%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA138-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:48 PM UTC 2026
% Result : Unsatisfiable 1.03s 1.30s
% Output : Proof 3.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA138-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:08:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 1.03/1.30 % SZS status Unsatisfiable
% 1.03/1.30 % SZS output start Proof
% 1.03/1.30 tff(r_type, type, (
% 1.03/1.30 r: ( $i * $i ) > $o)).
% 1.03/1.30 tff(elem_1_type, type, (
% 1.03/1.30 elem_1: $i)).
% 1.03/1.30 tff(s_type, type, (
% 1.03/1.30 s: $i > $i)).
% 1.03/1.30 tff(z_type, type, (
% 1.03/1.30 z: $i)).
% 1.03/1.30 tff(b_type, type, (
% 1.03/1.30 b: ( $i * $i ) > $o)).
% 1.03/1.30 tff(inj_0_type, type, (
% 1.03/1.30 inj_0: $i > $i)).
% 1.03/1.30 tff(1,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.03/1.30 tff(2,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.03/1.30 tff(3,plain,
% 1.03/1.30 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.03/1.30 inference(bind,[status(th)],[])).
% 1.03/1.30 tff(4,plain,
% 1.03/1.30 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.03/1.30 inference(quant_intro,[status(thm)],[3])).
% 1.03/1.30 tff(5,plain,
% 1.03/1.30 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.03/1.30 inference(rewrite,[status(thm)],[])).
% 1.03/1.30 tff(6,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.03/1.30 tff(7,plain,
% 1.03/1.30 (![X: $i] : (~(s(X) = z))),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.03/1.30 tff(8,plain,(
% 1.03/1.30 ![X: $i] : (~(s(X) = z))),
% 1.03/1.30 inference(skolemize,[status(sab)],[7])).
% 1.03/1.30 tff(9,plain,
% 1.03/1.30 (![X: $i] : (~(s(X) = z))),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.03/1.30 tff(10,plain,
% 1.03/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.03/1.30 inference(quant_inst,[status(thm)],[])).
% 1.03/1.30 tff(11,plain,
% 1.03/1.30 (~(s(z) = z)),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[10, 9])).
% 1.03/1.30 tff(12,plain,
% 1.03/1.30 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.03/1.30 inference(bind,[status(th)],[])).
% 1.03/1.30 tff(13,plain,
% 1.03/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(quant_intro,[status(thm)],[12])).
% 1.03/1.30 tff(14,plain,
% 1.03/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(rewrite,[status(thm)],[])).
% 1.03/1.30 tff(15,plain,
% 1.03/1.30 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.03/1.30 inference(bind,[status(th)],[])).
% 1.03/1.30 tff(16,plain,
% 1.03/1.30 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(quant_intro,[status(thm)],[15])).
% 1.03/1.30 tff(17,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.03/1.30 tff(18,plain,
% 1.03/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.03/1.30 tff(19,plain,
% 1.03/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.03/1.30 tff(20,plain,(
% 1.03/1.30 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(skolemize,[status(sab)],[19])).
% 1.03/1.30 tff(21,plain,
% 1.03/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.03/1.30 tff(22,plain,
% 1.03/1.30 (((~![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))),
% 1.03/1.30 inference(rewrite,[status(thm)],[])).
% 1.03/1.30 tff(23,plain,
% 1.03/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.03/1.30 inference(quant_inst,[status(thm)],[])).
% 1.03/1.30 tff(24,plain,
% 1.03/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.03/1.30 tff(25,plain,
% 1.03/1.30 (b(s(z), z) | r(s(z), z)),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 1.03/1.30 tff(26,plain,
% 1.03/1.30 (r(s(z), z)),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[25, 2])).
% 1.03/1.30 tff(27,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.03/1.30 tff(28,plain,
% 1.03/1.30 (s(s(s(elem!1))) = z),
% 1.03/1.30 inference(symmetry,[status(thm)],[27])).
% 1.03/1.30 tff(29,plain,
% 1.03/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.03/1.30 inference(quant_inst,[status(thm)],[])).
% 1.03/1.30 tff(30,plain,
% 1.03/1.30 (~(s(s(s(elem!1))) = z)),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[29, 9])).
% 1.03/1.30 tff(31,plain,
% 1.03/1.30 ($false),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[30, 28])).
% 1.03/1.30 tff(32,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.30 tff(33,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.30 tff(34,plain,
% 1.13/1.30 (((~![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)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(35,plain,
% 1.13/1.30 ((~![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)))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(36,plain,
% 1.13/1.30 ((~![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))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.13/1.30 tff(37,plain,
% 1.13/1.30 (r(z, s(s(s(elem!1))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[36, 21, 33, 32])).
% 1.13/1.30 tff(38,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.13/1.30 tff(39,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.13/1.30 tff(40,plain,
% 1.13/1.30 (s(z) = s(s(s(elem!1)))),
% 1.13/1.30 inference(symmetry,[status(thm)],[39])).
% 1.13/1.30 tff(41,plain,
% 1.13/1.30 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(42,plain,
% 1.13/1.30 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(43,plain,
% 1.13/1.30 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(44,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.13/1.30 tff(45,plain,
% 1.13/1.30 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.13/1.30 tff(46,plain,(
% 1.13/1.30 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.13/1.30 inference(skolemize,[status(sab)],[45])).
% 1.13/1.30 tff(47,plain,
% 1.13/1.30 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[46, 42])).
% 1.13/1.30 tff(48,plain,
% 1.13/1.30 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[47, 41])).
% 1.13/1.30 tff(49,plain,
% 1.13/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(50,plain,
% 1.13/1.30 (inj_0(s(z)) = z),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.13/1.30 tff(51,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.30 tff(52,plain,
% 1.13/1.30 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[51])).
% 1.13/1.30 tff(53,plain,
% 1.13/1.30 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.13/1.30 inference(symmetry,[status(thm)],[52])).
% 1.13/1.30 tff(54,plain,
% 1.13/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(55,plain,
% 1.13/1.30 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[54, 48])).
% 1.13/1.30 tff(56,plain,
% 1.13/1.30 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[55])).
% 1.13/1.30 tff(57,plain,
% 1.13/1.30 (s(s(elem!1)) = z),
% 1.13/1.30 inference(transitivity,[status(thm)],[56, 53, 50])).
% 1.13/1.30 tff(58,plain,
% 1.13/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(59,plain,
% 1.13/1.30 (~(s(s(elem!1)) = z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[58, 9])).
% 1.13/1.30 tff(60,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[59, 57])).
% 1.13/1.30 tff(61,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(62,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[61, 40])).
% 1.13/1.30 tff(63,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(64,plain,
% 1.13/1.30 (((~![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)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(65,plain,
% 1.13/1.30 ((~![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)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(66,plain,
% 1.13/1.30 ((~![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))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.13/1.30 tff(67,plain,
% 1.13/1.30 (b(s(s(s(elem!1))), s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[66, 21, 38, 63])).
% 1.13/1.30 tff(68,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.30 tff(69,plain,
% 1.13/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(70,plain,
% 1.13/1.30 (inj_0(s(elem!1)) = elem!1),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[69, 48])).
% 1.13/1.30 tff(71,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.13/1.30 tff(72,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.13/1.30 tff(73,plain,
% 1.13/1.30 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[72])).
% 1.13/1.30 tff(74,plain,
% 1.13/1.30 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[73])).
% 1.13/1.30 tff(75,plain,
% 1.13/1.30 (elem!1 = inj_0(s(elem!1))),
% 1.13/1.30 inference(symmetry,[status(thm)],[70])).
% 1.13/1.30 tff(76,plain,
% 1.13/1.30 (elem!1 = s(s(elem!1))),
% 1.13/1.30 inference(transitivity,[status(thm)],[75, 74, 55])).
% 1.13/1.30 tff(77,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[68, 76])).
% 1.13/1.30 tff(78,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(79,plain,
% 1.13/1.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[78, 68])).
% 1.13/1.30 tff(80,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.30 tff(81,plain,
% 1.13/1.30 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.30 inference(symmetry,[status(thm)],[80])).
% 1.13/1.30 tff(82,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.13/1.30 tff(83,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[82, 81])).
% 1.13/1.30 tff(84,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(85,plain,
% 1.13/1.30 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[84, 79])).
% 1.13/1.30 tff(86,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.13/1.30 tff(87,plain,
% 1.13/1.30 (s(s(s(z))) = s(z)),
% 1.13/1.30 inference(symmetry,[status(thm)],[86])).
% 1.13/1.30 tff(88,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.13/1.30 tff(89,plain,
% 1.13/1.30 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[88])).
% 1.13/1.30 tff(90,plain,
% 1.13/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(91,plain,
% 1.13/1.30 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[90, 48])).
% 1.13/1.30 tff(92,plain,
% 1.13/1.30 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[91])).
% 1.13/1.30 tff(93,plain,
% 1.13/1.30 (s(s(z)) = z),
% 1.13/1.30 inference(transitivity,[status(thm)],[92, 89, 50])).
% 1.13/1.30 tff(94,plain,
% 1.13/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(95,plain,
% 1.13/1.30 (~(s(s(z)) = z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[94, 9])).
% 1.13/1.30 tff(96,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[95, 93])).
% 1.13/1.30 tff(97,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(98,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[97, 87])).
% 1.13/1.30 tff(99,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(100,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.13/1.30 tff(101,plain,
% 1.13/1.30 (((~![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)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(102,plain,
% 1.13/1.30 ((~![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)))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(103,plain,
% 1.13/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.13/1.30 tff(104,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[103, 21, 71, 100, 99])).
% 1.13/1.30 tff(105,plain,(b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(106,plain,
% 1.13/1.30 (r(s(z), s(s(s(z))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[105, 71])).
% 1.13/1.30 tff(107,assumption,(z = elem!1), introduced(assumption)).
% 1.13/1.30 tff(108,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.13/1.30 tff(109,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.13/1.30 tff(110,assumption,(r(s(z), z)), introduced(assumption)).
% 1.13/1.30 tff(111,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.30 tff(112,plain,
% 1.13/1.30 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(113,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[112])).
% 1.13/1.30 tff(114,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(115,plain,
% 1.13/1.30 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(116,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[115])).
% 1.13/1.30 tff(117,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.13/1.30 tff(118,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.13/1.30 tff(119,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[118, 114])).
% 1.13/1.30 tff(120,plain,(
% 1.13/1.30 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(skolemize,[status(sab)],[119])).
% 1.13/1.30 tff(121,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[120, 113])).
% 1.13/1.30 tff(122,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(123,plain,
% 1.13/1.30 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(124,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[123])).
% 1.13/1.30 tff(125,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[124, 122])).
% 1.13/1.30 tff(126,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(127,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.13/1.30 tff(128,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[127, 121, 111, 110, 109, 108])).
% 1.13/1.30 tff(129,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(130,plain,
% 1.13/1.30 (~r(s(s(s(z))), z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[129, 108, 26, 37])).
% 1.13/1.30 tff(131,plain,
% 1.13/1.30 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.30 tff(132,plain,
% 1.13/1.30 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.13/1.30 inference(symmetry,[status(thm)],[131])).
% 1.13/1.30 tff(133,plain,
% 1.13/1.30 (s(z) = s(elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.30 tff(134,plain,
% 1.13/1.30 (s(s(z)) = s(s(elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[133])).
% 1.13/1.30 tff(135,plain,
% 1.13/1.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[134])).
% 1.13/1.30 tff(136,plain,
% 1.13/1.30 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[135])).
% 1.13/1.30 tff(137,plain,
% 1.13/1.30 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.13/1.30 inference(symmetry,[status(thm)],[136])).
% 1.13/1.30 tff(138,plain,
% 1.13/1.30 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.13/1.30 inference(transitivity,[status(thm)],[137, 132])).
% 1.13/1.30 tff(139,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(140,plain,
% 1.13/1.30 (r(s(s(s(z))), z)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.13/1.30 tff(141,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.13/1.30 tff(142,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[141, 140])).
% 1.13/1.30 tff(143,plain,(r(s(s(s(z))), z) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(144,plain,
% 1.13/1.30 (~r(s(s(s(elem!1))), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[143, 107, 130])).
% 1.13/1.30 tff(145,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(146,plain,
% 1.13/1.30 (r(s(s(s(elem!1))), elem!1)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[145, 136])).
% 1.13/1.30 tff(147,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(148,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[147, 146])).
% 1.13/1.30 tff(149,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(150,plain,
% 1.13/1.30 (~r(s(s(s(z))), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[149, 144, 107])).
% 1.13/1.30 tff(151,plain,
% 1.13/1.30 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[133])).
% 1.13/1.30 tff(152,plain,
% 1.13/1.30 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.13/1.30 inference(symmetry,[status(thm)],[151])).
% 1.13/1.30 tff(153,plain,
% 1.13/1.30 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[135])).
% 1.13/1.30 tff(154,plain,
% 1.13/1.30 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.13/1.30 inference(symmetry,[status(thm)],[153])).
% 1.13/1.30 tff(155,plain,
% 1.13/1.30 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.13/1.30 inference(transitivity,[status(thm)],[154, 152])).
% 1.13/1.30 tff(156,plain,
% 1.13/1.30 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[133])).
% 1.13/1.30 tff(157,plain,
% 1.13/1.30 (b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[67, 156])).
% 1.13/1.30 tff(158,plain,
% 1.13/1.30 (b(s(s(s(z))), s(z))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[157, 155])).
% 1.13/1.30 tff(159,plain,
% 1.13/1.30 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.13/1.30 inference(commutativity,[status(thm)],[])).
% 1.13/1.30 tff(160,plain,
% 1.13/1.30 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.30 inference(symmetry,[status(thm)],[159])).
% 1.13/1.30 tff(161,plain,
% 1.13/1.30 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.30 tff(162,plain,
% 1.13/1.30 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[161, 159])).
% 1.13/1.30 tff(163,plain,
% 1.13/1.30 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.30 inference(transitivity,[status(thm)],[162, 160])).
% 1.13/1.30 tff(164,plain,
% 1.13/1.30 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[163])).
% 1.13/1.30 tff(165,plain,
% 1.13/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(166,plain,
% 1.13/1.30 (~(s(s(s(z))) = z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[165, 9])).
% 1.13/1.30 tff(167,plain,
% 1.13/1.30 (~(s(s(s(z))) = elem!1)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[166, 164])).
% 1.13/1.30 tff(168,plain,
% 1.13/1.30 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[135])).
% 1.13/1.30 tff(169,plain,
% 1.13/1.30 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[168])).
% 1.13/1.30 tff(170,plain,
% 1.13/1.30 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[169])).
% 1.13/1.30 tff(171,plain,
% 1.13/1.30 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(172,plain,
% 1.13/1.30 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[171])).
% 1.13/1.30 tff(173,plain,
% 1.13/1.30 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(174,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 1.13/1.30 tff(175,plain,
% 1.13/1.30 (![X: $i] : (~r(X, X))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.13/1.30 tff(176,plain,(
% 1.13/1.30 ![X: $i] : (~r(X, X))),
% 1.13/1.30 inference(skolemize,[status(sab)],[175])).
% 1.13/1.30 tff(177,plain,
% 1.13/1.30 (![X: $i] : (~r(X, X))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.13/1.30 tff(178,plain,
% 1.13/1.30 ((~![X: $i] : (~r(X, X))) | (~r(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(179,plain,
% 1.13/1.30 (~r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[178, 177])).
% 1.13/1.30 tff(180,plain,
% 1.13/1.30 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[179, 170])).
% 1.13/1.30 tff(181,plain,
% 1.13/1.30 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.30 tff(182,plain,
% 1.13/1.30 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 1.13/1.30 inference(symmetry,[status(thm)],[181])).
% 1.13/1.30 tff(183,plain,
% 1.13/1.30 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[182])).
% 1.13/1.30 tff(184,plain,
% 1.13/1.30 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(185,plain,
% 1.13/1.30 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[184])).
% 1.13/1.30 tff(186,plain,
% 1.13/1.30 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(187,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.13/1.30 tff(188,plain,
% 1.13/1.30 (![X: $i] : (~b(X, X))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.13/1.30 tff(189,plain,(
% 1.13/1.30 ![X: $i] : (~b(X, X))),
% 1.13/1.30 inference(skolemize,[status(sab)],[188])).
% 1.13/1.30 tff(190,plain,
% 1.13/1.30 (![X: $i] : (~b(X, X))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.13/1.30 tff(191,plain,
% 1.13/1.30 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(192,plain,
% 1.13/1.30 (~b(elem!1, elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[191, 190])).
% 1.13/1.30 tff(193,plain,
% 1.13/1.30 (~b(z, elem!1)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[192, 183])).
% 1.13/1.30 tff(194,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.13/1.30 tff(195,plain,
% 1.13/1.30 (elem!1 = s(s(elem!1))),
% 1.13/1.30 inference(symmetry,[status(thm)],[194])).
% 1.13/1.30 tff(196,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[68, 195])).
% 1.13/1.30 tff(197,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(198,plain,
% 1.13/1.30 (~(s(s(elem!1)) = elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[197, 68])).
% 1.13/1.30 tff(199,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.13/1.30 tff(200,plain,
% 1.13/1.30 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.13/1.30 inference(commutativity,[status(thm)],[])).
% 1.13/1.30 tff(201,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.30 tff(202,plain,
% 1.13/1.30 (s(s(elem!1)) = s(elem!1)),
% 1.13/1.30 inference(symmetry,[status(thm)],[201])).
% 1.13/1.30 tff(203,plain,
% 1.13/1.30 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[202])).
% 1.13/1.30 tff(204,plain,
% 1.13/1.30 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.13/1.30 inference(transitivity,[status(thm)],[203, 200])).
% 1.13/1.30 tff(205,plain,
% 1.13/1.30 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[204])).
% 1.13/1.30 tff(206,plain,
% 1.13/1.30 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[202])).
% 1.13/1.30 tff(207,plain,
% 1.13/1.30 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.30 inference(transitivity,[status(thm)],[206, 202])).
% 1.13/1.30 tff(208,plain,
% 1.13/1.30 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[207, 205])).
% 1.13/1.30 tff(209,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1, 208])).
% 1.13/1.30 tff(210,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(211,plain,
% 1.13/1.30 (~(s(elem!1) = s(s(elem!1)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[210, 1])).
% 1.13/1.30 tff(212,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.13/1.30 tff(213,plain,
% 1.13/1.30 (s(elem!1) = elem!1),
% 1.13/1.30 inference(symmetry,[status(thm)],[212])).
% 1.13/1.30 tff(214,plain,
% 1.13/1.30 (s(s(elem!1)) = s(elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[213])).
% 1.13/1.30 tff(215,plain,
% 1.13/1.30 (s(elem!1) = s(s(elem!1))),
% 1.13/1.30 inference(symmetry,[status(thm)],[214])).
% 1.13/1.30 tff(216,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.30 tff(217,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[216, 215])).
% 1.13/1.30 tff(218,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(219,plain,
% 1.13/1.30 (~(elem!1 = s(elem!1))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[218, 211])).
% 1.13/1.30 tff(220,assumption,(b(z, s(z))), introduced(assumption)).
% 1.13/1.30 tff(221,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(222,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.13/1.30 tff(223,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.13/1.30 tff(224,plain,
% 1.13/1.30 (b(z, s(z)) <=> b(z, elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.30 tff(225,plain,
% 1.13/1.30 (b(z, elem!1) <=> b(z, s(z))),
% 1.13/1.30 inference(symmetry,[status(thm)],[224])).
% 1.13/1.30 tff(226,plain,
% 1.13/1.30 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[225])).
% 1.13/1.30 tff(227,plain,
% 1.13/1.30 (~b(z, s(z))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[199, 226])).
% 1.13/1.30 tff(228,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[220, 227])).
% 1.13/1.30 tff(229,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(230,plain,
% 1.13/1.30 (~(s(z) = elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[229, 199, 220])).
% 1.13/1.30 tff(231,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.13/1.30 tff(232,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(233,plain,
% 1.13/1.30 (((~![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))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(234,plain,
% 1.13/1.30 ((~![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))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(235,plain,
% 1.13/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.13/1.30 tff(236,plain,
% 1.13/1.30 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[235, 21])).
% 1.13/1.30 tff(237,plain,
% 1.13/1.30 (b(s(z), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[236, 232, 231])).
% 1.13/1.30 tff(238,plain,
% 1.13/1.30 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.13/1.30 inference(commutativity,[status(thm)],[])).
% 1.13/1.30 tff(239,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.13/1.30 tff(240,plain,
% 1.13/1.30 (s(z) = elem!1),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.13/1.30 tff(241,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[231, 240])).
% 1.13/1.30 tff(242,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(243,plain,
% 1.13/1.30 (~(elem!1 = s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[242, 231])).
% 1.13/1.30 tff(244,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.13/1.30 tff(245,plain,
% 1.13/1.30 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[244])).
% 1.13/1.30 tff(246,plain,
% 1.13/1.30 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[245])).
% 1.13/1.30 tff(247,plain,
% 1.13/1.30 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(z)))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[246])).
% 1.13/1.30 tff(248,plain,
% 1.13/1.30 (~r(s(z), s(s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[232, 247])).
% 1.13/1.30 tff(249,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[108, 248])).
% 1.13/1.30 tff(250,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(z))))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(251,plain,
% 1.13/1.30 (~(s(s(s(z))) = elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[250, 232, 108])).
% 1.13/1.30 tff(252,plain,
% 1.13/1.30 (((~![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))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(253,plain,
% 1.13/1.30 ((~![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))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(254,plain,
% 1.13/1.30 ((~![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)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.13/1.30 tff(255,plain,
% 1.13/1.30 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[254, 21])).
% 1.13/1.30 tff(256,plain,
% 1.13/1.30 (b(s(s(s(z))), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[255, 251, 221])).
% 1.13/1.30 tff(257,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(258,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.13/1.30 tff(259,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.13/1.30 tff(260,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.13/1.30 tff(261,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.13/1.30 tff(262,plain,
% 1.13/1.30 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(263,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[262])).
% 1.13/1.30 tff(264,plain,
% 1.13/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(265,plain,
% 1.13/1.31 (^[X0: $i, X3: $i, X2: $i, X1: $i] : 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)))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(266,plain,
% 1.13/1.31 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[265])).
% 1.13/1.31 tff(267,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.13/1.31 tff(268,plain,
% 1.13/1.31 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.13/1.31 tff(269,plain,
% 1.13/1.31 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[268, 264])).
% 1.13/1.31 tff(270,plain,(
% 1.13/1.31 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.31 inference(skolemize,[status(sab)],[269])).
% 1.13/1.31 tff(271,plain,
% 1.13/1.31 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[270, 263])).
% 1.13/1.31 tff(272,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(273,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(274,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.13/1.31 tff(275,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[274, 271, 260, 261, 222, 257])).
% 1.13/1.31 tff(276,plain,((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(277,plain,
% 1.13/1.31 (~b(elem!1, z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[276, 260, 222, 257])).
% 1.13/1.31 tff(278,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.13/1.31 tff(279,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.13/1.31 tff(280,plain,
% 1.13/1.31 (((~![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))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(281,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(282,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.13/1.31 tff(283,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[282, 21, 279, 278, 259])).
% 1.13/1.31 tff(284,plain,(r(elem!1, z) | b(elem!1, z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(285,plain,
% 1.13/1.31 (r(elem!1, z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[284, 277, 259])).
% 1.13/1.31 tff(286,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(287,plain,
% 1.13/1.31 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(288,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[287])).
% 1.13/1.31 tff(289,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[288, 286])).
% 1.13/1.31 tff(290,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(291,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.13/1.31 tff(292,plain,
% 1.13/1.31 (~r(elem!1, s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[291, 121, 111, 110, 285])).
% 1.13/1.31 tff(293,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.13/1.31 tff(294,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.13/1.31 tff(295,plain,
% 1.13/1.31 (((~![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)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(296,plain,
% 1.13/1.31 ((~![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)))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(297,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.13/1.31 tff(298,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[297, 21, 294, 293, 258])).
% 1.13/1.31 tff(299,plain,(r(elem!1, s(z)) | b(elem!1, s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(300,plain,
% 1.13/1.31 (b(elem!1, s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[299, 292, 258])).
% 1.13/1.31 tff(301,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(302,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(303,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[302, 301])).
% 1.13/1.31 tff(304,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[303, 271, 260, 300, 222, 257])).
% 1.13/1.31 tff(305,plain,((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(306,plain,
% 1.13/1.31 (elem!1 = z),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[305, 256, 243, 237, 111, 110, 222])).
% 1.13/1.31 tff(307,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.13/1.31 tff(308,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(309,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(310,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.13/1.31 tff(311,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[310, 271, 307, 260, 222, 257])).
% 1.13/1.31 tff(312,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(313,plain,
% 1.13/1.31 (~b(elem!1, s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[312, 237, 256, 222])).
% 1.13/1.31 tff(314,plain,
% 1.13/1.31 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[133])).
% 1.13/1.31 tff(315,plain,
% 1.13/1.31 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.13/1.31 inference(symmetry,[status(thm)],[314])).
% 1.13/1.31 tff(316,plain,
% 1.13/1.31 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(z)))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[315])).
% 1.13/1.31 tff(317,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.13/1.31 tff(318,plain,
% 1.13/1.31 (~b(elem!1, s(z))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[317, 316])).
% 1.13/1.31 tff(319,plain,
% 1.13/1.31 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.31 tff(320,plain,
% 1.13/1.31 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.13/1.31 inference(symmetry,[status(thm)],[319])).
% 1.13/1.31 tff(321,plain,
% 1.13/1.31 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[320])).
% 1.13/1.31 tff(322,plain,
% 1.13/1.31 (~b(z, s(z))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[294, 321])).
% 1.13/1.31 tff(323,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[220, 322])).
% 1.13/1.31 tff(324,plain,((~(z = elem!1)) | (~b(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(325,plain,
% 1.13/1.31 (b(elem!1, s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[324, 107, 220])).
% 1.13/1.31 tff(326,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[325, 318])).
% 1.13/1.31 tff(327,plain,((~(z = elem!1)) | b(elem!1, s(elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(328,plain,
% 1.13/1.31 (~(z = elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[327, 313, 220])).
% 1.13/1.31 tff(329,assumption,(elem!1 = z), introduced(assumption)).
% 1.13/1.31 tff(330,plain,
% 1.13/1.31 (z = elem!1),
% 1.13/1.31 inference(symmetry,[status(thm)],[329])).
% 1.13/1.31 tff(331,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.13/1.31 tff(332,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[331, 330])).
% 1.13/1.31 tff(333,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(334,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[333, 328, 306])).
% 1.13/1.31 tff(335,plain,(r(s(z), elem!1) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | r(s(s(s(z))), elem!1) | (s(z) = elem!1) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(336,plain,
% 1.13/1.31 (r(s(z), elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[335, 230, 111, 110, 222, 221, 220, 108])).
% 1.13/1.31 tff(337,plain,
% 1.13/1.31 (~(elem!1 = s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[242, 230])).
% 1.13/1.31 tff(338,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.13/1.31 tff(339,plain,
% 1.13/1.31 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[338])).
% 1.13/1.31 tff(340,plain,
% 1.13/1.31 (z = inj_0(s(z))),
% 1.13/1.31 inference(symmetry,[status(thm)],[50])).
% 1.13/1.31 tff(341,plain,
% 1.13/1.31 (z = elem!1),
% 1.13/1.31 inference(transitivity,[status(thm)],[340, 339, 70])).
% 1.13/1.31 tff(342,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[331, 341])).
% 1.13/1.31 tff(343,plain,((~(s(z) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(344,plain,
% 1.13/1.31 (~(s(z) = s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[343, 331])).
% 1.13/1.31 tff(345,plain,
% 1.13/1.31 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.13/1.31 inference(commutativity,[status(thm)],[])).
% 1.13/1.31 tff(346,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.13/1.31 tff(347,plain,
% 1.13/1.31 (s(z) = s(elem!1)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.13/1.31 tff(348,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.13/1.31 tff(349,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[348, 347])).
% 1.13/1.31 tff(350,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(351,plain,
% 1.13/1.31 (~(s(elem!1) = s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[350, 344])).
% 1.13/1.31 tff(352,plain,
% 1.13/1.31 (((~![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))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(353,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(354,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.13/1.31 tff(355,plain,
% 1.13/1.31 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[354, 21])).
% 1.13/1.31 tff(356,plain,
% 1.13/1.31 (r(z, elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[355, 331, 199])).
% 1.13/1.31 tff(357,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.13/1.31 tff(358,plain,
% 1.13/1.31 (~(elem!1 = z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[333, 331])).
% 1.13/1.31 tff(359,plain,
% 1.13/1.31 (r(elem!1, z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[284, 259, 279])).
% 1.13/1.31 tff(360,plain,
% 1.13/1.31 ((elem!1 = z) <=> (z = elem!1)),
% 1.13/1.31 inference(commutativity,[status(thm)],[])).
% 1.13/1.31 tff(361,plain,
% 1.13/1.31 ((z = elem!1) <=> (elem!1 = z)),
% 1.13/1.31 inference(symmetry,[status(thm)],[360])).
% 1.13/1.31 tff(362,plain,
% 1.13/1.31 (elem!1 = z),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[107, 361])).
% 1.13/1.31 tff(363,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[259, 362])).
% 1.13/1.31 tff(364,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(365,plain,
% 1.13/1.31 (~(z = elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[364, 259])).
% 1.13/1.31 tff(366,plain,
% 1.13/1.31 (r(z, elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[355, 365, 199])).
% 1.13/1.31 tff(367,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(368,plain,
% 1.13/1.31 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(369,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[368])).
% 1.13/1.31 tff(370,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(transitivity,[status(thm)],[369, 367])).
% 1.13/1.31 tff(371,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(372,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.13/1.31 tff(373,plain,
% 1.13/1.31 ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[372, 121])).
% 1.13/1.31 tff(374,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[373, 366, 359, 110, 357])).
% 1.13/1.31 tff(375,plain,((elem!1 = z) | (~r(s(z), z)) | (~r(s(z), elem!1)) | b(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(376,plain,
% 1.13/1.31 (b(elem!1, z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[375, 358, 199, 357, 110])).
% 1.13/1.31 tff(377,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.13/1.31 tff(378,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.13/1.31 tff(379,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.13/1.31 tff(380,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(381,plain,
% 1.13/1.31 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(382,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[381])).
% 1.13/1.31 tff(383,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.31 inference(transitivity,[status(thm)],[382, 380])).
% 1.13/1.31 tff(384,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(385,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.13/1.31 tff(386,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[385, 121, 379, 378, 357, 110])).
% 1.13/1.31 tff(387,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(388,plain,
% 1.13/1.31 (~r(elem!1, s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[387, 356, 110, 357])).
% 1.13/1.31 tff(389,plain,
% 1.13/1.31 (((~![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)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(390,plain,
% 1.13/1.31 ((~![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)))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(391,plain,
% 1.13/1.31 ((~![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))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.13/1.31 tff(392,plain,
% 1.13/1.31 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[391, 21])).
% 1.13/1.31 tff(393,plain,
% 1.13/1.31 (b(elem!1, s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[392, 388, 377])).
% 1.13/1.31 tff(394,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.13/1.31 tff(395,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(396,plain,
% 1.13/1.31 (((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(397,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(z)))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[396])).
% 1.13/1.31 tff(398,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(z))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[397, 395])).
% 1.13/1.31 tff(399,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(400,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.13/1.31 tff(401,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[400, 271, 307, 394, 261, 220])).
% 1.13/1.31 tff(402,plain,((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(403,plain,
% 1.13/1.31 (~b(s(elem!1), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[402, 393, 220, 376])).
% 1.13/1.31 tff(404,plain,
% 1.13/1.31 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(405,plain,
% 1.13/1.31 (~(s(elem!1) = z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[404, 9])).
% 1.13/1.31 tff(406,plain,
% 1.13/1.31 (((~![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))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(407,plain,
% 1.13/1.32 ((~![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))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(408,plain,
% 1.13/1.32 ((~![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)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.13/1.32 tff(409,plain,
% 1.13/1.32 (b(s(elem!1), z) | r(s(elem!1), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[408, 21, 405])).
% 1.13/1.32 tff(410,plain,
% 1.13/1.32 (r(s(elem!1), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[409, 403])).
% 1.13/1.32 tff(411,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.13/1.32 tff(412,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.13/1.32 tff(413,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(414,plain,
% 1.13/1.32 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(415,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[414])).
% 1.13/1.32 tff(416,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.32 inference(transitivity,[status(thm)],[415, 413])).
% 1.13/1.32 tff(417,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(418,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.13/1.32 tff(419,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[418, 121, 378, 110, 412, 411])).
% 1.13/1.32 tff(420,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(421,plain,
% 1.13/1.32 (~r(s(elem!1), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[420, 410, 110, 356])).
% 1.13/1.32 tff(422,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.13/1.32 tff(423,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.13/1.32 tff(424,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 1.13/1.32 tff(425,plain,
% 1.13/1.32 (((~![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)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(426,plain,
% 1.13/1.32 ((~![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)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(427,plain,
% 1.13/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.13/1.32 tff(428,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[427, 21, 424, 423, 422])).
% 1.13/1.32 tff(429,plain,(b(s(elem!1), s(z)) | r(s(elem!1), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(430,plain,
% 1.13/1.32 (b(s(elem!1), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[429, 421, 351])).
% 1.13/1.32 tff(431,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.13/1.32 tff(432,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(433,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(434,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.13/1.32 tff(435,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[434, 121, 378, 110, 431, 412])).
% 1.13/1.32 tff(436,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(437,plain,
% 1.13/1.32 (~r(s(z), s(elem!1))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[436, 410, 110, 356])).
% 1.13/1.32 tff(438,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.13/1.32 tff(439,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.13/1.32 tff(440,plain,
% 1.13/1.32 (((~![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)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(441,plain,
% 1.13/1.32 ((~![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)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(442,plain,
% 1.13/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.13/1.32 tff(443,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[442, 21, 348, 439, 438])).
% 1.13/1.32 tff(444,plain,(r(s(z), s(elem!1)) | (s(z) = s(elem!1)) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(445,plain,
% 1.13/1.32 (b(s(z), s(elem!1))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[444, 437, 344])).
% 1.13/1.32 tff(446,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.13/1.32 tff(447,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.13/1.32 tff(448,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.13/1.32 tff(449,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(450,plain,
% 1.13/1.32 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(451,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[450])).
% 1.13/1.32 tff(452,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[451, 449])).
% 1.13/1.32 tff(453,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(454,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.13/1.32 tff(455,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[454, 271, 307, 448, 447, 446])).
% 1.13/1.32 tff(456,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(457,plain,
% 1.13/1.32 (~b(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[456, 445, 393, 430])).
% 1.13/1.32 tff(458,plain,
% 1.13/1.32 (r(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[299, 457, 337])).
% 1.13/1.32 tff(459,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(460,plain,
% 1.13/1.32 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(461,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[460])).
% 1.13/1.32 tff(462,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.32 inference(transitivity,[status(thm)],[461, 459])).
% 1.13/1.32 tff(463,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(464,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[463, 462])).
% 1.13/1.32 tff(465,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[464, 121, 356, 357, 110, 458])).
% 1.13/1.32 tff(466,plain,((z = elem!1) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(467,plain,
% 1.13/1.32 (z = elem!1),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[466, 336, 110, 220, 219, 199])).
% 1.13/1.32 tff(468,plain,
% 1.13/1.32 (s(z) = s(elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[467])).
% 1.13/1.32 tff(469,plain,
% 1.13/1.32 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[468])).
% 1.13/1.32 tff(470,plain,
% 1.13/1.32 (r(s(elem!1), elem!1)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[336, 469])).
% 1.13/1.32 tff(471,plain,
% 1.13/1.32 (b(elem!1, s(elem!1))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[327, 467, 220])).
% 1.13/1.32 tff(472,plain,
% 1.13/1.32 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), z))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[132])).
% 1.13/1.32 tff(473,plain,
% 1.13/1.32 (~r(s(s(s(z))), z)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[221, 472])).
% 1.13/1.32 tff(474,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[109, 473])).
% 1.13/1.32 tff(475,plain,((~(z = elem!1)) | (~r(s(s(s(z))), z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(476,plain,
% 1.13/1.32 (~r(s(s(s(z))), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[475, 467, 221])).
% 1.13/1.32 tff(477,plain,
% 1.13/1.32 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.32 tff(478,plain,
% 1.13/1.32 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 1.13/1.32 inference(symmetry,[status(thm)],[477])).
% 1.13/1.32 tff(479,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.13/1.32 tff(480,plain,
% 1.13/1.32 (~r(s(s(s(elem!1))), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[143, 107, 141])).
% 1.13/1.32 tff(481,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.13/1.32 tff(482,plain,
% 1.13/1.32 (((~![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))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(483,plain,
% 1.13/1.32 ((~![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))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(484,plain,
% 1.13/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.13/1.32 tff(485,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[484, 21, 147, 481, 479])).
% 1.13/1.32 tff(486,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(487,plain,
% 1.13/1.32 (s(s(s(elem!1))) = elem!1),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[486, 480, 479])).
% 1.13/1.32 tff(488,plain,
% 1.13/1.32 (s(s(s(elem!1))) = z),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[487, 478])).
% 1.13/1.32 tff(489,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[30, 488])).
% 1.13/1.32 tff(490,plain,((~(z = elem!1)) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(491,plain,
% 1.13/1.32 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[490, 467, 476])).
% 1.13/1.32 tff(492,plain,
% 1.13/1.32 (s(s(z)) = s(s(elem!1))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[468])).
% 1.13/1.32 tff(493,plain,
% 1.13/1.32 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[492])).
% 1.13/1.32 tff(494,plain,
% 1.13/1.32 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[467])).
% 1.13/1.32 tff(495,plain,
% 1.13/1.32 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.13/1.32 inference(transitivity,[status(thm)],[494, 493])).
% 1.13/1.32 tff(496,plain,
% 1.13/1.32 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[495])).
% 1.13/1.32 tff(497,plain,
% 1.13/1.32 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[468, 492])).
% 1.13/1.32 tff(498,plain,
% 1.13/1.32 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.13/1.32 inference(symmetry,[status(thm)],[497])).
% 1.13/1.32 tff(499,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[348, 133])).
% 1.13/1.32 tff(500,plain,((~(z = elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(501,plain,
% 1.13/1.32 (s(z) = s(elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[500, 467])).
% 1.13/1.32 tff(502,plain,
% 1.13/1.32 (b(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[324, 467, 220])).
% 1.13/1.32 tff(503,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.13/1.32 tff(504,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.13/1.32 tff(505,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.32 tff(506,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(507,plain,
% 1.13/1.32 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(508,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[507])).
% 1.13/1.32 tff(509,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[508, 506])).
% 1.13/1.32 tff(510,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(511,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[510, 509])).
% 1.13/1.32 tff(512,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[511, 271, 505, 448, 504, 503])).
% 1.13/1.32 tff(513,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(514,plain,
% 1.13/1.32 (~b(s(z), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[513, 491, 503, 502])).
% 1.13/1.32 tff(515,plain,
% 1.13/1.32 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[338])).
% 1.13/1.32 tff(516,plain,
% 1.13/1.32 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.13/1.32 inference(symmetry,[status(thm)],[515])).
% 1.13/1.32 tff(517,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.32 tff(518,plain,
% 1.13/1.32 (b(s(z), s(s(elem!1)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.13/1.32 tff(519,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.32 tff(520,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[519, 518])).
% 1.13/1.32 tff(521,plain,((~(s(z) = s(elem!1))) | b(s(z), s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(522,plain,
% 1.13/1.32 (~b(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[521, 514, 501])).
% 1.13/1.32 tff(523,plain,
% 1.13/1.32 (((~![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))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(524,plain,
% 1.13/1.32 ((~![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))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(525,plain,
% 1.13/1.32 ((~![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)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.13/1.32 tff(526,plain,
% 1.13/1.32 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[525, 21])).
% 1.13/1.32 tff(527,plain,
% 1.13/1.32 (r(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[526, 522, 211])).
% 1.13/1.32 tff(528,plain,
% 1.13/1.32 (r(s(z), s(s(z)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[527, 498])).
% 1.13/1.32 tff(529,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(530,plain,
% 1.13/1.32 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(531,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[530])).
% 1.13/1.32 tff(532,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[531, 529])).
% 1.13/1.32 tff(533,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(534,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.13/1.32 tff(535,plain,
% 1.13/1.32 ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[534, 121])).
% 1.13/1.32 tff(536,plain,
% 1.13/1.32 (~r(s(s(z)), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[535, 528, 111, 110])).
% 1.13/1.32 tff(537,plain,
% 1.13/1.32 (~r(s(s(elem!1)), elem!1)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[536, 496])).
% 1.13/1.32 tff(538,plain,
% 1.13/1.32 (((~![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))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(539,plain,
% 1.13/1.32 ((~![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))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(540,plain,
% 1.13/1.32 ((~![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)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.13/1.32 tff(541,plain,
% 1.13/1.32 (b(s(s(elem!1)), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[540, 21, 537, 198])).
% 1.13/1.32 tff(542,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.13/1.32 tff(543,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.33 tff(544,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(545,plain,
% 1.13/1.33 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(546,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[545])).
% 1.13/1.33 tff(547,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[546, 544])).
% 1.13/1.33 tff(548,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(549,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.13/1.33 tff(550,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[549, 271, 307, 543, 504, 542])).
% 1.13/1.33 tff(551,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(552,plain,
% 1.13/1.33 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[551, 541, 471, 491])).
% 1.13/1.33 tff(553,plain,
% 1.13/1.33 (((~![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)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(554,plain,
% 1.13/1.33 ((~![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)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(555,plain,
% 1.13/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.13/1.33 tff(556,plain,
% 1.13/1.33 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[555, 21])).
% 1.13/1.33 tff(557,plain,
% 1.13/1.33 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[556, 552, 1])).
% 1.13/1.33 tff(558,plain,
% 1.13/1.33 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.13/1.33 inference(commutativity,[status(thm)],[])).
% 1.13/1.33 tff(559,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.33 tff(560,plain,
% 1.13/1.33 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[559, 558])).
% 1.13/1.33 tff(561,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1, 560])).
% 1.13/1.33 tff(562,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(563,plain,
% 1.13/1.33 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[562, 1])).
% 1.13/1.33 tff(564,plain,
% 1.13/1.33 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[468])).
% 1.13/1.33 tff(565,plain,
% 1.13/1.33 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.13/1.33 inference(symmetry,[status(thm)],[564])).
% 1.13/1.33 tff(566,plain,
% 1.13/1.33 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[492])).
% 1.13/1.33 tff(567,plain,
% 1.13/1.33 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[566])).
% 1.13/1.33 tff(568,plain,
% 1.13/1.33 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[567, 565])).
% 1.13/1.33 tff(569,plain,
% 1.13/1.33 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[468])).
% 1.13/1.33 tff(570,plain,
% 1.13/1.33 (r(s(elem!1), s(s(s(z))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[108, 569])).
% 1.13/1.33 tff(571,plain,
% 1.13/1.33 (r(s(z), s(s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[570, 568])).
% 1.13/1.33 tff(572,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.33 tff(573,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.33 tff(574,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(575,plain,
% 1.13/1.33 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(576,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[575])).
% 1.13/1.33 tff(577,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[576, 574])).
% 1.13/1.33 tff(578,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(579,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.13/1.33 tff(580,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[579, 121, 111, 573, 572, 110])).
% 1.13/1.33 tff(581,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(582,plain,
% 1.13/1.33 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[581, 571, 111, 110])).
% 1.13/1.33 tff(583,plain,
% 1.13/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(584,plain,
% 1.13/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(585,plain,
% 1.13/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.13/1.33 tff(586,plain,
% 1.13/1.33 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[585, 21])).
% 1.13/1.33 tff(587,plain,
% 1.13/1.33 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[586, 582, 563])).
% 1.13/1.33 tff(588,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.13/1.33 tff(589,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.33 tff(590,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(591,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(592,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[591, 590])).
% 1.13/1.33 tff(593,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[592, 271, 589, 588, 504, 542])).
% 1.13/1.33 tff(594,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(595,plain,
% 1.13/1.33 (~b(elem!1, s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[594, 541, 491, 587])).
% 1.13/1.33 tff(596,plain,
% 1.13/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(597,plain,
% 1.13/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(598,plain,
% 1.13/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.13/1.33 tff(599,plain,
% 1.13/1.33 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[598, 21])).
% 1.13/1.33 tff(600,plain,
% 1.13/1.33 (r(elem!1, s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[599, 595, 68])).
% 1.13/1.33 tff(601,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.33 tff(602,plain,
% 1.13/1.33 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[601])).
% 1.13/1.33 tff(603,plain,
% 1.13/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(604,plain,
% 1.13/1.33 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[603, 48])).
% 1.13/1.33 tff(605,plain,
% 1.13/1.33 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.13/1.33 inference(symmetry,[status(thm)],[604])).
% 1.13/1.33 tff(606,plain,
% 1.13/1.33 (s(elem!1) = s(s(elem!1))),
% 1.13/1.33 inference(transitivity,[status(thm)],[605, 602, 55])).
% 1.13/1.33 tff(607,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[216, 606])).
% 1.13/1.33 tff(608,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(609,plain,
% 1.13/1.33 (s(elem!1) = s(s(elem!1))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[608, 601])).
% 1.13/1.33 tff(610,plain,
% 1.13/1.33 (s(s(elem!1)) = s(elem!1)),
% 1.13/1.33 inference(symmetry,[status(thm)],[609])).
% 1.13/1.33 tff(611,plain,
% 1.13/1.33 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.13/1.33 inference(symmetry,[status(thm)],[601])).
% 1.13/1.33 tff(612,plain,
% 1.13/1.33 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.33 inference(transitivity,[status(thm)],[611, 610])).
% 1.13/1.33 tff(613,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[82, 612])).
% 1.13/1.33 tff(614,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(615,plain,
% 1.13/1.33 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[614, 82])).
% 1.13/1.33 tff(616,plain,
% 1.13/1.33 (~(s(elem!1) = s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[210, 615])).
% 1.13/1.33 tff(617,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.13/1.33 tff(618,plain,
% 1.13/1.33 (s(elem!1) = s(s(elem!1))),
% 1.13/1.33 inference(symmetry,[status(thm)],[617])).
% 1.13/1.33 tff(619,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[216, 618])).
% 1.13/1.33 tff(620,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(621,plain,
% 1.13/1.33 (~(s(s(elem!1)) = s(elem!1))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[620, 616])).
% 1.13/1.33 tff(622,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.13/1.33 tff(623,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.33 tff(624,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.13/1.33 tff(625,plain,
% 1.13/1.33 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[477])).
% 1.13/1.33 tff(626,plain,
% 1.13/1.33 (~(s(s(s(elem!1))) = elem!1)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[30, 625])).
% 1.13/1.33 tff(627,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.33 tff(628,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(629,plain,
% 1.13/1.33 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(630,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[629])).
% 1.13/1.33 tff(631,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[630, 628])).
% 1.13/1.33 tff(632,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(633,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[632, 631])).
% 1.13/1.33 tff(634,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[633, 121, 622, 623, 627, 624])).
% 1.13/1.33 tff(635,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(636,plain,
% 1.13/1.33 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[635, 622, 623, 624])).
% 1.13/1.33 tff(637,plain,
% 1.13/1.33 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[526, 636, 616])).
% 1.13/1.33 tff(638,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.13/1.33 tff(639,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(640,plain,
% 1.13/1.33 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(641,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[640])).
% 1.13/1.33 tff(642,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[641, 639])).
% 1.13/1.33 tff(643,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(644,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.13/1.33 tff(645,plain,
% 1.13/1.33 (~b(s(s(s(elem!1))), elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[644, 271, 307, 517, 638])).
% 1.13/1.33 tff(646,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(647,plain,
% 1.13/1.33 (((~b(s(elem!1), 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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(648,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[647])).
% 1.13/1.33 tff(649,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[648, 646])).
% 1.13/1.33 tff(650,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(651,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.13/1.33 tff(652,plain,
% 1.13/1.33 (~b(elem!1, s(s(s(elem!1))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[651, 271, 307, 517, 638])).
% 1.13/1.33 tff(653,plain,
% 1.13/1.33 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.13/1.33 inference(commutativity,[status(thm)],[])).
% 1.13/1.33 tff(654,plain,
% 1.13/1.33 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.13/1.33 inference(symmetry,[status(thm)],[653])).
% 1.13/1.33 tff(655,plain,
% 1.13/1.33 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[654])).
% 1.13/1.33 tff(656,plain,
% 1.13/1.33 (~(elem!1 = s(s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[481, 655])).
% 1.13/1.33 tff(657,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.33 tff(658,plain,
% 1.13/1.33 (((~![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)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(659,plain,
% 1.13/1.33 ((~![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)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(660,plain,
% 1.13/1.34 ((~![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))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.13/1.34 tff(661,plain,
% 1.13/1.34 ((elem!1 = s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[660, 21, 657])).
% 1.13/1.34 tff(662,plain,
% 1.13/1.34 (r(elem!1, s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[661, 656])).
% 1.13/1.34 tff(663,plain,
% 1.13/1.34 (r(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[486, 481, 479])).
% 1.13/1.34 tff(664,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(665,plain,
% 1.13/1.34 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(666,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[665])).
% 1.13/1.34 tff(667,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[666, 664])).
% 1.13/1.34 tff(668,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(669,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.13/1.34 tff(670,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[669, 121, 623, 624, 663, 662])).
% 1.13/1.34 tff(671,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(672,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[671, 652, 645, 624, 481, 623])).
% 1.13/1.34 tff(673,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(674,plain,
% 1.13/1.34 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[673, 637, 626, 623, 307, 624])).
% 1.13/1.34 tff(675,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(676,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(677,plain,
% 1.13/1.34 (((~![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)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(678,plain,
% 1.13/1.34 ((~![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)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(679,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.13/1.34 tff(680,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[679, 21, 676, 82, 675])).
% 1.13/1.34 tff(681,plain,(r(s(s(s(elem!1))), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(682,plain,
% 1.13/1.34 (r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[681, 674, 82])).
% 1.13/1.34 tff(683,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(684,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(685,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(686,plain,
% 1.13/1.34 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(687,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[686])).
% 1.13/1.34 tff(688,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[687, 685])).
% 1.13/1.34 tff(689,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(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))))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(690,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[689, 688])).
% 1.13/1.34 tff(691,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[690, 121, 622, 623, 684, 683])).
% 1.13/1.34 tff(692,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(693,plain,
% 1.13/1.34 (~r(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[692, 682, 623, 622])).
% 1.13/1.34 tff(694,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(695,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(696,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(697,plain,
% 1.13/1.34 (((~![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)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(698,plain,
% 1.13/1.34 ((~![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)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(699,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.13/1.34 tff(700,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[699, 21, 696, 695, 694])).
% 1.13/1.34 tff(701,plain,(b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(702,plain,
% 1.13/1.34 (b(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[701, 693, 621])).
% 1.13/1.34 tff(703,plain,
% 1.13/1.34 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[135])).
% 1.13/1.34 tff(704,plain,
% 1.13/1.34 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[703])).
% 1.13/1.34 tff(705,plain,
% 1.13/1.34 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[704])).
% 1.13/1.34 tff(706,plain,
% 1.13/1.34 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[705])).
% 1.13/1.34 tff(707,plain,
% 1.13/1.34 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.13/1.34 inference(symmetry,[status(thm)],[706])).
% 1.13/1.34 tff(708,plain,
% 1.13/1.34 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.34 tff(709,plain,
% 1.13/1.34 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[708])).
% 1.13/1.34 tff(710,plain,
% 1.13/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(711,plain,
% 1.13/1.34 (~(s(s(s(s(s(z))))) = z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[710, 9])).
% 1.13/1.34 tff(712,plain,
% 1.13/1.34 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[711, 709])).
% 1.13/1.34 tff(713,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(714,plain,
% 1.13/1.34 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(715,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[714])).
% 1.13/1.34 tff(716,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.34 inference(transitivity,[status(thm)],[715, 713])).
% 1.13/1.34 tff(717,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(718,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.13/1.34 tff(719,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[718, 121, 622, 684, 624, 139])).
% 1.13/1.34 tff(720,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(721,plain,
% 1.13/1.34 (~r(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[720, 682, 622, 624])).
% 1.13/1.34 tff(722,plain,
% 1.13/1.34 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[486, 721, 626])).
% 1.13/1.34 tff(723,plain,
% 1.13/1.34 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[133])).
% 1.13/1.34 tff(724,plain,
% 1.13/1.34 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[477, 654])).
% 1.13/1.34 tff(725,plain,
% 1.13/1.34 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[724])).
% 1.13/1.34 tff(726,plain,
% 1.13/1.34 (~(elem!1 = s(s(s(elem!1))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[30, 725])).
% 1.13/1.34 tff(727,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.34 tff(728,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(729,plain,
% 1.13/1.34 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(730,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[729])).
% 1.13/1.34 tff(731,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[730, 728])).
% 1.13/1.34 tff(732,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(733,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[732, 731])).
% 1.13/1.34 tff(734,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[733, 121, 623, 684, 624, 727])).
% 1.13/1.34 tff(735,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(736,plain,
% 1.13/1.34 (~r(elem!1, s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[735, 682, 623, 624])).
% 1.13/1.34 tff(737,plain,
% 1.13/1.34 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[660, 21, 736, 726])).
% 1.13/1.34 tff(738,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.34 tff(739,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.34 tff(740,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(741,plain,
% 1.13/1.34 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(742,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[741])).
% 1.13/1.34 tff(743,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.34 inference(transitivity,[status(thm)],[742, 740])).
% 1.13/1.34 tff(744,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(745,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[744, 743])).
% 1.13/1.34 tff(746,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[745, 271, 307, 739, 504, 738])).
% 1.13/1.34 tff(747,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(748,plain,
% 1.13/1.34 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[747, 737, 307, 722])).
% 1.13/1.34 tff(749,plain,
% 1.13/1.34 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[133])).
% 1.13/1.34 tff(750,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.34 tff(751,plain,
% 1.13/1.34 (b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.13/1.34 tff(752,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.34 tff(753,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[752, 751])).
% 1.13/1.34 tff(754,plain,((~b(s(z), s(s(s(elem!1))))) | b(s(elem!1), s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(755,plain,
% 1.13/1.34 (~b(s(z), s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[754, 748, 107])).
% 1.13/1.34 tff(756,plain,
% 1.13/1.34 (((~![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)))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(757,plain,
% 1.13/1.34 ((~![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)))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(758,plain,
% 1.13/1.34 ((~![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))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[757, 756])).
% 1.13/1.34 tff(759,plain,
% 1.13/1.34 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[758, 21])).
% 1.13/1.34 tff(760,plain,
% 1.13/1.34 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[759, 61])).
% 1.13/1.34 tff(761,plain,
% 1.13/1.34 (r(s(z), s(s(s(elem!1))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[760, 755])).
% 1.13/1.34 tff(762,plain,
% 1.13/1.34 (r(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[761, 723])).
% 1.13/1.34 tff(763,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(764,plain,
% 1.13/1.34 (inj_0(s(s(z))) = s(z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[763, 48])).
% 1.13/1.34 tff(765,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(766,plain,
% 1.13/1.34 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[765, 48])).
% 1.13/1.34 tff(767,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 1.13/1.34 tff(768,plain,
% 1.13/1.34 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[767])).
% 1.13/1.34 tff(769,plain,
% 1.13/1.34 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[768])).
% 1.13/1.34 tff(770,plain,
% 1.13/1.34 (s(s(z)) = s(s(s(s(z))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[92, 769, 766])).
% 1.13/1.34 tff(771,plain,
% 1.13/1.34 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[770])).
% 1.13/1.34 tff(772,plain,
% 1.13/1.34 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.13/1.34 inference(symmetry,[status(thm)],[771])).
% 1.13/1.34 tff(773,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(774,plain,
% 1.13/1.34 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[773, 48])).
% 1.13/1.34 tff(775,plain,
% 1.13/1.34 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[774])).
% 1.13/1.34 tff(776,plain,
% 1.13/1.34 (s(s(s(z))) = s(z)),
% 1.13/1.34 inference(transitivity,[status(thm)],[775, 772, 764])).
% 1.13/1.34 tff(777,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[97, 776])).
% 1.13/1.34 tff(778,plain,(~(s(s(s(s(s(z))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(779,plain,
% 1.13/1.34 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.13/1.34 inference(symmetry,[status(thm)],[135])).
% 1.13/1.34 tff(780,plain,
% 1.13/1.34 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[705, 779])).
% 1.13/1.35 tff(781,plain,
% 1.13/1.35 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[780])).
% 1.13/1.35 tff(782,assumption,(~(s(s(s(s(s(z))))) = s(s(s(z))))), introduced(assumption)).
% 1.13/1.35 tff(783,plain,
% 1.13/1.35 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[705, 779])).
% 1.13/1.35 tff(784,plain,
% 1.13/1.35 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[783])).
% 1.13/1.35 tff(785,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.13/1.35 tff(786,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(787,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(788,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[787, 786])).
% 1.13/1.35 tff(789,plain,
% 1.13/1.35 ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[788, 271, 307, 504])).
% 1.13/1.35 tff(790,plain,
% 1.13/1.35 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[789, 785])).
% 1.13/1.35 tff(791,plain,
% 1.13/1.35 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[790, 784])).
% 1.13/1.35 tff(792,plain,
% 1.13/1.35 (((~![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)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(793,plain,
% 1.13/1.35 ((~![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)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(794,plain,
% 1.13/1.35 ((~![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))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.13/1.35 tff(795,plain,
% 1.13/1.35 ((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))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[794, 21])).
% 1.13/1.35 tff(796,plain,
% 1.13/1.35 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[795, 791, 782])).
% 1.13/1.35 tff(797,plain,
% 1.13/1.35 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[796, 781])).
% 1.13/1.35 tff(798,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.35 tff(799,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(800,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(801,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.13/1.35 tff(802,plain,
% 1.13/1.35 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[801, 121, 684, 798])).
% 1.13/1.35 tff(803,plain,
% 1.13/1.35 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[802, 797])).
% 1.13/1.35 tff(804,plain,
% 1.13/1.35 (elem!1 = z),
% 1.13/1.35 inference(symmetry,[status(thm)],[107])).
% 1.13/1.35 tff(805,assumption,(s(s(s(s(s(elem!1))))) = s(elem!1)), introduced(assumption)).
% 1.13/1.35 tff(806,plain,
% 1.13/1.35 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[805])).
% 1.13/1.35 tff(807,plain,
% 1.13/1.35 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(808,plain,
% 1.13/1.35 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[807, 48])).
% 1.13/1.35 tff(809,plain,
% 1.13/1.35 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[808])).
% 1.13/1.35 tff(810,plain,
% 1.13/1.35 (s(s(s(s(elem!1)))) = z),
% 1.13/1.35 inference(transitivity,[status(thm)],[809, 806, 70, 804])).
% 1.13/1.35 tff(811,plain,
% 1.13/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(812,plain,
% 1.13/1.35 (~(s(s(s(s(elem!1)))) = z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[811, 9])).
% 1.13/1.35 tff(813,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[812, 810])).
% 1.13/1.35 tff(814,plain,((~(s(s(s(s(s(elem!1))))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(815,plain,
% 1.13/1.35 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[814, 107])).
% 1.13/1.35 tff(816,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(817,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(818,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[817, 816])).
% 1.13/1.35 tff(819,plain,
% 1.13/1.35 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[818, 21, 815, 803])).
% 1.13/1.35 tff(820,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(821,plain,
% 1.13/1.35 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(822,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[821])).
% 1.13/1.35 tff(823,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[822, 820])).
% 1.13/1.35 tff(824,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(825,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[824, 823])).
% 1.13/1.35 tff(826,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[825, 271, 307, 517, 785, 819])).
% 1.13/1.35 tff(827,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(z)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(828,plain,
% 1.13/1.35 ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[827, 778])).
% 1.13/1.35 tff(829,plain,
% 1.13/1.35 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[828, 762, 107, 637, 682, 307, 722])).
% 1.13/1.35 tff(830,plain,
% 1.13/1.35 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[704])).
% 1.13/1.35 tff(831,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.13/1.35 tff(832,plain,
% 1.13/1.35 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[831, 830])).
% 1.13/1.35 tff(833,assumption,(~b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.13/1.35 tff(834,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[833, 832])).
% 1.13/1.35 tff(835,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(836,plain,
% 1.13/1.35 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[835, 829, 107])).
% 1.13/1.35 tff(837,plain,
% 1.13/1.35 (((~![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))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(838,plain,
% 1.13/1.35 ((~![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))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(839,plain,
% 1.13/1.35 ((~![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)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.13/1.35 tff(840,plain,
% 1.13/1.35 ((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)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[839, 21])).
% 1.13/1.35 tff(841,plain,
% 1.13/1.35 (r(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[840, 836, 712])).
% 1.13/1.35 tff(842,plain,
% 1.13/1.35 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[841, 707])).
% 1.13/1.35 tff(843,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(844,plain,
% 1.13/1.35 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(845,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[844])).
% 1.13/1.35 tff(846,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[845, 843])).
% 1.13/1.35 tff(847,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(848,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.13/1.35 tff(849,plain,
% 1.13/1.35 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[848, 121, 622, 624, 842])).
% 1.13/1.35 tff(850,plain,
% 1.13/1.35 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[818, 21, 815, 849])).
% 1.13/1.35 tff(851,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.13/1.35 tff(852,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(853,plain,
% 1.13/1.35 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(854,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[853])).
% 1.13/1.35 tff(855,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[854, 852])).
% 1.13/1.35 tff(856,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(857,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.13/1.35 tff(858,plain,
% 1.13/1.35 (~b(s(s(elem!1)), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[857, 271, 307, 637, 702])).
% 1.13/1.35 tff(859,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.13/1.35 tff(860,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.13/1.35 tff(861,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[540, 21, 860, 859, 851])).
% 1.13/1.35 tff(862,plain,(r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(863,plain,
% 1.13/1.35 (r(s(s(elem!1)), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[862, 858, 851])).
% 1.13/1.35 tff(864,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(865,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(866,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[865, 864])).
% 1.13/1.35 tff(867,plain,
% 1.13/1.35 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[866, 121, 624, 863, 842])).
% 1.13/1.35 tff(868,plain,
% 1.13/1.35 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[704, 134])).
% 1.13/1.35 tff(869,plain,
% 1.13/1.35 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[868])).
% 1.13/1.35 tff(870,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.13/1.35 tff(871,plain,
% 1.13/1.35 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[870])).
% 1.13/1.35 tff(872,plain,
% 1.13/1.35 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[766])).
% 1.13/1.35 tff(873,plain,
% 1.13/1.35 (s(s(s(s(z)))) = s(z)),
% 1.13/1.35 inference(transitivity,[status(thm)],[872, 871, 764])).
% 1.13/1.35 tff(874,plain,
% 1.13/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[873])).
% 1.13/1.35 tff(875,plain,
% 1.13/1.35 (s(s(s(z))) = z),
% 1.13/1.35 inference(transitivity,[status(thm)],[775, 874, 50])).
% 1.13/1.35 tff(876,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[166, 875])).
% 1.13/1.35 tff(877,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(878,plain,
% 1.13/1.35 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[877, 869])).
% 1.13/1.35 tff(879,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(880,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(881,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[880, 879])).
% 1.13/1.35 tff(882,plain,
% 1.13/1.35 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[881, 21, 878, 867])).
% 1.13/1.35 tff(883,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(884,plain,
% 1.13/1.35 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(885,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[884])).
% 1.13/1.35 tff(886,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[885, 883])).
% 1.13/1.35 tff(887,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(888,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.13/1.36 tff(889,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[888, 271, 637, 882, 850, 702])).
% 1.13/1.36 tff(890,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(891,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[890, 600, 557, 467, 471, 79, 470, 198])).
% 1.13/1.36 tff(892,plain,(b(z, elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(893,plain,
% 1.13/1.36 (~b(z, s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[892, 158, 1, 37, 26, 108, 67, 68, 150, 193])).
% 1.13/1.36 tff(894,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.13/1.36 tff(895,assumption,(z = s(z)), introduced(assumption)).
% 1.13/1.36 tff(896,plain,
% 1.13/1.36 (s(z) = z),
% 1.13/1.36 inference(symmetry,[status(thm)],[895])).
% 1.13/1.36 tff(897,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[11, 896])).
% 1.13/1.36 tff(898,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(899,assumption,(~r(z, s(z))), introduced(assumption)).
% 1.13/1.36 tff(900,plain,
% 1.13/1.36 (((~![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)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(901,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(902,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[901, 900])).
% 1.13/1.36 tff(903,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[902, 21, 894, 899, 898])).
% 1.13/1.36 tff(904,plain,(b(z, s(z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(905,plain,
% 1.13/1.36 (r(z, s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[904, 894])).
% 1.13/1.36 tff(906,assumption,(~r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.36 tff(907,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.13/1.36 tff(908,plain,
% 1.13/1.36 (b(s(s(s(z))), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[255, 907, 221])).
% 1.13/1.36 tff(909,assumption,(r(z, s(z))), introduced(assumption)).
% 1.13/1.36 tff(910,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.13/1.36 tff(911,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.13/1.36 tff(912,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(913,plain,
% 1.13/1.36 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(914,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[913])).
% 1.13/1.36 tff(915,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[914, 912])).
% 1.13/1.36 tff(916,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(917,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[916, 915])).
% 1.13/1.36 tff(918,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[917, 121, 110, 909, 911, 910])).
% 1.13/1.36 tff(919,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(920,plain,
% 1.13/1.36 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[919, 910, 909, 110])).
% 1.13/1.36 tff(921,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.13/1.36 tff(922,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.13/1.36 tff(923,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.13/1.36 tff(924,plain,
% 1.13/1.36 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[923])).
% 1.13/1.36 tff(925,plain,
% 1.13/1.36 (s(s(s(z))) = z),
% 1.13/1.36 inference(transitivity,[status(thm)],[775, 924, 50])).
% 1.13/1.36 tff(926,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[166, 925])).
% 1.13/1.36 tff(927,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(928,plain,
% 1.13/1.36 (((~![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)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(929,plain,
% 1.13/1.36 ((~![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)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(930,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.13/1.36 tff(931,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[930, 21, 927, 922, 921])).
% 1.13/1.36 tff(932,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(933,plain,
% 1.13/1.36 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[932, 920])).
% 1.13/1.36 tff(934,plain,
% 1.13/1.36 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.13/1.36 inference(commutativity,[status(thm)],[])).
% 1.13/1.36 tff(935,plain,
% 1.13/1.36 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[934])).
% 1.13/1.36 tff(936,plain,
% 1.13/1.36 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[935])).
% 1.13/1.36 tff(937,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.13/1.36 tff(938,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 1.13/1.36 tff(939,plain,
% 1.13/1.36 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[938])).
% 1.13/1.36 tff(940,plain,
% 1.13/1.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.13/1.36 inference(symmetry,[status(thm)],[939])).
% 1.13/1.36 tff(941,plain,
% 1.13/1.36 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.13/1.36 inference(symmetry,[status(thm)],[938])).
% 1.13/1.36 tff(942,plain,
% 1.13/1.36 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[941])).
% 1.13/1.36 tff(943,plain,
% 1.13/1.36 (s(s(s(z))) = s(s(elem!1))),
% 1.13/1.36 inference(transitivity,[status(thm)],[775, 942, 55])).
% 1.13/1.36 tff(944,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.36 tff(945,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[944, 943])).
% 1.13/1.36 tff(946,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(947,plain,
% 1.13/1.36 (s(s(s(z))) = s(s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[946, 938])).
% 1.13/1.36 tff(948,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(949,plain,
% 1.13/1.36 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[948])).
% 1.13/1.36 tff(950,plain,
% 1.13/1.36 (s(s(z)) = s(elem!1)),
% 1.13/1.36 inference(transitivity,[status(thm)],[92, 949, 604])).
% 1.13/1.36 tff(951,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(952,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[951, 950])).
% 1.13/1.36 tff(953,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(954,plain,
% 1.13/1.36 (s(s(z)) = s(elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[953, 947])).
% 1.13/1.36 tff(955,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 1.13/1.36 tff(956,plain,
% 1.13/1.36 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[955])).
% 1.13/1.36 tff(957,plain,
% 1.13/1.36 (s(z) = inj_0(s(s(z)))),
% 1.13/1.36 inference(symmetry,[status(thm)],[764])).
% 1.13/1.36 tff(958,plain,
% 1.13/1.36 (s(z) = elem!1),
% 1.13/1.36 inference(transitivity,[status(thm)],[957, 956, 70])).
% 1.13/1.36 tff(959,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[231, 958])).
% 1.13/1.36 tff(960,plain,((~(s(s(z)) = s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(961,plain,
% 1.13/1.36 (s(z) = elem!1),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[960, 954])).
% 1.13/1.36 tff(962,plain,
% 1.13/1.36 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[961])).
% 1.13/1.36 tff(963,plain,
% 1.13/1.36 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.13/1.36 inference(transitivity,[status(thm)],[962, 940])).
% 1.13/1.36 tff(964,plain,
% 1.13/1.36 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[937, 963])).
% 1.13/1.36 tff(965,plain,
% 1.13/1.36 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[961])).
% 1.13/1.36 tff(966,plain,
% 1.13/1.36 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(symmetry,[status(thm)],[965])).
% 1.13/1.36 tff(967,plain,
% 1.13/1.36 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[938])).
% 1.13/1.36 tff(968,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(z)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[56, 967, 774])).
% 1.13/1.36 tff(969,plain,
% 1.13/1.36 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[968])).
% 1.13/1.36 tff(970,plain,
% 1.13/1.36 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.13/1.36 inference(symmetry,[status(thm)],[969])).
% 1.13/1.36 tff(971,plain,
% 1.13/1.36 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(transitivity,[status(thm)],[970, 966])).
% 1.13/1.36 tff(972,plain,
% 1.13/1.36 (b(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[257, 971])).
% 1.13/1.36 tff(973,plain,
% 1.13/1.36 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[968, 938])).
% 1.13/1.36 tff(974,plain,
% 1.13/1.36 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[973])).
% 1.13/1.36 tff(975,plain,
% 1.13/1.36 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[974])).
% 1.13/1.36 tff(976,plain,
% 1.13/1.36 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[938])).
% 1.13/1.36 tff(977,plain,
% 1.13/1.36 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[976])).
% 1.13/1.36 tff(978,plain,
% 1.13/1.36 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[906, 977])).
% 1.13/1.36 tff(979,plain,
% 1.13/1.36 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[978, 975])).
% 1.13/1.36 tff(980,plain,
% 1.13/1.36 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[556, 979, 1])).
% 1.13/1.36 tff(981,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.13/1.36 tff(982,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(983,plain,
% 1.13/1.36 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(984,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[983])).
% 1.13/1.36 tff(985,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[984, 982])).
% 1.13/1.36 tff(986,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(987,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.13/1.36 tff(988,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[987, 271, 543, 750, 504, 981])).
% 1.13/1.36 tff(989,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(990,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[989, 980, 972, 750, 964])).
% 1.13/1.36 tff(991,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(992,plain,
% 1.13/1.36 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[991, 750, 1, 257, 937, 906])).
% 1.13/1.36 tff(993,plain,
% 1.13/1.36 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[992, 936])).
% 1.13/1.36 tff(994,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(995,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(996,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[995, 994])).
% 1.13/1.36 tff(997,plain,
% 1.13/1.36 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[996, 271, 750, 503, 937])).
% 1.13/1.36 tff(998,plain,
% 1.13/1.36 (((~![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)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(999,plain,
% 1.13/1.36 ((~![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)))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(1000,plain,
% 1.13/1.36 ((~![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))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[999, 998])).
% 1.13/1.36 tff(1001,plain,
% 1.13/1.36 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1000, 21, 997])).
% 1.13/1.36 tff(1002,plain,
% 1.13/1.36 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1001, 993])).
% 1.13/1.36 tff(1003,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(1004,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(1005,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 1.13/1.36 tff(1006,plain,
% 1.13/1.36 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1005, 271, 750, 503, 937])).
% 1.13/1.36 tff(1007,assumption,(~r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.36 tff(1008,assumption,(~(s(s(s(elem!1))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.36 tff(1009,assumption,(~b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.36 tff(1010,plain,
% 1.13/1.36 (((~![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))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(1011,plain,
% 1.13/1.36 ((~![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))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(1012,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 1.13/1.36 tff(1013,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1012, 21, 1009, 1008, 1007])).
% 1.13/1.36 tff(1014,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(1015,plain,
% 1.13/1.36 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1014, 992, 1006])).
% 1.13/1.36 tff(1016,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(1017,plain,
% 1.13/1.36 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(1018,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[1017])).
% 1.13/1.36 tff(1019,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[1018, 1016])).
% 1.13/1.36 tff(1020,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(1021,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 1.13/1.36 tff(1022,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1021, 121, 111, 910, 1015, 1002])).
% 1.13/1.36 tff(1023,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(1024,plain,
% 1.13/1.36 (~b(s(z), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1023, 910, 111, 1, 257, 933, 906, 503])).
% 1.13/1.36 tff(1025,plain,
% 1.13/1.36 (r(s(z), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[760, 1024])).
% 1.13/1.36 tff(1026,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.36 tff(1027,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1028,plain,
% 1.13/1.37 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1029,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1028])).
% 1.13/1.37 tff(1030,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.13/1.37 tff(1031,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1032,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.13/1.37 tff(1033,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1032, 121, 111, 110, 1026, 910])).
% 1.13/1.37 tff(1034,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1035,plain,
% 1.13/1.37 (~r(s(z), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1034, 910, 110, 111])).
% 1.13/1.37 tff(1036,plain,
% 1.13/1.37 (s(s(z)) = s(elem!1)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.37 tff(1037,plain,
% 1.13/1.37 (s(s(s(z))) = s(s(elem!1))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1036])).
% 1.13/1.37 tff(1038,plain,
% 1.13/1.37 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1037])).
% 1.13/1.37 tff(1039,plain,
% 1.13/1.37 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1038])).
% 1.13/1.37 tff(1040,plain,
% 1.13/1.37 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[1039])).
% 1.13/1.37 tff(1041,plain,
% 1.13/1.37 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.37 tff(1042,plain,
% 1.13/1.37 (r(elem!1, s(s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[572, 1041])).
% 1.13/1.37 tff(1043,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(1044,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1043, 1042])).
% 1.13/1.37 tff(1045,plain,((~r(s(z), s(s(s(elem!1))))) | r(elem!1, s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1046,plain,
% 1.13/1.37 (r(elem!1, s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1045, 223, 572])).
% 1.13/1.37 tff(1047,plain,
% 1.13/1.37 (r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1046, 1040])).
% 1.13/1.37 tff(1048,plain,
% 1.13/1.37 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.37 tff(1049,plain,
% 1.13/1.37 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1048])).
% 1.13/1.37 tff(1050,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(1051,plain,
% 1.13/1.37 (~r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 1.13/1.37 tff(1052,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1051, 1047])).
% 1.13/1.37 tff(1053,plain,((~(s(z) = elem!1)) | r(s(z), s(s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1054,plain,
% 1.13/1.37 (~(s(z) = elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1053, 1035, 1025])).
% 1.13/1.37 tff(1055,plain,
% 1.13/1.37 (~(s(s(z)) = s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[960, 1054])).
% 1.13/1.37 tff(1056,plain,
% 1.13/1.37 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[953, 1055])).
% 1.13/1.37 tff(1057,plain,
% 1.13/1.37 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[946, 1056])).
% 1.13/1.37 tff(1058,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.13/1.37 tff(1059,plain,
% 1.13/1.37 (s(s(s(s(z)))) = s(z)),
% 1.13/1.37 inference(symmetry,[status(thm)],[1058])).
% 1.13/1.37 tff(1060,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[927, 1059])).
% 1.13/1.37 tff(1061,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1062,plain,
% 1.13/1.37 (((~![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))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1063,plain,
% 1.13/1.37 ((~![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))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1064,plain,
% 1.13/1.37 ((~![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)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.13/1.37 tff(1065,plain,
% 1.13/1.37 (b(s(z), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1064, 21, 1035, 1061])).
% 1.13/1.37 tff(1066,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(1067,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(1068,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1069,plain,
% 1.13/1.37 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1070,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1069])).
% 1.13/1.37 tff(1071,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[1070, 1068])).
% 1.13/1.37 tff(1072,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1073,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.13/1.37 tff(1074,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1073, 271, 503, 937, 1067, 1066])).
% 1.13/1.37 tff(1075,plain,((~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(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1076,plain,
% 1.13/1.37 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1075, 1065, 503, 933])).
% 1.13/1.37 tff(1077,plain,
% 1.13/1.37 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1014, 1076, 1057])).
% 1.13/1.37 tff(1078,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1079,plain,
% 1.13/1.37 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1080,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1079])).
% 1.13/1.37 tff(1081,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[1080, 1078])).
% 1.13/1.37 tff(1082,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1083,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 1.13/1.37 tff(1084,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1083, 121, 111, 1025, 110, 1077])).
% 1.13/1.37 tff(1085,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1086,plain,
% 1.13/1.37 (~r(s(s(s(s(z)))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1085, 908, 26, 67, 1, 37, 906, 905])).
% 1.13/1.37 tff(1087,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.13/1.37 tff(1088,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.13/1.37 tff(1089,plain,
% 1.13/1.37 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1090,plain,
% 1.13/1.37 (~(s(s(s(s(z)))) = z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1089, 9])).
% 1.13/1.37 tff(1091,plain,
% 1.13/1.37 (((~![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))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1092,plain,
% 1.13/1.37 ((~![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))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1093,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 1.13/1.37 tff(1094,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1093, 21, 1090, 1088, 1087])).
% 1.13/1.37 tff(1095,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1096,plain,
% 1.13/1.37 (b(s(s(s(s(z)))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1095, 1086])).
% 1.13/1.37 tff(1097,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(1098,plain,
% 1.13/1.37 (s(s(s(z))) = elem!1),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1097, 160])).
% 1.13/1.37 tff(1099,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[907, 1098])).
% 1.13/1.37 tff(1100,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1101,plain,
% 1.13/1.37 (~(elem!1 = s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1100, 907])).
% 1.13/1.37 tff(1102,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.13/1.37 tff(1103,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.13/1.37 tff(1104,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1105,plain,
% 1.13/1.37 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1106,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1105])).
% 1.13/1.37 tff(1107,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.13/1.37 tff(1108,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1109,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.13/1.37 tff(1110,plain,
% 1.13/1.37 (~r(z, s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1109, 121, 110, 909, 911])).
% 1.13/1.37 tff(1111,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 1.13/1.37 tff(1112,plain,
% 1.13/1.37 (s(s(s(s(z)))) = z),
% 1.13/1.37 inference(symmetry,[status(thm)],[1111])).
% 1.13/1.37 tff(1113,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1090, 1112])).
% 1.13/1.37 tff(1114,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1115,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(1116,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(1117,plain,
% 1.13/1.37 (((~![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))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1118,plain,
% 1.13/1.37 ((~![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))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1119,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.13/1.37 tff(1120,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1119, 21, 1116, 1115, 1114])).
% 1.13/1.37 tff(1121,plain,(b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1122,plain,
% 1.13/1.37 (b(z, s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1121, 1110])).
% 1.13/1.37 tff(1123,plain,
% 1.13/1.37 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.13/1.37 inference(commutativity,[status(thm)],[])).
% 1.13/1.37 tff(1124,plain,
% 1.13/1.37 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[1123])).
% 1.13/1.37 tff(1125,plain,
% 1.13/1.37 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1124])).
% 1.13/1.37 tff(1126,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(1127,plain,
% 1.13/1.37 (s(s(s(z))) = s(s(s(s(z))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[1126])).
% 1.13/1.37 tff(1128,plain,
% 1.13/1.37 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1127])).
% 1.13/1.37 tff(1129,plain,
% 1.13/1.37 (s(s(z)) = s(s(s(z)))),
% 1.13/1.37 inference(transitivity,[status(thm)],[92, 1128, 774])).
% 1.13/1.37 tff(1130,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(1131,plain,
% 1.13/1.37 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1130])).
% 1.13/1.37 tff(1132,plain,
% 1.13/1.37 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.13/1.37 inference(symmetry,[status(thm)],[1131])).
% 1.13/1.37 tff(1133,plain,
% 1.13/1.37 (s(s(s(z))) = s(s(z))),
% 1.13/1.37 inference(symmetry,[status(thm)],[1130])).
% 1.13/1.37 tff(1134,plain,
% 1.13/1.37 (s(s(s(z))) = s(z)),
% 1.13/1.37 inference(transitivity,[status(thm)],[1133, 92, 1132, 764])).
% 1.13/1.37 tff(1135,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[97, 1134])).
% 1.13/1.37 tff(1136,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1137,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1136, 1129])).
% 1.13/1.37 tff(1138,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1139,plain,
% 1.13/1.37 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1138, 1125])).
% 1.13/1.37 tff(1140,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.13/1.37 tff(1141,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1142,plain,
% 1.13/1.37 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1143,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1142])).
% 1.13/1.37 tff(1144,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[1143, 1141])).
% 1.13/1.37 tff(1145,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1146,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.13/1.37 tff(1147,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1146, 121, 909, 109, 1140, 108])).
% 1.13/1.37 tff(1148,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1149,plain,
% 1.13/1.37 (~r(s(s(s(z))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1148, 1140, 108, 909])).
% 1.13/1.37 tff(1150,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.13/1.37 tff(1151,plain,
% 1.13/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![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))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1152,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(1153,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.13/1.37 tff(1154,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1153, 21, 166, 141, 1150])).
% 1.13/1.37 tff(1155,plain,(b(s(s(s(z))), z) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(1156,plain,
% 1.13/1.37 (b(s(s(s(z))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1155, 1149])).
% 1.13/1.37 tff(1157,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(1158,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), z)) | (~b(s(s(s(z))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1159,plain,
% 1.13/1.37 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~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)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(1160,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), z)) | (~b(s(s(s(z))), z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1159])).
% 1.13/1.37 tff(1161,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), z)) | (~b(s(s(s(z))), z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[1160, 1158])).
% 1.13/1.38 tff(1162,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1163,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), z)) | (~b(s(s(s(z))), z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 1.13/1.38 tff(1164,plain,
% 1.13/1.38 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1163, 271, 1157, 1156, 1103])).
% 1.13/1.38 tff(1165,plain,
% 1.13/1.38 (((~![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))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1166,plain,
% 1.13/1.38 ((~![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))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1167,plain,
% 1.13/1.38 ((~![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)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 1.13/1.38 tff(1168,plain,
% 1.13/1.38 ((s(s(s(z))) = s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1167, 21, 1164])).
% 1.13/1.38 tff(1169,plain,
% 1.13/1.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1168, 1139])).
% 1.13/1.38 tff(1170,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1171,plain,
% 1.13/1.38 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1172,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1171])).
% 1.13/1.38 tff(1173,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[1172, 1170])).
% 1.13/1.38 tff(1174,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1175,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 1.13/1.38 tff(1176,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1175, 121, 110, 1140, 108, 1169])).
% 1.13/1.38 tff(1177,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1178,plain,
% 1.13/1.38 (~r(z, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1177, 1122, 108, 110, 1103, 909])).
% 1.13/1.38 tff(1179,plain,
% 1.13/1.38 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.38 tff(1180,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[1179])).
% 1.13/1.38 tff(1181,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 1.13/1.38 tff(1182,plain,
% 1.13/1.38 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[107])).
% 1.13/1.38 tff(1183,plain,
% 1.13/1.38 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[1182])).
% 1.13/1.38 tff(1184,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.13/1.38 tff(1185,plain,
% 1.13/1.38 (r(z, s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 1.13/1.38 tff(1186,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1181, 1185])).
% 1.13/1.38 tff(1187,plain,((~r(elem!1, s(s(s(z))))) | r(z, s(s(s(z)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1188,plain,
% 1.13/1.38 (~r(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1187, 107, 1181])).
% 1.13/1.38 tff(1189,plain,
% 1.13/1.38 (((~![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)))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1190,plain,
% 1.13/1.38 ((~![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)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1191,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.13/1.38 tff(1192,plain,
% 1.13/1.38 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1191, 21])).
% 1.13/1.38 tff(1193,plain,
% 1.13/1.38 (b(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1192, 1188, 1102])).
% 1.13/1.38 tff(1194,plain,
% 1.13/1.38 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[135])).
% 1.13/1.38 tff(1195,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.13/1.38 tff(1196,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.13/1.38 tff(1197,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[657, 1196])).
% 1.13/1.38 tff(1198,plain,((~b(elem!1, s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1199,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1198, 1193, 107])).
% 1.13/1.38 tff(1200,plain,
% 1.13/1.38 (b(z, s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1199, 1180])).
% 1.13/1.38 tff(1201,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[33, 1200])).
% 1.13/1.38 tff(1202,plain,((~(z = elem!1)) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(z)))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1203,plain,
% 1.13/1.38 (~(z = elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1202, 1178, 1102, 33])).
% 1.13/1.38 tff(1204,plain,
% 1.13/1.38 (~(elem!1 = z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[333, 1203])).
% 1.13/1.38 tff(1205,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 1.13/1.38 tff(1206,plain,
% 1.13/1.38 (s(s(s(z))) = z),
% 1.13/1.38 inference(symmetry,[status(thm)],[1205])).
% 1.13/1.38 tff(1207,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[166, 1206])).
% 1.13/1.38 tff(1208,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1209,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.13/1.38 tff(1210,plain,
% 1.13/1.38 (((~![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)))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1211,plain,
% 1.13/1.38 ((~![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)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1212,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 1.13/1.38 tff(1213,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1212, 21, 1209, 1181, 1208])).
% 1.13/1.38 tff(1214,plain,(b(z, s(s(s(z)))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1215,plain,
% 1.13/1.38 (b(z, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1214, 1178])).
% 1.13/1.38 tff(1216,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.38 tff(1217,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.13/1.38 inference(symmetry,[status(thm)],[1216])).
% 1.13/1.38 tff(1218,plain,
% 1.13/1.38 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.13/1.38 inference(symmetry,[status(thm)],[238])).
% 1.13/1.38 tff(1219,plain,
% 1.13/1.38 (elem!1 = s(z)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[223, 1218])).
% 1.13/1.38 tff(1220,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[258, 1219])).
% 1.13/1.38 tff(1221,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1222,plain,
% 1.13/1.38 (elem!1 = s(z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1221, 223])).
% 1.13/1.38 tff(1223,plain,
% 1.13/1.38 (s(elem!1) = s(s(z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[239])).
% 1.13/1.38 tff(1224,plain,
% 1.13/1.38 (s(s(elem!1)) = s(s(s(z)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1223])).
% 1.13/1.38 tff(1225,plain,
% 1.13/1.38 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1224])).
% 1.13/1.38 tff(1226,plain,
% 1.13/1.38 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.13/1.38 inference(symmetry,[status(thm)],[1225])).
% 1.13/1.38 tff(1227,plain,
% 1.13/1.38 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1226])).
% 1.13/1.38 tff(1228,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(symmetry,[status(thm)],[1227])).
% 1.13/1.38 tff(1229,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[239])).
% 1.13/1.38 tff(1230,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(transitivity,[status(thm)],[1229, 1228])).
% 1.13/1.38 tff(1231,plain,
% 1.13/1.38 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(z)))), s(z)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1230])).
% 1.13/1.38 tff(1232,plain,
% 1.13/1.38 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[147, 1231])).
% 1.13/1.38 tff(1233,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[911, 1232])).
% 1.13/1.38 tff(1234,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1235,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1234, 1222, 911])).
% 1.13/1.38 tff(1236,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), s(z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1235, 1217])).
% 1.13/1.38 tff(1237,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[38, 1236])).
% 1.13/1.38 tff(1238,plain,((~(s(z) = elem!1)) | r(s(s(s(elem!1))), s(z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1239,plain,
% 1.13/1.38 (~(s(z) = elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1238, 911, 38])).
% 1.13/1.38 tff(1240,plain,
% 1.13/1.38 (~(elem!1 = s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[242, 1239])).
% 1.13/1.38 tff(1241,plain,
% 1.13/1.38 (~b(s(z), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[305, 1240, 257, 1204, 37, 110, 222])).
% 1.13/1.38 tff(1242,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.13/1.38 tff(1243,plain,
% 1.13/1.38 (r(z, elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[355, 199, 331])).
% 1.13/1.38 tff(1244,plain,
% 1.13/1.38 (r(s(z), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[236, 231, 1242])).
% 1.13/1.38 tff(1245,plain,
% 1.13/1.38 (~r(elem!1, s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[387, 1244, 110, 1243])).
% 1.13/1.38 tff(1246,plain,
% 1.13/1.38 (b(elem!1, s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[392, 1245, 377])).
% 1.13/1.38 tff(1247,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1248,plain,
% 1.13/1.38 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1249,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1248])).
% 1.13/1.38 tff(1250,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[1249, 1247])).
% 1.13/1.38 tff(1251,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1252,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 1.13/1.38 tff(1253,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1252, 121, 357, 909, 412, 411])).
% 1.13/1.38 tff(1254,plain,((~r(s(elem!1), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1255,plain,
% 1.13/1.38 (~r(s(elem!1), s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1254, 1244, 909, 412])).
% 1.13/1.38 tff(1256,plain,
% 1.13/1.38 (r(elem!1, s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[299, 258, 294])).
% 1.13/1.38 tff(1257,plain,
% 1.13/1.38 (~(s(z) = elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1221, 258])).
% 1.13/1.38 tff(1258,plain,
% 1.13/1.38 (r(s(z), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[236, 1257, 1242])).
% 1.13/1.38 tff(1259,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1260,plain,
% 1.13/1.38 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1261,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1260])).
% 1.13/1.38 tff(1262,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[1261, 1259])).
% 1.13/1.38 tff(1263,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1264,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 1.13/1.38 tff(1265,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1264, 121, 378, 1258, 909, 1256])).
% 1.13/1.38 tff(1266,plain,((elem!1 = s(z)) | (~r(z, elem!1)) | (~r(z, s(z))) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1267,plain,
% 1.13/1.38 (b(elem!1, s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1266, 243, 909, 1242, 378])).
% 1.13/1.38 tff(1268,plain,
% 1.13/1.38 (~b(s(elem!1), s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[456, 1267, 307, 446])).
% 1.13/1.38 tff(1269,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[429, 1268, 1255, 422])).
% 1.13/1.38 tff(1270,plain,((s(z) = elem!1) | (s(elem!1) = s(z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | b(s(z), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1271,plain,
% 1.13/1.38 (~b(s(z), s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1270, 1242, 231, 307, 909, 412, 1243, 351])).
% 1.13/1.38 tff(1272,plain,
% 1.13/1.38 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.38 tff(1273,plain,
% 1.13/1.38 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.13/1.38 inference(symmetry,[status(thm)],[1272])).
% 1.13/1.38 tff(1274,plain,
% 1.13/1.38 (b(s(z), s(elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[307, 1273])).
% 1.13/1.38 tff(1275,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[439, 1274])).
% 1.13/1.38 tff(1276,plain,((~(s(z) = elem!1)) | b(s(z), s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1277,plain,
% 1.13/1.38 (~(s(z) = elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1276, 439, 307])).
% 1.13/1.38 tff(1278,plain,
% 1.13/1.38 (~(elem!1 = s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[242, 1277])).
% 1.13/1.38 tff(1279,plain,
% 1.13/1.38 (r(s(z), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[236, 1242, 1257])).
% 1.13/1.38 tff(1280,plain,
% 1.13/1.38 (~r(s(elem!1), s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1254, 1279, 909, 412])).
% 1.13/1.38 tff(1281,assumption,(b(s(z), z)), introduced(assumption)).
% 1.13/1.38 tff(1282,plain,
% 1.13/1.38 (b(elem!1, s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1266, 1242, 909, 258, 378])).
% 1.13/1.38 tff(1283,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1284,plain,
% 1.13/1.38 (((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1285,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1284])).
% 1.13/1.38 tff(1286,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[1285, 1283])).
% 1.13/1.38 tff(1287,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1288,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.13/1.38 tff(1289,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1288, 271, 307, 1281, 448, 447])).
% 1.13/1.38 tff(1290,plain,((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1291,plain,
% 1.13/1.38 (~b(s(elem!1), s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1290, 1282, 307, 1281])).
% 1.13/1.38 tff(1292,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[429, 1291, 1280, 422])).
% 1.13/1.38 tff(1293,plain,(b(s(z), elem!1) | (s(elem!1) = s(z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1294,plain,
% 1.13/1.38 (~b(s(z), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1293, 351, 307, 1242, 909, 412, 1278, 356])).
% 1.13/1.38 tff(1295,plain,
% 1.13/1.38 (r(s(z), s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[444, 344, 439])).
% 1.13/1.38 tff(1296,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(1297,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(1298,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.13/1.38 tff(1299,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1298, 121, 110, 909, 412, 431])).
% 1.13/1.38 tff(1300,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1301,plain,
% 1.13/1.38 (~r(s(z), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1300, 1295, 412, 909])).
% 1.13/1.38 tff(1302,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[25, 1301, 1294])).
% 1.13/1.38 tff(1303,plain,((z = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | b(s(z), elem!1) | b(s(z), s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1304,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1303, 1271, 1242, 909, 307, 331, 412, 199])).
% 1.13/1.38 tff(1305,plain,(b(s(z), elem!1) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (z = elem!1) | (~r(s(elem!1), z)) | b(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(1306,plain,
% 1.13/1.38 (~r(s(elem!1), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1305, 1246, 909, 231, 199, 331, 1242])).
% 1.13/1.38 tff(1307,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.13/1.38 tff(1308,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1309,plain,
% 1.13/1.39 (((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1310,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(z)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1309])).
% 1.13/1.39 tff(1311,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(z))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[1310, 1308])).
% 1.13/1.39 tff(1312,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1313,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(z)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 1.13/1.39 tff(1314,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1313, 271, 307, 394, 261, 1307])).
% 1.13/1.39 tff(1315,plain,((~b(z, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1316,plain,
% 1.13/1.39 (~b(elem!1, z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1315, 307, 394, 1307])).
% 1.13/1.39 tff(1317,plain,
% 1.13/1.39 (r(elem!1, z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[284, 1316, 259])).
% 1.13/1.39 tff(1318,plain,
% 1.13/1.39 (~b(s(z), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[312, 307, 257, 222])).
% 1.13/1.39 tff(1319,plain,
% 1.13/1.39 (r(s(z), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[236, 1318, 231])).
% 1.13/1.39 tff(1320,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[373, 1319, 1317, 110, 378])).
% 1.13/1.39 tff(1321,plain,((~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (s(z) = elem!1) | (elem!1 = z) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1322,plain,
% 1.13/1.39 (~b(s(elem!1), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1321, 1246, 1243, 231, 358, 257, 222, 110, 1307])).
% 1.13/1.39 tff(1323,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[409, 1322, 1306])).
% 1.13/1.39 tff(1324,plain,((s(z) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | b(z, elem!1) | (z = elem!1) | b(s(z), elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1325,plain,
% 1.13/1.39 (b(z, elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1324, 1241, 222, 110, 1215, 909, 257, 1203, 1239, 377])).
% 1.13/1.39 tff(1326,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.13/1.39 tff(1327,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1328,plain,
% 1.13/1.39 (((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1329,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1328])).
% 1.13/1.39 tff(1330,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[1329, 1327])).
% 1.13/1.39 tff(1331,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1332,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 1.13/1.39 tff(1333,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1332, 271, 1326, 261, 1307, 257])).
% 1.13/1.39 tff(1334,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1335,plain,
% 1.13/1.39 (~b(elem!1, z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1334, 1325, 1215, 257])).
% 1.13/1.39 tff(1336,plain,
% 1.13/1.39 (r(elem!1, z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[284, 1335, 1204])).
% 1.13/1.39 tff(1337,plain,
% 1.13/1.39 (r(s(z), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[236, 1241, 1239])).
% 1.13/1.39 tff(1338,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1339,plain,
% 1.13/1.39 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1340,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1339])).
% 1.13/1.39 tff(1341,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[1340, 1338])).
% 1.13/1.39 tff(1342,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1343,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 1.13/1.39 tff(1344,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1343, 121, 1337, 37, 110, 1336])).
% 1.13/1.39 tff(1345,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (elem!1 = s(elem!1)) | r(s(s(s(elem!1))), s(z)) | (elem!1 = s(s(s(z)))) | b(z, s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1346,plain,
% 1.13/1.39 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1345, 908, 26, 222, 905, 219, 38, 1101, 33, 108, 1096])).
% 1.13/1.39 tff(1347,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[932, 922])).
% 1.13/1.39 tff(1348,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.13/1.39 tff(1349,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1350,plain,
% 1.13/1.39 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1351,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1350])).
% 1.13/1.39 tff(1352,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[1351, 1349])).
% 1.13/1.39 tff(1353,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1354,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.13/1.39 tff(1355,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1354, 121, 110, 1140, 108, 1348])).
% 1.13/1.39 tff(1356,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1357,plain,
% 1.13/1.39 (~r(s(s(s(z))), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1356, 1140, 108, 26])).
% 1.13/1.39 tff(1358,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.13/1.39 tff(1359,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.13/1.39 tff(1360,plain,
% 1.13/1.39 (s(s(z)) = s(s(s(z)))),
% 1.13/1.39 inference(symmetry,[status(thm)],[1359])).
% 1.13/1.39 tff(1361,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1136, 1360])).
% 1.13/1.39 tff(1362,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1363,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.13/1.39 tff(1364,plain,
% 1.13/1.39 (((~![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))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1365,plain,
% 1.13/1.39 ((~![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))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1366,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 1.13/1.39 tff(1367,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1366, 21, 1363, 1362, 1358])).
% 1.13/1.39 tff(1368,plain,(b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1369,plain,
% 1.13/1.39 (b(s(s(s(z))), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1368, 1357])).
% 1.13/1.39 tff(1370,plain,
% 1.13/1.39 (~r(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1148, 1140, 108, 905])).
% 1.13/1.39 tff(1371,plain,
% 1.13/1.39 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1036])).
% 1.13/1.39 tff(1372,plain,
% 1.13/1.39 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.39 inference(symmetry,[status(thm)],[1371])).
% 1.13/1.39 tff(1373,plain,
% 1.13/1.39 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.13/1.39 inference(symmetry,[status(thm)],[1038])).
% 1.13/1.39 tff(1374,plain,
% 1.13/1.39 (~b(s(z), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[991, 1373, 1, 257, 937, 906])).
% 1.13/1.39 tff(1375,plain,
% 1.13/1.39 (r(s(z), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[760, 1374])).
% 1.13/1.39 tff(1376,plain,
% 1.13/1.39 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[581, 1375, 111, 110])).
% 1.13/1.39 tff(1377,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[586, 1376, 563])).
% 1.13/1.39 tff(1378,plain,
% 1.13/1.39 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1037])).
% 1.13/1.39 tff(1379,plain,
% 1.13/1.39 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1378])).
% 1.13/1.39 tff(1380,plain,
% 1.13/1.39 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[906, 1379])).
% 1.13/1.39 tff(1381,plain,
% 1.13/1.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[556, 1380, 1])).
% 1.13/1.39 tff(1382,plain,
% 1.13/1.39 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1037])).
% 1.13/1.39 tff(1383,plain,
% 1.13/1.39 (b(s(s(elem!1)), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[257, 1382])).
% 1.13/1.39 tff(1384,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.13/1.39 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.39 tff(1385,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[503, 1384])).
% 1.13/1.39 tff(1386,plain,
% 1.13/1.39 (~b(elem!1, s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[551, 1381, 1385, 1383])).
% 1.13/1.39 tff(1387,plain,
% 1.13/1.39 (r(elem!1, s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[392, 1386, 219])).
% 1.13/1.39 tff(1388,plain,
% 1.13/1.39 ((s(z) = z) <=> (elem!1 = z)),
% 1.13/1.39 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.39 tff(1389,plain,
% 1.13/1.39 ((s(z) = z) <=> (z = elem!1)),
% 1.13/1.39 inference(transitivity,[status(thm)],[1388, 360])).
% 1.13/1.39 tff(1390,plain,
% 1.13/1.39 ((z = elem!1) <=> (s(z) = z)),
% 1.13/1.39 inference(symmetry,[status(thm)],[1389])).
% 1.13/1.39 tff(1391,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.13/1.39 tff(1392,plain,
% 1.13/1.39 (b(z, elem!1) <=> b(z, s(z))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[239])).
% 1.13/1.39 tff(1393,plain,
% 1.13/1.39 (b(z, s(z)) <=> b(z, elem!1)),
% 1.13/1.39 inference(symmetry,[status(thm)],[1392])).
% 1.13/1.39 tff(1394,plain,
% 1.13/1.39 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1393])).
% 1.13/1.39 tff(1395,plain,
% 1.13/1.39 (~b(z, elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[894, 1394])).
% 1.13/1.39 tff(1396,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1326, 1395])).
% 1.13/1.39 tff(1397,plain,((~(elem!1 = s(z))) | (~b(z, elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1398,plain,
% 1.13/1.39 (~b(z, elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1397, 1222, 894])).
% 1.13/1.39 tff(1399,plain,
% 1.13/1.39 (z = elem!1),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[355, 1398, 1391])).
% 1.13/1.39 tff(1400,plain,
% 1.13/1.39 (s(z) = z),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1399, 1390])).
% 1.13/1.39 tff(1401,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[11, 1400])).
% 1.13/1.39 tff(1402,plain,((~(s(z) = elem!1)) | r(z, elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1403,plain,
% 1.13/1.39 (r(z, elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1402, 223, 894])).
% 1.13/1.39 tff(1404,plain,
% 1.13/1.39 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1036])).
% 1.13/1.39 tff(1405,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.13/1.39 tff(1406,plain,
% 1.13/1.39 (b(s(s(s(z))), s(elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.13/1.39 tff(1407,plain,
% 1.13/1.39 (r(s(z), z) <=> r(elem!1, z)),
% 1.13/1.39 inference(monotonicity,[status(thm)],[223])).
% 1.13/1.39 tff(1408,plain,
% 1.13/1.39 (r(elem!1, z)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[110, 1407])).
% 1.13/1.39 tff(1409,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.13/1.39 tff(1410,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1411,plain,
% 1.13/1.39 (((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1412,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1411])).
% 1.13/1.39 tff(1413,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[1412, 1410])).
% 1.13/1.39 tff(1414,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1415,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.13/1.39 tff(1416,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1415, 121, 379, 909, 1409, 412])).
% 1.13/1.39 tff(1417,plain,((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1418,plain,
% 1.13/1.39 (~r(s(elem!1), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1417, 1387, 1408, 905])).
% 1.13/1.39 tff(1419,plain,
% 1.13/1.39 (b(s(elem!1), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[409, 1418])).
% 1.13/1.39 tff(1420,plain,
% 1.13/1.39 (b(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1153, 21, 166, 141])).
% 1.13/1.39 tff(1421,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.13/1.39 tff(1422,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.13/1.39 tff(1423,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1424,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1425,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.13/1.39 tff(1426,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1425, 271, 394, 1422, 1421, 1420])).
% 1.13/1.39 tff(1427,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1428,plain,
% 1.13/1.39 (~b(z, s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1427, 1419, 141, 1406])).
% 1.13/1.39 tff(1429,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 1.13/1.39 tff(1430,assumption,(z = s(elem!1)), introduced(assumption)).
% 1.13/1.39 tff(1431,plain,
% 1.13/1.39 (s(elem!1) = z),
% 1.13/1.39 inference(symmetry,[status(thm)],[1430])).
% 1.13/1.39 tff(1432,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[405, 1431])).
% 1.13/1.39 tff(1433,plain,(~(z = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1434,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 1.13/1.39 tff(1435,plain,
% 1.13/1.39 (((~![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)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1436,plain,
% 1.13/1.39 ((~![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)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(1437,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 1.13/1.39 tff(1438,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1437, 21, 1434, 1433, 1429])).
% 1.13/1.39 tff(1439,plain,(r(z, s(elem!1)) | b(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(1440,plain,
% 1.13/1.39 (r(z, s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1439, 1428])).
% 1.13/1.39 tff(1441,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.13/1.39 tff(1442,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1443,plain,
% 1.13/1.39 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(1444,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1443])).
% 1.13/1.39 tff(1445,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.13/1.40 inference(transitivity,[status(thm)],[1444, 1442])).
% 1.13/1.40 tff(1446,plain,
% 1.13/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.13/1.40 inference(quant_inst,[status(thm)],[])).
% 1.13/1.40 tff(1447,plain,
% 1.13/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1))),
% 1.13/1.40 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 1.13/1.40 tff(1448,plain,
% 1.13/1.40 ($false),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[1447, 121, 379, 378, 1441, 627])).
% 1.13/1.40 tff(1449,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.40 tff(1450,plain,
% 1.13/1.40 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[1449, 1440, 1403, 1387])).
% 1.13/1.40 tff(1451,plain,
% 1.13/1.40 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[526, 1450, 211])).
% 1.13/1.40 tff(1452,plain,
% 1.13/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.40 inference(rewrite,[status(thm)],[])).
% 1.13/1.40 tff(1453,plain,
% 1.13/1.40 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.40 inference(rewrite,[status(thm)],[])).
% 1.13/1.40 tff(1454,plain,
% 1.13/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.13/1.40 inference(monotonicity,[status(thm)],[1453])).
% 1.13/1.40 tff(1455,plain,
% 1.13/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.40 inference(transitivity,[status(thm)],[1454, 1452])).
% 1.13/1.40 tff(1456,plain,
% 1.13/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.40 inference(quant_inst,[status(thm)],[])).
% 1.13/1.40 tff(1457,plain,
% 1.13/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.13/1.40 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.13/1.40 tff(1458,plain,
% 1.13/1.40 ($false),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[1457, 271, 543, 517, 589, 638])).
% 1.13/1.40 tff(1459,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1460,plain,
% 1.23/1.40 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1459, 1451, 1381, 1377])).
% 1.23/1.40 tff(1461,plain,
% 1.23/1.40 (r(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[681, 1460, 82])).
% 1.23/1.40 tff(1462,plain,
% 1.23/1.40 (r(s(s(s(elem!1))), s(s(z)))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1461, 1372])).
% 1.23/1.40 tff(1463,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.23/1.40 tff(1464,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1465,plain,
% 1.23/1.40 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1466,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1465])).
% 1.23/1.40 tff(1467,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[1466, 1464])).
% 1.23/1.40 tff(1468,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(1469,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.23/1.40 tff(1470,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1469, 121, 111, 572, 110, 1463])).
% 1.23/1.40 tff(1471,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1472,plain,
% 1.23/1.40 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1471, 1375, 111, 110])).
% 1.23/1.40 tff(1473,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1472, 1462])).
% 1.23/1.40 tff(1474,plain,((~(s(z) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(z))), z) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1475,plain,
% 1.23/1.40 (~(s(z) = elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1474, 1370, 79, 111, 26, 1, 257, 1347, 906, 1369, 503, 894])).
% 1.23/1.40 tff(1476,plain,
% 1.23/1.40 (~(elem!1 = s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[242, 1475])).
% 1.23/1.40 tff(1477,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.40 tff(1478,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1479,plain,
% 1.23/1.40 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1480,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1479])).
% 1.23/1.40 tff(1481,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[1480, 1478])).
% 1.23/1.40 tff(1482,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(1483,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.23/1.40 tff(1484,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1483, 121, 110, 1477, 1140, 108])).
% 1.23/1.40 tff(1485,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1486,plain,
% 1.23/1.40 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1485, 1140, 26, 108])).
% 1.23/1.40 tff(1487,plain,
% 1.23/1.40 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.23/1.40 inference(commutativity,[status(thm)],[])).
% 1.23/1.40 tff(1488,plain,
% 1.23/1.40 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1487])).
% 1.23/1.40 tff(1489,plain,
% 1.23/1.40 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[778, 1488])).
% 1.23/1.40 tff(1490,plain,
% 1.23/1.40 (((~![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)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1491,plain,
% 1.23/1.40 ((~![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)))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(1492,plain,
% 1.23/1.40 ((~![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))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.23/1.40 tff(1493,plain,
% 1.23/1.40 ((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))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1492, 21])).
% 1.23/1.40 tff(1494,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1493, 1489])).
% 1.23/1.40 tff(1495,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1494, 1486])).
% 1.23/1.40 tff(1496,plain,
% 1.23/1.40 (~r(s(s(s(s(z)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1085, 257, 26, 503, 1, 111, 906, 905])).
% 1.23/1.40 tff(1497,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1095, 1496])).
% 1.23/1.40 tff(1498,plain,
% 1.23/1.40 (~b(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1177, 1140, 108, 26, 1497, 905])).
% 1.23/1.40 tff(1499,plain,
% 1.23/1.40 (r(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1121, 1498])).
% 1.23/1.40 tff(1500,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.23/1.40 tff(1501,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1502,plain,
% 1.23/1.40 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1503,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1502])).
% 1.23/1.40 tff(1504,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[1503, 1501])).
% 1.23/1.40 tff(1505,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(1506,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.23/1.40 tff(1507,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1506, 121, 909, 1500, 1140, 108])).
% 1.23/1.40 tff(1508,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1509,plain,
% 1.23/1.40 (~r(s(s(s(z))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1508, 1140, 108, 905])).
% 1.23/1.40 tff(1510,assumption,(~r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.23/1.40 tff(1511,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 1.23/1.40 tff(1512,plain,
% 1.23/1.40 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1511])).
% 1.23/1.40 tff(1513,plain,
% 1.23/1.40 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1512])).
% 1.23/1.40 tff(1514,plain,
% 1.23/1.40 (elem!1 = s(s(s(z)))),
% 1.23/1.40 inference(transitivity,[status(thm)],[75, 1513, 774])).
% 1.23/1.40 tff(1515,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1102, 1514])).
% 1.23/1.40 tff(1516,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1517,plain,
% 1.23/1.40 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1516, 1102])).
% 1.23/1.40 tff(1518,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.40 tff(1519,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.40 tff(1520,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[134])).
% 1.23/1.40 tff(1521,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1520])).
% 1.23/1.40 tff(1522,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[135])).
% 1.23/1.40 tff(1523,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.23/1.40 inference(transitivity,[status(thm)],[1522, 1521])).
% 1.23/1.40 tff(1524,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[134])).
% 1.23/1.40 tff(1525,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1405, 1524])).
% 1.23/1.40 tff(1526,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), s(s(z)))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1525, 1523])).
% 1.23/1.40 tff(1527,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.23/1.40 inference(monotonicity,[status(thm)],[107])).
% 1.23/1.40 tff(1528,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.23/1.40 inference(symmetry,[status(thm)],[1527])).
% 1.23/1.40 tff(1529,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[490, 107, 141])).
% 1.23/1.40 tff(1530,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), z)),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 1.23/1.40 tff(1531,plain,
% 1.23/1.40 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.23/1.40 inference(monotonicity,[status(thm)],[107])).
% 1.23/1.40 tff(1532,plain,
% 1.23/1.40 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.23/1.40 inference(symmetry,[status(thm)],[1531])).
% 1.23/1.40 tff(1533,plain,
% 1.23/1.40 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.23/1.40 inference(monotonicity,[status(thm)],[134])).
% 1.23/1.40 tff(1534,plain,
% 1.23/1.40 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.23/1.40 inference(symmetry,[status(thm)],[1533])).
% 1.23/1.40 tff(1535,plain,
% 1.23/1.40 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.23/1.40 inference(transitivity,[status(thm)],[1534, 1532])).
% 1.23/1.40 tff(1536,plain,
% 1.23/1.40 (s(z) = s(elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[500, 107])).
% 1.23/1.40 tff(1537,plain,
% 1.23/1.40 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1536])).
% 1.23/1.40 tff(1538,plain,
% 1.23/1.40 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1537])).
% 1.23/1.40 tff(1539,plain,
% 1.23/1.40 (b(elem!1, s(z))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[307, 1538])).
% 1.23/1.40 tff(1540,plain,
% 1.23/1.40 ((~b(z, s(z))) <=> (~b(elem!1, s(z)))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[319])).
% 1.23/1.40 tff(1541,plain,
% 1.23/1.40 (~b(elem!1, s(z))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[894, 1540])).
% 1.23/1.40 tff(1542,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1541, 1539])).
% 1.23/1.40 tff(1543,plain,((~(z = elem!1)) | (~b(elem!1, s(elem!1))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1544,plain,
% 1.23/1.40 (~b(elem!1, s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1543, 107, 894])).
% 1.23/1.40 tff(1545,plain,
% 1.23/1.40 (r(elem!1, s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[392, 1544, 219])).
% 1.23/1.40 tff(1546,plain,
% 1.23/1.40 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[133])).
% 1.23/1.40 tff(1547,plain,
% 1.23/1.40 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1546])).
% 1.23/1.40 tff(1548,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 1.23/1.40 tff(1549,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[338])).
% 1.23/1.40 tff(1550,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1549])).
% 1.23/1.40 tff(1551,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.23/1.40 tff(1552,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 1.23/1.40 tff(1553,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[922, 1552])).
% 1.23/1.40 tff(1554,plain,((~r(s(s(s(s(z)))), s(elem!1))) | r(s(s(s(s(z)))), s(z)) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1555,plain,
% 1.23/1.40 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1554, 1536, 922])).
% 1.23/1.40 tff(1556,plain,
% 1.23/1.40 (((~![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)))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(1557,plain,
% 1.23/1.40 ((~![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)))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(1558,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 1.23/1.40 tff(1559,plain,
% 1.23/1.40 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1558, 21])).
% 1.23/1.40 tff(1560,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1559, 1555, 1548])).
% 1.23/1.40 tff(1561,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[703])).
% 1.23/1.40 tff(1562,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.23/1.40 tff(1563,plain,
% 1.23/1.40 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.23/1.40 tff(1564,assumption,(~b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.23/1.40 tff(1565,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1564, 1563])).
% 1.23/1.40 tff(1566,plain,((~b(s(s(s(s(z)))), s(elem!1))) | b(s(s(s(s(elem!1)))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1567,plain,
% 1.23/1.40 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1566, 1560, 107])).
% 1.23/1.40 tff(1568,plain,
% 1.23/1.40 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[503, 156])).
% 1.23/1.40 tff(1569,plain,
% 1.23/1.40 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(1570,plain,
% 1.23/1.40 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1569, 48])).
% 1.23/1.40 tff(1571,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.23/1.40 tff(1572,plain,
% 1.23/1.40 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1571])).
% 1.23/1.40 tff(1573,plain,
% 1.23/1.40 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1572])).
% 1.23/1.40 tff(1574,plain,
% 1.23/1.40 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.23/1.40 inference(transitivity,[status(thm)],[56, 1573, 1570])).
% 1.23/1.40 tff(1575,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1, 1574])).
% 1.23/1.40 tff(1576,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(1577,plain,
% 1.23/1.40 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1576, 1])).
% 1.23/1.40 tff(1578,plain,
% 1.23/1.40 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.23/1.40 inference(symmetry,[status(thm)],[703])).
% 1.23/1.40 tff(1579,plain,
% 1.23/1.40 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[1578])).
% 1.23/1.40 tff(1580,plain,
% 1.23/1.40 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(symmetry,[status(thm)],[1579])).
% 1.23/1.40 tff(1581,plain,
% 1.23/1.40 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[107])).
% 1.23/1.40 tff(1582,plain,
% 1.23/1.40 (r(elem!1, s(s(s(s(z)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1518, 1581])).
% 1.23/1.40 tff(1583,plain,
% 1.23/1.40 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1582, 1580])).
% 1.23/1.40 tff(1584,plain,
% 1.23/1.40 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[107])).
% 1.23/1.40 tff(1585,plain,
% 1.23/1.40 (r(elem!1, s(s(s(elem!1))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[111, 1584])).
% 1.23/1.40 tff(1586,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.23/1.41 tff(1587,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1588,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1589,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.23/1.41 tff(1590,plain,
% 1.23/1.41 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1589, 271, 517, 638, 1586])).
% 1.23/1.41 tff(1591,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.41 tff(1592,plain,
% 1.23/1.41 (((~![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)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1593,plain,
% 1.23/1.41 ((~![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)))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1594,plain,
% 1.23/1.41 ((~![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))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.23/1.41 tff(1595,plain,
% 1.23/1.41 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1594, 21, 1591, 1590])).
% 1.23/1.41 tff(1596,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.41 tff(1597,plain,
% 1.23/1.41 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.23/1.41 inference(commutativity,[status(thm)],[])).
% 1.23/1.41 tff(1598,plain,
% 1.23/1.41 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(symmetry,[status(thm)],[1597])).
% 1.23/1.41 tff(1599,plain,
% 1.23/1.41 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1598])).
% 1.23/1.41 tff(1600,plain,
% 1.23/1.41 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1591, 1599])).
% 1.23/1.41 tff(1601,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1602,plain,
% 1.23/1.41 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1603,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1602])).
% 1.23/1.41 tff(1604,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1603, 1601])).
% 1.23/1.41 tff(1605,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1606,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 1.23/1.41 tff(1607,plain,
% 1.23/1.41 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1606, 271, 517, 638, 1586])).
% 1.23/1.41 tff(1608,plain,
% 1.23/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1609,plain,
% 1.23/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1610,plain,
% 1.23/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.23/1.41 tff(1611,plain,
% 1.23/1.41 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1610, 21, 1607])).
% 1.23/1.41 tff(1612,plain,
% 1.23/1.41 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1611, 1600])).
% 1.23/1.41 tff(1613,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1614,plain,
% 1.23/1.41 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1615,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1614])).
% 1.23/1.41 tff(1616,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1615, 1613])).
% 1.23/1.41 tff(1617,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1618,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.23/1.41 tff(1619,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1618, 121, 727, 1612, 1596, 1595])).
% 1.23/1.41 tff(1620,plain,((~b(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1621,plain,
% 1.23/1.41 (~b(s(elem!1), s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1620, 1585, 1583, 1577, 1568, 1567])).
% 1.23/1.41 tff(1622,plain,
% 1.23/1.41 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[526, 1621, 211])).
% 1.23/1.41 tff(1623,plain,
% 1.23/1.41 (r(s(z), s(s(elem!1)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1622, 1547])).
% 1.23/1.41 tff(1624,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.23/1.41 tff(1625,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.23/1.41 tff(1626,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1627,plain,
% 1.23/1.41 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1628,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1627])).
% 1.23/1.41 tff(1629,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1628, 1626])).
% 1.23/1.41 tff(1630,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1631,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.23/1.41 tff(1632,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1631, 121, 379, 357, 1625, 1624])).
% 1.23/1.41 tff(1633,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1634,plain,
% 1.23/1.41 (~r(s(s(elem!1)), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1633, 1623, 357, 1545])).
% 1.23/1.41 tff(1635,plain,
% 1.23/1.41 (b(s(s(elem!1)), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[862, 1634, 198])).
% 1.23/1.41 tff(1636,plain,
% 1.23/1.41 (b(s(s(z)), z)),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1635, 1535])).
% 1.23/1.41 tff(1637,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.23/1.41 tff(1638,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.23/1.41 tff(1639,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.41 tff(1640,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.23/1.41 tff(1641,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1642,plain,
% 1.23/1.41 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1643,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1642])).
% 1.23/1.41 tff(1644,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1643, 1641])).
% 1.23/1.41 tff(1645,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1646,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 1.23/1.41 tff(1647,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1646, 271, 1640, 1639, 1638, 1637])).
% 1.23/1.41 tff(1648,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1649,plain,
% 1.23/1.41 (~b(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1648, 1636, 1530, 1526])).
% 1.23/1.41 tff(1650,plain,
% 1.23/1.41 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.23/1.41 inference(commutativity,[status(thm)],[])).
% 1.23/1.41 tff(1651,plain,
% 1.23/1.41 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.23/1.41 inference(symmetry,[status(thm)],[1650])).
% 1.23/1.41 tff(1652,plain,
% 1.23/1.41 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1651])).
% 1.23/1.41 tff(1653,plain,
% 1.23/1.41 (~(z = s(s(s(s(s(z))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[711, 1652])).
% 1.23/1.41 tff(1654,plain,
% 1.23/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1655,plain,
% 1.23/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1656,plain,
% 1.23/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 1.23/1.41 tff(1657,plain,
% 1.23/1.41 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1656, 21])).
% 1.23/1.41 tff(1658,plain,
% 1.23/1.41 (b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1657, 1653])).
% 1.23/1.41 tff(1659,plain,
% 1.23/1.41 (r(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1658, 1649])).
% 1.23/1.41 tff(1660,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.23/1.41 tff(1661,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.41 tff(1662,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1663,plain,
% 1.23/1.41 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1664,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1663])).
% 1.23/1.41 tff(1665,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1664, 1662])).
% 1.23/1.41 tff(1666,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1667,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 1.23/1.41 tff(1668,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1667, 121, 110, 909, 1661, 1660])).
% 1.23/1.41 tff(1669,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1670,plain,
% 1.23/1.41 (~r(s(s(s(s(s(z))))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1669, 1659, 110, 905])).
% 1.23/1.41 tff(1671,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.23/1.41 tff(1672,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.23/1.41 tff(1673,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.23/1.41 tff(1674,plain,
% 1.23/1.41 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1673])).
% 1.23/1.41 tff(1675,plain,
% 1.23/1.41 (s(s(s(s(z)))) = z),
% 1.23/1.41 inference(transitivity,[status(thm)],[872, 1674, 50])).
% 1.23/1.41 tff(1676,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1090, 1675])).
% 1.23/1.41 tff(1677,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1678,plain,
% 1.23/1.41 (((~![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)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1679,plain,
% 1.23/1.41 ((~![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)))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1680,plain,
% 1.23/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.23/1.41 tff(1681,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1680, 21, 1677, 1672, 1671])).
% 1.23/1.41 tff(1682,plain,(b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1683,plain,
% 1.23/1.41 (b(s(s(s(s(s(z))))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1682, 1670])).
% 1.23/1.41 tff(1684,plain,
% 1.23/1.41 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[135])).
% 1.23/1.41 tff(1685,plain,
% 1.23/1.41 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.41 inference(symmetry,[status(thm)],[1684])).
% 1.23/1.41 tff(1686,plain,
% 1.23/1.41 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.23/1.41 inference(monotonicity,[status(thm)],[133])).
% 1.23/1.41 tff(1687,plain,
% 1.23/1.41 (r(s(elem!1), elem!1)),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[357, 1686])).
% 1.23/1.41 tff(1688,plain,
% 1.23/1.41 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1525, 1522])).
% 1.23/1.41 tff(1689,plain,
% 1.23/1.41 (~b(elem!1, s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[594, 1635, 1688, 1529])).
% 1.23/1.41 tff(1690,plain,
% 1.23/1.41 (r(elem!1, s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[599, 1689, 68])).
% 1.23/1.41 tff(1691,plain,
% 1.23/1.41 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[635, 1690, 1687, 1622])).
% 1.23/1.41 tff(1692,plain,
% 1.23/1.41 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[556, 1691, 1])).
% 1.23/1.41 tff(1693,plain,
% 1.23/1.41 (b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1692, 1685])).
% 1.23/1.41 tff(1694,assumption,(r(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.23/1.41 tff(1695,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1696,plain,
% 1.23/1.42 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1697,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1696])).
% 1.23/1.42 tff(1698,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1697, 1695])).
% 1.23/1.42 tff(1699,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1700,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 1.23/1.42 tff(1701,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1700, 121, 379, 627, 624, 1694])).
% 1.23/1.42 tff(1702,plain,((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1703,plain,
% 1.23/1.42 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1702, 1545, 1622, 1690])).
% 1.23/1.42 tff(1704,plain,
% 1.23/1.42 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.23/1.42 inference(commutativity,[status(thm)],[])).
% 1.23/1.42 tff(1705,plain,
% 1.23/1.42 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(symmetry,[status(thm)],[1704])).
% 1.23/1.42 tff(1706,plain,
% 1.23/1.42 ((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1705])).
% 1.23/1.42 tff(1707,plain,
% 1.23/1.42 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[878, 1706])).
% 1.23/1.42 tff(1708,plain,
% 1.23/1.42 (b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[705])).
% 1.23/1.42 tff(1709,plain,
% 1.23/1.42 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(symmetry,[status(thm)],[1708])).
% 1.23/1.42 tff(1710,plain,
% 1.23/1.42 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1709])).
% 1.23/1.42 tff(1711,assumption,(~b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1712,plain,
% 1.23/1.42 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 1.23/1.42 tff(1713,assumption,(~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.23/1.42 tff(1714,plain,
% 1.23/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1715,plain,
% 1.23/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1716,plain,
% 1.23/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 1.23/1.42 tff(1717,plain,
% 1.23/1.42 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1716, 21, 1713])).
% 1.23/1.42 tff(1718,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1717, 1712, 1707])).
% 1.23/1.42 tff(1719,plain,(r(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1720,plain,
% 1.23/1.42 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1719, 1703, 107])).
% 1.23/1.42 tff(1721,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.23/1.42 tff(1722,assumption,(b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1723,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.42 tff(1724,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1725,plain,
% 1.23/1.42 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(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(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1726,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1725])).
% 1.23/1.42 tff(1727,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1726, 1724])).
% 1.23/1.42 tff(1728,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1729,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 1.23/1.42 tff(1730,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1729, 271, 1519, 1723, 1722, 1721])).
% 1.23/1.42 tff(1731,plain,((~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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1732,plain,
% 1.23/1.42 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1731, 1720, 1519, 1693])).
% 1.23/1.42 tff(1733,plain,
% 1.23/1.42 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[795, 778])).
% 1.23/1.42 tff(1734,plain,
% 1.23/1.42 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1733, 1732])).
% 1.23/1.42 tff(1735,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1736,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.42 tff(1737,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1738,plain,
% 1.23/1.42 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1739,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1738])).
% 1.23/1.42 tff(1740,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1739, 1737])).
% 1.23/1.42 tff(1741,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1742,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 1.23/1.42 tff(1743,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1742, 121, 110, 1661, 1736, 1735])).
% 1.23/1.42 tff(1744,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1745,plain,
% 1.23/1.42 (~r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1744, 1734, 110, 1659])).
% 1.23/1.42 tff(1746,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.42 tff(1747,plain,
% 1.23/1.42 (s(s(s(s(s(z))))) = s(z)),
% 1.23/1.42 inference(symmetry,[status(thm)],[1746])).
% 1.23/1.42 tff(1748,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1677, 1747])).
% 1.23/1.42 tff(1749,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1750,assumption,(~r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1751,assumption,(~b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1752,plain,
% 1.23/1.42 (((~![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)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1753,plain,
% 1.23/1.42 ((~![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)))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1754,plain,
% 1.23/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.23/1.42 tff(1755,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1754, 21, 1751, 1750, 1749])).
% 1.23/1.42 tff(1756,plain,(b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1757,plain,
% 1.23/1.42 (b(s(z), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1756, 1745])).
% 1.23/1.42 tff(1758,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1759,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1760,plain,
% 1.23/1.42 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1761,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1760])).
% 1.23/1.42 tff(1762,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1761, 1759])).
% 1.23/1.42 tff(1763,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1764,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.23/1.42 tff(1765,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1764, 121, 1758, 1661, 1736, 1518])).
% 1.23/1.42 tff(1766,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1767,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1766, 1734, 1518, 1659])).
% 1.23/1.42 tff(1768,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.42 tff(1769,plain,
% 1.23/1.42 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1768])).
% 1.23/1.42 tff(1770,plain,
% 1.23/1.42 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[775, 1769, 766, 1768])).
% 1.23/1.42 tff(1771,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1489, 1770])).
% 1.23/1.42 tff(1772,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1773,plain,
% 1.23/1.42 (((~![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)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1774,plain,
% 1.23/1.42 ((~![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)))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1775,plain,
% 1.23/1.42 ((~![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))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 1.23/1.42 tff(1776,plain,
% 1.23/1.42 ((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))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1775, 21])).
% 1.23/1.42 tff(1777,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1776, 1772])).
% 1.23/1.42 tff(1778,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1777, 1767])).
% 1.23/1.42 tff(1779,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1780,plain,
% 1.23/1.42 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1781,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1780])).
% 1.23/1.42 tff(1782,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1781, 1779])).
% 1.23/1.42 tff(1783,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1784,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 1.23/1.42 tff(1785,plain,
% 1.23/1.42 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1784, 271])).
% 1.23/1.42 tff(1786,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1785, 1778, 1757, 1347, 1683])).
% 1.23/1.42 tff(1787,plain,((~(z = elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(z)) | r(s(s(s(z))), z) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1788,plain,
% 1.23/1.42 (~(z = elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1787, 1244, 110, 1519, 1, 68, 1518, 1405, 503, 111, 1517, 922, 141, 894])).
% 1.23/1.42 tff(1789,plain,
% 1.23/1.42 (r(z, elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[355, 1788, 199])).
% 1.23/1.42 tff(1790,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1791,plain,
% 1.23/1.42 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1792,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1791])).
% 1.23/1.42 tff(1793,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1792, 1790])).
% 1.23/1.42 tff(1794,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1795,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 1.23/1.42 tff(1796,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1795, 121, 378, 357, 110, 1184])).
% 1.23/1.42 tff(1797,plain,((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1798,plain,
% 1.23/1.42 (~r(elem!1, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1797, 1789, 110, 1244])).
% 1.23/1.42 tff(1799,plain,
% 1.23/1.42 (b(elem!1, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1192, 1798, 1102])).
% 1.23/1.42 tff(1800,plain,
% 1.23/1.42 (~r(elem!1, s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[387, 1789, 110, 1244])).
% 1.23/1.43 tff(1801,plain,
% 1.23/1.43 (b(elem!1, s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[392, 1800, 219])).
% 1.23/1.43 tff(1802,plain,
% 1.23/1.43 (~r(s(elem!1), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1305, 1801, 905, 199, 231, 1788, 1242])).
% 1.23/1.43 tff(1803,plain,
% 1.23/1.43 (b(s(elem!1), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[409, 1802])).
% 1.23/1.43 tff(1804,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1805,plain,
% 1.23/1.43 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1806,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z)))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1805])).
% 1.23/1.43 tff(1807,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1806, 1804])).
% 1.23/1.43 tff(1808,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1809,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.23/1.43 tff(1810,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1809, 271, 307, 394, 1195, 1422])).
% 1.23/1.43 tff(1811,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1812,plain,
% 1.23/1.43 (~b(s(s(s(z))), s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1811, 1803, 1801, 1799])).
% 1.23/1.43 tff(1813,plain,
% 1.23/1.43 (((~![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)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1814,plain,
% 1.23/1.43 ((~![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)))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1815,plain,
% 1.23/1.43 ((~![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))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.23/1.43 tff(1816,plain,
% 1.23/1.43 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1815, 21])).
% 1.23/1.43 tff(1817,plain,
% 1.23/1.43 (s(s(s(z))) = s(elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1816, 1812, 1510])).
% 1.23/1.43 tff(1818,plain,
% 1.23/1.43 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1817])).
% 1.23/1.43 tff(1819,plain,
% 1.23/1.43 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1818])).
% 1.23/1.43 tff(1820,plain,
% 1.23/1.43 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1819])).
% 1.23/1.43 tff(1821,plain,
% 1.23/1.43 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1820])).
% 1.23/1.43 tff(1822,plain,
% 1.23/1.43 (b(s(s(s(s(s(z))))), s(z))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[503, 1821])).
% 1.23/1.43 tff(1823,plain,
% 1.23/1.43 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1819])).
% 1.23/1.43 tff(1824,plain,
% 1.23/1.43 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1823])).
% 1.23/1.43 tff(1825,plain,
% 1.23/1.43 (r(z, s(s(s(s(s(z))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[111, 1824])).
% 1.23/1.43 tff(1826,assumption,(r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.43 tff(1827,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1828,plain,
% 1.23/1.43 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1829,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1828])).
% 1.23/1.43 tff(1830,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1829, 1827])).
% 1.23/1.43 tff(1831,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1832,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 1.23/1.43 tff(1833,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1832, 121, 378, 357, 110, 1826])).
% 1.23/1.43 tff(1834,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1835,plain,
% 1.23/1.43 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1834, 1789, 110, 1244])).
% 1.23/1.43 tff(1836,plain,
% 1.23/1.43 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.43 inference(commutativity,[status(thm)],[])).
% 1.23/1.43 tff(1837,plain,
% 1.23/1.43 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1836])).
% 1.23/1.43 tff(1838,plain,
% 1.23/1.43 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1817])).
% 1.23/1.43 tff(1839,plain,
% 1.23/1.43 (s(s(z)) = elem!1),
% 1.23/1.43 inference(transitivity,[status(thm)],[92, 1838, 70])).
% 1.23/1.43 tff(1840,plain,
% 1.23/1.43 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1839])).
% 1.23/1.43 tff(1841,plain,
% 1.23/1.43 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1840, 1837])).
% 1.23/1.43 tff(1842,plain,
% 1.23/1.43 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1841])).
% 1.23/1.43 tff(1843,plain,
% 1.23/1.43 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[877, 1842])).
% 1.23/1.43 tff(1844,plain,
% 1.23/1.43 (((~![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)))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1845,plain,
% 1.23/1.43 ((~![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)))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1846,plain,
% 1.23/1.43 ((~![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))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.23/1.43 tff(1847,plain,
% 1.23/1.43 ((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))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1846, 21])).
% 1.23/1.43 tff(1848,plain,
% 1.23/1.43 (b(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1847, 1843, 1835])).
% 1.23/1.43 tff(1849,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.43 tff(1850,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1851,plain,
% 1.23/1.43 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1852,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1851])).
% 1.23/1.43 tff(1853,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1852, 1850])).
% 1.23/1.43 tff(1854,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1855,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.23/1.43 tff(1856,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1855, 271, 1195, 1849, 257, 1723])).
% 1.23/1.43 tff(1857,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1858,plain,
% 1.23/1.43 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1857, 1848, 257, 1799])).
% 1.23/1.43 tff(1859,plain,
% 1.23/1.43 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1733, 1858])).
% 1.23/1.43 tff(1860,plain,
% 1.23/1.43 (~r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1744, 1859, 110, 1825])).
% 1.23/1.43 tff(1861,plain,
% 1.23/1.43 (b(s(z), s(s(s(s(s(z))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1756, 1860])).
% 1.23/1.43 tff(1862,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1766, 1859, 1518, 1825])).
% 1.23/1.43 tff(1863,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1777, 1862])).
% 1.23/1.43 tff(1864,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1785, 1863, 1861, 1347, 1822])).
% 1.23/1.43 tff(1865,plain,((s(z) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(z))), s(elem!1)) | b(z, elem!1) | b(s(z), elem!1) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | r(s(s(s(s(z)))), s(z)) | r(s(s(s(z))), z) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1866,plain,
% 1.23/1.43 (b(s(z), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1865, 1475, 26, 257, 503, 111, 1509, 199, 1499, 1102, 1495, 1, 68, 1369, 922, 1370, 894])).
% 1.23/1.43 tff(1867,plain,
% 1.23/1.43 (elem!1 = z),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[305, 1866, 257, 1476, 111, 26, 222])).
% 1.23/1.43 tff(1868,plain,
% 1.23/1.43 (z = elem!1),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[333, 1867])).
% 1.23/1.43 tff(1869,plain,
% 1.23/1.43 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1868])).
% 1.23/1.43 tff(1870,plain,
% 1.23/1.43 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.23/1.43 inference(symmetry,[status(thm)],[1869])).
% 1.23/1.43 tff(1871,plain,
% 1.23/1.43 (b(s(z), z)),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1866, 1870])).
% 1.23/1.43 tff(1872,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2, 1871])).
% 1.23/1.43 tff(1873,plain,((~r(z, s(s(s(z))))) | b(s(z), z) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(z, elem!1) | (elem!1 = s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | r(s(s(s(s(z)))), s(z)) | b(z, s(z)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1874,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1873, 199, 257, 37, 222, 503, 2, 1102, 1, 68, 922, 894, 906, 108])).
% 1.23/1.43 tff(1875,plain,
% 1.23/1.43 (b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1214, 1874])).
% 1.23/1.43 tff(1876,plain,
% 1.23/1.43 (~(z = elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1202, 1874, 1102, 33])).
% 1.23/1.43 tff(1877,plain,
% 1.23/1.43 (b(s(z), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1324, 231, 222, 110, 199, 909, 257, 331, 1307, 377])).
% 1.23/1.43 tff(1878,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[305, 1877, 243, 257, 358, 111, 110, 222])).
% 1.23/1.43 tff(1879,plain,((s(z) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | b(z, elem!1) | (~r(z, s(z))) | (z = elem!1) | (~b(z, s(s(s(z))))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1880,plain,
% 1.23/1.43 (s(z) = elem!1),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1879, 199, 37, 26, 222, 257, 905, 1876, 1875, 219])).
% 1.23/1.43 tff(1881,plain,
% 1.23/1.43 (s(s(z)) = s(elem!1)),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1880])).
% 1.23/1.43 tff(1882,plain,
% 1.23/1.43 (s(s(s(z))) = s(s(elem!1))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1881])).
% 1.23/1.43 tff(1883,plain,
% 1.23/1.43 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1882])).
% 1.23/1.43 tff(1884,plain,
% 1.23/1.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1883])).
% 1.23/1.43 tff(1885,plain,
% 1.23/1.43 (~b(s(z), s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[991, 1884, 1, 257, 1347, 906])).
% 1.23/1.43 tff(1886,plain,
% 1.23/1.43 (r(s(z), s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[760, 1885])).
% 1.23/1.43 tff(1887,plain,
% 1.23/1.43 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[581, 1886, 37, 26])).
% 1.23/1.43 tff(1888,plain,
% 1.23/1.43 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1882])).
% 1.23/1.43 tff(1889,plain,
% 1.23/1.43 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1888])).
% 1.23/1.43 tff(1890,plain,
% 1.23/1.43 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[906, 1889])).
% 1.23/1.43 tff(1891,plain,
% 1.23/1.43 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[556, 1890, 1])).
% 1.23/1.43 tff(1892,plain,
% 1.23/1.43 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1882])).
% 1.23/1.43 tff(1893,plain,
% 1.23/1.43 (b(z, s(s(elem!1)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1875, 1892])).
% 1.23/1.43 tff(1894,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.23/1.43 tff(1895,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1896,plain,
% 1.23/1.43 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1897,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1896])).
% 1.23/1.43 tff(1898,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.23/1.43 tff(1899,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1900,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.23/1.43 tff(1901,plain,
% 1.23/1.43 (~b(s(s(s(elem!1))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1900, 271, 543, 589, 1894])).
% 1.23/1.43 tff(1902,plain,
% 1.23/1.43 (((~![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))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1903,plain,
% 1.23/1.43 ((~![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))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1904,plain,
% 1.23/1.43 ((~![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)),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.23/1.43 tff(1905,plain,
% 1.23/1.43 (r(s(s(s(elem!1))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1904, 21, 30, 1901])).
% 1.23/1.43 tff(1906,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1907,plain,
% 1.23/1.43 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1908,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1907])).
% 1.23/1.43 tff(1909,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1908, 1906])).
% 1.23/1.43 tff(1910,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1911,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.23/1.43 tff(1912,plain,
% 1.23/1.43 (~b(z, s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1911, 271, 543, 589, 1894])).
% 1.23/1.43 tff(1913,plain,
% 1.23/1.43 (r(z, s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[36, 21, 1912, 32])).
% 1.23/1.43 tff(1914,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1915,plain,
% 1.23/1.43 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1916,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1915])).
% 1.23/1.44 tff(1917,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.23/1.44 tff(1918,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1919,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.23/1.44 tff(1920,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1919, 121, 1913, 572, 110, 1905])).
% 1.23/1.44 tff(1921,plain,((~b(z, s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1922,plain,
% 1.23/1.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1921, 1886, 26, 1893, 1891])).
% 1.23/1.44 tff(1923,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[586, 1922, 1887, 563])).
% 1.23/1.44 tff(1924,plain,(b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | b(z, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | (elem!1 = s(s(elem!1))) | r(s(s(s(s(z)))), s(z)) | b(z, s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1925,plain,
% 1.23/1.44 (b(z, elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1924, 908, 1, 906, 222, 1101, 33, 67, 2, 68, 1346, 894, 108])).
% 1.23/1.44 tff(1926,plain,
% 1.23/1.44 (~(elem!1 = s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1397, 1925, 894])).
% 1.23/1.44 tff(1927,plain,
% 1.23/1.44 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.23/1.44 inference(commutativity,[status(thm)],[])).
% 1.23/1.44 tff(1928,plain,
% 1.23/1.44 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1927])).
% 1.23/1.44 tff(1929,plain,
% 1.23/1.44 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1517, 1928])).
% 1.23/1.44 tff(1930,plain,
% 1.23/1.44 (~r(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1085, 257, 110, 503, 1, 111, 906, 909])).
% 1.23/1.44 tff(1931,plain,
% 1.23/1.44 (b(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1095, 1930])).
% 1.23/1.44 tff(1932,plain,
% 1.23/1.44 (~b(s(z), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[305, 358, 257, 258, 111, 110, 222])).
% 1.23/1.44 tff(1933,plain,
% 1.23/1.44 (r(s(z), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[236, 1932, 1257])).
% 1.23/1.44 tff(1934,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1508, 1140, 108, 909])).
% 1.23/1.44 tff(1935,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.23/1.44 tff(1936,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1937,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1938,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.23/1.44 tff(1939,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1938, 271, 307, 1326, 257, 1935])).
% 1.23/1.44 tff(1940,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1941,plain,
% 1.23/1.44 (~b(elem!1, s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1940, 1156, 257, 1326])).
% 1.23/1.44 tff(1942,plain,
% 1.23/1.44 (r(elem!1, s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[392, 1941, 377])).
% 1.23/1.44 tff(1943,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1944,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1945,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.23/1.44 tff(1946,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1945, 271, 1326, 261, 257, 1935])).
% 1.23/1.44 tff(1947,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1948,plain,
% 1.23/1.44 (~b(elem!1, z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1947, 1156, 257, 1326])).
% 1.23/1.44 tff(1949,plain,
% 1.23/1.44 (r(elem!1, z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[284, 1948, 259])).
% 1.23/1.44 tff(1950,plain,
% 1.23/1.44 (~r(s(elem!1), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1417, 1949, 1942, 909])).
% 1.23/1.44 tff(1951,plain,
% 1.23/1.44 (b(s(elem!1), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[409, 1950])).
% 1.23/1.44 tff(1952,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1953,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1954,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 1.23/1.44 tff(1955,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1954, 271, 1326, 394, 1422, 1935])).
% 1.23/1.44 tff(1956,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1957,plain,
% 1.23/1.44 (~b(s(s(s(z))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1956, 1951, 1326, 1156])).
% 1.23/1.44 tff(1958,plain,
% 1.23/1.44 (s(s(s(z))) = s(elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1816, 1957, 1934])).
% 1.23/1.44 tff(1959,plain,
% 1.23/1.44 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1958])).
% 1.23/1.44 tff(1960,plain,
% 1.23/1.44 (s(s(z)) = elem!1),
% 1.23/1.44 inference(transitivity,[status(thm)],[92, 1959, 70])).
% 1.23/1.44 tff(1961,plain,
% 1.23/1.44 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1960])).
% 1.23/1.44 tff(1962,plain,
% 1.23/1.44 (r(elem!1, z) <=> r(s(s(z)), z)),
% 1.23/1.44 inference(symmetry,[status(thm)],[1961])).
% 1.23/1.44 tff(1963,plain,
% 1.23/1.44 (r(s(s(z)), z)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1949, 1962])).
% 1.23/1.44 tff(1964,plain,
% 1.23/1.44 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1960])).
% 1.23/1.44 tff(1965,plain,
% 1.23/1.44 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1964])).
% 1.23/1.44 tff(1966,plain,
% 1.23/1.44 (r(s(z), s(s(z)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[357, 1965])).
% 1.23/1.44 tff(1967,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[535, 1966, 1963, 111, 110])).
% 1.23/1.44 tff(1968,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~r(z, s(z))) | (elem!1 = z) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1969,plain,
% 1.23/1.44 (~r(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1968, 1933, 110, 111, 1326, 909, 358, 257, 219, 108])).
% 1.23/1.44 tff(1970,plain,
% 1.23/1.44 (b(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1214, 1969])).
% 1.23/1.44 tff(1971,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1972,plain,
% 1.23/1.44 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1973,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1972])).
% 1.23/1.44 tff(1974,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1973, 1971])).
% 1.23/1.44 tff(1975,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1976,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 1.23/1.44 tff(1977,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1976, 271, 307, 1326, 1307, 257])).
% 1.23/1.44 tff(1978,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1979,plain,
% 1.23/1.44 (~b(elem!1, s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1978, 1970, 1326, 257])).
% 1.23/1.44 tff(1980,plain,
% 1.23/1.44 (r(elem!1, s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[392, 1979, 219])).
% 1.23/1.44 tff(1981,plain,
% 1.23/1.44 (~b(elem!1, z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1334, 1970, 1326, 257])).
% 1.23/1.44 tff(1982,plain,
% 1.23/1.44 (r(elem!1, z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[284, 1981, 358])).
% 1.23/1.44 tff(1983,plain,
% 1.23/1.44 (~r(s(elem!1), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1417, 1982, 1980, 909])).
% 1.23/1.44 tff(1984,plain,
% 1.23/1.44 (b(s(elem!1), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[409, 1983])).
% 1.23/1.44 tff(1985,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1986,plain,
% 1.23/1.44 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1987,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1986])).
% 1.23/1.44 tff(1988,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1987, 1985])).
% 1.23/1.44 tff(1989,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1990,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.23/1.44 tff(1991,plain,
% 1.23/1.44 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1990, 271, 1326, 1984, 1931])).
% 1.23/1.44 tff(1992,plain,
% 1.23/1.44 (((~![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))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1993,plain,
% 1.23/1.44 ((~![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))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1994,plain,
% 1.23/1.44 ((~![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)))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.23/1.44 tff(1995,plain,
% 1.23/1.44 ((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)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1994, 21])).
% 1.23/1.44 tff(1996,plain,
% 1.23/1.44 (r(s(elem!1), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1995, 1991, 1929])).
% 1.23/1.44 tff(1997,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.23/1.44 tff(1998,plain,
% 1.23/1.44 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1997])).
% 1.23/1.44 tff(1999,plain,
% 1.23/1.44 (r(s(z), s(elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[108, 1998])).
% 1.23/1.44 tff(2000,plain,
% 1.23/1.44 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1997])).
% 1.23/1.44 tff(2001,plain,
% 1.23/1.44 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[2000])).
% 1.23/1.44 tff(2002,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.44 tff(2003,plain,
% 1.23/1.44 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 1.23/1.44 tff(2004,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(2005,plain,
% 1.23/1.44 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(2006,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[2005])).
% 1.23/1.44 tff(2007,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[2006, 2004])).
% 1.23/1.44 tff(2008,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(2009,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 1.23/1.44 tff(2010,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2009, 121, 379, 357, 2003, 1999])).
% 1.23/1.44 tff(2011,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(2012,plain,
% 1.23/1.44 (~(s(s(s(z))) = s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2011, 1980, 1933, 1996, 108])).
% 1.23/1.44 tff(2013,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(2014,plain,
% 1.23/1.44 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(2015,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[2014])).
% 1.23/1.44 tff(2016,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[2015, 2013])).
% 1.23/1.44 tff(2017,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(2018,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.23/1.44 tff(2019,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2018, 271, 1326, 1195, 1307, 257])).
% 1.23/1.44 tff(2020,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(2021,plain,
% 1.23/1.44 (~b(elem!1, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2020, 1970, 1326, 257])).
% 1.23/1.44 tff(2022,plain,
% 1.23/1.44 (r(elem!1, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1192, 2021, 1102])).
% 1.23/1.44 tff(2023,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(2024,plain,
% 1.23/1.44 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(2025,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[2024])).
% 1.23/1.44 tff(2026,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[2025, 2023])).
% 1.23/1.44 tff(2027,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(2028,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 1.23/1.45 tff(2029,plain,
% 1.23/1.45 ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2028, 271])).
% 1.23/1.45 tff(2030,plain,
% 1.23/1.45 (~b(s(elem!1), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2029, 1984, 1970, 222])).
% 1.23/1.45 tff(2031,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.23/1.45 tff(2032,plain,
% 1.23/1.45 (s(s(s(z))) = s(elem!1)),
% 1.23/1.45 inference(symmetry,[status(thm)],[2031])).
% 1.23/1.45 tff(2033,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.23/1.45 tff(2034,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2033, 2032])).
% 1.23/1.45 tff(2035,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2036,plain,
% 1.23/1.45 (~(s(elem!1) = s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2035, 2012])).
% 1.23/1.45 tff(2037,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.23/1.45 tff(2038,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.23/1.45 tff(2039,assumption,(~b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.23/1.45 tff(2040,plain,
% 1.23/1.45 (((~![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)))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2041,plain,
% 1.23/1.45 ((~![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)))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2042,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 1.23/1.45 tff(2043,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2042, 21, 2039, 2038, 2037])).
% 1.23/1.45 tff(2044,plain,(b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2045,plain,
% 1.23/1.45 (r(s(elem!1), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2044, 2036, 2030])).
% 1.23/1.45 tff(2046,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.23/1.45 tff(2047,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2048,plain,
% 1.23/1.45 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2049,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2048])).
% 1.23/1.45 tff(2050,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[2049, 2047])).
% 1.23/1.45 tff(2051,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2052,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 1.23/1.45 tff(2053,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2052, 121, 379, 1184, 1500, 2046])).
% 1.23/1.45 tff(2054,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2055,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2054, 2045, 2022, 1980])).
% 1.23/1.45 tff(2056,plain,
% 1.23/1.45 (b(s(s(s(z))), s(elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1816, 2055, 2012])).
% 1.23/1.45 tff(2057,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.23/1.45 tff(2058,plain,
% 1.23/1.45 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2057])).
% 1.23/1.45 tff(2059,plain,
% 1.23/1.45 (s(s(z)) = s(s(elem!1))),
% 1.23/1.45 inference(transitivity,[status(thm)],[92, 2058, 55])).
% 1.23/1.45 tff(2060,plain,
% 1.23/1.45 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2059])).
% 1.23/1.45 tff(2061,plain,
% 1.23/1.45 (s(z) = s(elem!1)),
% 1.23/1.45 inference(transitivity,[status(thm)],[957, 2060, 604])).
% 1.23/1.45 tff(2062,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[348, 2061])).
% 1.23/1.45 tff(2063,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2064,plain,
% 1.23/1.45 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2063, 344])).
% 1.23/1.45 tff(2065,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.45 tff(2066,assumption,(~b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.45 tff(2067,plain,
% 1.23/1.45 (((~![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)))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2068,plain,
% 1.23/1.45 ((~![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)))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2069,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 1.23/1.45 tff(2070,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2069, 21, 2066, 2065, 906])).
% 1.23/1.45 tff(2071,plain,(b(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2072,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2071, 2064, 906])).
% 1.23/1.45 tff(2073,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.45 tff(2074,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2075,plain,
% 1.23/1.45 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2076,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2075])).
% 1.23/1.45 tff(2077,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[2076, 2074])).
% 1.23/1.45 tff(2078,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2079,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 1.23/1.45 tff(2080,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2079, 271, 750, 2073, 222, 503])).
% 1.23/1.45 tff(2081,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2082,plain,
% 1.23/1.45 (~b(s(z), s(s(s(elem!1))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2081, 2072, 222, 503])).
% 1.23/1.45 tff(2083,plain,
% 1.23/1.45 (r(s(z), s(s(s(elem!1))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[760, 2082])).
% 1.23/1.45 tff(2084,plain,
% 1.23/1.45 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[581, 2083, 111, 110])).
% 1.23/1.45 tff(2085,plain,
% 1.23/1.45 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[586, 2084, 563])).
% 1.23/1.45 tff(2086,plain,
% 1.23/1.45 (~b(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1956, 2056, 1326, 1984])).
% 1.23/1.45 tff(2087,plain,
% 1.23/1.45 (r(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1155, 2086])).
% 1.23/1.45 tff(2088,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.23/1.45 tff(2089,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2090,plain,
% 1.23/1.45 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2091,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2090])).
% 1.23/1.45 tff(2092,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[2091, 2089])).
% 1.23/1.45 tff(2093,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2094,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.23/1.45 tff(2095,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2094, 121, 2088, 110, 109, 108])).
% 1.23/1.45 tff(2096,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2097,plain,
% 1.23/1.45 (~r(z, s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2096, 2087, 108, 110])).
% 1.23/1.45 tff(2098,plain,
% 1.23/1.45 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(2099,plain,
% 1.23/1.45 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.23/1.45 inference(symmetry,[status(thm)],[2098])).
% 1.23/1.45 tff(2100,plain,
% 1.23/1.45 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2099])).
% 1.23/1.45 tff(2101,plain,
% 1.23/1.45 (~(z = s(s(elem!1)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[59, 2100])).
% 1.23/1.45 tff(2102,plain,
% 1.23/1.45 (((~![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))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2103,plain,
% 1.23/1.45 ((~![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))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2104,plain,
% 1.23/1.45 ((~![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)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 1.23/1.45 tff(2105,plain,
% 1.23/1.45 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2104, 21])).
% 1.23/1.45 tff(2106,plain,
% 1.23/1.45 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2105, 2101])).
% 1.23/1.45 tff(2107,plain,
% 1.23/1.45 (b(z, s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2106, 2097])).
% 1.23/1.45 tff(2108,plain,
% 1.23/1.45 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1921, 2107, 110, 2083, 2085])).
% 1.23/1.45 tff(2109,plain,
% 1.23/1.45 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[556, 2108, 1])).
% 1.23/1.45 tff(2110,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2111,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2112,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 1.23/1.45 tff(2113,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2112, 271, 394, 1422, 2073, 638])).
% 1.23/1.45 tff(2114,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2115,plain,
% 1.23/1.45 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2114, 1984, 2056, 2072])).
% 1.23/1.45 tff(2116,plain,
% 1.23/1.45 (r(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[681, 2115, 79])).
% 1.23/1.45 tff(2117,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.23/1.45 tff(2118,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2119,plain,
% 1.23/1.45 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2120,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2119])).
% 1.23/1.45 tff(2121,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.23/1.45 tff(2122,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2123,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.23/1.45 tff(2124,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2123, 121, 623, 684, 572, 2117])).
% 1.23/1.45 tff(2125,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2126,plain,
% 1.23/1.45 (~r(s(s(elem!1)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2125, 684, 572, 623])).
% 1.23/1.45 tff(2127,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.23/1.45 tff(2128,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.23/1.45 tff(2129,plain,
% 1.23/1.45 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(2130,plain,
% 1.23/1.45 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[2129])).
% 1.23/1.45 tff(2131,plain,
% 1.23/1.45 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2130])).
% 1.23/1.45 tff(2132,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.23/1.45 tff(2133,plain,
% 1.23/1.45 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2132])).
% 1.23/1.45 tff(2134,plain,
% 1.23/1.45 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[2133])).
% 1.23/1.45 tff(2135,plain,
% 1.23/1.45 (s(elem!1) = z),
% 1.23/1.45 inference(transitivity,[status(thm)],[605, 2134, 50])).
% 1.23/1.45 tff(2136,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[405, 2135])).
% 1.23/1.45 tff(2137,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2138,plain,
% 1.23/1.45 (~(s(s(elem!1)) = s(z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2137, 2131])).
% 1.23/1.45 tff(2139,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2140,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2141,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.23/1.45 tff(2142,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 2128, 2127])).
% 1.23/1.45 tff(2143,plain,(b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(2144,plain,
% 1.23/1.45 (b(s(s(elem!1)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2143, 2126])).
% 1.23/1.45 tff(2145,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2146,plain,
% 1.23/1.45 (((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(2147,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[2146])).
% 1.23/1.45 tff(2148,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[2147, 2145])).
% 1.23/1.45 tff(2149,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(2150,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.23/1.45 tff(2151,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2150, 271, 517, 1894, 1421, 981])).
% 1.23/1.45 tff(2152,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2153,plain,
% 1.23/1.46 (~b(z, s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2152, 2144, 1894, 517])).
% 1.23/1.46 tff(2154,plain,
% 1.23/1.46 (~r(s(s(elem!1)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2125, 572, 623, 684])).
% 1.23/1.46 tff(2155,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2143, 2154])).
% 1.23/1.46 tff(2156,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2157,plain,
% 1.23/1.46 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2158,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2157])).
% 1.23/1.46 tff(2159,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2158, 2156])).
% 1.23/1.46 tff(2160,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2161,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 1.23/1.46 tff(2162,plain,
% 1.23/1.46 (~r(s(z), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2161, 121, 623, 684, 572])).
% 1.23/1.46 tff(2163,plain,
% 1.23/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2164,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2165,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2164, 2163])).
% 1.23/1.46 tff(2166,plain,
% 1.23/1.46 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2165, 21])).
% 1.23/1.46 tff(2167,plain,
% 1.23/1.46 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2166, 2137])).
% 1.23/1.46 tff(2168,plain,
% 1.23/1.46 (b(s(z), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2167, 2162])).
% 1.23/1.46 tff(2169,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2170,plain,
% 1.23/1.46 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2171,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2170])).
% 1.23/1.46 tff(2172,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.23/1.46 tff(2173,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2174,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.23/1.46 tff(2175,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2174, 271, 2168, 517, 447, 2155])).
% 1.23/1.46 tff(2176,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2177,plain,
% 1.23/1.46 (~b(s(elem!1), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2176, 684, 572, 623, 517])).
% 1.23/1.46 tff(2178,plain,
% 1.23/1.46 (r(s(elem!1), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[429, 2177, 422])).
% 1.23/1.46 tff(2179,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2180,plain,
% 1.23/1.46 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2181,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2180])).
% 1.23/1.46 tff(2182,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2181, 2179])).
% 1.23/1.46 tff(2183,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2184,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 1.23/1.46 tff(2185,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2184, 121, 1441, 909, 411, 108])).
% 1.23/1.46 tff(2186,plain,((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2187,plain,
% 1.23/1.46 (~r(z, s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2186, 2178, 108, 909])).
% 1.23/1.46 tff(2188,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1439, 2187, 2153])).
% 1.23/1.46 tff(2189,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2190,plain,
% 1.23/1.46 (~b(s(elem!1), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2189, 2116, 909, 2107, 108, 351, 2083, 2109])).
% 1.23/1.46 tff(2191,plain,
% 1.23/1.46 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[526, 2190, 211])).
% 1.23/1.46 tff(2192,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2193,plain,
% 1.23/1.46 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2194,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2193])).
% 1.23/1.46 tff(2195,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2194, 2192])).
% 1.23/1.46 tff(2196,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2197,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 1.23/1.46 tff(2198,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2197, 121, 379, 623, 627, 624])).
% 1.23/1.46 tff(2199,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2200,plain,
% 1.23/1.46 (~r(elem!1, s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2199, 2191, 2109, 1980])).
% 1.23/1.46 tff(2201,plain,
% 1.23/1.46 (b(elem!1, s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[599, 2200, 68])).
% 1.23/1.46 tff(2202,plain,
% 1.23/1.46 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.23/1.46 inference(commutativity,[status(thm)],[])).
% 1.23/1.46 tff(2203,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.23/1.46 tff(2204,plain,
% 1.23/1.46 (elem!1 = s(elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 1.23/1.46 tff(2205,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[377, 2204])).
% 1.23/1.46 tff(2206,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2207,plain,
% 1.23/1.46 (~(s(elem!1) = elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2206, 219])).
% 1.23/1.46 tff(2208,plain,
% 1.23/1.46 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[614, 79])).
% 1.23/1.46 tff(2209,plain,
% 1.23/1.46 (~(s(elem!1) = s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[210, 2208])).
% 1.23/1.46 tff(2210,plain,
% 1.23/1.46 (~(s(s(elem!1)) = s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[620, 2209])).
% 1.23/1.46 tff(2211,plain,
% 1.23/1.46 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.23/1.46 inference(commutativity,[status(thm)],[])).
% 1.23/1.46 tff(2212,plain,
% 1.23/1.46 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.23/1.46 inference(symmetry,[status(thm)],[2211])).
% 1.23/1.46 tff(2213,plain,
% 1.23/1.46 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2212])).
% 1.23/1.46 tff(2214,plain,
% 1.23/1.46 (~(s(s(elem!1)) = elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[68, 2213])).
% 1.23/1.46 tff(2215,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2216,plain,
% 1.23/1.46 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2217,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2216])).
% 1.23/1.46 tff(2218,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2217, 2215])).
% 1.23/1.46 tff(2219,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2220,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 1.23/1.46 tff(2221,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2220, 271, 1326, 1894, 588, 542])).
% 1.23/1.46 tff(2222,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2223,plain,
% 1.23/1.46 (~b(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2222, 1326, 1894, 588])).
% 1.23/1.46 tff(2224,plain,
% 1.23/1.46 ((s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[540, 21, 2223])).
% 1.23/1.46 tff(2225,plain,
% 1.23/1.46 (r(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2224, 2214])).
% 1.23/1.46 tff(2226,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2227,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2228,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.23/1.46 tff(2229,plain,
% 1.23/1.46 (~r(s(s(elem!1)), s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2228, 121, 379, 622, 2225])).
% 1.23/1.46 tff(2230,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[699, 21, 2229, 2210])).
% 1.23/1.46 tff(2231,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2232,plain,
% 1.23/1.46 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2233,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2232])).
% 1.23/1.46 tff(2234,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2233, 2231])).
% 1.23/1.46 tff(2235,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2236,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2235, 2234])).
% 1.23/1.46 tff(2237,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2236, 271, 1326, 1894, 588, 2230])).
% 1.23/1.46 tff(2238,plain,((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(2239,plain,
% 1.23/1.46 (~r(s(elem!1), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2238, 2201, 1326, 1980, 2107, 68])).
% 1.23/1.46 tff(2240,plain,
% 1.23/1.46 (((~![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))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2241,plain,
% 1.23/1.46 ((~![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))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(2242,plain,
% 1.23/1.46 ((~![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)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.23/1.46 tff(2243,plain,
% 1.23/1.46 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2242, 21])).
% 1.23/1.46 tff(2244,plain,
% 1.23/1.46 (b(s(elem!1), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2243, 2239, 2207])).
% 1.23/1.46 tff(2245,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2246,plain,
% 1.23/1.46 (((~b(elem!1, s(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(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(2247,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[2246])).
% 1.23/1.46 tff(2248,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[2247, 2245])).
% 1.23/1.46 tff(2249,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2250,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 1.23/1.47 tff(2251,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2250, 271, 2244, 2201, 2056, 257])).
% 1.23/1.47 tff(2252,plain,((z = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2253,plain,
% 1.23/1.47 (z = elem!1),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2252, 908, 1925, 68, 905, 108, 1, 26, 222, 1101, 37, 67, 906, 1926])).
% 1.23/1.47 tff(2254,plain,
% 1.23/1.47 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2253])).
% 1.23/1.47 tff(2255,plain,
% 1.23/1.47 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 1.23/1.47 inference(symmetry,[status(thm)],[2254])).
% 1.23/1.47 tff(2256,plain,
% 1.23/1.47 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2255])).
% 1.23/1.47 tff(2257,plain,
% 1.23/1.47 (~b(z, elem!1)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[192, 2256])).
% 1.23/1.47 tff(2258,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1925, 2257])).
% 1.23/1.47 tff(2259,plain,((s(s(s(z))) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(z, s(z)) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2260,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2259, 893, 180, 108, 1, 167, 158, 68, 33, 2, 38, 150])).
% 1.23/1.47 tff(2261,plain,((~(z = elem!1)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2262,plain,
% 1.23/1.47 (~(z = elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2261, 106, 1, 68, 33, 2, 38])).
% 1.23/1.47 tff(2263,plain,
% 1.23/1.47 (~(s(z) = s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[343, 2262])).
% 1.23/1.47 tff(2264,plain,
% 1.23/1.47 (~r(s(s(s(z))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[129, 106, 26, 37])).
% 1.23/1.47 tff(2265,plain,
% 1.23/1.47 (b(s(s(s(z))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1155, 2264])).
% 1.23/1.47 tff(2266,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2267,plain,
% 1.23/1.47 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2268,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2267])).
% 1.23/1.47 tff(2269,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2268, 2266])).
% 1.23/1.47 tff(2270,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2271,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 1.23/1.47 tff(2272,plain,
% 1.23/1.47 (~r(s(elem!1), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2271, 121, 111, 110, 412])).
% 1.23/1.47 tff(2273,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2274,plain,
% 1.23/1.47 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2275,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2274])).
% 1.23/1.47 tff(2276,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2275, 2273])).
% 1.23/1.47 tff(2277,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2278,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 1.23/1.47 tff(2279,plain,
% 1.23/1.47 (~r(s(z), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2278, 121, 111, 110, 412])).
% 1.23/1.47 tff(2280,plain,
% 1.23/1.47 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[84, 82])).
% 1.23/1.47 tff(2281,plain,
% 1.23/1.47 (b(s(z), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[444, 348, 438])).
% 1.23/1.47 tff(2282,plain,
% 1.23/1.47 (~(s(elem!1) = s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[350, 348])).
% 1.23/1.47 tff(2283,plain,
% 1.23/1.47 (b(s(elem!1), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[429, 2282, 423])).
% 1.23/1.47 tff(2284,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2285,plain,
% 1.23/1.47 (((~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(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2286,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2285])).
% 1.23/1.47 tff(2287,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2286, 2284])).
% 1.23/1.47 tff(2288,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2289,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 1.23/1.47 tff(2290,plain,
% 1.23/1.47 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2289, 271, 2283, 2281, 503])).
% 1.23/1.47 tff(2291,plain,
% 1.23/1.47 (((~![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)))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2292,plain,
% 1.23/1.47 ((~![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)))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2293,plain,
% 1.23/1.47 ((~![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))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.23/1.47 tff(2294,plain,
% 1.23/1.47 (r(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2293, 21, 2290, 2280])).
% 1.23/1.47 tff(2295,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2296,plain,
% 1.23/1.47 (((~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(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2297,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2296])).
% 1.23/1.47 tff(2298,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2297, 2295])).
% 1.23/1.47 tff(2299,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2300,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 1.23/1.47 tff(2301,plain,
% 1.23/1.47 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2300, 271, 2283, 2281, 503])).
% 1.23/1.47 tff(2302,plain,
% 1.23/1.47 (r(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[681, 2301, 82])).
% 1.23/1.47 tff(2303,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2304,plain,
% 1.23/1.47 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2305,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2304])).
% 1.23/1.47 tff(2306,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.23/1.47 tff(2307,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2308,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.23/1.47 tff(2309,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2308, 121, 2302, 111, 412, 2294])).
% 1.23/1.47 tff(2310,plain,((s(z) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | r(s(elem!1), s(z)) | r(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2311,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2310, 2279, 2272, 111, 82, 503, 348, 412])).
% 1.23/1.47 tff(2312,plain,((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2313,plain,
% 1.23/1.47 (~r(s(elem!1), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2312, 2263, 79, 67, 37, 26])).
% 1.23/1.47 tff(2314,plain,
% 1.23/1.47 (b(s(elem!1), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[409, 2313])).
% 1.23/1.47 tff(2315,plain,
% 1.23/1.47 (~(elem!1 = z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[333, 2262])).
% 1.23/1.47 tff(2316,plain,
% 1.23/1.47 (~(s(s(s(z))) = elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[250, 232, 106])).
% 1.23/1.47 tff(2317,plain,
% 1.23/1.47 (~r(s(s(s(z))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[129, 106, 110, 37])).
% 1.23/1.47 tff(2318,plain,
% 1.23/1.47 (b(s(s(s(z))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1155, 2317])).
% 1.23/1.47 tff(2319,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.23/1.47 tff(2320,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.23/1.47 tff(2321,plain,
% 1.23/1.47 (((~![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)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2322,plain,
% 1.23/1.47 ((~![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)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2323,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 1.23/1.47 tff(2324,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2323, 21, 2319, 97, 2320])).
% 1.23/1.47 tff(2325,plain,(b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2326,plain,
% 1.23/1.47 (r(s(s(s(z))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2325, 2319])).
% 1.23/1.47 tff(2327,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.23/1.47 tff(2328,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2329,plain,
% 1.23/1.47 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2330,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2329])).
% 1.23/1.47 tff(2331,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2330, 2328])).
% 1.23/1.47 tff(2332,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2333,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 1.23/1.47 tff(2334,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2333, 121, 909, 2327, 1140, 108])).
% 1.23/1.47 tff(2335,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(2336,plain,
% 1.23/1.47 (~r(z, s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2335, 2326, 106, 905])).
% 1.23/1.47 tff(2337,plain,
% 1.23/1.47 (b(z, s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1214, 2336])).
% 1.23/1.47 tff(2338,plain,
% 1.23/1.47 (~(elem!1 = s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1100, 2316])).
% 1.23/1.47 tff(2339,plain,
% 1.23/1.47 (~(z = elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1202, 2336, 2338, 33])).
% 1.23/1.47 tff(2340,plain,
% 1.23/1.47 (~(s(z) = s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[343, 2339])).
% 1.23/1.47 tff(2341,plain,
% 1.23/1.47 (r(z, elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[355, 2339, 199])).
% 1.23/1.47 tff(2342,plain,
% 1.23/1.47 (~r(s(s(s(z))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[129, 106, 110, 111])).
% 1.23/1.47 tff(2343,plain,
% 1.23/1.47 (b(s(s(s(z))), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1155, 2342])).
% 1.23/1.47 tff(2344,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.23/1.47 tff(2345,plain,
% 1.23/1.47 (b(elem!1, s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[392, 2344, 219])).
% 1.23/1.47 tff(2346,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.23/1.47 tff(2347,plain,
% 1.23/1.47 (~r(z, s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2335, 2327, 108, 909])).
% 1.23/1.47 tff(2348,plain,
% 1.23/1.47 (b(z, s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1214, 2347])).
% 1.23/1.47 tff(2349,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2350,plain,
% 1.23/1.47 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(2351,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[2350])).
% 1.23/1.47 tff(2352,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[2351, 2349])).
% 1.23/1.47 tff(2353,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(2354,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 1.23/1.47 tff(2355,plain,
% 1.23/1.47 (~b(s(elem!1), s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2354, 271, 394, 2348, 1935])).
% 1.23/1.48 tff(2356,plain,
% 1.23/1.48 (r(s(s(s(z))), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[255, 2346, 251])).
% 1.23/1.48 tff(2357,plain,
% 1.23/1.48 (~(elem!1 = s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1100, 251])).
% 1.23/1.48 tff(2358,plain,
% 1.23/1.48 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1516, 2357])).
% 1.23/1.48 tff(2359,plain,
% 1.23/1.48 (s(z) = elem!1),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[242, 239])).
% 1.23/1.48 tff(2360,plain,
% 1.23/1.48 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2359])).
% 1.23/1.48 tff(2361,plain,
% 1.23/1.48 (b(s(s(s(elem!1))), elem!1)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[503, 2360])).
% 1.23/1.48 tff(2362,plain,
% 1.23/1.48 (s(s(z)) = s(elem!1)),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2359])).
% 1.23/1.48 tff(2363,plain,
% 1.23/1.48 (s(s(s(z))) = s(s(elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2362])).
% 1.23/1.48 tff(2364,plain,
% 1.23/1.48 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2363])).
% 1.23/1.48 tff(2365,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2364])).
% 1.23/1.48 tff(2366,plain,
% 1.23/1.48 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1224])).
% 1.23/1.48 tff(2367,plain,
% 1.23/1.48 (b(s(elem!1), s(s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[517, 2366])).
% 1.23/1.48 tff(2368,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2039, 2367])).
% 1.23/1.48 tff(2369,plain,((~b(s(elem!1), s(s(elem!1)))) | b(s(elem!1), s(s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2370,plain,
% 1.23/1.48 (~b(s(elem!1), s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2369, 239, 2039])).
% 1.23/1.48 tff(2371,plain,
% 1.23/1.48 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[526, 2370, 216])).
% 1.23/1.48 tff(2372,plain,
% 1.23/1.48 (s(s(s(z))) = s(s(elem!1))),
% 1.23/1.48 inference(symmetry,[status(thm)],[1224])).
% 1.23/1.48 tff(2373,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1226, 2372])).
% 1.23/1.48 tff(2374,plain,
% 1.23/1.48 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[2373])).
% 1.23/1.48 tff(2375,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[573, 2374])).
% 1.23/1.48 tff(2376,plain,
% 1.23/1.48 (s(s(z)) = s(elem!1)),
% 1.23/1.48 inference(symmetry,[status(thm)],[1223])).
% 1.23/1.48 tff(2377,plain,
% 1.23/1.48 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2376, 2372])).
% 1.23/1.48 tff(2378,plain,
% 1.23/1.48 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[2377])).
% 1.23/1.48 tff(2379,plain,
% 1.23/1.48 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[627, 2378])).
% 1.23/1.48 tff(2380,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2376])).
% 1.23/1.48 tff(2381,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.48 inference(symmetry,[status(thm)],[2380])).
% 1.23/1.48 tff(2382,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1551, 2381])).
% 1.23/1.48 tff(2383,plain,
% 1.23/1.48 (s(z) = elem!1),
% 1.23/1.48 inference(symmetry,[status(thm)],[239])).
% 1.23/1.48 tff(2384,plain,
% 1.23/1.48 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2383])).
% 1.23/1.48 tff(2385,plain,
% 1.23/1.48 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.23/1.48 inference(symmetry,[status(thm)],[2384])).
% 1.23/1.48 tff(2386,plain,
% 1.23/1.48 (r(s(s(s(z))), s(z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[145, 2385])).
% 1.23/1.48 tff(2387,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2388,plain,
% 1.23/1.48 (((~r(s(s(s(z))), s(z))) | (~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(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2389,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2388])).
% 1.23/1.48 tff(2390,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[2389, 2387])).
% 1.23/1.48 tff(2391,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2392,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.23/1.48 tff(2393,plain,
% 1.23/1.48 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2392, 121])).
% 1.23/1.48 tff(2394,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2393, 2386, 2382, 2379, 2375])).
% 1.23/1.48 tff(2395,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2396,plain,
% 1.23/1.48 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2395, 2371, 239, 145, 573])).
% 1.23/1.48 tff(2397,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1559, 2396, 1548])).
% 1.23/1.48 tff(2398,plain,
% 1.23/1.48 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2397, 2365])).
% 1.23/1.48 tff(2399,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2400,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2401,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.23/1.48 tff(2402,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2401, 271, 307, 394, 2398, 2361])).
% 1.23/1.48 tff(2403,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2404,plain,
% 1.23/1.48 (~(elem!1 = s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2403, 394, 2345, 503, 2358, 2356, 573, 211, 2355])).
% 1.23/1.48 tff(2405,plain,
% 1.23/1.48 (~(s(z) = elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1221, 2404])).
% 1.23/1.48 tff(2406,plain,
% 1.23/1.48 (b(s(z), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[236, 2405, 232])).
% 1.23/1.48 tff(2407,plain,
% 1.23/1.48 (~(s(s(z)) = s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[960, 2405])).
% 1.23/1.48 tff(2408,plain,
% 1.23/1.48 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[953, 2407])).
% 1.23/1.48 tff(2409,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2410,plain,
% 1.23/1.48 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2411,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2410])).
% 1.23/1.48 tff(2412,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[2411, 2409])).
% 1.23/1.48 tff(2413,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2414,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 1.23/1.48 tff(2415,plain,
% 1.23/1.48 (~b(s(s(elem!1)), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2414, 271, 543, 750, 503])).
% 1.23/1.48 tff(2416,plain,
% 1.23/1.48 (r(s(s(elem!1)), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2143, 2415])).
% 1.23/1.48 tff(2417,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.23/1.48 tff(2418,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2419,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2420,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2419, 2418])).
% 1.23/1.48 tff(2421,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2420, 121, 110, 2117, 909, 2417])).
% 1.23/1.48 tff(2422,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2423,plain,
% 1.23/1.48 (~r(s(s(elem!1)), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2422, 2416, 110, 909])).
% 1.23/1.48 tff(2424,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.23/1.48 tff(2425,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.23/1.48 tff(2426,plain,
% 1.23/1.48 (((~![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))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2427,plain,
% 1.23/1.48 ((~![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))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2428,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2427, 2426])).
% 1.23/1.48 tff(2429,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2428, 21, 59, 2425, 2424])).
% 1.23/1.48 tff(2430,plain,(b(s(s(elem!1)), z) | r(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2431,plain,
% 1.23/1.48 (b(s(s(elem!1)), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2430, 2423])).
% 1.23/1.48 tff(2432,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2433,plain,
% 1.23/1.48 (((~b(s(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(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2434,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2433])).
% 1.23/1.48 tff(2435,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.23/1.48 tff(2436,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(elem!1)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2437,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.23/1.48 tff(2438,plain,
% 1.23/1.48 (~b(s(z), s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2437, 271, 543, 750, 503])).
% 1.23/1.48 tff(2439,plain,
% 1.23/1.48 (r(s(z), s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2167, 2438])).
% 1.23/1.48 tff(2440,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2441,plain,
% 1.23/1.48 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2442,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2441])).
% 1.23/1.48 tff(2443,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[2442, 2440])).
% 1.23/1.48 tff(2444,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2445,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 1.23/1.48 tff(2446,plain,
% 1.23/1.48 (~r(z, s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2445, 121, 2439, 2416, 909])).
% 1.23/1.48 tff(2447,plain,
% 1.23/1.48 (b(z, s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2106, 2446])).
% 1.23/1.48 tff(2448,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.23/1.48 tff(2449,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.23/1.48 tff(2450,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2451,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2452,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.23/1.48 tff(2453,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2452, 271, 1894, 2449, 2448, 1935])).
% 1.23/1.48 tff(2454,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2455,plain,
% 1.23/1.48 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2454, 2447, 1935, 2431])).
% 1.23/1.48 tff(2456,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2457,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2458,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.23/1.48 tff(2459,plain,
% 1.23/1.48 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2458, 121, 2439, 2416, 2327])).
% 1.23/1.48 tff(2460,plain,
% 1.23/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(2461,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(2462,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 1.23/1.48 tff(2463,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2462, 21, 2459, 2455, 944])).
% 1.23/1.48 tff(2464,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(2465,plain,
% 1.23/1.48 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2464, 2408, 1935, 2327, 909, 110, 750, 503])).
% 1.23/1.48 tff(2466,plain,
% 1.23/1.48 (b(elem!1, s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[392, 219, 2344])).
% 1.23/1.48 tff(2467,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.23/1.48 tff(2468,plain,
% 1.23/1.48 (r(s(elem!1), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[2243, 2207, 2467])).
% 1.23/1.48 tff(2469,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.48 tff(2470,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.23/1.48 tff(2471,plain,
% 1.23/1.48 (s(elem!1) = s(s(s(elem!1)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2470])).
% 1.23/1.48 tff(2472,plain,
% 1.23/1.48 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2471])).
% 1.23/1.48 tff(2473,plain,
% 1.23/1.48 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.23/1.48 inference(symmetry,[status(thm)],[2472])).
% 1.23/1.48 tff(2474,plain,
% 1.23/1.48 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2473])).
% 1.23/1.48 tff(2475,plain,
% 1.23/1.48 (~b(s(s(elem!1)), s(elem!1))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[2469, 2474])).
% 1.23/1.48 tff(2476,plain,
% 1.23/1.48 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[2470])).
% 1.23/1.49 tff(2477,plain,
% 1.23/1.49 (b(s(s(elem!1)), s(elem!1))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[307, 2476])).
% 1.23/1.49 tff(2478,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2477, 2475])).
% 1.23/1.49 tff(2479,plain,((~(elem!1 = s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2480,plain,
% 1.23/1.49 (~(elem!1 = s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2479, 2466, 2469])).
% 1.23/1.49 tff(2481,plain,
% 1.23/1.49 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[78, 2480])).
% 1.23/1.49 tff(2482,plain,
% 1.23/1.49 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[556, 1, 2469])).
% 1.23/1.49 tff(2483,plain,
% 1.23/1.49 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[107])).
% 1.23/1.49 tff(2484,plain,
% 1.23/1.49 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.23/1.49 inference(symmetry,[status(thm)],[2483])).
% 1.23/1.49 tff(2485,plain,
% 1.23/1.49 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), z))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2484])).
% 1.23/1.49 tff(2486,plain,
% 1.23/1.49 (~b(s(elem!1), z)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2467, 2485])).
% 1.23/1.49 tff(2487,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[394, 2486])).
% 1.23/1.49 tff(2488,plain,((~(z = elem!1)) | (~b(s(elem!1), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2489,plain,
% 1.23/1.49 (~(z = elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2488, 2467, 394])).
% 1.23/1.49 tff(2490,plain,
% 1.23/1.49 (~(s(s(elem!1)) = elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[197, 2480])).
% 1.23/1.49 tff(2491,plain,
% 1.23/1.49 (~(elem!1 = s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[218, 616])).
% 1.23/1.49 tff(2492,plain,
% 1.23/1.49 (b(elem!1, s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[392, 2344, 2491])).
% 1.23/1.49 tff(2493,plain,
% 1.23/1.49 (~(s(elem!1) = elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2206, 2491])).
% 1.23/1.49 tff(2494,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.23/1.49 tff(2495,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2496,plain,
% 1.23/1.49 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2497,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2496])).
% 1.23/1.49 tff(2498,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2497, 2495])).
% 1.23/1.49 tff(2499,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2500,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2499, 2498])).
% 1.23/1.49 tff(2501,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2500, 121, 378, 623, 2088, 624])).
% 1.23/1.49 tff(2502,plain,((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2503,plain,
% 1.23/1.49 (~r(z, s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2502, 378, 623, 624])).
% 1.23/1.49 tff(2504,plain,
% 1.23/1.49 (b(z, s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2106, 2503])).
% 1.23/1.49 tff(2505,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.23/1.49 tff(2506,plain,
% 1.23/1.49 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2505])).
% 1.23/1.49 tff(2507,plain,
% 1.23/1.49 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[2506])).
% 1.23/1.49 tff(2508,plain,
% 1.23/1.49 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2507])).
% 1.23/1.49 tff(2509,plain,
% 1.23/1.49 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[860, 2508])).
% 1.23/1.49 tff(2510,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[623, 2509])).
% 1.23/1.49 tff(2511,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2512,plain,
% 1.23/1.49 (r(s(s(elem!1)), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2511, 2505, 623])).
% 1.23/1.49 tff(2513,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2514,plain,
% 1.23/1.49 (((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2515,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2514])).
% 1.23/1.49 tff(2516,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2515, 2513])).
% 1.23/1.49 tff(2517,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2518,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 1.23/1.49 tff(2519,plain,
% 1.23/1.49 (~r(s(s(elem!1)), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2518, 121, 378, 624, 2512])).
% 1.23/1.49 tff(2520,plain,
% 1.23/1.49 (b(s(s(elem!1)), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2430, 2519])).
% 1.23/1.49 tff(2521,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2522,plain,
% 1.23/1.49 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2523,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2522])).
% 1.23/1.49 tff(2524,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2523, 2521])).
% 1.23/1.49 tff(2525,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2526,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 1.23/1.49 tff(2527,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2526, 271, 394, 1894, 2449, 2494])).
% 1.23/1.49 tff(2528,plain,((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2529,plain,
% 1.23/1.49 (~b(s(elem!1), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2528, 2520, 2494, 2504])).
% 1.23/1.49 tff(2530,plain,
% 1.23/1.49 (r(s(elem!1), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[409, 2529])).
% 1.23/1.49 tff(2531,plain,
% 1.23/1.49 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2505])).
% 1.23/1.49 tff(2532,plain,
% 1.23/1.49 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.49 inference(symmetry,[status(thm)],[2531])).
% 1.23/1.49 tff(2533,plain,
% 1.23/1.49 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[624, 2532])).
% 1.23/1.49 tff(2534,plain,
% 1.23/1.49 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2505])).
% 1.23/1.49 tff(2535,plain,
% 1.23/1.49 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[2534])).
% 1.23/1.49 tff(2536,plain,
% 1.23/1.49 (r(z, s(s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[378, 2535])).
% 1.23/1.49 tff(2537,plain,
% 1.23/1.49 (~r(s(z), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[579, 121, 111, 573, 572])).
% 1.23/1.49 tff(2538,plain,
% 1.23/1.49 (b(s(z), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[25, 2537])).
% 1.23/1.49 tff(2539,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2540,plain,
% 1.23/1.49 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2541,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2540])).
% 1.23/1.49 tff(2542,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2541, 2539])).
% 1.23/1.49 tff(2543,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2544,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 1.23/1.49 tff(2545,plain,
% 1.23/1.49 (~r(s(z), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2544, 121, 623, 573, 572])).
% 1.23/1.49 tff(2546,plain,
% 1.23/1.49 (b(s(z), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2167, 2545])).
% 1.23/1.49 tff(2547,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2548,plain,
% 1.23/1.49 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2549,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2548])).
% 1.23/1.49 tff(2550,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.23/1.49 tff(2551,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2552,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.23/1.49 tff(2553,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2552, 271, 2546, 1894, 2538, 2449])).
% 1.23/1.49 tff(2554,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2555,plain,
% 1.23/1.49 (~r(s(z), s(s(s(elem!1))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2554, 2520, 623, 2536, 2533, 2504])).
% 1.23/1.49 tff(2556,plain,
% 1.23/1.49 (b(s(z), s(s(s(elem!1))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[760, 2555])).
% 1.23/1.49 tff(2557,plain,
% 1.23/1.49 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2505])).
% 1.23/1.49 tff(2558,plain,
% 1.23/1.49 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[2557])).
% 1.23/1.49 tff(2559,plain,
% 1.23/1.49 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2558])).
% 1.23/1.49 tff(2560,plain,
% 1.23/1.49 (~b(s(z), s(s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1242, 2559])).
% 1.23/1.49 tff(2561,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[750, 2560])).
% 1.23/1.49 tff(2562,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(s(s(elem!1))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2563,plain,
% 1.23/1.49 (b(s(z), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2562, 2556, 2505])).
% 1.23/1.49 tff(2564,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.23/1.49 tff(2565,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2566,plain,
% 1.23/1.49 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2567,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2566])).
% 1.23/1.49 tff(2568,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.23/1.49 tff(2569,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2570,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.23/1.49 tff(2571,plain,
% 1.23/1.49 (~b(z, s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2570, 271, 517, 2504, 2520])).
% 1.23/1.49 tff(2572,plain,
% 1.23/1.49 (r(z, s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1439, 2571])).
% 1.23/1.49 tff(2573,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2574,plain,
% 1.23/1.49 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2575,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[2574])).
% 1.23/1.49 tff(2576,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.23/1.49 inference(transitivity,[status(thm)],[2575, 2573])).
% 1.23/1.49 tff(2577,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2578,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 1.23/1.49 tff(2579,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2578, 121, 622, 378, 1441, 624])).
% 1.23/1.49 tff(2580,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(2581,plain,
% 1.23/1.49 (~r(s(elem!1), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2580, 2572, 624, 378])).
% 1.23/1.49 tff(2582,plain,
% 1.23/1.49 (b(s(elem!1), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2243, 2581, 2564])).
% 1.23/1.49 tff(2583,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(2584,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(2585,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 1.23/1.49 tff(2586,plain,
% 1.23/1.49 (~b(s(z), s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2585, 271, 307, 2582, 2563])).
% 1.23/1.50 tff(2587,plain,
% 1.23/1.50 (r(s(z), s(elem!1))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[444, 2586, 348])).
% 1.23/1.50 tff(2588,plain,
% 1.23/1.50 (~r(s(z), z)),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[436, 2587, 378, 2530])).
% 1.23/1.50 tff(2589,plain,
% 1.23/1.50 (b(s(z), z)),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[25, 2588])).
% 1.23/1.50 tff(2590,plain,
% 1.23/1.50 (elem!1 = s(s(s(elem!1)))),
% 1.23/1.50 inference(symmetry,[status(thm)],[2505])).
% 1.23/1.50 tff(2591,plain,
% 1.23/1.50 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[1997])).
% 1.23/1.50 tff(2592,plain,
% 1.23/1.50 (s(s(z)) = s(s(s(elem!1)))),
% 1.23/1.50 inference(transitivity,[status(thm)],[92, 2591, 70, 2590])).
% 1.23/1.50 tff(2593,plain,
% 1.23/1.50 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[2592])).
% 1.23/1.50 tff(2594,plain,
% 1.23/1.50 (s(z) = s(s(elem!1))),
% 1.23/1.50 inference(transitivity,[status(thm)],[957, 2593, 55])).
% 1.23/1.50 tff(2595,plain,
% 1.23/1.50 ($false),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[2137, 2594])).
% 1.23/1.50 tff(2596,plain,((~(s(s(s(z))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.50 tff(2597,plain,
% 1.23/1.50 (~(s(s(s(z))) = s(elem!1))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[2596, 2505])).
% 1.23/1.50 tff(2598,plain,
% 1.23/1.50 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.23/1.50 inference(transitivity,[status(thm)],[244, 2590])).
% 1.23/1.50 tff(2599,plain,
% 1.23/1.50 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[2598])).
% 1.23/1.50 tff(2600,plain,
% 1.23/1.50 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.23/1.50 inference(symmetry,[status(thm)],[2599])).
% 1.23/1.50 tff(2601,plain,
% 1.23/1.50 (s(s(s(s(z)))) = s(elem!1)),
% 1.23/1.50 inference(monotonicity,[status(thm)],[244])).
% 1.23/1.50 tff(2602,plain,
% 1.23/1.50 (s(elem!1) = s(s(s(s(z))))),
% 1.23/1.50 inference(symmetry,[status(thm)],[2601])).
% 1.23/1.50 tff(2603,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.50 tff(2604,plain,
% 1.23/1.50 ($false),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[2603, 2602])).
% 1.23/1.50 tff(2605,plain,((~(s(s(s(z))) = elem!1)) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.50 tff(2606,plain,
% 1.23/1.50 (s(elem!1) = s(s(s(s(z))))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[2605, 244])).
% 1.23/1.50 tff(2607,plain,
% 1.23/1.50 (s(s(s(s(z)))) = s(elem!1)),
% 1.23/1.50 inference(symmetry,[status(thm)],[2606])).
% 1.23/1.50 tff(2608,plain,
% 1.23/1.50 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[2607])).
% 1.23/1.50 tff(2609,plain,
% 1.23/1.50 (s(s(s(s(s(z))))) = s(s(z))),
% 1.23/1.50 inference(transitivity,[status(thm)],[2608, 56, 2600, 91])).
% 1.23/1.50 tff(2610,plain,
% 1.23/1.50 ($false),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[877, 2609])).
% 1.23/1.50 tff(2611,plain,((~(s(s(s(z))) = elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.50 tff(2612,plain,
% 1.23/1.50 (~(s(s(s(z))) = elem!1)),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[2611, 2505])).
% 1.23/1.50 tff(2613,plain,
% 1.23/1.50 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.23/1.50 inference(monotonicity,[status(thm)],[2505])).
% 1.23/1.50 tff(2614,plain,
% 1.23/1.50 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[2613])).
% 1.23/1.50 tff(2615,plain,
% 1.23/1.50 (~(s(z) = elem!1)),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[61, 2614])).
% 1.23/1.50 tff(2616,plain,
% 1.23/1.50 (~(s(s(z)) = s(elem!1))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[960, 2615])).
% 1.23/1.50 tff(2617,plain,
% 1.23/1.50 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[953, 2616])).
% 1.23/1.50 tff(2618,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.23/1.50 tff(2619,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(2620,plain,
% 1.23/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2621,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 1.33/1.50 tff(2622,plain,
% 1.33/1.50 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2621, 271, 2618, 1422, 2494])).
% 1.33/1.50 tff(2623,plain,
% 1.33/1.50 (r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2462, 21, 2622, 944])).
% 1.33/1.50 tff(2624,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2625,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2626,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 1.33/1.50 tff(2627,plain,
% 1.33/1.50 (~b(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2626, 271, 307, 2618, 1422])).
% 1.33/1.50 tff(2628,plain,
% 1.33/1.50 (r(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[255, 2627, 907])).
% 1.33/1.50 tff(2629,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2630,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2631,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.33/1.50 tff(2632,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2631, 121, 624, 2628, 1624, 2623])).
% 1.33/1.50 tff(2633,plain,((~b(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(2634,plain,
% 1.33/1.50 (~b(s(s(s(z))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2633, 2512, 624, 2617, 2612, 2582, 2494, 307])).
% 1.33/1.50 tff(2635,plain,
% 1.33/1.50 (r(s(s(s(z))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1816, 2634, 2597])).
% 1.33/1.50 tff(2636,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2637,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2638,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 1.33/1.50 tff(2639,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2638, 121, 412, 431, 1500, 2327])).
% 1.33/1.50 tff(2640,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(2641,plain,
% 1.33/1.50 (~r(s(s(s(z))), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2640, 2635, 2587, 2530])).
% 1.33/1.50 tff(2642,plain,
% 1.33/1.50 (b(s(s(s(z))), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2325, 2641])).
% 1.33/1.50 tff(2643,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2644,plain,
% 1.33/1.50 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2645,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2644])).
% 1.33/1.50 tff(2646,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2645, 2643])).
% 1.33/1.50 tff(2647,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2648,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 1.33/1.50 tff(2649,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2648, 271, 1894, 1281, 222, 1935])).
% 1.33/1.50 tff(2650,plain,((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(2651,plain,
% 1.33/1.50 (~b(s(s(s(z))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2650, 2642, 2504, 2589])).
% 1.33/1.50 tff(2652,plain,
% 1.33/1.50 (r(s(s(s(z))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1155, 2651])).
% 1.33/1.50 tff(2653,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2654,plain,
% 1.33/1.50 (((~r(s(elem!1), z)) | (~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))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2655,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2654])).
% 1.33/1.50 tff(2656,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2655, 2653])).
% 1.33/1.50 tff(2657,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2658,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 1.33/1.50 tff(2659,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2658, 121, 2572, 2530, 2635, 2652])).
% 1.33/1.50 tff(2660,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = elem!1) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(2661,plain,
% 1.33/1.50 (~(s(s(s(elem!1))) = elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2660, 2494, 624, 307, 378, 348, 2493, 517, 623])).
% 1.33/1.50 tff(2662,plain,
% 1.33/1.50 (r(s(s(s(elem!1))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[486, 2661, 479])).
% 1.33/1.50 tff(2663,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2664,plain,
% 1.33/1.50 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2665,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2664])).
% 1.33/1.50 tff(2666,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2665, 2663])).
% 1.33/1.50 tff(2667,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2668,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 1.33/1.50 tff(2669,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2668, 121, 623, 624, 139, 1624])).
% 1.33/1.50 tff(2670,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(2671,plain,
% 1.33/1.50 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2670, 2662, 624, 623])).
% 1.33/1.50 tff(2672,plain,
% 1.33/1.50 (b(s(s(elem!1)), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[862, 2671, 851])).
% 1.33/1.50 tff(2673,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2674,plain,
% 1.33/1.50 (((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2675,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2674])).
% 1.33/1.50 tff(2676,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2675, 2673])).
% 1.33/1.50 tff(2677,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2678,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.33/1.50 tff(2679,plain,
% 1.33/1.50 (~r(s(s(s(elem!1))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2678, 121, 378, 624, 139])).
% 1.33/1.50 tff(2680,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1904, 21, 30, 2679])).
% 1.33/1.50 tff(2681,plain,
% 1.33/1.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[720, 139, 622, 624])).
% 1.33/1.50 tff(2682,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[681, 2681, 82])).
% 1.33/1.50 tff(2683,plain,
% 1.33/1.50 (~r(z, s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2580, 622, 624, 378])).
% 1.33/1.50 tff(2684,plain,
% 1.33/1.50 (b(z, s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1439, 2683])).
% 1.33/1.50 tff(2685,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2686,plain,
% 1.33/1.50 (((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2687,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2686])).
% 1.33/1.50 tff(2688,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2687, 2685])).
% 1.33/1.50 tff(2689,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2690,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 1.33/1.50 tff(2691,plain,
% 1.33/1.50 (~r(s(elem!1), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2690, 121, 622, 378, 624])).
% 1.33/1.50 tff(2692,plain,
% 1.33/1.50 (b(s(elem!1), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[409, 2691])).
% 1.33/1.50 tff(2693,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2694,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2695,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.33/1.50 tff(2696,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2695, 271, 2692, 2684, 2682, 2680])).
% 1.33/1.50 tff(2697,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(2698,plain,
% 1.33/1.50 (~r(s(elem!1), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2697, 2662, 624, 82, 378])).
% 1.33/1.51 tff(2699,plain,
% 1.33/1.51 (b(s(elem!1), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2243, 2698, 2493])).
% 1.33/1.51 tff(2700,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2701,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2702,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 1.33/1.51 tff(2703,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2702, 271, 307, 2699, 2672, 2494])).
% 1.33/1.51 tff(2704,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2705,plain,
% 1.33/1.51 (~b(s(s(elem!1)), s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2704, 645, 851, 624, 82, 378, 623, 307, 348, 517])).
% 1.33/1.51 tff(2706,plain,
% 1.33/1.51 (r(s(s(elem!1)), s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[701, 2705, 621])).
% 1.33/1.51 tff(2707,plain,
% 1.33/1.51 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2697, 622, 624, 82, 378])).
% 1.33/1.51 tff(2708,plain,
% 1.33/1.51 (s(s(s(elem!1))) = elem!1),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[486, 2707, 479])).
% 1.33/1.51 tff(2709,plain,
% 1.33/1.51 (r(s(s(elem!1)), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2511, 2708, 623])).
% 1.33/1.51 tff(2710,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2711,plain,
% 1.33/1.51 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2712,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2711])).
% 1.33/1.51 tff(2713,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2712, 2710])).
% 1.33/1.51 tff(2714,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2715,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 1.33/1.51 tff(2716,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2715, 121, 622, 624, 2709, 683])).
% 1.33/1.51 tff(2717,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2718,plain,
% 1.33/1.51 (~r(s(elem!1), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2717, 2706, 624, 623, 645, 82, 378])).
% 1.33/1.51 tff(2719,plain,
% 1.33/1.51 (b(s(elem!1), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2243, 2718, 2493])).
% 1.33/1.51 tff(2720,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2721,plain,
% 1.33/1.51 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2722,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2721])).
% 1.33/1.51 tff(2723,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2722, 2720])).
% 1.33/1.51 tff(2724,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2725,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 1.33/1.51 tff(2726,plain,
% 1.33/1.51 (~b(s(z), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2725, 271, 1894, 1281, 1638])).
% 1.33/1.51 tff(2727,plain,
% 1.33/1.51 (r(s(z), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[760, 2726])).
% 1.33/1.51 tff(2728,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2729,plain,
% 1.33/1.51 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2730,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2729])).
% 1.33/1.51 tff(2731,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2730, 2728])).
% 1.33/1.51 tff(2732,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2733,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.33/1.51 tff(2734,plain,
% 1.33/1.51 (~r(s(s(elem!1)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2733, 121, 623, 2727, 139])).
% 1.33/1.51 tff(2735,plain,
% 1.33/1.51 (b(s(s(elem!1)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2143, 2734])).
% 1.33/1.51 tff(2736,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2737,plain,
% 1.33/1.51 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2738,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2737])).
% 1.33/1.51 tff(2739,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2738, 2736])).
% 1.33/1.51 tff(2740,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2741,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.33/1.51 tff(2742,plain,
% 1.33/1.51 (~r(s(z), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2741, 121, 623, 2727, 139])).
% 1.33/1.51 tff(2743,plain,
% 1.33/1.51 (b(s(z), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2167, 2742])).
% 1.33/1.51 tff(2744,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2745,plain,
% 1.33/1.51 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2746,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2745])).
% 1.33/1.51 tff(2747,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2746, 2744])).
% 1.33/1.51 tff(2748,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2749,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 1.33/1.51 tff(2750,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2749, 271, 2743, 1894, 1281, 2735])).
% 1.33/1.51 tff(2751,plain,((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2752,plain,
% 1.33/1.51 (~b(s(z), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2751, 139, 623, 2504, 2680])).
% 1.33/1.51 tff(2753,plain,
% 1.33/1.51 (r(s(z), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[25, 2752])).
% 1.33/1.51 tff(2754,plain,
% 1.33/1.51 (~r(s(z), s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[436, 110, 378, 412])).
% 1.33/1.51 tff(2755,plain,
% 1.33/1.51 (b(s(z), s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[444, 2754, 348])).
% 1.33/1.51 tff(2756,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2757,plain,
% 1.33/1.51 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2758,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2757])).
% 1.33/1.51 tff(2759,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2758, 2756])).
% 1.33/1.51 tff(2760,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2761,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.33/1.51 tff(2762,plain,
% 1.33/1.51 (~b(s(z), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2761, 271, 2618, 2755, 638])).
% 1.33/1.51 tff(2763,plain,
% 1.33/1.51 (r(s(z), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[760, 2762])).
% 1.33/1.51 tff(2764,plain,
% 1.33/1.51 (~r(s(s(elem!1)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2733, 121, 623, 2763, 139])).
% 1.33/1.51 tff(2765,plain,
% 1.33/1.51 (b(s(s(elem!1)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2143, 2764])).
% 1.33/1.51 tff(2766,plain,
% 1.33/1.51 (~r(s(elem!1), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[418, 121, 378, 110, 412])).
% 1.33/1.51 tff(2767,plain,
% 1.33/1.51 (b(s(elem!1), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[427, 21, 2766, 2282])).
% 1.33/1.51 tff(2768,plain,
% 1.33/1.51 (~r(s(z), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2741, 121, 623, 2763, 139])).
% 1.33/1.51 tff(2769,plain,
% 1.33/1.51 (b(s(z), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2167, 2768])).
% 1.33/1.51 tff(2770,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2174, 271, 2769, 517, 2767, 2765])).
% 1.33/1.51 tff(2771,plain,((~r(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2772,plain,
% 1.33/1.51 (~r(s(elem!1), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2771, 2753, 623, 139, 2618, 638, 378, 517, 348])).
% 1.33/1.51 tff(2773,plain,
% 1.33/1.51 (b(s(elem!1), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[409, 2772])).
% 1.33/1.51 tff(2774,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2775,plain,
% 1.33/1.51 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2776,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2775])).
% 1.33/1.51 tff(2777,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2776, 2774])).
% 1.33/1.51 tff(2778,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2779,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 1.33/1.51 tff(2780,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2779, 271, 2773, 2504, 638, 2680])).
% 1.33/1.51 tff(2781,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2782,plain,
% 1.33/1.51 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2781, 638, 623, 2719, 378, 517, 348, 624])).
% 1.33/1.51 tff(2783,plain,
% 1.33/1.51 (s(s(s(elem!1))) = elem!1),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[486, 2782, 645])).
% 1.33/1.51 tff(2784,plain,
% 1.33/1.51 (r(s(s(elem!1)), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2511, 2783, 623])).
% 1.33/1.51 tff(2785,plain,
% 1.33/1.51 (~r(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2518, 121, 378, 624, 2784])).
% 1.33/1.51 tff(2786,plain,
% 1.33/1.51 (b(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2430, 2785])).
% 1.33/1.51 tff(2787,plain,
% 1.33/1.51 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2783])).
% 1.33/1.51 tff(2788,plain,
% 1.33/1.51 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.51 inference(symmetry,[status(thm)],[2787])).
% 1.33/1.51 tff(2789,plain,
% 1.33/1.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[624, 2788])).
% 1.33/1.51 tff(2790,plain,
% 1.33/1.51 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2783])).
% 1.33/1.51 tff(2791,plain,
% 1.33/1.51 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.33/1.51 inference(symmetry,[status(thm)],[2790])).
% 1.33/1.51 tff(2792,plain,
% 1.33/1.51 (r(z, s(s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[378, 2791])).
% 1.33/1.51 tff(2793,plain,
% 1.33/1.51 (~r(s(z), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2554, 2786, 623, 2792, 2789, 2504])).
% 1.33/1.51 tff(2794,plain,
% 1.33/1.51 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[760, 2793])).
% 1.33/1.51 tff(2795,plain,
% 1.33/1.51 (b(s(z), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2562, 2794, 2783])).
% 1.33/1.52 tff(2796,plain,
% 1.33/1.52 (~b(s(z), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2585, 271, 307, 2719, 2795])).
% 1.33/1.52 tff(2797,plain,
% 1.33/1.52 (r(s(z), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[444, 2796, 348])).
% 1.33/1.52 tff(2798,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2799,plain,
% 1.33/1.52 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2800,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2799])).
% 1.33/1.52 tff(2801,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2800, 2798])).
% 1.33/1.52 tff(2802,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2803,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2802, 2801])).
% 1.33/1.52 tff(2804,plain,
% 1.33/1.52 (~b(s(elem!1), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2803, 271, 517, 2504, 2786])).
% 1.33/1.52 tff(2805,plain,
% 1.33/1.52 (r(s(elem!1), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[409, 2804])).
% 1.33/1.52 tff(2806,plain,
% 1.33/1.52 (~r(s(z), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[436, 2805, 378, 2797])).
% 1.33/1.52 tff(2807,plain,
% 1.33/1.52 (b(s(z), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[25, 2806])).
% 1.33/1.52 tff(2808,plain,
% 1.33/1.52 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2809,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2808])).
% 1.33/1.52 tff(2810,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2809, 2547])).
% 1.33/1.52 tff(2811,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2812,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 1.33/1.52 tff(2813,plain,
% 1.33/1.52 (~b(s(z), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2812, 271, 2504, 2807, 2786])).
% 1.33/1.52 tff(2814,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2815,plain,
% 1.33/1.52 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2816,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2815])).
% 1.33/1.52 tff(2817,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2816, 2814])).
% 1.33/1.52 tff(2818,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2819,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 1.33/1.52 tff(2820,plain,
% 1.33/1.52 (~r(s(z), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2819, 121, 2805, 2797, 2706])).
% 1.33/1.52 tff(2821,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2167, 2820, 2813])).
% 1.33/1.52 tff(2822,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2823,plain,
% 1.33/1.52 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2822, 517, 378, 344, 2492, 623, 624, 82, 851])).
% 1.33/1.52 tff(2824,plain,
% 1.33/1.52 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[681, 2823, 82])).
% 1.33/1.52 tff(2825,plain,
% 1.33/1.52 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2505])).
% 1.33/1.52 tff(2826,plain,
% 1.33/1.52 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2825])).
% 1.33/1.52 tff(2827,plain,
% 1.33/1.52 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2826])).
% 1.33/1.52 tff(2828,plain,
% 1.33/1.52 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2344, 2827])).
% 1.33/1.52 tff(2829,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[684, 2828])).
% 1.33/1.52 tff(2830,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2831,plain,
% 1.33/1.52 (~(s(s(s(elem!1))) = elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2830, 2824, 2344])).
% 1.33/1.52 tff(2832,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 1.33/1.52 tff(2833,plain,
% 1.33/1.52 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2832])).
% 1.33/1.52 tff(2834,plain,
% 1.33/1.52 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[1570])).
% 1.33/1.52 tff(2835,plain,
% 1.33/1.52 (s(s(s(elem!1))) = elem!1),
% 1.33/1.52 inference(transitivity,[status(thm)],[2834, 2833, 70])).
% 1.33/1.52 tff(2836,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[481, 2835])).
% 1.33/1.52 tff(2837,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2838,plain,
% 1.33/1.52 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2837, 2831])).
% 1.33/1.52 tff(2839,plain,
% 1.33/1.52 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[200])).
% 1.33/1.52 tff(2840,plain,
% 1.33/1.52 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2839])).
% 1.33/1.52 tff(2841,plain,
% 1.33/1.52 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[82, 2840])).
% 1.33/1.52 tff(2842,plain,
% 1.33/1.52 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2822, 517, 378, 344, 307, 623, 624, 82, 851])).
% 1.33/1.52 tff(2843,plain,
% 1.33/1.52 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[681, 2842, 82])).
% 1.33/1.52 tff(2844,plain,
% 1.33/1.52 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[692, 622, 623, 684])).
% 1.33/1.52 tff(2845,plain,
% 1.33/1.52 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[701, 2844, 694])).
% 1.33/1.52 tff(2846,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2847,plain,
% 1.33/1.52 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2848,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2847])).
% 1.33/1.52 tff(2849,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2848, 2846])).
% 1.33/1.52 tff(2850,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2851,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2850, 2849])).
% 1.33/1.52 tff(2852,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2851, 271, 394, 1421, 2449, 2494])).
% 1.33/1.52 tff(2853,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2854,plain,
% 1.33/1.52 (~b(s(s(elem!1)), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2853, 2692, 2684, 2845])).
% 1.33/1.52 tff(2855,plain,
% 1.33/1.52 (r(s(s(elem!1)), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2430, 2854])).
% 1.33/1.52 tff(2856,plain,
% 1.33/1.52 (~b(s(s(elem!1)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2152, 2684, 2504, 517])).
% 1.33/1.52 tff(2857,plain,
% 1.33/1.52 (r(s(s(elem!1)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2143, 2856])).
% 1.33/1.52 tff(2858,plain,
% 1.33/1.52 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.33/1.52 inference(commutativity,[status(thm)],[])).
% 1.33/1.52 tff(2859,plain,
% 1.33/1.52 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2858])).
% 1.33/1.52 tff(2860,plain,
% 1.33/1.52 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2859])).
% 1.33/1.52 tff(2861,plain,
% 1.33/1.52 (~(s(s(s(elem!1))) = s(z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[61, 2860])).
% 1.33/1.52 tff(2862,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2863,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2864,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.33/1.52 tff(2865,plain,
% 1.33/1.52 (~b(s(s(s(elem!1))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2864, 271, 307, 260, 504])).
% 1.33/1.52 tff(2866,plain,
% 1.33/1.52 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[66, 21, 2865])).
% 1.33/1.52 tff(2867,plain,
% 1.33/1.52 (r(s(s(s(elem!1))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2866, 2861])).
% 1.33/1.52 tff(2868,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2869,plain,
% 1.33/1.52 (((~b(elem!1, 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(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2870,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2869])).
% 1.33/1.52 tff(2871,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2870, 2868])).
% 1.33/1.52 tff(2872,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2873,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 1.33/1.52 tff(2874,plain,
% 1.33/1.52 (~b(s(z), s(s(s(elem!1))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2873, 271, 307, 260, 504])).
% 1.33/1.52 tff(2875,plain,
% 1.33/1.52 (r(s(z), s(s(s(elem!1))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[760, 2874])).
% 1.33/1.52 tff(2876,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2877,plain,
% 1.33/1.52 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2878,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2877])).
% 1.33/1.52 tff(2879,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2878, 2876])).
% 1.33/1.52 tff(2880,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2881,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 1.33/1.52 tff(2882,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2881, 121, 623, 2875, 2117, 2867])).
% 1.33/1.52 tff(2883,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2884,plain,
% 1.33/1.52 (~b(s(z), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2883, 2857, 623, 307, 504])).
% 1.33/1.52 tff(2885,plain,
% 1.33/1.52 ((~(z = elem!1)) <=> (~(elem!1 = z))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[361])).
% 1.33/1.52 tff(2886,plain,
% 1.33/1.52 (~(elem!1 = z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[331, 2885])).
% 1.33/1.52 tff(2887,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2888,plain,
% 1.33/1.52 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2889,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2888])).
% 1.33/1.52 tff(2890,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.33/1.52 tff(2891,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2892,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.33/1.52 tff(2893,plain,
% 1.33/1.52 (~b(elem!1, z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2892, 271, 307, 2692, 2684])).
% 1.33/1.52 tff(2894,plain,
% 1.33/1.52 ((elem!1 = z) | r(elem!1, z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[282, 21, 2893])).
% 1.33/1.52 tff(2895,plain,
% 1.33/1.52 (r(elem!1, z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2894, 2886])).
% 1.33/1.52 tff(2896,plain,
% 1.33/1.52 (~r(s(z), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[373, 357, 378, 1409])).
% 1.33/1.52 tff(2897,plain,
% 1.33/1.52 (b(s(z), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[25, 2896])).
% 1.33/1.52 tff(2898,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2899,plain,
% 1.33/1.52 (((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2900,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2899])).
% 1.33/1.53 tff(2901,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2900, 2898])).
% 1.33/1.53 tff(2902,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2903,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 1.33/1.53 tff(2904,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2903, 271, 517, 1281, 446, 1421])).
% 1.33/1.53 tff(2905,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2906,plain,
% 1.33/1.53 (~b(s(z), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2905, 2897, 2684, 517])).
% 1.33/1.53 tff(2907,plain,
% 1.33/1.53 (r(s(z), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[444, 2906, 348])).
% 1.33/1.53 tff(2908,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2909,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2910,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 1.33/1.53 tff(2911,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2910, 121, 622, 357, 624, 2907])).
% 1.33/1.53 tff(2912,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2913,plain,
% 1.33/1.53 (~r(s(z), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2912, 2895, 624, 344, 517, 378, 622])).
% 1.33/1.53 tff(2914,plain,
% 1.33/1.53 (s(z) = elem!1),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[236, 2913, 2884])).
% 1.33/1.53 tff(2915,plain,
% 1.33/1.53 (r(s(z), z) <=> r(elem!1, z)),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2914])).
% 1.33/1.53 tff(2916,plain,
% 1.33/1.53 (r(elem!1, z) <=> r(s(z), z)),
% 1.33/1.53 inference(symmetry,[status(thm)],[2915])).
% 1.33/1.53 tff(2917,plain,
% 1.33/1.53 (r(s(z), z)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2895, 2916])).
% 1.33/1.53 tff(2918,plain,
% 1.33/1.53 (r(z, s(z)) <=> r(z, elem!1)),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2914])).
% 1.33/1.53 tff(2919,plain,
% 1.33/1.53 (r(z, elem!1) <=> r(z, s(z))),
% 1.33/1.53 inference(symmetry,[status(thm)],[2918])).
% 1.33/1.53 tff(2920,plain,
% 1.33/1.53 (r(z, s(z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[378, 2919])).
% 1.33/1.53 tff(2921,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2422, 2920, 2917, 2857, 2855])).
% 1.33/1.53 tff(2922,plain,((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (z = elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2923,plain,
% 1.33/1.53 (~r(s(elem!1), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2922, 504, 624, 517, 331, 307, 623, 378, 621, 2843])).
% 1.33/1.53 tff(2924,plain,
% 1.33/1.53 (b(s(elem!1), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2243, 2923, 2493])).
% 1.33/1.53 tff(2925,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2926,plain,
% 1.33/1.53 (((~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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2927,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2926])).
% 1.33/1.53 tff(2928,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2927, 2925])).
% 1.33/1.53 tff(2929,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2930,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.33/1.53 tff(2931,plain,
% 1.33/1.53 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2930, 271, 307, 2924, 504])).
% 1.33/1.53 tff(2932,plain,
% 1.33/1.53 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2293, 21, 2931])).
% 1.33/1.53 tff(2933,plain,
% 1.33/1.53 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2932, 2841])).
% 1.33/1.53 tff(2934,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2935,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2936,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 1.33/1.53 tff(2937,plain,
% 1.33/1.53 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2936, 121, 623, 2843, 2933])).
% 1.33/1.53 tff(2938,plain,
% 1.33/1.53 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[701, 2937, 621])).
% 1.33/1.53 tff(2939,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2940,plain,
% 1.33/1.53 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2941,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2940])).
% 1.33/1.53 tff(2942,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2941, 2939])).
% 1.33/1.53 tff(2943,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2944,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 1.33/1.53 tff(2945,plain,
% 1.33/1.53 (~b(s(elem!1), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2944, 271, 517, 2504, 2938])).
% 1.33/1.53 tff(2946,plain,
% 1.33/1.53 (r(s(elem!1), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[409, 2945])).
% 1.33/1.53 tff(2947,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2948,plain,
% 1.33/1.53 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2949,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2948])).
% 1.33/1.53 tff(2950,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2949, 2947])).
% 1.33/1.53 tff(2951,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2952,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 1.33/1.53 tff(2953,plain,
% 1.33/1.53 (~b(z, s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2952, 271, 517, 2504, 2938])).
% 1.33/1.53 tff(2954,plain,
% 1.33/1.53 (r(z, s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[1439, 2953])).
% 1.33/1.53 tff(2955,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2956,plain,
% 1.33/1.53 (((~r(s(elem!1), z)) | (~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))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2957,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2956])).
% 1.33/1.53 tff(2958,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2957, 2955])).
% 1.33/1.53 tff(2959,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2960,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 1.33/1.53 tff(2961,plain,
% 1.33/1.53 (~r(s(s(s(elem!1))), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2960, 121, 2843, 2954, 2946])).
% 1.33/1.53 tff(2962,plain,
% 1.33/1.53 (b(s(s(s(elem!1))), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[1904, 21, 30, 2961])).
% 1.33/1.53 tff(2963,plain,
% 1.33/1.53 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2702, 271, 307, 2924, 2938])).
% 1.33/1.53 tff(2964,plain,
% 1.33/1.53 (r(s(s(elem!1)), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[862, 2963, 851])).
% 1.33/1.53 tff(2965,plain,
% 1.33/1.53 (~r(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2518, 121, 378, 624, 2964])).
% 1.33/1.53 tff(2966,plain,
% 1.33/1.53 (b(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2430, 2965])).
% 1.33/1.53 tff(2967,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2968,plain,
% 1.33/1.53 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2969,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2968])).
% 1.33/1.53 tff(2970,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2969, 2967])).
% 1.33/1.53 tff(2971,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2972,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2971, 2970])).
% 1.33/1.53 tff(2973,plain,
% 1.33/1.53 (~b(s(s(elem!1)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2972, 271, 1894, 1281, 2449])).
% 1.33/1.53 tff(2974,plain,
% 1.33/1.53 (r(s(s(elem!1)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2143, 2973])).
% 1.33/1.53 tff(2975,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2125, 2974, 2727, 623, 684])).
% 1.33/1.53 tff(2976,plain,((~b(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2977,plain,
% 1.33/1.53 (~b(s(z), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2976, 2966, 2843, 2504, 623, 2962])).
% 1.33/1.53 tff(2978,plain,
% 1.33/1.53 (r(s(z), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[25, 2977])).
% 1.33/1.53 tff(2979,plain,
% 1.33/1.53 (~r(s(z), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[436, 2978, 378, 2946])).
% 1.33/1.53 tff(2980,plain,
% 1.33/1.53 (b(s(z), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[444, 2979, 344])).
% 1.33/1.53 tff(2981,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2982,plain,
% 1.33/1.53 (((~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(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2983,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2982])).
% 1.33/1.53 tff(2984,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.33/1.53 tff(2985,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2986,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.33/1.53 tff(2987,plain,
% 1.33/1.53 (~b(s(z), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2986, 271, 307, 2924, 2980])).
% 1.33/1.53 tff(2988,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2989,plain,
% 1.33/1.53 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2990,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2989])).
% 1.33/1.53 tff(2991,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2990, 2988])).
% 1.33/1.53 tff(2992,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2993,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 1.33/1.54 tff(2994,plain,
% 1.33/1.54 (~b(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2993, 271, 2924, 2980, 2938])).
% 1.33/1.54 tff(2995,plain,
% 1.33/1.54 (r(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2167, 2994])).
% 1.33/1.54 tff(2996,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2997,plain,
% 1.33/1.54 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2998,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2997])).
% 1.33/1.54 tff(2999,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2998, 2996])).
% 1.33/1.54 tff(3000,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3001,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.33/1.54 tff(3002,plain,
% 1.33/1.54 (~r(s(z), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3001, 121, 623, 2995, 624])).
% 1.33/1.54 tff(3003,plain,
% 1.33/1.54 (s(z) = elem!1),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[236, 3002, 2987])).
% 1.33/1.54 tff(3004,plain,
% 1.33/1.54 (s(s(z)) = s(elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3003])).
% 1.33/1.54 tff(3005,plain,
% 1.33/1.54 (s(s(s(z))) = s(s(elem!1))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3004])).
% 1.33/1.54 tff(3006,plain,
% 1.33/1.54 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3005])).
% 1.33/1.54 tff(3007,plain,
% 1.33/1.54 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3006])).
% 1.33/1.54 tff(3008,plain,
% 1.33/1.54 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3007])).
% 1.33/1.54 tff(3009,plain,
% 1.33/1.54 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3006])).
% 1.33/1.54 tff(3010,plain,
% 1.33/1.54 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3009, 3008])).
% 1.33/1.54 tff(3011,plain,
% 1.33/1.54 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3010])).
% 1.33/1.54 tff(3012,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3013,plain,
% 1.33/1.54 (((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3014,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3013])).
% 1.33/1.54 tff(3015,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[3014, 3012])).
% 1.33/1.54 tff(3016,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(z))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3017,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3016, 3015])).
% 1.33/1.54 tff(3018,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3017, 271, 307, 2618, 448, 446])).
% 1.33/1.54 tff(3019,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(3020,plain,
% 1.33/1.54 (~b(elem!1, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3019, 2980, 307, 2924])).
% 1.33/1.54 tff(3021,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3022,plain,
% 1.33/1.54 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3023,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3022])).
% 1.33/1.54 tff(3024,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[3023, 3021])).
% 1.33/1.54 tff(3025,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3026,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 1.33/1.54 tff(3027,plain,
% 1.33/1.54 (~r(elem!1, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3026, 121, 623, 2995, 624])).
% 1.33/1.54 tff(3028,plain,
% 1.33/1.54 (elem!1 = s(z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[299, 3027, 3020])).
% 1.33/1.54 tff(3029,plain,
% 1.33/1.54 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[1225])).
% 1.33/1.54 tff(3030,plain,
% 1.33/1.54 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3029])).
% 1.33/1.54 tff(3031,plain,
% 1.33/1.54 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[1768, 3030])).
% 1.33/1.54 tff(3032,plain,
% 1.33/1.54 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3031])).
% 1.33/1.54 tff(3033,plain,
% 1.33/1.54 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.33/1.54 inference(transitivity,[status(thm)],[1224, 775, 3032, 1570])).
% 1.33/1.54 tff(3034,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1, 3033])).
% 1.33/1.54 tff(3035,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(3036,plain,
% 1.33/1.54 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3035, 3028, 615])).
% 1.33/1.54 tff(3037,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3009, 3008])).
% 1.33/1.54 tff(3038,plain,
% 1.33/1.54 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3037])).
% 1.33/1.54 tff(3039,plain,
% 1.33/1.54 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3007])).
% 1.33/1.54 tff(3040,plain,
% 1.33/1.54 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[1373])).
% 1.33/1.54 tff(3041,plain,
% 1.33/1.54 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3040])).
% 1.33/1.54 tff(3042,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 1.33/1.54 tff(3043,plain,
% 1.33/1.54 (elem!1 = s(s(s(s(s(z)))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3042])).
% 1.33/1.54 tff(3044,plain,
% 1.33/1.54 (s(z) = s(s(s(s(elem!1))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[223, 3043, 3041])).
% 1.33/1.54 tff(3045,plain,
% 1.33/1.54 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3044])).
% 1.33/1.54 tff(3046,plain,
% 1.33/1.54 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3045])).
% 1.33/1.54 tff(3047,plain,
% 1.33/1.54 (s(s(s(elem!1))) = z),
% 1.33/1.54 inference(transitivity,[status(thm)],[2834, 3046, 50])).
% 1.33/1.54 tff(3048,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[30, 3047])).
% 1.33/1.54 tff(3049,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(3050,plain,
% 1.33/1.54 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3049, 3003])).
% 1.33/1.54 tff(3051,plain,
% 1.33/1.54 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3005])).
% 1.33/1.54 tff(3052,plain,
% 1.33/1.54 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(symmetry,[status(thm)],[3051])).
% 1.33/1.54 tff(3053,plain,
% 1.33/1.54 (r(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2964, 3052])).
% 1.33/1.54 tff(3054,plain,
% 1.33/1.54 (r(s(z), z) <=> r(elem!1, z)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3003])).
% 1.33/1.54 tff(3055,plain,
% 1.33/1.54 (r(elem!1, z)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2978, 3054])).
% 1.33/1.54 tff(3056,plain,
% 1.33/1.54 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[1038])).
% 1.33/1.54 tff(3057,plain,
% 1.33/1.54 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3056])).
% 1.33/1.54 tff(3058,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3057])).
% 1.33/1.54 tff(3059,plain,
% 1.33/1.54 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[3058])).
% 1.33/1.54 tff(3060,plain,
% 1.33/1.54 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[1037])).
% 1.33/1.54 tff(3061,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.33/1.54 tff(3062,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3063,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3064,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3063, 3062])).
% 1.33/1.54 tff(3065,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3064, 121, 1409, 3061, 145, 1736])).
% 1.33/1.54 tff(3066,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(3067,plain,
% 1.33/1.54 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3066, 3061, 1409, 145])).
% 1.33/1.54 tff(3068,plain,
% 1.33/1.54 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1733, 3067])).
% 1.33/1.54 tff(3069,plain,
% 1.33/1.54 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3068, 3060])).
% 1.33/1.54 tff(3070,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3069, 3059])).
% 1.33/1.54 tff(3071,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3072,plain,
% 1.33/1.54 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3073,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3072])).
% 1.33/1.54 tff(3074,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[3073, 3071])).
% 1.33/1.54 tff(3075,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3076,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 1.33/1.54 tff(3077,plain,
% 1.33/1.54 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3076, 271, 1894, 2449])).
% 1.33/1.54 tff(3078,plain,
% 1.33/1.54 (~b(s(s(s(s(elem!1)))), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3077, 3070])).
% 1.33/1.54 tff(3079,plain,
% 1.33/1.54 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3057])).
% 1.33/1.54 tff(3080,plain,
% 1.33/1.54 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.54 inference(symmetry,[status(thm)],[3079])).
% 1.33/1.54 tff(3081,plain,
% 1.33/1.54 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3061, 3080])).
% 1.33/1.54 tff(3082,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3083,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3084,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 1.33/1.54 tff(3085,plain,
% 1.33/1.54 ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3084, 121, 378, 624])).
% 1.33/1.54 tff(3086,plain,
% 1.33/1.54 (~r(s(s(s(s(elem!1)))), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3085, 3081])).
% 1.33/1.54 tff(3087,plain,
% 1.33/1.54 (((~![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))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3088,plain,
% 1.33/1.54 ((~![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))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3089,plain,
% 1.33/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 1.33/1.54 tff(3090,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3089, 21, 812, 3086, 3078])).
% 1.33/1.54 tff(3091,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(3092,plain,
% 1.33/1.54 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3091, 2966, 2504, 378, 624, 3003, 3055, 3053])).
% 1.33/1.54 tff(3093,plain,
% 1.33/1.54 (b(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[840, 3092, 3050])).
% 1.33/1.54 tff(3094,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3093, 3039])).
% 1.33/1.54 tff(3095,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3096,plain,
% 1.33/1.54 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(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(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3097,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[3096])).
% 1.33/1.54 tff(3098,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[3097, 3095])).
% 1.33/1.54 tff(3099,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(3100,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 1.33/1.54 tff(3101,plain,
% 1.33/1.54 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3100, 271, 307, 504, 3094])).
% 1.33/1.54 tff(3102,plain,
% 1.33/1.54 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3101, 3038])).
% 1.33/1.54 tff(3103,plain,
% 1.33/1.54 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1776, 3102, 3036])).
% 1.33/1.54 tff(3104,plain,
% 1.33/1.54 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3103, 3011])).
% 1.33/1.54 tff(3105,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(3106,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3107,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3106, 3105])).
% 1.33/1.55 tff(3108,plain,
% 1.33/1.55 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3107, 271, 307, 2924, 3094])).
% 1.33/1.55 tff(3109,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 1.33/1.55 tff(3110,plain,
% 1.33/1.55 (((~![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)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3111,plain,
% 1.33/1.55 ((~![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)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3112,plain,
% 1.33/1.55 ((~![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))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 1.33/1.55 tff(3113,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3112, 21, 3109, 3108])).
% 1.33/1.55 tff(3114,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3115,plain,
% 1.33/1.55 (((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3116,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3115])).
% 1.33/1.55 tff(3117,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[3116, 3114])).
% 1.33/1.55 tff(3118,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3119,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 1.33/1.55 tff(3120,plain,
% 1.33/1.55 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3119, 121, 2843, 2946, 3113])).
% 1.33/1.55 tff(3121,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3120, 3104])).
% 1.33/1.55 tff(3122,plain,((~b(s(s(s(elem!1))), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(3123,plain,
% 1.33/1.55 (~b(s(s(s(elem!1))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3122, 2838, 2492, 378, 624, 623, 851, 517, 82, 331])).
% 1.33/1.55 tff(3124,plain,
% 1.33/1.55 (r(s(s(s(elem!1))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[486, 3123, 2831])).
% 1.33/1.55 tff(3125,plain,
% 1.33/1.55 (~r(s(s(s(elem!1))), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2678, 121, 378, 624, 3124])).
% 1.33/1.55 tff(3126,plain,
% 1.33/1.55 (b(s(s(s(elem!1))), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1904, 21, 30, 3125])).
% 1.33/1.55 tff(3127,plain,
% 1.33/1.55 (~b(s(z), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2751, 3126, 623, 2504, 3124])).
% 1.33/1.55 tff(3128,plain,
% 1.33/1.55 (r(s(z), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[25, 3127])).
% 1.33/1.55 tff(3129,plain,
% 1.33/1.55 (~b(s(s(elem!1)), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2704, 3123, 851, 624, 82, 378, 623, 2492, 344, 517])).
% 1.33/1.55 tff(3130,plain,
% 1.33/1.55 (r(s(s(elem!1)), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[701, 3129, 621])).
% 1.33/1.55 tff(3131,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2936, 121, 623, 684, 798, 683])).
% 1.33/1.55 tff(3132,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(3133,plain,
% 1.33/1.55 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3132, 2824, 623, 3130])).
% 1.33/1.55 tff(3134,plain,
% 1.33/1.55 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2293, 21, 3133])).
% 1.33/1.55 tff(3135,plain,
% 1.33/1.55 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3134, 2841])).
% 1.33/1.55 tff(3136,plain,
% 1.33/1.55 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.33/1.55 inference(commutativity,[status(thm)],[])).
% 1.33/1.55 tff(3137,plain,
% 1.33/1.55 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.33/1.55 inference(symmetry,[status(thm)],[3136])).
% 1.33/1.55 tff(3138,plain,
% 1.33/1.55 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3137])).
% 1.33/1.55 tff(3139,plain,
% 1.33/1.55 (~(z = s(s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[30, 3138])).
% 1.33/1.55 tff(3140,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3141,plain,
% 1.33/1.55 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3142,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3141])).
% 1.33/1.55 tff(3143,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.33/1.55 inference(transitivity,[status(thm)],[3142, 3140])).
% 1.33/1.55 tff(3144,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3145,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3144, 3143])).
% 1.33/1.55 tff(3146,plain,
% 1.33/1.55 (~r(z, s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3145, 121, 378, 624, 3124])).
% 1.33/1.55 tff(3147,plain,
% 1.33/1.55 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[36, 21, 3146])).
% 1.33/1.55 tff(3148,plain,
% 1.33/1.55 (b(z, s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3147, 3139])).
% 1.33/1.55 tff(3149,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3150,plain,
% 1.33/1.55 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3151,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3150])).
% 1.33/1.55 tff(3152,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.55 inference(transitivity,[status(thm)],[3151, 3149])).
% 1.33/1.55 tff(3153,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3154,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 1.33/1.55 tff(3155,plain,
% 1.33/1.55 (~b(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3154, 271, 3148, 3135, 3126])).
% 1.33/1.55 tff(3156,plain,
% 1.33/1.55 (r(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[409, 3155])).
% 1.33/1.55 tff(3157,plain,
% 1.33/1.55 (~r(s(z), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[436, 3156, 378, 3128])).
% 1.33/1.55 tff(3158,plain,
% 1.33/1.55 (b(s(z), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[444, 3157, 344])).
% 1.33/1.55 tff(3159,plain,
% 1.33/1.55 (~r(s(elem!1), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[418, 121, 378, 3128, 3156])).
% 1.33/1.55 tff(3160,plain,
% 1.33/1.55 (b(s(elem!1), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[427, 21, 3159, 351])).
% 1.33/1.55 tff(3161,plain,
% 1.33/1.55 (~r(s(z), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2176, 517, 3160, 623, 2824])).
% 1.33/1.55 tff(3162,plain,
% 1.33/1.55 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[760, 3161])).
% 1.33/1.55 tff(3163,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3164,plain,
% 1.33/1.55 (((~b(s(s(s(elem!1))), z)) | (~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(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3165,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3164])).
% 1.33/1.55 tff(3166,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.55 inference(transitivity,[status(thm)],[3165, 3163])).
% 1.33/1.55 tff(3167,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3168,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3167, 3166])).
% 1.33/1.55 tff(3169,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3168, 271, 3162, 3135, 3158, 3126])).
% 1.33/1.55 tff(3170,plain,((~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (z = elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(3171,plain,
% 1.33/1.55 (~b(s(elem!1), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3170, 356, 623, 82, 624, 851, 331, 2344])).
% 1.33/1.55 tff(3172,plain,
% 1.33/1.55 (r(s(elem!1), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[526, 3171, 616])).
% 1.33/1.55 tff(3173,plain,
% 1.33/1.55 (~r(s(elem!1), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[635, 3172, 623, 624])).
% 1.33/1.55 tff(3174,plain,
% 1.33/1.55 (b(s(elem!1), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2243, 3173, 2493])).
% 1.33/1.55 tff(3175,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3176,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3177,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 1.33/1.55 tff(3178,plain,
% 1.33/1.55 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3177, 271, 307, 2618, 504])).
% 1.33/1.55 tff(3179,plain,
% 1.33/1.55 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2930, 271, 307, 2618, 504])).
% 1.33/1.55 tff(3180,plain,
% 1.33/1.55 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2293, 21, 752])).
% 1.33/1.55 tff(3181,plain,
% 1.33/1.55 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3180, 2841])).
% 1.33/1.55 tff(3182,plain,
% 1.33/1.55 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[679, 21, 82, 675])).
% 1.33/1.55 tff(3183,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3184,plain,
% 1.33/1.55 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3185,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3184])).
% 1.33/1.55 tff(3186,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[3185, 3183])).
% 1.33/1.55 tff(3187,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3188,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3187, 3186])).
% 1.33/1.55 tff(3189,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3188, 121, 623, 3182, 627, 3181])).
% 1.33/1.55 tff(3190,plain,(b(s(elem!1), s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(3191,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3190, 3179, 3178, 623, 82, 627])).
% 1.33/1.55 tff(3192,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(3193,plain,
% 1.33/1.55 (~b(s(s(s(elem!1))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3192, 3174, 82, 623, 2492, 3172])).
% 1.33/1.55 tff(3194,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3195,plain,
% 1.33/1.55 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(3196,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[3195])).
% 1.33/1.55 tff(3197,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[3196, 3194])).
% 1.33/1.55 tff(3198,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(3199,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 1.33/1.55 tff(3200,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3199, 121, 623, 684, 627, 683])).
% 1.33/1.55 tff(3201,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(3202,plain,
% 1.33/1.55 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3201, 684, 623, 627])).
% 1.33/1.55 tff(3203,plain,
% 1.33/1.55 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[699, 21, 3202, 694])).
% 1.33/1.55 tff(3204,plain,
% 1.33/1.56 (~(s(s(s(elem!1))) = elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2830, 684, 2344])).
% 1.33/1.56 tff(3205,plain,
% 1.33/1.56 (r(s(s(s(elem!1))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[486, 3204, 479])).
% 1.33/1.56 tff(3206,plain,
% 1.33/1.56 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2670, 3205, 624, 623])).
% 1.33/1.56 tff(3207,plain,
% 1.33/1.56 (b(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[862, 3206, 851])).
% 1.33/1.56 tff(3208,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2702, 271, 307, 2618, 3207, 3203])).
% 1.33/1.56 tff(3209,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3210,plain,
% 1.33/1.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3209, 3174, 3172, 621, 623, 2492, 851, 624, 3193, 2344])).
% 1.33/1.56 tff(3211,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[681, 3210, 82])).
% 1.33/1.56 tff(3212,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3213,plain,
% 1.33/1.56 (((~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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3214,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3213])).
% 1.33/1.56 tff(3215,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[3214, 3212])).
% 1.33/1.56 tff(3216,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3217,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 1.33/1.56 tff(3218,plain,
% 1.33/1.56 (~b(elem!1, s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3217, 271, 2492, 3174, 3211])).
% 1.33/1.56 tff(3219,plain,
% 1.33/1.56 (s(s(s(elem!1))) = elem!1),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[671, 3218, 624, 623, 3193])).
% 1.33/1.56 tff(3220,plain,
% 1.33/1.56 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3219])).
% 1.33/1.56 tff(3221,plain,
% 1.33/1.56 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3220])).
% 1.33/1.56 tff(3222,plain,
% 1.33/1.56 (~(s(z) = elem!1)),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[61, 3221])).
% 1.33/1.56 tff(3223,plain,
% 1.33/1.56 (~(s(s(z)) = s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[960, 3222])).
% 1.33/1.56 tff(3224,plain,
% 1.33/1.56 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[953, 3223])).
% 1.33/1.56 tff(3225,plain,
% 1.33/1.56 (r(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2511, 3219, 623])).
% 1.33/1.56 tff(3226,plain,
% 1.33/1.56 (~r(s(s(elem!1)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2518, 121, 356, 624, 3225])).
% 1.33/1.56 tff(3227,plain,
% 1.33/1.56 (b(s(s(elem!1)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2430, 3226])).
% 1.33/1.56 tff(3228,plain,
% 1.33/1.56 (~r(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2502, 356, 623, 624])).
% 1.33/1.56 tff(3229,plain,
% 1.33/1.56 (b(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2106, 3228])).
% 1.33/1.56 tff(3230,plain,
% 1.33/1.56 (~(s(s(s(z))) = elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2611, 3219])).
% 1.33/1.56 tff(3231,plain,
% 1.33/1.56 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3219])).
% 1.33/1.56 tff(3232,plain,
% 1.33/1.56 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.56 inference(symmetry,[status(thm)],[3231])).
% 1.33/1.56 tff(3233,plain,
% 1.33/1.56 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[624, 3232])).
% 1.33/1.56 tff(3234,plain,
% 1.33/1.56 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3219])).
% 1.33/1.56 tff(3235,plain,
% 1.33/1.56 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[3234])).
% 1.33/1.56 tff(3236,plain,
% 1.33/1.56 (r(z, s(s(s(elem!1))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[356, 3235])).
% 1.33/1.56 tff(3237,plain,
% 1.33/1.56 (~r(s(z), s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2554, 3227, 623, 3236, 3233, 3229])).
% 1.33/1.56 tff(3238,plain,
% 1.33/1.56 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[760, 3237])).
% 1.33/1.56 tff(3239,plain,
% 1.33/1.56 (b(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2562, 3238, 3219])).
% 1.33/1.56 tff(3240,plain,
% 1.33/1.56 (~b(s(z), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2585, 271, 2492, 3174, 3239])).
% 1.33/1.56 tff(3241,plain,
% 1.33/1.56 (r(s(z), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[444, 3240, 344])).
% 1.33/1.56 tff(3242,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3243,plain,
% 1.33/1.56 (((~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(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3244,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3243])).
% 1.33/1.56 tff(3245,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[3244, 3242])).
% 1.33/1.56 tff(3246,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3247,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3246, 3245])).
% 1.33/1.56 tff(3248,plain,
% 1.33/1.56 (~b(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3247, 271, 307, 2618, 2563])).
% 1.33/1.56 tff(3249,plain,
% 1.33/1.56 (r(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[427, 21, 3248, 2282])).
% 1.33/1.56 tff(3250,plain,
% 1.33/1.56 (~b(s(z), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2585, 271, 307, 2618, 2563])).
% 1.33/1.56 tff(3251,plain,
% 1.33/1.56 (r(s(z), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[444, 3250, 348])).
% 1.33/1.56 tff(3252,plain,
% 1.33/1.56 (~r(s(z), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[436, 3251, 378, 2530])).
% 1.33/1.56 tff(3253,plain,
% 1.33/1.56 (b(s(z), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[25, 3252])).
% 1.33/1.56 tff(3254,plain,
% 1.33/1.56 (~b(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2812, 271, 2504, 3253, 2520])).
% 1.33/1.56 tff(3255,plain,
% 1.33/1.56 (r(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2167, 3254])).
% 1.33/1.56 tff(3256,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3257,plain,
% 1.33/1.56 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3258,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3257])).
% 1.33/1.56 tff(3259,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[3258, 3256])).
% 1.33/1.56 tff(3260,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3261,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 1.33/1.56 tff(3262,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3261, 121, 623, 1625, 627, 411])).
% 1.33/1.56 tff(3263,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3264,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3263, 3255, 3249, 623, 627])).
% 1.33/1.56 tff(3265,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3266,plain,
% 1.33/1.56 (~b(s(s(elem!1)), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3265, 3219, 3172, 356, 344, 2492, 3174, 623, 624])).
% 1.33/1.56 tff(3267,plain,
% 1.33/1.56 (r(s(s(elem!1)), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[701, 3266, 621])).
% 1.33/1.56 tff(3268,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3269,plain,
% 1.33/1.56 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3270,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3269])).
% 1.33/1.56 tff(3271,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[3270, 3268])).
% 1.33/1.56 tff(3272,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3273,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 1.33/1.56 tff(3274,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3273, 121, 1625, 627, 431, 683])).
% 1.33/1.56 tff(3275,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3276,plain,
% 1.33/1.56 (~r(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3275, 3241, 3172, 3267])).
% 1.33/1.56 tff(3277,plain,
% 1.33/1.56 (b(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2167, 3276])).
% 1.33/1.56 tff(3278,plain,
% 1.33/1.56 (~b(s(z), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2552, 271, 3277, 3229, 3227])).
% 1.33/1.56 tff(3279,plain,
% 1.33/1.56 (r(s(z), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[25, 3278])).
% 1.33/1.56 tff(3280,plain,
% 1.33/1.56 (~r(s(elem!1), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[436, 3279, 356, 3241])).
% 1.33/1.56 tff(3281,plain,
% 1.33/1.56 (b(s(elem!1), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[409, 3280])).
% 1.33/1.56 tff(3282,plain,
% 1.33/1.56 (~(s(s(s(z))) = s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2596, 3219])).
% 1.33/1.56 tff(3283,plain,
% 1.33/1.56 (~b(s(s(s(z))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[310, 271, 307, 260, 257])).
% 1.33/1.56 tff(3284,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3285,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3286,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3285, 3284])).
% 1.33/1.56 tff(3287,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3286, 271, 307, 394, 1422, 257])).
% 1.33/1.56 tff(3288,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3289,plain,
% 1.33/1.56 (~b(s(s(s(z))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3288, 257, 394, 307])).
% 1.33/1.56 tff(3290,plain,
% 1.33/1.56 (r(s(s(s(z))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1816, 3289, 2033])).
% 1.33/1.56 tff(3291,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3292,plain,
% 1.33/1.56 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3293,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[3292])).
% 1.33/1.56 tff(3294,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[3293, 3291])).
% 1.33/1.56 tff(3295,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3296,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3295, 3294])).
% 1.33/1.56 tff(3297,plain,
% 1.33/1.56 (~r(s(s(s(z))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3296, 121, 627, 431, 3290])).
% 1.33/1.56 tff(3298,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2325, 3297, 3283])).
% 1.33/1.56 tff(3299,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3300,plain,
% 1.33/1.56 (~b(s(s(s(z))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3299, 3172, 3241, 2492, 3239, 3282, 3281])).
% 1.33/1.56 tff(3301,plain,
% 1.33/1.56 (r(s(s(s(z))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[255, 3300, 3230])).
% 1.33/1.56 tff(3302,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3303,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(3304,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.33/1.56 tff(3305,plain,
% 1.33/1.56 (~r(s(s(s(z))), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3304, 121, 356, 624, 3301])).
% 1.33/1.56 tff(3306,plain,
% 1.33/1.56 (b(s(s(s(z))), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1155, 3305])).
% 1.33/1.56 tff(3307,plain,
% 1.33/1.56 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2454, 3306, 3229, 3227])).
% 1.33/1.56 tff(3308,plain,
% 1.33/1.56 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2631, 121, 624, 3301, 3225])).
% 1.33/1.56 tff(3309,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2462, 21, 3308, 3307, 3224])).
% 1.33/1.56 tff(3310,plain,((z = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = elem!1) | r(elem!1, s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(3311,plain,
% 1.33/1.56 (~r(elem!1, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3310, 2490, 199, 2489, 2482, 2344, 2481])).
% 1.33/1.56 tff(3312,plain,
% 1.33/1.56 (b(elem!1, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[599, 3311, 2480])).
% 1.33/1.56 tff(3313,plain,
% 1.33/1.56 (~(s(s(elem!1)) = s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[620, 211])).
% 1.33/1.56 tff(3314,plain,
% 1.33/1.56 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[681, 2481, 675])).
% 1.33/1.56 tff(3315,plain,
% 1.33/1.56 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[692, 3314, 2482, 2468])).
% 1.33/1.56 tff(3316,plain,
% 1.33/1.56 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[701, 3315, 3313])).
% 1.33/1.56 tff(3317,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3318,plain,
% 1.33/1.56 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(3319,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3318])).
% 1.33/1.57 tff(3320,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3319, 3317])).
% 1.33/1.57 tff(3321,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3322,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3321, 3320])).
% 1.33/1.57 tff(3323,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3322, 271, 307, 394, 588, 2494])).
% 1.33/1.57 tff(3324,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3325,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3324, 3316, 3312, 394, 2466])).
% 1.33/1.57 tff(3326,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | b(z, elem!1) | r(elem!1, s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3327,plain,
% 1.33/1.57 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3326, 1, 199, 2344, 394, 2469, 2467])).
% 1.33/1.57 tff(3328,plain,
% 1.33/1.57 (~(elem!1 = z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[333, 2489])).
% 1.33/1.57 tff(3329,plain,
% 1.33/1.57 (~b(s(s(elem!1)), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3324, 3312, 394, 2466])).
% 1.33/1.57 tff(3330,plain,
% 1.33/1.57 (r(s(s(elem!1)), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[701, 3329, 3313])).
% 1.33/1.57 tff(3331,plain,
% 1.33/1.57 (~b(s(s(s(elem!1))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2401, 271, 307, 394, 638])).
% 1.33/1.57 tff(3332,plain,
% 1.33/1.57 (~b(s(s(s(elem!1))), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2695, 271, 394, 1421, 638])).
% 1.33/1.57 tff(3333,plain,
% 1.33/1.57 (r(s(s(s(elem!1))), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1904, 21, 30, 3332])).
% 1.33/1.57 tff(3334,plain,
% 1.33/1.57 (~b(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2892, 271, 307, 394, 1421])).
% 1.33/1.57 tff(3335,plain,
% 1.33/1.57 (r(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[284, 3334, 259])).
% 1.33/1.57 tff(3336,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3337,plain,
% 1.33/1.57 (((~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(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3338,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3337])).
% 1.33/1.57 tff(3339,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3338, 3336])).
% 1.33/1.57 tff(3340,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3341,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 1.33/1.57 tff(3342,plain,
% 1.33/1.57 (~b(z, s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3341, 271, 394, 1421, 638])).
% 1.33/1.57 tff(3343,plain,
% 1.33/1.57 (r(z, s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[36, 21, 3342, 32])).
% 1.33/1.57 tff(3344,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3345,plain,
% 1.33/1.57 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3346,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3345])).
% 1.33/1.57 tff(3347,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3346, 3344])).
% 1.33/1.57 tff(3348,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3349,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 1.33/1.57 tff(3350,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3349, 121, 3343, 3335, 139, 3333])).
% 1.33/1.57 tff(3351,plain,((~b(z, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3352,plain,
% 1.33/1.57 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3351, 1421, 259, 394, 638, 307])).
% 1.33/1.57 tff(3353,plain,
% 1.33/1.57 (s(s(s(elem!1))) = elem!1),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[486, 3352, 3331])).
% 1.33/1.57 tff(3354,plain,
% 1.33/1.57 (r(s(s(elem!1)), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2511, 3353, 623])).
% 1.33/1.57 tff(3355,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3356,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3357,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3356, 3355])).
% 1.33/1.57 tff(3358,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3357, 121, 622, 3335, 3354, 683])).
% 1.33/1.57 tff(3359,plain,((~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = z) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3360,plain,
% 1.33/1.57 (~b(z, s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3359, 3330, 2468, 3328, 2466, 394, 2482, 3327])).
% 1.33/1.57 tff(3361,plain,
% 1.33/1.57 (r(z, s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1439, 3360])).
% 1.33/1.57 tff(3362,plain,
% 1.33/1.57 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.33/1.57 inference(monotonicity,[status(thm)],[1997])).
% 1.33/1.57 tff(3363,plain,
% 1.33/1.57 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.33/1.57 inference(symmetry,[status(thm)],[3362])).
% 1.33/1.57 tff(3364,plain,
% 1.33/1.57 (r(s(s(s(z))), elem!1)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[622, 3363])).
% 1.33/1.57 tff(3365,plain,
% 1.33/1.57 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[1997])).
% 1.33/1.57 tff(3366,plain,
% 1.33/1.57 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.33/1.57 inference(symmetry,[status(thm)],[3365])).
% 1.33/1.57 tff(3367,plain,
% 1.33/1.57 (r(z, s(s(s(z))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[1441, 3366])).
% 1.33/1.57 tff(3368,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3369,plain,
% 1.33/1.57 (((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3370,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3369])).
% 1.33/1.57 tff(3371,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.33/1.57 tff(3372,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3373,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.33/1.57 tff(3374,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3373, 121, 110, 145, 1140, 108])).
% 1.33/1.57 tff(3375,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3376,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3375, 3367, 3364, 108, 110])).
% 1.33/1.57 tff(3377,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3378,plain,
% 1.33/1.57 (~(s(s(s(z))) = s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3377, 3361, 110, 108, 2468])).
% 1.33/1.57 tff(3379,plain,
% 1.33/1.57 (r(z, elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[355, 2489, 199])).
% 1.33/1.57 tff(3380,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3381,plain,
% 1.33/1.57 (((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3382,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3381])).
% 1.33/1.57 tff(3383,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3382, 3380])).
% 1.33/1.57 tff(3384,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3385,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.33/1.57 tff(3386,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3385, 121, 622, 378, 1441, 1409])).
% 1.33/1.57 tff(3387,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3388,plain,
% 1.33/1.57 (~r(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3387, 2468, 3379, 3361])).
% 1.33/1.57 tff(3389,plain,
% 1.33/1.57 (b(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[284, 3388, 3328])).
% 1.33/1.57 tff(3390,plain,
% 1.33/1.57 (~b(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[402, 3389, 394, 2466])).
% 1.33/1.57 tff(3391,plain,
% 1.33/1.57 (r(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[902, 21, 3390, 898])).
% 1.33/1.57 tff(3392,plain,
% 1.33/1.57 (~b(z, s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1315, 2466, 394, 3389])).
% 1.33/1.57 tff(3393,plain,
% 1.33/1.57 (r(z, s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1214, 3392])).
% 1.33/1.57 tff(3394,plain,
% 1.33/1.57 (~r(s(s(s(z))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1508, 3393, 108, 3391])).
% 1.33/1.57 tff(3395,plain,
% 1.33/1.57 (b(s(s(s(z))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1816, 3394, 3378])).
% 1.33/1.57 tff(3396,plain,
% 1.33/1.57 (~b(s(s(s(elem!1))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2401, 271, 2466, 394, 3327])).
% 1.33/1.57 tff(3397,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3398,plain,
% 1.33/1.57 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3399,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3398])).
% 1.33/1.57 tff(3400,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3399, 3397])).
% 1.33/1.57 tff(3401,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3402,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3401, 3400])).
% 1.33/1.57 tff(3403,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3402, 271, 307, 394, 1894, 261])).
% 1.33/1.57 tff(3404,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3405,plain,
% 1.33/1.57 (~b(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3404, 2466, 394, 3389])).
% 1.33/1.57 tff(3406,plain,
% 1.33/1.57 (r(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2106, 3405])).
% 1.33/1.57 tff(3407,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.57 tff(3408,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3409,plain,
% 1.33/1.57 (((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3410,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3409])).
% 1.33/1.57 tff(3411,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3410, 3408])).
% 1.33/1.57 tff(3412,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(3413,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.33/1.57 tff(3414,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3413, 271, 307, 394, 261, 3407])).
% 1.33/1.57 tff(3415,plain,((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(3416,plain,
% 1.33/1.57 (~b(z, s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3415, 2466, 394, 3389])).
% 1.33/1.57 tff(3417,plain,
% 1.33/1.57 (r(z, s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[36, 21, 3416, 32])).
% 1.33/1.57 tff(3418,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3419,plain,
% 1.33/1.57 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(3420,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[3419])).
% 1.33/1.57 tff(3421,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[3420, 3418])).
% 1.33/1.57 tff(3422,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3423,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 1.33/1.58 tff(3424,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3423, 121, 623, 111, 2088, 139])).
% 1.33/1.58 tff(3425,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3426,plain,
% 1.33/1.58 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3425, 2482, 3417, 3406])).
% 1.33/1.58 tff(3427,plain,
% 1.33/1.58 (s(s(s(elem!1))) = elem!1),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[486, 3426, 3396])).
% 1.33/1.58 tff(3428,plain,
% 1.33/1.58 (~(s(s(s(z))) = elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2611, 3427])).
% 1.33/1.58 tff(3429,plain,
% 1.33/1.58 (~r(s(s(s(z))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3375, 3393, 108, 110])).
% 1.33/1.58 tff(3430,plain,
% 1.33/1.58 (b(s(s(s(z))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[255, 3429, 3428])).
% 1.33/1.58 tff(3431,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3288, 3430, 3395, 394, 2466])).
% 1.33/1.58 tff(3432,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | b(z, elem!1) | r(elem!1, s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3433,plain,
% 1.33/1.58 (b(s(elem!1), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3432, 2465, 110, 1, 108, 199, 394, 2344])).
% 1.33/1.58 tff(3434,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2585, 271, 307, 2618, 260, 446])).
% 1.33/1.58 tff(3435,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3436,plain,
% 1.33/1.58 (~b(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3435, 3433, 2345, 2406])).
% 1.33/1.58 tff(3437,plain,
% 1.33/1.58 (r(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[444, 3436, 348])).
% 1.33/1.58 tff(3438,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3439,plain,
% 1.33/1.58 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3440,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3439])).
% 1.33/1.58 tff(3441,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3440, 3438])).
% 1.33/1.58 tff(3442,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3443,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 1.33/1.58 tff(3444,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3443, 121, 431, 145, 108, 2046])).
% 1.33/1.58 tff(3445,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3446,plain,
% 1.33/1.58 (~r(s(elem!1), s(s(s(z))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3445, 3437, 108, 2356])).
% 1.33/1.58 tff(3447,plain,
% 1.33/1.58 (s(elem!1) = s(s(s(z)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2044, 3446, 2355])).
% 1.33/1.58 tff(3448,plain,
% 1.33/1.58 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3447])).
% 1.33/1.58 tff(3449,plain,
% 1.33/1.58 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.33/1.58 inference(symmetry,[status(thm)],[3448])).
% 1.33/1.58 tff(3450,plain,
% 1.33/1.58 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3449])).
% 1.33/1.58 tff(3451,plain,
% 1.33/1.58 (~b(s(elem!1), elem!1)),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2346, 3450])).
% 1.33/1.58 tff(3452,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3433, 3451])).
% 1.33/1.58 tff(3453,plain,((~b(s(elem!1), z)) | b(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3454,plain,
% 1.33/1.58 (~b(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3453, 2346, 106, 348, 110, 1, 199, 2344, 1935, 2327, 905, 750, 503, 232, 573])).
% 1.33/1.58 tff(3455,plain,
% 1.33/1.58 (r(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[409, 3454])).
% 1.33/1.58 tff(3456,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.33/1.58 tff(3457,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3458,plain,
% 1.33/1.58 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3459,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3458])).
% 1.33/1.58 tff(3460,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3459, 3457])).
% 1.33/1.58 tff(3461,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3462,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.33/1.58 tff(3463,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3462, 121, 378, 909, 3456, 108])).
% 1.33/1.58 tff(3464,plain,((~r(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3465,plain,
% 1.33/1.58 (~r(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3464, 108, 909, 378])).
% 1.33/1.58 tff(3466,plain,
% 1.33/1.58 (b(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[299, 3465, 258])).
% 1.33/1.58 tff(3467,plain,
% 1.33/1.58 (~b(s(elem!1), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[456, 3466, 446, 307])).
% 1.33/1.58 tff(3468,plain,
% 1.33/1.58 (r(s(elem!1), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[429, 3467, 422])).
% 1.33/1.58 tff(3469,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3470,plain,
% 1.33/1.58 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3471,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3470])).
% 1.33/1.58 tff(3472,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3471, 3469])).
% 1.33/1.58 tff(3473,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3474,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3473, 3472])).
% 1.33/1.58 tff(3475,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3474, 121, 909, 412, 3468, 108])).
% 1.33/1.58 tff(3476,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3477,plain,
% 1.33/1.58 (~b(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3476, 108, 412, 909, 422, 307, 258, 378])).
% 1.33/1.58 tff(3478,plain,
% 1.33/1.58 (r(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[444, 3477, 348])).
% 1.33/1.58 tff(3479,plain,
% 1.33/1.58 (~r(s(z), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1300, 3478, 412, 909])).
% 1.33/1.58 tff(3480,plain,
% 1.33/1.58 (b(s(z), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[25, 3479])).
% 1.33/1.58 tff(3481,plain,
% 1.33/1.58 (~b(s(elem!1), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1290, 3480, 307, 3466])).
% 1.33/1.58 tff(3482,plain,
% 1.33/1.58 (r(s(elem!1), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[429, 3481, 422])).
% 1.33/1.58 tff(3483,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3484,plain,
% 1.33/1.58 (((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3485,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3484])).
% 1.33/1.58 tff(3486,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3485, 3483])).
% 1.33/1.58 tff(3487,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3488,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3487, 3486])).
% 1.33/1.58 tff(3489,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3488, 121, 909, 412, 3478, 3482])).
% 1.33/1.58 tff(3490,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3491,plain,
% 1.33/1.58 (elem!1 = s(z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3490, 3455, 106, 905, 378, 348, 2282, 2345])).
% 1.33/1.58 tff(3492,plain,
% 1.33/1.58 (s(z) = elem!1),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[242, 3491])).
% 1.33/1.58 tff(3493,plain,
% 1.33/1.58 (s(s(z)) = s(elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3492])).
% 1.33/1.58 tff(3494,plain,
% 1.33/1.58 (s(s(s(z))) = s(s(elem!1))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3493])).
% 1.33/1.58 tff(3495,plain,
% 1.33/1.58 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3494])).
% 1.33/1.58 tff(3496,plain,
% 1.33/1.58 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3495])).
% 1.33/1.58 tff(3497,plain,
% 1.33/1.58 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3496])).
% 1.33/1.58 tff(3498,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.33/1.58 tff(3499,assumption,(~b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.33/1.58 tff(3500,plain,
% 1.33/1.58 (~(s(elem!1) = elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2206, 377])).
% 1.33/1.58 tff(3501,plain,
% 1.33/1.58 (r(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[409, 3498])).
% 1.33/1.58 tff(3502,plain,
% 1.33/1.58 (r(elem!1, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[392, 317, 377])).
% 1.33/1.58 tff(3503,plain,
% 1.33/1.58 (~(s(s(z)) = s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[960, 231])).
% 1.33/1.58 tff(3504,plain,
% 1.33/1.58 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[953, 3503])).
% 1.33/1.58 tff(3505,plain,
% 1.33/1.58 (r(z, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[902, 21, 894, 898])).
% 1.33/1.58 tff(3506,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.33/1.58 tff(3507,plain,
% 1.33/1.58 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[153])).
% 1.33/1.58 tff(3508,plain,
% 1.33/1.58 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3506, 3507])).
% 1.33/1.58 tff(3509,plain,
% 1.33/1.58 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[133])).
% 1.33/1.58 tff(3510,plain,
% 1.33/1.58 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3509, 200])).
% 1.33/1.58 tff(3511,plain,
% 1.33/1.58 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3510])).
% 1.33/1.58 tff(3512,plain,
% 1.33/1.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[61, 3511])).
% 1.33/1.58 tff(3513,plain,
% 1.33/1.58 (r(s(s(s(z))), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[490, 107, 479])).
% 1.33/1.58 tff(3514,plain,
% 1.33/1.58 (r(s(s(s(z))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[475, 107, 3513])).
% 1.33/1.58 tff(3515,plain,
% 1.33/1.58 (r(s(s(s(elem!1))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[149, 3514, 107])).
% 1.33/1.58 tff(3516,plain,
% 1.33/1.58 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[107])).
% 1.33/1.58 tff(3517,plain,
% 1.33/1.58 (r(s(elem!1), elem!1)),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[412, 3516])).
% 1.33/1.58 tff(3518,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3519,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3520,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3519, 3518])).
% 1.33/1.58 tff(3521,plain,
% 1.33/1.58 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3520, 121, 379, 3517, 3515])).
% 1.33/1.58 tff(3522,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[679, 21, 3521, 3512, 3508])).
% 1.33/1.58 tff(3523,plain,((~(z = elem!1)) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(3524,plain,
% 1.33/1.58 (~(z = elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3523, 3502, 3506, 412, 479])).
% 1.33/1.58 tff(3525,plain,
% 1.33/1.58 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[239])).
% 1.33/1.58 tff(3526,plain,
% 1.33/1.58 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 1.33/1.58 inference(symmetry,[status(thm)],[3525])).
% 1.33/1.58 tff(3527,plain,
% 1.33/1.58 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3526])).
% 1.33/1.58 tff(3528,plain,
% 1.33/1.58 ((~![X: $i] : (~b(X, X))) | (~b(s(z), s(z)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(3529,plain,
% 1.33/1.58 (~b(s(z), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3528, 190])).
% 1.33/1.58 tff(3530,plain,
% 1.33/1.58 (~b(s(z), elem!1)),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3529, 3527])).
% 1.33/1.58 tff(3531,plain,
% 1.33/1.58 (b(elem!1, s(z)) <=> b(s(z), s(z))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[239])).
% 1.33/1.58 tff(3532,plain,
% 1.33/1.58 (b(s(z), s(z)) <=> b(elem!1, s(z))),
% 1.33/1.58 inference(symmetry,[status(thm)],[3531])).
% 1.33/1.58 tff(3533,plain,
% 1.33/1.58 ((~b(s(z), s(z))) <=> (~b(elem!1, s(z)))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3532])).
% 1.33/1.58 tff(3534,plain,
% 1.33/1.58 (~b(elem!1, s(z))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[3529, 3533])).
% 1.33/1.58 tff(3535,plain,
% 1.33/1.58 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.33/1.58 inference(commutativity,[status(thm)],[])).
% 1.33/1.58 tff(3536,plain,
% 1.33/1.58 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2376])).
% 1.33/1.58 tff(3537,plain,
% 1.33/1.58 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3536, 3535])).
% 1.33/1.58 tff(3538,plain,
% 1.33/1.58 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3537])).
% 1.33/1.58 tff(3539,plain,
% 1.33/1.58 (~(s(s(s(z))) = s(elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[1136, 3538])).
% 1.33/1.58 tff(3540,plain,
% 1.33/1.58 (r(s(s(s(z))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1816, 3539, 3506])).
% 1.33/1.58 tff(3541,plain,
% 1.33/1.58 ((z = s(z)) <=> (s(z) = z)),
% 1.33/1.58 inference(commutativity,[status(thm)],[])).
% 1.33/1.58 tff(3542,plain,
% 1.33/1.58 ((z = elem!1) <=> (z = s(z))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[239])).
% 1.33/1.58 tff(3543,plain,
% 1.33/1.58 ((z = elem!1) <=> (s(z) = z)),
% 1.33/1.58 inference(transitivity,[status(thm)],[3542, 3541])).
% 1.33/1.58 tff(3544,plain,
% 1.33/1.58 ((s(z) = z) <=> (z = elem!1)),
% 1.33/1.58 inference(symmetry,[status(thm)],[3543])).
% 1.33/1.58 tff(3545,plain,
% 1.33/1.58 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3544])).
% 1.33/1.58 tff(3546,plain,
% 1.33/1.58 (~(z = elem!1)),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[11, 3545])).
% 1.33/1.58 tff(3547,plain,
% 1.33/1.58 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.33/1.58 inference(symmetry,[status(thm)],[3535])).
% 1.33/1.58 tff(3548,plain,
% 1.33/1.58 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[3537, 3547])).
% 1.33/1.58 tff(3549,plain,
% 1.33/1.58 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3548])).
% 1.33/1.58 tff(3550,plain,
% 1.33/1.58 (~(s(elem!1) = s(s(s(z))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[1136, 3549])).
% 1.33/1.58 tff(3551,plain,
% 1.33/1.58 (elem!1 = s(z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1266, 1242, 909, 1243, 294])).
% 1.33/1.58 tff(3552,plain,
% 1.33/1.58 (s(elem!1) = s(s(z))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3551])).
% 1.33/1.58 tff(3553,plain,
% 1.33/1.58 (s(s(z)) = s(elem!1)),
% 1.33/1.58 inference(symmetry,[status(thm)],[3552])).
% 1.33/1.58 tff(3554,plain,
% 1.33/1.58 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(elem!1))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3553])).
% 1.33/1.58 tff(3555,plain,
% 1.33/1.58 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.33/1.58 inference(symmetry,[status(thm)],[3554])).
% 1.33/1.58 tff(3556,plain,
% 1.33/1.58 (r(s(s(s(z))), s(s(z)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[1500, 3555])).
% 1.33/1.58 tff(3557,plain,
% 1.33/1.58 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3553])).
% 1.33/1.58 tff(3558,plain,
% 1.33/1.58 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.33/1.58 inference(symmetry,[status(thm)],[3557])).
% 1.33/1.58 tff(3559,plain,
% 1.33/1.58 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3551])).
% 1.33/1.58 tff(3560,plain,
% 1.33/1.58 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3559])).
% 1.33/1.58 tff(3561,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3562,plain,
% 1.33/1.58 (((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(3563,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[3562])).
% 1.33/1.58 tff(3564,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3563, 3561])).
% 1.33/1.59 tff(3565,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3566,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.33/1.59 tff(3567,plain,
% 1.33/1.59 (~r(elem!1, s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3566, 121, 379, 412, 1500])).
% 1.33/1.59 tff(3568,plain,
% 1.33/1.59 (~r(s(z), s(s(s(z))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3567, 3560])).
% 1.33/1.59 tff(3569,plain,
% 1.33/1.59 (b(s(z), s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[103, 21, 3568, 99])).
% 1.33/1.59 tff(3570,plain,
% 1.33/1.59 (b(s(z), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[444, 344, 438])).
% 1.33/1.59 tff(3571,plain,
% 1.33/1.59 (elem!1 = s(z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1266, 356, 909, 294, 1242])).
% 1.33/1.59 tff(3572,plain,
% 1.33/1.59 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[239])).
% 1.33/1.59 tff(3573,plain,
% 1.33/1.59 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.33/1.59 inference(symmetry,[status(thm)],[3572])).
% 1.33/1.59 tff(3574,plain,
% 1.33/1.59 (b(elem!1, s(elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[446, 3573])).
% 1.33/1.59 tff(3575,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[317, 3574])).
% 1.33/1.59 tff(3576,plain,((~(elem!1 = s(z))) | b(elem!1, s(elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3577,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3576, 3571, 3570, 317])).
% 1.33/1.59 tff(3578,plain,((z = elem!1) | b(elem!1, s(elem!1)) | (~r(z, s(z))) | b(elem!1, s(z)) | b(s(z), elem!1) | r(s(z), s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3579,plain,
% 1.33/1.59 (r(s(z), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3578, 1242, 909, 331, 317, 294, 199])).
% 1.33/1.59 tff(3580,plain,
% 1.33/1.59 (~r(s(s(s(z))), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2640, 3579, 412, 1500])).
% 1.33/1.59 tff(3581,plain,
% 1.33/1.59 (b(s(s(s(z))), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2325, 3580])).
% 1.33/1.59 tff(3582,plain,
% 1.33/1.59 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3552])).
% 1.33/1.59 tff(3583,plain,
% 1.33/1.59 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.33/1.59 inference(symmetry,[status(thm)],[3582])).
% 1.33/1.59 tff(3584,plain,
% 1.33/1.59 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3551])).
% 1.33/1.59 tff(3585,plain,
% 1.33/1.59 (b(s(s(z)), elem!1) <=> b(s(elem!1), s(z))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3584, 3583])).
% 1.33/1.59 tff(3586,plain,
% 1.33/1.59 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3551])).
% 1.33/1.59 tff(3587,plain,
% 1.33/1.59 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 1.33/1.59 inference(symmetry,[status(thm)],[3586])).
% 1.33/1.59 tff(3588,plain,
% 1.33/1.59 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3587])).
% 1.33/1.59 tff(3589,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.33/1.59 tff(3590,plain,
% 1.33/1.59 (s(z) = s(s(z))),
% 1.33/1.59 inference(symmetry,[status(thm)],[3589])).
% 1.33/1.59 tff(3591,plain,
% 1.33/1.59 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3590])).
% 1.33/1.59 tff(3592,plain,
% 1.33/1.59 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.33/1.59 inference(symmetry,[status(thm)],[3591])).
% 1.33/1.59 tff(3593,plain,
% 1.33/1.59 (s(z) = z),
% 1.33/1.59 inference(transitivity,[status(thm)],[957, 3592, 50])).
% 1.33/1.59 tff(3594,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[11, 3593])).
% 1.33/1.59 tff(3595,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3596,plain,
% 1.33/1.59 (~(s(s(z)) = elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3595, 3588])).
% 1.33/1.59 tff(3597,plain,
% 1.33/1.59 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3552])).
% 1.33/1.59 tff(3598,plain,
% 1.33/1.59 (r(s(s(z)), z)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[412, 3597])).
% 1.33/1.59 tff(3599,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.33/1.59 tff(3600,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.33/1.59 tff(3601,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3602,plain,
% 1.33/1.59 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3603,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3602])).
% 1.33/1.59 tff(3604,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3603, 3601])).
% 1.33/1.59 tff(3605,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3606,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3605, 3604])).
% 1.33/1.59 tff(3607,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3606, 121, 379, 378, 3600, 3599])).
% 1.33/1.59 tff(3608,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3609,plain,
% 1.33/1.59 (~r(s(s(z)), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3608, 3598, 1243, 379])).
% 1.33/1.59 tff(3610,plain,
% 1.33/1.59 (((~![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))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3611,plain,
% 1.33/1.59 ((~![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))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3612,plain,
% 1.33/1.59 ((~![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)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 1.33/1.59 tff(3613,plain,
% 1.33/1.59 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3612, 21])).
% 1.33/1.59 tff(3614,plain,
% 1.33/1.59 (b(s(s(z)), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3613, 3609, 3596])).
% 1.33/1.59 tff(3615,plain,
% 1.33/1.59 (b(s(elem!1), s(z))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3614, 3585])).
% 1.33/1.59 tff(3616,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3617,plain,
% 1.33/1.59 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3618,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3617])).
% 1.33/1.59 tff(3619,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3618, 3616])).
% 1.33/1.59 tff(3620,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3621,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 1.33/1.59 tff(3622,plain,
% 1.33/1.59 ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3621, 271])).
% 1.33/1.59 tff(3623,plain,
% 1.33/1.59 (~b(s(elem!1), s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3622, 3615, 3581, 3569])).
% 1.33/1.59 tff(3624,plain,
% 1.33/1.59 (r(s(elem!1), s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2044, 3623, 2037])).
% 1.33/1.59 tff(3625,plain,
% 1.33/1.59 (r(s(s(z)), s(s(s(z))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3624, 3558])).
% 1.33/1.59 tff(3626,plain,
% 1.33/1.59 (s(s(elem!1)) = s(s(s(z)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3552])).
% 1.33/1.59 tff(3627,plain,
% 1.33/1.59 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3626])).
% 1.33/1.59 tff(3628,plain,
% 1.33/1.59 (~r(s(z), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[436, 3579, 412, 1243])).
% 1.33/1.59 tff(3629,plain,
% 1.33/1.59 (b(s(z), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[25, 3628])).
% 1.33/1.59 tff(3630,plain,
% 1.33/1.59 (~b(z, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2650, 3581, 1935, 3629])).
% 1.33/1.59 tff(3631,plain,
% 1.33/1.59 (r(z, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2106, 3630])).
% 1.33/1.59 tff(3632,plain,
% 1.33/1.59 (r(z, s(s(s(z))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3631, 3627])).
% 1.33/1.59 tff(3633,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3634,plain,
% 1.33/1.59 (((~r(s(s(s(z))), s(s(z)))) | (~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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3635,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3634])).
% 1.33/1.59 tff(3636,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3635, 3633])).
% 1.33/1.59 tff(3637,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3638,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3637, 3636])).
% 1.33/1.59 tff(3639,plain,
% 1.33/1.59 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3638, 121, 3598, 3632])).
% 1.33/1.59 tff(3640,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3639, 3625, 3556])).
% 1.33/1.59 tff(3641,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | b(elem!1, s(z)) | (z = elem!1) | b(elem!1, s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3642,plain,
% 1.33/1.59 (~b(s(s(s(z))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3641, 3550, 3546, 199, 412, 317, 909, 3540, 379, 3534, 3530])).
% 1.33/1.59 tff(3643,plain,
% 1.33/1.59 (r(z, elem!1) <=> r(z, s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[239])).
% 1.33/1.59 tff(3644,plain,
% 1.33/1.59 (r(z, s(z)) <=> r(z, elem!1)),
% 1.33/1.59 inference(symmetry,[status(thm)],[3643])).
% 1.33/1.59 tff(3645,plain,
% 1.33/1.59 (r(z, elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[909, 3644])).
% 1.33/1.59 tff(3646,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3647,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3648,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 1.33/1.59 tff(3649,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3648, 121, 378, 412, 1500, 109])).
% 1.33/1.59 tff(3650,plain,((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3651,plain,
% 1.33/1.59 (~r(s(s(s(z))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3650, 3540, 412, 3645])).
% 1.33/1.59 tff(3652,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1155, 3651, 3642])).
% 1.33/1.59 tff(3653,plain,((~(elem!1 = s(z))) | (~r(s(elem!1), z)) | b(z, elem!1) | b(elem!1, s(elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3654,plain,
% 1.33/1.59 (~(elem!1 = s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3653, 199, 412, 317, 909, 379, 3506])).
% 1.33/1.59 tff(3655,plain,
% 1.33/1.59 (b(elem!1, s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[299, 258, 293])).
% 1.33/1.59 tff(3656,plain,
% 1.33/1.59 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[346])).
% 1.33/1.59 tff(3657,plain,
% 1.33/1.59 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.33/1.59 inference(symmetry,[status(thm)],[3656])).
% 1.33/1.59 tff(3658,plain,
% 1.33/1.59 (b(elem!1, s(elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[448, 3657])).
% 1.33/1.59 tff(3659,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[317, 3658])).
% 1.33/1.59 tff(3660,plain,((~(s(elem!1) = s(z))) | b(elem!1, s(elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3661,plain,
% 1.33/1.59 (~(s(elem!1) = s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3660, 3655, 317])).
% 1.33/1.59 tff(3662,plain,
% 1.33/1.59 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[345])).
% 1.33/1.59 tff(3663,plain,
% 1.33/1.59 (~(s(z) = s(elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3661, 3662])).
% 1.33/1.59 tff(3664,plain,
% 1.33/1.59 (~(z = elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[500, 3663])).
% 1.33/1.59 tff(3665,plain,
% 1.33/1.59 (r(z, elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[355, 3664, 199])).
% 1.33/1.59 tff(3666,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3667,plain,
% 1.33/1.59 (((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3668,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3667])).
% 1.33/1.59 tff(3669,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3668, 3666])).
% 1.33/1.59 tff(3670,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3671,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3670, 3669])).
% 1.33/1.59 tff(3672,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3671, 121, 379, 378, 357, 909])).
% 1.33/1.59 tff(3673,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3674,plain,
% 1.33/1.59 (~r(s(z), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3673, 3665, 379, 909])).
% 1.33/1.59 tff(3675,plain,
% 1.33/1.59 (b(s(z), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[236, 3674, 1257])).
% 1.33/1.59 tff(3676,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3677,plain,
% 1.33/1.59 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3678,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3677])).
% 1.33/1.59 tff(3679,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3678, 3676])).
% 1.33/1.59 tff(3680,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(3681,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[3680, 3679])).
% 1.33/1.59 tff(3682,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3681, 121, 379, 622, 378, 412])).
% 1.33/1.59 tff(3683,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(3684,plain,
% 1.33/1.59 (~r(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3683, 3665, 379, 412])).
% 1.33/1.59 tff(3685,plain,
% 1.33/1.59 (b(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2243, 3684, 2564])).
% 1.33/1.59 tff(3686,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3687,plain,
% 1.33/1.59 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(3688,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[3687])).
% 1.33/1.59 tff(3689,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[3688, 3686])).
% 1.33/1.59 tff(3690,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.33/1.60 inference(quant_inst,[status(thm)],[])).
% 1.33/1.60 tff(3691,plain,
% 1.33/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.33/1.60 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 1.33/1.60 tff(3692,plain,
% 1.33/1.60 (~b(s(elem!1), s(z))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[3691, 271, 3685, 3675, 3655])).
% 1.33/1.60 tff(3693,plain,
% 1.33/1.60 (r(s(elem!1), s(z))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[429, 3692, 3661])).
% 1.33/1.60 tff(3694,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(3695,plain,
% 1.33/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.33/1.60 inference(quant_inst,[status(thm)],[])).
% 1.33/1.60 tff(3696,plain,
% 1.33/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.33/1.60 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 1.33/1.60 tff(3697,plain,
% 1.33/1.60 (~b(s(z), s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[3696, 271, 3685, 3675, 3655])).
% 1.33/1.60 tff(3698,plain,
% 1.33/1.60 (r(s(z), s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[444, 3697, 3663])).
% 1.33/1.60 tff(3699,plain,
% 1.33/1.60 ($false),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[3488, 121, 909, 412, 3698, 3693])).
% 1.33/1.60 tff(3700,plain,((elem!1 = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | b(z, elem!1) | b(elem!1, s(elem!1)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.60 tff(3701,plain,
% 1.33/1.60 (r(elem!1, s(z))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[3700, 199, 412, 2564, 379, 3654, 317, 909])).
% 1.33/1.60 tff(3702,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(3703,plain,
% 1.33/1.60 (((~r(s(elem!1), z)) | (~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))) | (~r(s(elem!1), z)))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(3704,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.33/1.60 inference(monotonicity,[status(thm)],[3703])).
% 1.33/1.60 tff(3705,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.33/1.60 inference(transitivity,[status(thm)],[3704, 3702])).
% 1.33/1.60 tff(3706,plain,
% 1.33/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3707,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 1.43/1.60 tff(3708,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3707, 121, 379, 3456, 412, 431])).
% 1.43/1.60 tff(3709,plain,((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3710,plain,
% 1.43/1.60 (~r(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3709, 3701, 379, 412])).
% 1.43/1.60 tff(3711,plain,
% 1.43/1.60 (b(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[444, 3710, 344])).
% 1.43/1.60 tff(3712,plain,
% 1.43/1.60 (~r(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1417, 379, 909, 412])).
% 1.43/1.60 tff(3713,plain,
% 1.43/1.60 ((elem!1 = z) | b(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[282, 21, 3712])).
% 1.43/1.60 tff(3714,plain,
% 1.43/1.60 (b(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3713, 2886])).
% 1.43/1.60 tff(3715,plain,
% 1.43/1.60 (~(s(z) = elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1221, 3654])).
% 1.43/1.60 tff(3716,plain,
% 1.43/1.60 (~r(s(z), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3673, 1243, 379, 909])).
% 1.43/1.60 tff(3717,plain,
% 1.43/1.60 (b(s(z), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[236, 3716, 3715])).
% 1.43/1.60 tff(3718,plain,
% 1.43/1.60 (~r(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3683, 1243, 379, 412])).
% 1.43/1.60 tff(3719,plain,
% 1.43/1.60 (b(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2243, 3718, 2564])).
% 1.43/1.60 tff(3720,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3721,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3722,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3721, 3720])).
% 1.43/1.60 tff(3723,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3722, 271, 3719, 3717, 3714, 3711])).
% 1.43/1.60 tff(3724,plain,(b(z, elem!1) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(elem!1, s(elem!1)) | (z = elem!1) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3725,plain,
% 1.43/1.60 (b(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3724, 3502, 3500, 412, 3505, 317, 3524, 3506])).
% 1.43/1.60 tff(3726,plain,
% 1.43/1.60 (~(z = elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3523, 379, 3506, 412, 479])).
% 1.43/1.60 tff(3727,plain,
% 1.43/1.60 (r(elem!1, s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3700, 3654, 412, 2564, 379, 199, 317, 909])).
% 1.43/1.60 tff(3728,plain,
% 1.43/1.60 (~r(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3709, 3727, 379, 412])).
% 1.43/1.60 tff(3729,plain,
% 1.43/1.60 (b(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[444, 3728, 344])).
% 1.43/1.60 tff(3730,plain,
% 1.43/1.60 (b(s(z), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1266, 1243, 909, 3654, 294])).
% 1.43/1.60 tff(3731,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3722, 271, 3719, 3730, 3714, 3729])).
% 1.43/1.60 tff(3732,plain,(b(z, elem!1) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(elem!1, s(z)) | b(elem!1, s(elem!1)) | (z = elem!1) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3733,plain,
% 1.43/1.60 (b(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3732, 294, 379, 412, 3505, 2564, 317, 3726, 3506])).
% 1.43/1.60 tff(3734,plain,
% 1.43/1.60 (~(elem!1 = s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1397, 3733, 894])).
% 1.43/1.60 tff(3735,plain,
% 1.43/1.60 (r(elem!1, s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[299, 3734, 294])).
% 1.43/1.60 tff(3736,plain,
% 1.43/1.60 (~(s(z) = elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1221, 3734])).
% 1.43/1.60 tff(3737,plain,
% 1.43/1.60 (~(s(z) = s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[343, 3726])).
% 1.43/1.60 tff(3738,plain,
% 1.43/1.60 (~r(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3709, 3735, 379, 412])).
% 1.43/1.60 tff(3739,plain,
% 1.43/1.60 (b(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[444, 3738, 3737])).
% 1.43/1.60 tff(3740,plain,
% 1.43/1.60 (~(elem!1 = z)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3726, 2885])).
% 1.43/1.60 tff(3741,plain,
% 1.43/1.60 (b(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3713, 3740])).
% 1.43/1.60 tff(3742,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3743,plain,
% 1.43/1.60 (((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3744,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3743])).
% 1.43/1.60 tff(3745,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[3744, 3742])).
% 1.43/1.60 tff(3746,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3747,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3746, 3745])).
% 1.43/1.60 tff(3748,plain,
% 1.43/1.60 (~b(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3747, 271, 2618, 1326, 3741])).
% 1.43/1.60 tff(3749,plain,
% 1.43/1.60 (r(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1439, 3748])).
% 1.43/1.60 tff(3750,plain,
% 1.43/1.60 (r(s(s(s(z))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1816, 2597, 3506])).
% 1.43/1.60 tff(3751,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3752,plain,
% 1.43/1.60 (((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3753,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3752])).
% 1.43/1.60 tff(3754,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[3753, 3751])).
% 1.43/1.60 tff(3755,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3756,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3755, 3754])).
% 1.43/1.60 tff(3757,plain,
% 1.43/1.60 (~r(s(s(s(z))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3756, 121, 379, 412, 1500])).
% 1.43/1.60 tff(3758,plain,
% 1.43/1.60 (b(s(s(s(z))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[255, 3757, 907])).
% 1.43/1.60 tff(3759,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3760,plain,
% 1.43/1.60 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3761,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3760])).
% 1.43/1.60 tff(3762,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[3761, 3759])).
% 1.43/1.60 tff(3763,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3764,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3763, 3762])).
% 1.43/1.60 tff(3765,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3764, 271, 1326, 3714, 3758, 1935])).
% 1.43/1.60 tff(3766,plain,((~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (z = elem!1) | (s(s(s(z))) = elem!1) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3767,plain,
% 1.43/1.60 (~b(s(s(s(z))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3766, 3750, 379, 331, 1326, 412, 2612, 909])).
% 1.43/1.60 tff(3768,plain,
% 1.43/1.60 (r(s(s(s(z))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1155, 3767])).
% 1.43/1.60 tff(3769,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2658, 121, 1441, 412, 3750, 3768])).
% 1.43/1.60 tff(3770,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (z = elem!1) | (~b(z, elem!1)) | (~r(z, s(z))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3771,plain,
% 1.43/1.60 (~(s(s(s(elem!1))) = elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3770, 3749, 412, 379, 3726, 1326, 909, 3506])).
% 1.43/1.60 tff(3772,plain,
% 1.43/1.60 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[486, 3771, 479])).
% 1.43/1.60 tff(3773,plain,
% 1.43/1.60 (~(s(elem!1) = s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[350, 3737])).
% 1.43/1.60 tff(3774,plain,
% 1.43/1.60 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[2471])).
% 1.43/1.60 tff(3775,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[3774])).
% 1.43/1.60 tff(3776,plain,
% 1.43/1.60 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3775])).
% 1.43/1.60 tff(3777,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[2470])).
% 1.43/1.60 tff(3778,plain,
% 1.43/1.60 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3777])).
% 1.43/1.60 tff(3779,plain,
% 1.43/1.60 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[479, 3778])).
% 1.43/1.60 tff(3780,plain,
% 1.43/1.60 (~b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3779, 3776])).
% 1.43/1.60 tff(3781,plain,
% 1.43/1.60 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[2470])).
% 1.43/1.60 tff(3782,plain,
% 1.43/1.60 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[3781])).
% 1.43/1.60 tff(3783,plain,
% 1.43/1.60 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3782])).
% 1.43/1.60 tff(3784,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.60 tff(3785,plain,
% 1.43/1.60 (~b(s(elem!1), elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 1.43/1.60 tff(3786,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2618, 3785])).
% 1.43/1.60 tff(3787,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | b(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3788,plain,
% 1.43/1.60 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3787, 2470, 2618])).
% 1.43/1.60 tff(3789,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3788, 3780])).
% 1.43/1.60 tff(3790,plain,((~(elem!1 = s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3791,plain,
% 1.43/1.60 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3790, 2618, 479])).
% 1.43/1.60 tff(3792,plain,
% 1.43/1.60 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[78, 3791])).
% 1.43/1.60 tff(3793,plain,
% 1.43/1.60 (~r(s(elem!1), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1254, 357, 909, 412])).
% 1.43/1.60 tff(3794,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3795,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3796,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3795, 3794])).
% 1.43/1.60 tff(3797,plain,
% 1.43/1.60 (~r(s(s(s(elem!1))), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3796, 121, 379, 357, 139])).
% 1.43/1.60 tff(3798,plain,
% 1.43/1.60 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[66, 21, 3797])).
% 1.43/1.60 tff(3799,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3798, 2861])).
% 1.43/1.60 tff(3800,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3801,plain,
% 1.43/1.60 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3802,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3801])).
% 1.43/1.60 tff(3803,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[3802, 3800])).
% 1.43/1.60 tff(3804,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3805,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 1.43/1.60 tff(3806,plain,
% 1.43/1.60 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3805, 121, 379, 357, 139])).
% 1.43/1.60 tff(3807,plain,
% 1.43/1.60 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[760, 3806])).
% 1.43/1.60 tff(3808,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3809,plain,
% 1.43/1.60 (((~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(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))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3810,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3809])).
% 1.43/1.61 tff(3811,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3810, 3808])).
% 1.43/1.61 tff(3812,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3813,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3812, 3811])).
% 1.43/1.61 tff(3814,plain,
% 1.43/1.61 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3813, 271, 3807, 447, 3799])).
% 1.43/1.61 tff(3815,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[681, 3814, 82])).
% 1.43/1.61 tff(3816,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3817,plain,
% 1.43/1.61 (((~r(s(elem!1), z)) | (~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)) | (~r(s(elem!1), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3818,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3817])).
% 1.43/1.61 tff(3819,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3818, 3816])).
% 1.43/1.61 tff(3820,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3821,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 1.43/1.61 tff(3822,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3821, 121, 379, 3815, 139, 412])).
% 1.43/1.61 tff(3823,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3824,plain,
% 1.43/1.61 (~b(s(elem!1), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3823, 357, 412, 379, 82, 139])).
% 1.43/1.61 tff(3825,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[429, 3824, 3793, 422])).
% 1.43/1.61 tff(3826,plain,((~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3827,plain,
% 1.43/1.61 (~r(s(z), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3826, 3792, 412, 379, 3773, 3772, 909])).
% 1.43/1.61 tff(3828,plain,
% 1.43/1.61 (b(s(z), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[236, 3827, 231])).
% 1.43/1.61 tff(3829,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3722, 271, 2618, 3828, 3741, 446])).
% 1.43/1.61 tff(3830,plain,((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (s(z) = elem!1) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | b(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3831,plain,
% 1.43/1.61 (~b(s(elem!1), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3830, 3739, 3736, 412, 379, 3505, 479, 3733, 3506])).
% 1.43/1.61 tff(3832,plain,
% 1.43/1.61 (r(s(elem!1), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2243, 3831, 2564])).
% 1.43/1.61 tff(3833,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3834,plain,
% 1.43/1.61 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3835,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3834])).
% 1.43/1.61 tff(3836,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3835, 3833])).
% 1.43/1.61 tff(3837,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3838,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3837, 3836])).
% 1.43/1.61 tff(3839,plain,
% 1.43/1.61 (~r(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3838, 121, 379, 622, 3750])).
% 1.43/1.61 tff(3840,plain,
% 1.43/1.61 (b(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[255, 3839, 2612])).
% 1.43/1.61 tff(3841,plain,
% 1.43/1.61 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2035, 2597])).
% 1.43/1.61 tff(3842,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3843,plain,
% 1.43/1.61 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3844,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3843])).
% 1.43/1.61 tff(3845,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3844, 3842])).
% 1.43/1.61 tff(3846,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3847,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3846, 3845])).
% 1.43/1.61 tff(3848,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3847, 121, 379, 622, 1184, 1500])).
% 1.43/1.61 tff(3849,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3850,plain,
% 1.43/1.61 (~r(elem!1, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3849, 3750, 622, 379])).
% 1.43/1.61 tff(3851,plain,
% 1.43/1.61 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[2505])).
% 1.43/1.61 tff(3852,plain,
% 1.43/1.61 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(z))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3851, 159])).
% 1.43/1.61 tff(3853,plain,
% 1.43/1.61 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3852])).
% 1.43/1.61 tff(3854,plain,
% 1.43/1.61 (~(elem!1 = s(s(s(z))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[2064, 3853])).
% 1.43/1.61 tff(3855,plain,
% 1.43/1.61 (b(elem!1, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1192, 3854, 3850])).
% 1.43/1.61 tff(3856,plain,
% 1.43/1.61 (~b(z, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2018, 271, 1326, 3855, 3840])).
% 1.43/1.61 tff(3857,plain,
% 1.43/1.61 (r(z, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1214, 3856])).
% 1.43/1.61 tff(3858,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3859,plain,
% 1.43/1.61 (((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3860,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3859])).
% 1.43/1.61 tff(3861,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3860, 3858])).
% 1.43/1.61 tff(3862,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3863,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 1.43/1.61 tff(3864,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3863, 121, 412, 1500, 1140, 2046])).
% 1.43/1.61 tff(3865,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3866,plain,
% 1.43/1.61 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3865, 3857, 3750, 412])).
% 1.43/1.61 tff(3867,plain,
% 1.43/1.61 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2044, 3866, 3841])).
% 1.43/1.61 tff(3868,plain,
% 1.43/1.61 (~r(s(z), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1148, 3857, 3768, 909])).
% 1.43/1.61 tff(3869,plain,
% 1.43/1.61 (b(s(z), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[105, 3868])).
% 1.43/1.61 tff(3870,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.43/1.61 tff(3871,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.43/1.61 tff(3872,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3873,plain,
% 1.43/1.61 (((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3874,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3873])).
% 1.43/1.61 tff(3875,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3874, 3872])).
% 1.43/1.61 tff(3876,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3877,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3876, 3875])).
% 1.43/1.61 tff(3878,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3877, 271, 3871, 3870, 446, 257])).
% 1.43/1.61 tff(3879,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3880,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3879, 3869, 3867, 3840, 446])).
% 1.43/1.61 tff(3881,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (z = elem!1) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3882,plain,
% 1.43/1.61 (~(s(s(s(elem!1))) = elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3881, 3739, 3505, 412, 3733, 379, 3832, 3726, 3506])).
% 1.43/1.61 tff(3883,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[486, 3882, 479])).
% 1.43/1.61 tff(3884,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3885,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3886,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 1.43/1.61 tff(3887,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3886, 121, 622, 684, 139, 3456])).
% 1.43/1.61 tff(3888,plain,((~r(elem!1, s(z))) | (~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,[]))).
% 1.43/1.61 tff(3889,plain,
% 1.43/1.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3888, 3883, 3735, 3832])).
% 1.43/1.61 tff(3890,plain,
% 1.43/1.61 (s(s(s(elem!1))) = s(elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[614, 601])).
% 1.43/1.61 tff(3891,plain,
% 1.43/1.61 (elem!1 = s(s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[78, 3890])).
% 1.43/1.61 tff(3892,plain,
% 1.43/1.61 (s(s(elem!1)) = elem!1),
% 1.43/1.61 inference(symmetry,[status(thm)],[3891])).
% 1.43/1.61 tff(3893,plain,
% 1.43/1.61 (s(s(s(elem!1))) = elem!1),
% 1.43/1.61 inference(transitivity,[status(thm)],[611, 3892])).
% 1.43/1.61 tff(3894,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[481, 3893])).
% 1.43/1.61 tff(3895,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3896,plain,
% 1.43/1.61 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3895, 3882])).
% 1.43/1.61 tff(3897,plain,
% 1.43/1.61 (~(s(elem!1) = s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[210, 3896])).
% 1.43/1.61 tff(3898,plain,
% 1.43/1.61 (~(s(s(z)) = s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[960, 3736])).
% 1.43/1.61 tff(3899,plain,
% 1.43/1.61 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[953, 3898])).
% 1.43/1.61 tff(3900,plain,
% 1.43/1.61 (s(s(s(z))) = s(s(elem!1))),
% 1.43/1.61 inference(transitivity,[status(thm)],[244, 2470])).
% 1.43/1.61 tff(3901,plain,
% 1.43/1.61 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3900])).
% 1.43/1.61 tff(3902,plain,
% 1.43/1.61 (s(s(z)) = s(s(s(elem!1)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[92, 3901, 604, 2471])).
% 1.43/1.61 tff(3903,plain,
% 1.43/1.61 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3902])).
% 1.43/1.61 tff(3904,plain,
% 1.43/1.61 (s(z) = s(s(elem!1))),
% 1.43/1.61 inference(transitivity,[status(thm)],[957, 3903, 55])).
% 1.43/1.61 tff(3905,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2137, 3904])).
% 1.43/1.61 tff(3906,plain,((~(s(s(s(z))) = elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3907,plain,
% 1.43/1.61 (~(s(s(s(z))) = elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3906, 2470])).
% 1.43/1.61 tff(3908,plain,
% 1.43/1.61 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[2470])).
% 1.43/1.61 tff(3909,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(symmetry,[status(thm)],[3908])).
% 1.43/1.61 tff(3910,plain,
% 1.43/1.61 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3909])).
% 1.43/1.61 tff(3911,plain,
% 1.43/1.61 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[2470])).
% 1.43/1.61 tff(3912,plain,
% 1.43/1.61 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[379, 3911])).
% 1.43/1.61 tff(3913,plain,
% 1.43/1.61 (s(s(z)) = s(s(elem!1))),
% 1.43/1.61 inference(transitivity,[status(thm)],[92, 2591, 70, 2470])).
% 1.43/1.61 tff(3914,plain,
% 1.43/1.61 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3913])).
% 1.43/1.61 tff(3915,plain,
% 1.43/1.61 (s(z) = s(elem!1)),
% 1.43/1.61 inference(transitivity,[status(thm)],[957, 3914, 604])).
% 1.43/1.61 tff(3916,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[348, 3915])).
% 1.43/1.61 tff(3917,plain,((~(s(s(s(z))) = s(elem!1))) | (s(z) = s(elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3918,plain,
% 1.43/1.61 (~(s(s(s(z))) = s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3917, 2470, 344])).
% 1.43/1.61 tff(3919,plain,
% 1.43/1.61 (r(s(s(s(z))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1816, 3918, 3506])).
% 1.43/1.61 tff(3920,plain,
% 1.43/1.61 (b(s(elem!1), elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[517, 3782])).
% 1.43/1.61 tff(3921,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2467, 3920])).
% 1.43/1.61 tff(3922,plain,((~(elem!1 = s(s(elem!1)))) | b(s(elem!1), elem!1) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3923,plain,
% 1.43/1.61 (~b(s(elem!1), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3922, 2470, 2467])).
% 1.43/1.61 tff(3924,plain,
% 1.43/1.61 (r(s(elem!1), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[526, 3923, 216])).
% 1.43/1.61 tff(3925,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3926,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3927,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 1.43/1.62 tff(3928,plain,
% 1.43/1.62 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3927, 121, 3924, 3919, 3912])).
% 1.43/1.62 tff(3929,plain,
% 1.43/1.62 (~r(s(s(s(z))), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3928, 3910])).
% 1.43/1.62 tff(3930,plain,
% 1.43/1.62 (b(s(s(s(z))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[255, 3929, 3907])).
% 1.43/1.62 tff(3931,plain,
% 1.43/1.62 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2035, 3918])).
% 1.43/1.62 tff(3932,plain,
% 1.43/1.62 (b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2462, 21, 3928, 944])).
% 1.43/1.62 tff(3933,plain,
% 1.43/1.62 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[2470])).
% 1.43/1.62 tff(3934,plain,
% 1.43/1.62 (b(s(s(elem!1)), z)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3714, 3933])).
% 1.43/1.62 tff(3935,plain,
% 1.43/1.62 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[2470])).
% 1.43/1.62 tff(3936,plain,
% 1.43/1.62 (b(z, s(s(elem!1)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1326, 3935])).
% 1.43/1.62 tff(3937,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3938,plain,
% 1.43/1.62 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3939,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3938])).
% 1.43/1.62 tff(3940,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3939, 3937])).
% 1.43/1.62 tff(3941,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3942,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3941, 3940])).
% 1.43/1.62 tff(3943,plain,
% 1.43/1.62 (~b(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3942, 271, 3936, 3934, 3932])).
% 1.43/1.62 tff(3944,plain,
% 1.43/1.62 (r(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1214, 3943])).
% 1.43/1.62 tff(3945,plain,
% 1.43/1.62 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3865, 3944, 3919, 412])).
% 1.43/1.62 tff(3946,plain,
% 1.43/1.62 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2044, 3945, 3931])).
% 1.43/1.62 tff(3947,plain,
% 1.43/1.62 (~b(s(s(s(z))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3766, 3919, 379, 331, 1326, 412, 3907, 909])).
% 1.43/1.62 tff(3948,plain,
% 1.43/1.62 (r(s(s(s(z))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1155, 3947])).
% 1.43/1.62 tff(3949,plain,
% 1.43/1.62 (~r(s(z), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1148, 3944, 3948, 909])).
% 1.43/1.62 tff(3950,plain,
% 1.43/1.62 (b(s(z), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[105, 3949])).
% 1.43/1.62 tff(3951,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3879, 3950, 3946, 3930, 446])).
% 1.43/1.62 tff(3952,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (z = elem!1) | (s(elem!1) = s(s(elem!1))) | b(s(s(s(z))), s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(3953,plain,
% 1.43/1.62 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3952, 3739, 3505, 412, 3899, 3733, 379, 3726, 3897, 3506, 3831])).
% 1.43/1.62 tff(3954,plain,
% 1.43/1.62 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[78, 3953])).
% 1.43/1.62 tff(3955,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[681, 3954, 3889])).
% 1.43/1.62 tff(3956,plain,
% 1.43/1.62 (~r(elem!1, z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1417, 379, 3505, 412])).
% 1.43/1.62 tff(3957,plain,
% 1.43/1.62 ((elem!1 = z) | b(elem!1, z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[282, 21, 3956])).
% 1.43/1.62 tff(3958,plain,
% 1.43/1.62 (b(elem!1, z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3957, 3740])).
% 1.43/1.62 tff(3959,plain,
% 1.43/1.62 (~r(s(z), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3826, 3954, 412, 379, 3773, 3883, 3505])).
% 1.43/1.62 tff(3960,plain,
% 1.43/1.62 (b(s(z), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[236, 3959, 3736])).
% 1.43/1.62 tff(3961,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3962,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3963,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 1.43/1.62 tff(3964,plain,
% 1.43/1.62 ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3963, 271])).
% 1.43/1.62 tff(3965,plain,
% 1.43/1.62 (~b(s(z), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3964, 3960, 3958, 3733])).
% 1.43/1.62 tff(3966,plain,
% 1.43/1.62 (r(s(z), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[25, 3965])).
% 1.43/1.62 tff(3967,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3968,plain,
% 1.43/1.62 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3969,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3968])).
% 1.43/1.62 tff(3970,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3969, 3967])).
% 1.43/1.62 tff(3971,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3972,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3971, 3970])).
% 1.43/1.62 tff(3973,plain,
% 1.43/1.62 (~r(s(elem!1), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3972, 121, 3966, 3505, 412])).
% 1.43/1.62 tff(3974,plain,
% 1.43/1.62 (b(s(elem!1), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[429, 3973, 3773])).
% 1.43/1.62 tff(3975,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3976,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3975, 2295])).
% 1.43/1.62 tff(3977,plain,
% 1.43/1.62 (~b(s(s(s(elem!1))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3976, 271, 3974, 3739, 3955])).
% 1.43/1.62 tff(3978,plain,
% 1.43/1.62 (r(s(s(s(elem!1))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[66, 21, 3977, 63])).
% 1.43/1.62 tff(3979,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3980,plain,
% 1.43/1.62 (((~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(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3981,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3980])).
% 1.43/1.62 tff(3982,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3981, 3979])).
% 1.43/1.62 tff(3983,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3984,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 1.43/1.62 tff(3985,plain,
% 1.43/1.62 (~b(s(z), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3984, 271, 3974, 3739, 3955])).
% 1.43/1.62 tff(3986,plain,
% 1.43/1.62 (r(s(z), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[760, 3985])).
% 1.43/1.62 tff(3987,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3988,plain,
% 1.43/1.62 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3989,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3988])).
% 1.43/1.62 tff(3990,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3989, 3987])).
% 1.43/1.62 tff(3991,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3992,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 1.43/1.62 tff(3993,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3992, 121, 3986, 3883, 3978, 3735])).
% 1.43/1.62 tff(3994,plain,(b(elem!1, s(z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | b(s(s(s(elem!1))), elem!1) | (s(elem!1) = elem!1) | b(z, s(z)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(3995,plain,
% 1.43/1.62 (b(elem!1, s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3994, 3502, 412, 3506, 479, 3500, 894, 317])).
% 1.43/1.62 tff(3996,plain,
% 1.43/1.62 (~(elem!1 = s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1397, 3725, 894])).
% 1.43/1.62 tff(3997,plain,
% 1.43/1.62 (~(s(z) = elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1221, 3996])).
% 1.43/1.62 tff(3998,plain,
% 1.43/1.62 (~(s(z) = s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[343, 3524])).
% 1.43/1.62 tff(3999,plain,
% 1.43/1.62 (~(z = elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[490, 141, 479])).
% 1.43/1.62 tff(4000,plain,
% 1.43/1.62 (~(s(z) = s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[343, 3999])).
% 1.43/1.62 tff(4001,plain,
% 1.43/1.62 (~(s(elem!1) = s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[350, 4000])).
% 1.43/1.62 tff(4002,plain,
% 1.43/1.62 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1997])).
% 1.43/1.62 tff(4003,plain,
% 1.43/1.62 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 1.43/1.62 inference(symmetry,[status(thm)],[4002])).
% 1.43/1.62 tff(4004,plain,
% 1.43/1.62 (r(s(s(s(z))), z)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[412, 4003])).
% 1.43/1.62 tff(4005,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[141, 4004])).
% 1.43/1.62 tff(4006,plain,((~(s(s(s(z))) = s(elem!1))) | r(s(s(s(z))), z) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(4007,plain,
% 1.43/1.62 (~(s(s(s(z))) = s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4006, 141, 412])).
% 1.43/1.62 tff(4008,plain,
% 1.43/1.62 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2035, 4007])).
% 1.43/1.62 tff(4009,plain,
% 1.43/1.62 (r(s(s(s(z))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1816, 4007, 3506])).
% 1.43/1.62 tff(4010,plain,
% 1.43/1.62 (b(s(s(s(z))), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1155, 141])).
% 1.43/1.62 tff(4011,plain,
% 1.43/1.62 (~(elem!1 = s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1397, 1326, 894])).
% 1.43/1.62 tff(4012,plain,
% 1.43/1.62 (~(s(z) = elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1221, 4011])).
% 1.43/1.62 tff(4013,plain,
% 1.43/1.62 (~r(s(s(s(z))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2640, 431, 412, 1500])).
% 1.43/1.62 tff(4014,plain,
% 1.43/1.62 (b(s(s(s(z))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2325, 4013])).
% 1.43/1.62 tff(4015,plain,
% 1.43/1.62 (~r(s(z), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1300, 431, 412, 909])).
% 1.43/1.62 tff(4016,plain,
% 1.43/1.62 (b(s(z), z)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[25, 4015])).
% 1.43/1.62 tff(4017,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(4018,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(4019,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[4018, 4017])).
% 1.43/1.62 tff(4020,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4019, 271, 1326, 4016, 4014, 1935])).
% 1.43/1.62 tff(4021,plain,((~r(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(4022,plain,
% 1.43/1.62 (~r(s(z), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4021, 1326, 1935, 412, 1500, 3505])).
% 1.43/1.62 tff(4023,plain,
% 1.43/1.62 (b(s(z), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[444, 4022, 344])).
% 1.43/1.62 tff(4024,assumption,(s(elem!1) = s(s(s(s(z))))), introduced(assumption)).
% 1.43/1.62 tff(4025,plain,
% 1.43/1.62 (s(s(s(s(z)))) = s(elem!1)),
% 1.43/1.62 inference(symmetry,[status(thm)],[4024])).
% 1.43/1.62 tff(4026,plain,
% 1.43/1.62 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4025])).
% 1.43/1.62 tff(4027,plain,
% 1.43/1.62 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 1.43/1.62 inference(symmetry,[status(thm)],[4026])).
% 1.43/1.62 tff(4028,plain,
% 1.43/1.62 (r(s(s(s(s(z)))), z)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[412, 4027])).
% 1.43/1.62 tff(4029,plain,
% 1.43/1.62 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(elem!1))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4025])).
% 1.43/1.62 tff(4030,plain,
% 1.43/1.62 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[4029])).
% 1.43/1.62 tff(4031,plain,
% 1.43/1.62 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1500, 4030])).
% 1.43/1.62 tff(4032,plain,
% 1.43/1.62 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.43/1.62 inference(commutativity,[status(thm)],[])).
% 1.43/1.62 tff(4033,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.43/1.62 tff(4034,plain,
% 1.43/1.62 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[4033, 4032])).
% 1.43/1.62 tff(4035,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.43/1.62 tff(4036,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4035, 4034])).
% 1.43/1.62 tff(4037,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(4038,plain,
% 1.43/1.62 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4037, 1772])).
% 1.43/1.62 tff(4039,plain,
% 1.43/1.62 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4024])).
% 1.43/1.62 tff(4040,plain,
% 1.43/1.62 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4039])).
% 1.43/1.62 tff(4041,plain,
% 1.43/1.62 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3499, 4040])).
% 1.43/1.62 tff(4042,plain,
% 1.43/1.62 (((~![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))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(4043,plain,
% 1.43/1.62 ((~![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))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(4044,plain,
% 1.43/1.62 ((~![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)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[4043, 4042])).
% 1.43/1.62 tff(4045,plain,
% 1.43/1.62 ((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)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4044, 21])).
% 1.43/1.62 tff(4046,plain,
% 1.43/1.62 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4045, 4041, 4038])).
% 1.43/1.62 tff(4047,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(4048,plain,
% 1.43/1.62 (((~r(s(s(s(s(z)))), 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(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(4049,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4048])).
% 1.43/1.62 tff(4050,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4049, 4047])).
% 1.43/1.63 tff(4051,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4052,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4051, 4050])).
% 1.43/1.63 tff(4053,plain,
% 1.43/1.63 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4052, 121, 4046])).
% 1.43/1.63 tff(4054,plain,
% 1.43/1.63 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4053, 4031, 4028])).
% 1.43/1.63 tff(4055,plain,
% 1.43/1.63 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1733, 4054])).
% 1.43/1.63 tff(4056,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4057,plain,
% 1.43/1.63 (((~r(s(s(s(s(z)))), z)) | (~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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4058,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4057])).
% 1.43/1.63 tff(4059,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4058, 4056])).
% 1.43/1.63 tff(4060,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(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))))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4061,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 1.43/1.63 tff(4062,plain,
% 1.43/1.63 ((~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(z)))), z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4061, 121, 4046])).
% 1.43/1.63 tff(4063,plain,
% 1.43/1.63 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4062, 4031, 4028])).
% 1.43/1.63 tff(4064,plain,
% 1.43/1.63 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1494, 4063])).
% 1.43/1.63 tff(4065,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4066,plain,
% 1.43/1.63 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4067,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4066])).
% 1.43/1.63 tff(4068,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.43/1.63 tff(4069,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4070,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.43/1.63 tff(4071,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4070, 271, 1639, 1519, 1723, 1935])).
% 1.43/1.63 tff(4072,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4073,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4072, 4064, 4055, 1639, 1935])).
% 1.43/1.63 tff(4074,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4075,plain,
% 1.43/1.63 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4074, 1935, 1639, 412, 1500, 3499])).
% 1.43/1.63 tff(4076,plain,
% 1.43/1.63 (~(s(s(s(z))) = elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[2605, 4075])).
% 1.43/1.63 tff(4077,plain,
% 1.43/1.63 (~r(elem!1, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3766, 1326, 1935, 331, 4076, 412, 1500, 3505])).
% 1.43/1.63 tff(4078,plain,
% 1.43/1.63 (b(elem!1, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[392, 4077, 377])).
% 1.43/1.63 tff(4079,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4080,plain,
% 1.43/1.63 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4081,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4080])).
% 1.43/1.63 tff(4082,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4081, 4079])).
% 1.43/1.63 tff(4083,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4084,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 1.43/1.63 tff(4085,plain,
% 1.43/1.63 (~b(s(z), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4084, 271, 307, 1326, 260])).
% 1.43/1.63 tff(4086,plain,
% 1.43/1.63 (r(s(z), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[25, 4085])).
% 1.43/1.63 tff(4087,plain,
% 1.43/1.63 (~r(s(elem!1), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3972, 121, 4086, 909, 412])).
% 1.43/1.63 tff(4088,plain,
% 1.43/1.63 (b(s(elem!1), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[429, 4087, 422])).
% 1.43/1.63 tff(4089,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4090,plain,
% 1.43/1.63 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4091,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4090])).
% 1.43/1.63 tff(4092,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4091, 4089])).
% 1.43/1.63 tff(4093,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4094,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4093, 4092])).
% 1.43/1.63 tff(4095,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4094, 271, 307, 260, 4088, 446])).
% 1.43/1.63 tff(4096,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4097,plain,
% 1.43/1.63 (~b(s(z), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4096, 4078, 4023, 351, 3505, 412, 1326])).
% 1.43/1.63 tff(4098,plain,
% 1.43/1.63 (r(s(z), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[236, 4097, 4012])).
% 1.43/1.63 tff(4099,plain,
% 1.43/1.63 (~r(s(elem!1), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1254, 4098, 3505, 412])).
% 1.43/1.63 tff(4100,plain,
% 1.43/1.63 (b(s(elem!1), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[429, 4099, 351])).
% 1.43/1.63 tff(4101,plain,
% 1.43/1.63 (~b(s(s(s(z))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1940, 4078, 1935, 1326])).
% 1.43/1.63 tff(4102,plain,
% 1.43/1.63 (r(s(s(s(z))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[255, 4101, 4076])).
% 1.43/1.63 tff(4103,plain,
% 1.43/1.63 (~b(elem!1, s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[456, 4100, 4023, 4078])).
% 1.43/1.63 tff(4104,plain,
% 1.43/1.63 (r(elem!1, s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[299, 4103, 4011])).
% 1.43/1.63 tff(4105,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4106,plain,
% 1.43/1.63 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4107,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4106])).
% 1.43/1.63 tff(4108,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4107, 4105])).
% 1.43/1.63 tff(4109,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4110,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 1.43/1.63 tff(4111,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4110, 121, 357, 3456, 145, 108])).
% 1.43/1.63 tff(4112,plain,((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4113,plain,
% 1.43/1.63 (~r(s(z), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4112, 4104, 4102, 4098])).
% 1.43/1.63 tff(4114,plain,
% 1.43/1.63 (b(s(z), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[105, 4113])).
% 1.43/1.63 tff(4115,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4116,plain,
% 1.43/1.63 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4117,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4116])).
% 1.43/1.63 tff(4118,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[4117, 4115])).
% 1.43/1.63 tff(4119,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4120,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4119, 4118])).
% 1.43/1.63 tff(4121,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4120, 271, 307, 1326, 447, 1421])).
% 1.43/1.63 tff(4122,plain,((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4123,plain,
% 1.43/1.63 (~b(z, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4122, 447, 1326, 307])).
% 1.43/1.63 tff(4124,assumption,(s(s(s(s(s(z))))) = s(elem!1)), introduced(assumption)).
% 1.43/1.63 tff(4125,plain,
% 1.43/1.63 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4124])).
% 1.43/1.63 tff(4126,plain,
% 1.43/1.63 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(z))))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[4125])).
% 1.43/1.63 tff(4127,plain,
% 1.43/1.63 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(s(s(z)))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4126])).
% 1.43/1.63 tff(4128,plain,
% 1.43/1.63 (~b(z, s(s(s(s(s(z))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1429, 4127])).
% 1.43/1.63 tff(4129,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1639, 4128])).
% 1.43/1.63 tff(4130,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | b(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4131,plain,
% 1.43/1.63 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4130, 4123, 1639])).
% 1.43/1.63 tff(4132,assumption,(~(s(s(s(s(s(z))))) = s(elem!1))), introduced(assumption)).
% 1.43/1.63 tff(4133,assumption,(~r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.43/1.63 tff(4134,plain,
% 1.43/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4135,plain,
% 1.43/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4136,plain,
% 1.43/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4135, 4134])).
% 1.43/1.63 tff(4137,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4136, 21, 3499, 4133, 4132])).
% 1.43/1.63 tff(4138,plain,(r(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(s(s(s(s(z))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4139,plain,
% 1.43/1.63 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4138, 4131, 3499])).
% 1.43/1.63 tff(4140,plain,
% 1.43/1.63 (~b(s(s(s(z))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1940, 307, 1935, 1326])).
% 1.43/1.63 tff(4141,plain,
% 1.43/1.63 (r(s(s(s(z))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[255, 4140, 4076])).
% 1.43/1.63 tff(4142,plain,
% 1.43/1.63 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3622, 447, 222, 3871])).
% 1.43/1.63 tff(4143,plain,
% 1.43/1.63 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[2044, 4142, 2037])).
% 1.43/1.63 tff(4144,plain,
% 1.43/1.63 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4072, 1519, 1639, 1935])).
% 1.43/1.63 tff(4145,plain,
% 1.43/1.63 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1733, 4144])).
% 1.43/1.63 tff(4146,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(4147,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(4148,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[4147, 4146])).
% 1.43/1.63 tff(4149,plain,
% 1.43/1.63 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4148, 121, 145, 4145, 2046])).
% 1.43/1.63 tff(4150,plain,
% 1.43/1.63 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4136, 21, 3499, 4149])).
% 1.43/1.63 tff(4151,plain,
% 1.43/1.63 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4150])).
% 1.43/1.63 tff(4152,plain,
% 1.43/1.63 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[4151])).
% 1.43/1.63 tff(4153,plain,
% 1.43/1.63 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4152])).
% 1.43/1.63 tff(4154,plain,
% 1.43/1.63 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3506, 4153])).
% 1.43/1.63 tff(4155,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1519, 4154])).
% 1.43/1.63 tff(4156,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | b(s(s(s(z))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(4157,plain,
% 1.43/1.63 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4156, 4143, 3499, 4141, 3506, 1639, 1935])).
% 1.43/1.63 tff(4158,plain,
% 1.43/1.63 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1494, 4157])).
% 1.43/1.64 tff(4159,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4160,plain,
% 1.43/1.64 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4161,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4160])).
% 1.43/1.64 tff(4162,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[4161, 4159])).
% 1.43/1.64 tff(4163,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(4164,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4163, 4162])).
% 1.43/1.64 tff(4165,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4164, 121, 412, 4158, 1500, 4139])).
% 1.43/1.64 tff(4166,plain,((~b(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4167,plain,
% 1.43/1.64 (~b(s(s(s(z))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4166, 4114, 1500, 3499, 1639, 1326, 4078, 3506, 1935, 2037, 412, 4100])).
% 1.43/1.64 tff(4168,plain,
% 1.43/1.64 (r(s(s(s(z))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2325, 4167])).
% 1.43/1.64 tff(4169,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4170,plain,
% 1.43/1.64 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4171,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4170])).
% 1.43/1.64 tff(4172,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[4171, 4169])).
% 1.43/1.64 tff(4173,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(4174,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 1.43/1.64 tff(4175,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4174, 121, 4098, 4104, 4102, 4168])).
% 1.43/1.64 tff(4176,plain,((~b(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(z, s(s(s(s(s(z))))))) | b(s(s(s(z))), s(elem!1)) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (z = elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4177,plain,
% 1.43/1.64 (~b(z, elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4176, 4009, 3499, 1639, 3506, 4010, 4008, 412, 377, 3999, 894])).
% 1.43/1.64 tff(4178,plain,
% 1.43/1.64 (~r(s(z), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[436, 431, 412, 378])).
% 1.43/1.64 tff(4179,plain,
% 1.43/1.64 (b(s(z), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[25, 4178])).
% 1.43/1.64 tff(4180,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4181,plain,
% 1.43/1.64 (((~b(z, s(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(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4182,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4181])).
% 1.43/1.64 tff(4183,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[4182, 4180])).
% 1.43/1.64 tff(4184,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(4185,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4184, 4183])).
% 1.43/1.64 tff(4186,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4185, 271, 4179, 4014, 1639, 1935])).
% 1.43/1.64 tff(4187,plain,((~r(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4188,plain,
% 1.43/1.64 (~r(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4187, 1243, 1935, 412, 1500, 1639])).
% 1.43/1.64 tff(4189,plain,
% 1.43/1.64 (b(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[444, 4188, 344])).
% 1.43/1.64 tff(4190,plain,
% 1.43/1.64 (b(s(z), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3641, 294, 2037, 379, 412, 1935, 909, 1500, 331, 317, 199])).
% 1.43/1.64 tff(4191,plain,
% 1.43/1.64 (~(elem!1 = s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3576, 446, 317])).
% 1.43/1.64 tff(4192,plain,
% 1.43/1.64 (r(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[299, 4191, 294])).
% 1.43/1.64 tff(4193,plain,
% 1.43/1.64 (~r(s(z), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3464, 4192, 909, 378])).
% 1.43/1.64 tff(4194,plain,
% 1.43/1.64 (b(s(z), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[105, 4193])).
% 1.43/1.64 tff(4195,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4196,plain,
% 1.43/1.64 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4197,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4196])).
% 1.43/1.64 tff(4198,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[4197, 4195])).
% 1.43/1.64 tff(4199,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(4200,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 1.43/1.64 tff(4201,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4200, 121, 378, 110, 909, 3456])).
% 1.43/1.64 tff(4202,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4203,plain,
% 1.43/1.64 (~r(s(z), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4202, 4192, 909, 378])).
% 1.43/1.64 tff(4204,plain,
% 1.43/1.64 (b(s(z), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[25, 4203])).
% 1.43/1.64 tff(4205,plain,
% 1.43/1.64 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[244])).
% 1.43/1.64 tff(4206,plain,
% 1.43/1.64 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[4205])).
% 1.43/1.64 tff(4207,plain,
% 1.43/1.64 ((~b(z, elem!1)) <=> (~b(z, s(s(s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4206])).
% 1.43/1.64 tff(4208,plain,
% 1.43/1.64 (~b(z, s(s(s(z))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[199, 4207])).
% 1.43/1.64 tff(4209,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1307, 4208])).
% 1.43/1.64 tff(4210,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(z))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4211,plain,
% 1.43/1.64 (~(s(s(s(z))) = elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4210, 1307, 199])).
% 1.43/1.64 tff(4212,plain,
% 1.43/1.64 (b(s(s(s(z))), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[255, 4211, 221])).
% 1.43/1.64 tff(4213,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4214,plain,
% 1.43/1.64 (((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4215,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4214])).
% 1.43/1.64 tff(4216,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[4215, 4213])).
% 1.43/1.64 tff(4217,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(4218,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 1.43/1.64 tff(4219,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4218, 271, 1281, 1307, 3871, 4212])).
% 1.43/1.64 tff(4220,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4221,plain,
% 1.43/1.64 (~b(z, s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4220, 4204, 4194, 221, 199])).
% 1.43/1.64 tff(4222,plain,
% 1.43/1.64 (r(z, s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1214, 4221])).
% 1.43/1.64 tff(4223,plain,
% 1.43/1.64 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3865, 4222, 1500, 412])).
% 1.43/1.64 tff(4224,plain,
% 1.43/1.64 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2044, 4223, 2037])).
% 1.43/1.64 tff(4225,plain,
% 1.43/1.64 (~b(s(s(s(z))), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3879, 4194, 4224, 446])).
% 1.43/1.64 tff(4226,plain,
% 1.43/1.64 (s(s(s(z))) = elem!1),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[255, 4225, 221])).
% 1.43/1.64 tff(4227,plain,
% 1.43/1.64 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4226])).
% 1.43/1.64 tff(4228,plain,
% 1.43/1.64 (b(elem!1, z)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1935, 4227])).
% 1.43/1.64 tff(4229,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4230,plain,
% 1.43/1.64 (((~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4231,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4230])).
% 1.43/1.64 tff(4232,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[4231, 4229])).
% 1.43/1.64 tff(4233,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(4234,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 1.43/1.64 tff(4235,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4234, 271, 260, 4204, 4228, 1639])).
% 1.43/1.64 tff(4236,plain,((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | r(s(s(s(z))), elem!1) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | b(z, elem!1) | (~r(z, s(z))) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4237,plain,
% 1.43/1.64 (~b(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4236, 4190, 1639, 1935, 3757, 2037, 1500, 412, 199, 909, 1243, 294, 317])).
% 1.43/1.64 tff(4238,plain,
% 1.43/1.64 (r(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[444, 4237, 344])).
% 1.43/1.64 tff(4239,plain,
% 1.43/1.64 (~r(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3709, 4238, 379, 412])).
% 1.43/1.64 tff(4240,plain,
% 1.43/1.64 (elem!1 = s(z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[299, 4239, 294])).
% 1.43/1.64 tff(4241,plain,
% 1.43/1.64 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4240])).
% 1.43/1.64 tff(4242,plain,
% 1.43/1.64 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 1.43/1.64 inference(symmetry,[status(thm)],[4241])).
% 1.43/1.64 tff(4243,plain,
% 1.43/1.64 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4242])).
% 1.43/1.64 tff(4244,plain,
% 1.43/1.64 (~b(s(z), elem!1)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3529, 4243])).
% 1.43/1.64 tff(4245,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4190, 4244])).
% 1.43/1.64 tff(4246,plain,(b(elem!1, s(z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | b(z, elem!1) | (~r(z, s(z))) | b(elem!1, s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4247,plain,
% 1.43/1.64 (b(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4246, 199, 412, 1639, 1935, 2037, 1500, 379, 909, 317, 331])).
% 1.43/1.64 tff(4248,plain,
% 1.43/1.64 (~(elem!1 = s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3576, 4189, 317])).
% 1.43/1.64 tff(4249,plain,
% 1.43/1.64 (~(s(z) = elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1221, 4248])).
% 1.43/1.64 tff(4250,plain,
% 1.43/1.64 (b(s(z), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[236, 3716, 4249])).
% 1.43/1.64 tff(4251,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3696, 271, 3719, 4250, 4247, 4189])).
% 1.43/1.64 tff(4252,plain,(b(z, elem!1) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(elem!1, s(elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (s(elem!1) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4253,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4252, 3502, 317, 3500, 412, 909, 199, 1935, 1500, 1639, 2037, 331])).
% 1.43/1.64 tff(4254,plain,(b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(z, elem!1) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (s(elem!1) = s(s(s(z)))) | (z = elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4255,plain,
% 1.43/1.64 (b(elem!1, s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4254, 4177, 3505, 412, 4010, 4009, 1639, 4008, 3999, 377])).
% 1.43/1.64 tff(4256,plain,
% 1.43/1.64 (r(z, elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[355, 4177, 3999])).
% 1.43/1.64 tff(4257,plain,
% 1.43/1.64 (~r(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4187, 4256, 4010, 412, 4009, 1639])).
% 1.43/1.64 tff(4258,plain,
% 1.43/1.64 (b(s(z), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[444, 4257, 4000])).
% 1.43/1.64 tff(4259,plain,
% 1.43/1.64 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1223])).
% 1.43/1.64 tff(4260,plain,
% 1.43/1.64 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.64 inference(symmetry,[status(thm)],[4259])).
% 1.43/1.64 tff(4261,plain,
% 1.43/1.64 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4260])).
% 1.43/1.64 tff(4262,plain,
% 1.43/1.64 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[877, 4261])).
% 1.43/1.64 tff(4263,plain,
% 1.43/1.64 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4138, 4262, 3499])).
% 1.43/1.64 tff(4264,plain,
% 1.43/1.64 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[2376])).
% 1.43/1.64 tff(4265,plain,
% 1.43/1.64 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.64 inference(symmetry,[status(thm)],[4264])).
% 1.43/1.64 tff(4266,assumption,(r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.43/1.64 tff(4267,plain,
% 1.43/1.64 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 1.43/1.64 tff(4268,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.43/1.64 tff(4269,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4268, 4267])).
% 1.43/1.64 tff(4270,plain,(r(s(s(s(s(s(z))))), s(s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(4271,plain,
% 1.43/1.64 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4270, 4263, 239])).
% 1.43/1.64 tff(4272,plain,
% 1.43/1.64 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(elem!1))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[2376])).
% 1.43/1.64 tff(4273,plain,
% 1.43/1.64 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.43/1.64 inference(symmetry,[status(thm)],[4272])).
% 1.43/1.64 tff(4274,plain,
% 1.43/1.64 (r(s(s(s(z))), s(s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1500, 4273])).
% 1.43/1.64 tff(4275,plain,
% 1.43/1.64 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1223])).
% 1.43/1.64 tff(4276,plain,
% 1.43/1.64 (r(s(s(z)), z)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[412, 4275])).
% 1.43/1.64 tff(4277,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(4278,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4279,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4278, 4277])).
% 1.43/1.65 tff(4280,plain,
% 1.43/1.65 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4279, 121, 4276, 4274, 4271])).
% 1.43/1.65 tff(4281,plain,
% 1.43/1.65 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1733, 4280])).
% 1.43/1.65 tff(4282,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4283,plain,
% 1.43/1.65 (((~r(s(s(z)), z)) | (~r(s(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(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4284,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4283])).
% 1.43/1.65 tff(4285,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4284, 4282])).
% 1.43/1.65 tff(4286,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4287,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4286, 4285])).
% 1.43/1.65 tff(4288,plain,
% 1.43/1.65 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4287, 121, 4276, 4274, 4271])).
% 1.43/1.65 tff(4289,plain,
% 1.43/1.65 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1494, 4288])).
% 1.43/1.65 tff(4290,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4072, 4289, 4281, 1639, 1935])).
% 1.43/1.65 tff(4291,plain,((~(elem!1 = s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(4292,plain,
% 1.43/1.65 (~(elem!1 = s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4291, 4010, 1639, 4009, 3499, 412])).
% 1.43/1.65 tff(4293,plain,
% 1.43/1.65 (~r(s(z), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3476, 4001, 412, 3505, 4258, 4255, 4292, 4256])).
% 1.43/1.65 tff(4294,plain,
% 1.43/1.65 (b(s(z), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[105, 4293])).
% 1.43/1.65 tff(4295,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4296,plain,
% 1.43/1.65 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4297,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4296])).
% 1.43/1.65 tff(4298,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4297, 4295])).
% 1.43/1.65 tff(4299,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4300,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4299, 4298])).
% 1.43/1.65 tff(4301,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4300, 271, 1281, 3871, 1639, 1935])).
% 1.43/1.65 tff(4302,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(4303,plain,
% 1.43/1.65 (~b(s(z), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4302, 4294, 1639, 4010])).
% 1.43/1.65 tff(4304,plain,
% 1.43/1.65 (r(s(z), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[25, 4303])).
% 1.43/1.65 tff(4305,plain,
% 1.43/1.65 (~r(elem!1, s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4202, 4304, 3505, 4256])).
% 1.43/1.65 tff(4306,plain,
% 1.43/1.65 (b(elem!1, s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[299, 4305, 4292])).
% 1.43/1.65 tff(4307,plain,
% 1.43/1.65 (~b(s(elem!1), s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[456, 4306, 4258, 4255])).
% 1.43/1.65 tff(4308,plain,
% 1.43/1.65 (r(s(elem!1), s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[429, 4307, 4001])).
% 1.43/1.65 tff(4309,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[418, 121, 4256, 4304, 412, 4308])).
% 1.43/1.65 tff(4310,plain,(r(s(s(s(z))), z) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(elem!1)) | (elem!1 = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | b(z, s(z)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(4311,plain,
% 1.43/1.65 (r(s(s(s(z))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4310, 1639, 412, 3499, 377, 3506, 894, 479])).
% 1.43/1.65 tff(4312,plain,
% 1.43/1.65 ((~r(s(z), s(s(s(z))))) <=> (~r(s(z), s(elem!1)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1998])).
% 1.43/1.65 tff(4313,plain,
% 1.43/1.65 (s(s(z)) = elem!1),
% 1.43/1.65 inference(transitivity,[status(thm)],[92, 2591, 70])).
% 1.43/1.65 tff(4314,plain,
% 1.43/1.65 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4313])).
% 1.43/1.65 tff(4315,plain,
% 1.43/1.65 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.43/1.65 inference(transitivity,[status(thm)],[4314, 360])).
% 1.43/1.65 tff(4316,plain,
% 1.43/1.65 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4315])).
% 1.43/1.65 tff(4317,plain,
% 1.43/1.65 (~(z = elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[95, 4316])).
% 1.43/1.65 tff(4318,plain,
% 1.43/1.65 (r(z, elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[355, 4317, 199])).
% 1.43/1.65 tff(4319,plain,
% 1.43/1.65 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4313])).
% 1.43/1.65 tff(4320,plain,
% 1.43/1.65 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 1.43/1.65 inference(transitivity,[status(thm)],[4319, 238])).
% 1.43/1.65 tff(4321,plain,
% 1.43/1.65 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4320, 1218])).
% 1.43/1.65 tff(4322,plain,
% 1.43/1.65 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4321])).
% 1.43/1.65 tff(4323,plain,
% 1.43/1.65 (~(elem!1 = s(z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3595, 4322])).
% 1.43/1.65 tff(4324,plain,
% 1.43/1.65 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1997])).
% 1.43/1.65 tff(4325,plain,
% 1.43/1.65 ((s(s(s(z))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4324, 345])).
% 1.43/1.65 tff(4326,plain,
% 1.43/1.65 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4325])).
% 1.43/1.65 tff(4327,plain,
% 1.43/1.65 (~(s(z) = s(elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[97, 4326])).
% 1.43/1.65 tff(4328,plain,
% 1.43/1.65 (~(s(s(s(elem!1))) = elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2596, 1997])).
% 1.43/1.65 tff(4329,plain,
% 1.43/1.65 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[2000])).
% 1.43/1.65 tff(4330,plain,
% 1.43/1.65 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4329])).
% 1.43/1.65 tff(4331,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.65 inference(symmetry,[status(thm)],[4330])).
% 1.43/1.65 tff(4332,plain,
% 1.43/1.65 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[638, 4331])).
% 1.43/1.65 tff(4333,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3499, 4332])).
% 1.43/1.65 tff(4334,plain,((~b(s(s(s(elem!1))), s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~(s(s(s(z))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(4335,plain,
% 1.43/1.65 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4334, 1997, 3499])).
% 1.43/1.65 tff(4336,plain,
% 1.43/1.65 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[4329])).
% 1.43/1.65 tff(4337,plain,
% 1.43/1.65 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4336])).
% 1.43/1.65 tff(4338,plain,
% 1.43/1.65 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.65 inference(symmetry,[status(thm)],[4337])).
% 1.43/1.65 tff(4339,plain,
% 1.43/1.65 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4338])).
% 1.43/1.65 tff(4340,plain,
% 1.43/1.65 (s(elem!1) = s(s(s(z)))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1997])).
% 1.43/1.65 tff(4341,plain,
% 1.43/1.65 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4340])).
% 1.43/1.65 tff(4342,plain,
% 1.43/1.65 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4341, 1487])).
% 1.43/1.65 tff(4343,plain,
% 1.43/1.65 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.65 inference(symmetry,[status(thm)],[4342])).
% 1.43/1.65 tff(4344,plain,
% 1.43/1.65 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4343])).
% 1.43/1.65 tff(4345,plain,
% 1.43/1.65 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1489, 4344])).
% 1.43/1.65 tff(4346,plain,
% 1.43/1.65 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4345, 4339])).
% 1.43/1.65 tff(4347,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[681, 4346, 4335])).
% 1.43/1.65 tff(4348,plain,
% 1.43/1.65 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4329])).
% 1.43/1.65 tff(4349,plain,
% 1.43/1.65 (b(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1639, 4348])).
% 1.43/1.65 tff(4350,plain,
% 1.43/1.65 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4336])).
% 1.43/1.65 tff(4351,plain,
% 1.43/1.65 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.43/1.65 inference(symmetry,[status(thm)],[4350])).
% 1.43/1.65 tff(4352,plain,
% 1.43/1.65 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4351, 654])).
% 1.43/1.65 tff(4353,plain,
% 1.43/1.65 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4352])).
% 1.43/1.65 tff(4354,plain,
% 1.43/1.65 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4313])).
% 1.43/1.65 tff(4355,plain,
% 1.43/1.65 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4354])).
% 1.43/1.65 tff(4356,plain,
% 1.43/1.65 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[877, 4355])).
% 1.43/1.65 tff(4357,plain,
% 1.43/1.65 (~(elem!1 = s(s(s(elem!1))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4356, 4353])).
% 1.43/1.65 tff(4358,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.65 tff(4359,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4360,plain,
% 1.43/1.65 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4361,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4360])).
% 1.43/1.65 tff(4362,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4361, 4359])).
% 1.43/1.65 tff(4363,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4364,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4363, 4362])).
% 1.43/1.65 tff(4365,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4364, 121, 379, 684, 412])).
% 1.43/1.65 tff(4366,plain,
% 1.43/1.65 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[660, 21, 4365, 4358])).
% 1.43/1.65 tff(4367,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3821, 121, 379, 684, 412])).
% 1.43/1.65 tff(4368,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[486, 4367, 481])).
% 1.43/1.65 tff(4369,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4370,plain,
% 1.43/1.65 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4371,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4370])).
% 1.43/1.65 tff(4372,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4371, 4369])).
% 1.43/1.65 tff(4373,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4374,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4373, 4372])).
% 1.43/1.65 tff(4375,plain,
% 1.43/1.65 (~b(elem!1, z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4374, 271, 3407, 4368, 4366])).
% 1.43/1.65 tff(4376,plain,
% 1.43/1.65 ((elem!1 = z) | r(elem!1, z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[282, 21, 4375])).
% 1.43/1.65 tff(4377,plain,
% 1.43/1.65 (r(elem!1, z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4376, 2886])).
% 1.43/1.65 tff(4378,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4379,plain,
% 1.43/1.65 (((~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(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4380,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4379])).
% 1.43/1.65 tff(4381,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4380, 4378])).
% 1.43/1.65 tff(4382,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4383,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4382, 4381])).
% 1.43/1.65 tff(4384,plain,
% 1.43/1.65 (~b(z, elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4383, 271, 3407, 4368, 4366])).
% 1.43/1.65 tff(4385,plain,
% 1.43/1.65 (r(z, elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[355, 4384, 331])).
% 1.43/1.65 tff(4386,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4387,plain,
% 1.43/1.65 (((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(4388,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4387])).
% 1.43/1.65 tff(4389,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4388, 4386])).
% 1.43/1.65 tff(4390,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(4391,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4390, 4389])).
% 1.43/1.65 tff(4392,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4391, 121, 379, 4385, 4377, 412])).
% 1.43/1.65 tff(4393,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (z = elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(4394,plain,
% 1.43/1.65 (~r(elem!1, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4393, 4357, 412, 4317, 4349, 4347, 4328])).
% 1.43/1.65 tff(4395,plain,
% 1.43/1.65 (b(elem!1, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[392, 4394, 377])).
% 1.43/1.65 tff(4396,plain,
% 1.43/1.65 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.43/1.65 inference(symmetry,[status(thm)],[345])).
% 1.43/1.65 tff(4397,plain,
% 1.43/1.65 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.43/1.65 inference(transitivity,[status(thm)],[4325, 4396])).
% 1.43/1.65 tff(4398,plain,
% 1.43/1.65 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[4397])).
% 1.43/1.65 tff(4399,plain,
% 1.43/1.65 (~(s(elem!1) = s(z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[97, 4398])).
% 1.43/1.65 tff(4400,plain,
% 1.43/1.65 (~r(s(z), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3490, 4399, 412, 909, 4395, 4327, 4323, 4318])).
% 1.43/1.65 tff(4401,plain,
% 1.43/1.65 (~r(s(z), s(elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[4400, 4312])).
% 1.43/1.66 tff(4402,plain,
% 1.43/1.66 (b(s(z), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[442, 21, 4327, 4401])).
% 1.43/1.66 tff(4403,plain,
% 1.43/1.66 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4320])).
% 1.43/1.66 tff(4404,plain,
% 1.43/1.66 (~(s(z) = elem!1)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3595, 4403])).
% 1.43/1.66 tff(4405,plain,
% 1.43/1.66 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3917, 4327, 1997])).
% 1.43/1.66 tff(4406,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[486, 4328, 479])).
% 1.43/1.66 tff(4407,plain,
% 1.43/1.66 (~r(s(z), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1254, 411, 909, 412])).
% 1.43/1.66 tff(4408,plain,
% 1.43/1.66 (b(s(z), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[236, 4407, 231])).
% 1.43/1.66 tff(4409,plain,
% 1.43/1.66 (~b(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3435, 4408, 307, 446])).
% 1.43/1.66 tff(4410,plain,
% 1.43/1.66 (r(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2243, 4409, 2564])).
% 1.43/1.66 tff(4411,plain,
% 1.43/1.66 (~r(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2697, 4410, 139, 82, 378])).
% 1.43/1.66 tff(4412,plain,
% 1.43/1.66 (b(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[599, 4411, 68])).
% 1.43/1.66 tff(4413,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[681, 82, 675])).
% 1.43/1.66 tff(4414,plain,
% 1.43/1.66 (~r(elem!1, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3888, 4410, 4413, 139])).
% 1.43/1.66 tff(4415,plain,
% 1.43/1.66 (b(elem!1, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[299, 4414, 258])).
% 1.43/1.66 tff(4416,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4417,plain,
% 1.43/1.66 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4418,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4417])).
% 1.43/1.66 tff(4419,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4418, 4416])).
% 1.43/1.66 tff(4420,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4421,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4420, 4419])).
% 1.43/1.66 tff(4422,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4421, 121, 1625, 909, 412, 411])).
% 1.43/1.66 tff(4423,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4424,plain,
% 1.43/1.66 (~r(s(z), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4423, 411, 412, 909])).
% 1.43/1.66 tff(4425,plain,
% 1.43/1.66 (b(s(z), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2167, 4424])).
% 1.43/1.66 tff(4426,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4427,plain,
% 1.43/1.66 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4428,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4427])).
% 1.43/1.66 tff(4429,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4428, 4426])).
% 1.43/1.66 tff(4430,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4431,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4430, 4429])).
% 1.43/1.66 tff(4432,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4431, 271, 543, 505, 588, 448])).
% 1.43/1.66 tff(4433,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4434,plain,
% 1.43/1.66 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4433, 4425, 4415, 4412])).
% 1.43/1.66 tff(4435,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.43/1.66 tff(4436,plain,
% 1.43/1.66 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3895, 481])).
% 1.43/1.66 tff(4437,plain,
% 1.43/1.66 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[556, 4436, 2469])).
% 1.43/1.66 tff(4438,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.66 tff(4439,plain,
% 1.43/1.66 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[562, 4436])).
% 1.43/1.66 tff(4440,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[586, 4439, 4438])).
% 1.43/1.66 tff(4441,plain,
% 1.43/1.66 (~(s(elem!1) = s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[210, 4436])).
% 1.43/1.66 tff(4442,plain,
% 1.43/1.66 (~(elem!1 = s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[218, 4441])).
% 1.43/1.66 tff(4443,plain,
% 1.43/1.66 (~(s(elem!1) = elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2206, 4442])).
% 1.43/1.66 tff(4444,plain,
% 1.43/1.66 (r(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2243, 4443, 2467])).
% 1.43/1.66 tff(4445,plain,
% 1.43/1.66 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.43/1.66 inference(commutativity,[status(thm)],[])).
% 1.43/1.66 tff(4446,plain,
% 1.43/1.66 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.43/1.66 inference(symmetry,[status(thm)],[4445])).
% 1.43/1.66 tff(4447,plain,
% 1.43/1.66 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4446])).
% 1.43/1.66 tff(4448,plain,
% 1.43/1.66 (~(s(s(elem!1)) = s(elem!1))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4441, 4447])).
% 1.43/1.66 tff(4449,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[681, 79, 675])).
% 1.43/1.66 tff(4450,plain,
% 1.43/1.66 (~r(s(s(elem!1)), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[692, 4449, 623, 622])).
% 1.43/1.66 tff(4451,plain,
% 1.43/1.66 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[699, 21, 4450])).
% 1.43/1.66 tff(4452,plain,
% 1.43/1.66 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4451, 4448])).
% 1.43/1.66 tff(4453,plain,
% 1.43/1.66 (b(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[599, 68, 4435])).
% 1.43/1.66 tff(4454,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4455,plain,
% 1.43/1.66 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4456,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4455])).
% 1.43/1.66 tff(4457,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4456, 4454])).
% 1.43/1.66 tff(4458,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4459,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4458, 4457])).
% 1.43/1.66 tff(4460,plain,
% 1.43/1.66 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4459, 271, 589, 4453, 4452])).
% 1.43/1.66 tff(4461,plain,
% 1.43/1.66 ((elem!1 = s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[660, 21, 4460])).
% 1.43/1.66 tff(4462,plain,
% 1.43/1.66 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4461, 656])).
% 1.43/1.66 tff(4463,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4464,plain,
% 1.43/1.66 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4465,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4464])).
% 1.43/1.66 tff(4466,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4465, 4463])).
% 1.43/1.66 tff(4467,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4468,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4467, 4466])).
% 1.43/1.66 tff(4469,plain,
% 1.43/1.66 (~b(s(s(s(elem!1))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4468, 271, 589, 4453, 4452])).
% 1.43/1.66 tff(4470,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[486, 4469, 481])).
% 1.43/1.66 tff(4471,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4472,plain,
% 1.43/1.66 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4473,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4472])).
% 1.43/1.66 tff(4474,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4473, 4471])).
% 1.43/1.66 tff(4475,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4476,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4475, 4474])).
% 1.43/1.66 tff(4477,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4476, 121, 622, 4449, 4470, 4462])).
% 1.43/1.66 tff(4478,plain,((elem!1 = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(elem!1)) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4479,plain,
% 1.43/1.66 (elem!1 = s(s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4478, 4444, 481, 4440, 4437, 675, 4435])).
% 1.43/1.66 tff(4480,plain,
% 1.43/1.66 (s(elem!1) = s(s(s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4479])).
% 1.43/1.66 tff(4481,plain,
% 1.43/1.66 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4480])).
% 1.43/1.66 tff(4482,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[4481])).
% 1.43/1.66 tff(4483,plain,
% 1.43/1.66 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4440, 4482])).
% 1.43/1.66 tff(4484,plain,
% 1.43/1.66 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4479])).
% 1.43/1.66 tff(4485,plain,
% 1.43/1.66 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4484])).
% 1.43/1.66 tff(4486,plain,
% 1.43/1.66 (~b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[2467, 4485])).
% 1.43/1.66 tff(4487,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4486, 4483])).
% 1.43/1.66 tff(4488,plain,((s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | b(s(s(s(elem!1))), s(elem!1)) | r(elem!1, s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4489,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4488, 4434, 4409, 481, 4411, 675])).
% 1.43/1.66 tff(4490,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4491,plain,
% 1.43/1.66 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4492,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4491])).
% 1.43/1.66 tff(4493,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4492, 4490])).
% 1.43/1.66 tff(4494,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4495,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4494, 4493])).
% 1.43/1.66 tff(4496,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4495, 271, 307, 260, 517, 446])).
% 1.43/1.66 tff(4497,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4498,plain,
% 1.43/1.66 (~b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4497, 4408, 307, 446])).
% 1.43/1.66 tff(4499,plain,
% 1.43/1.66 (r(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[526, 4498, 4441])).
% 1.43/1.66 tff(4500,plain,
% 1.43/1.66 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[556, 4434, 4436])).
% 1.43/1.66 tff(4501,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4502,plain,
% 1.43/1.66 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(4503,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[4502])).
% 1.43/1.66 tff(4504,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[4503, 4501])).
% 1.43/1.66 tff(4505,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(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))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(4506,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[4505, 4504])).
% 1.43/1.66 tff(4507,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4506, 121, 4500, 4413, 4499, 4489])).
% 1.43/1.66 tff(4508,plain,((~r(s(elem!1), s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (elem!1 = s(z)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4509,plain,
% 1.43/1.66 (~r(s(elem!1), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4508, 4328, 4335, 412, 909, 4395, 4402, 4323, 4406, 4405, 4346, 4318, 3500, 4404])).
% 1.43/1.66 tff(4510,plain,
% 1.43/1.66 (b(s(elem!1), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[429, 4509, 4399])).
% 1.43/1.66 tff(4511,plain,
% 1.43/1.66 (~b(elem!1, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[456, 4510, 4402, 4395])).
% 1.43/1.66 tff(4512,plain,
% 1.43/1.66 (b(s(z), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1266, 4511, 909, 4318, 4323])).
% 1.43/1.66 tff(4513,plain,
% 1.43/1.66 (~b(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3435, 4512, 4395, 4402])).
% 1.43/1.66 tff(4514,plain,
% 1.43/1.66 (r(elem!1, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[299, 4511, 4323])).
% 1.43/1.66 tff(4515,plain,
% 1.43/1.66 (~r(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3888, 4514, 4347, 4406])).
% 1.43/1.66 tff(4516,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2243, 4515, 4513, 3500])).
% 1.43/1.66 tff(4517,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | b(z, elem!1) | (~b(z, s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(4518,plain,
% 1.43/1.66 (~(s(s(s(z))) = s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4517, 199, 412, 377, 909, 1639, 479, 3499])).
% 1.43/1.66 tff(4519,plain,
% 1.43/1.66 (r(s(s(s(z))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1816, 4518, 3506])).
% 1.43/1.66 tff(4520,plain,
% 1.43/1.66 (~r(z, elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3650, 4519, 412, 109])).
% 1.43/1.66 tff(4521,plain,
% 1.43/1.66 (z = elem!1),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[355, 4520, 199])).
% 1.43/1.66 tff(4522,plain,
% 1.43/1.66 (r(s(s(s(z))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[475, 4521, 109])).
% 1.43/1.66 tff(4523,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[149, 4522, 4521])).
% 1.43/1.66 tff(4524,plain,
% 1.43/1.66 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[135])).
% 1.43/1.66 tff(4525,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1500, 4524])).
% 1.43/1.66 tff(4526,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[676, 4525])).
% 1.43/1.66 tff(4527,plain,((~r(s(s(s(z))), s(elem!1))) | r(s(s(s(elem!1))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(4528,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4527, 4521, 4519])).
% 1.43/1.67 tff(4529,plain,
% 1.43/1.67 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4521])).
% 1.43/1.67 tff(4530,plain,
% 1.43/1.67 (r(s(elem!1), elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[412, 4529])).
% 1.43/1.67 tff(4531,plain,
% 1.43/1.67 (s(z) = s(elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4521])).
% 1.43/1.67 tff(4532,plain,
% 1.43/1.67 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4531])).
% 1.43/1.67 tff(4533,plain,
% 1.43/1.67 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4521])).
% 1.43/1.67 tff(4534,plain,
% 1.43/1.67 (r(elem!1, s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[909, 4533])).
% 1.43/1.67 tff(4535,plain,
% 1.43/1.67 (r(elem!1, s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4534, 4532])).
% 1.43/1.67 tff(4536,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3520, 121, 4535, 4530, 4528, 4523])).
% 1.43/1.67 tff(4537,plain,(b(z, elem!1) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | b(s(s(s(z))), s(elem!1)) | (elem!1 = s(elem!1)) | (~b(z, s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(4538,plain,
% 1.43/1.67 (b(z, elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4537, 4311, 3505, 412, 3506, 377, 1639, 479, 3499])).
% 1.43/1.67 tff(4539,plain,
% 1.43/1.67 (~(elem!1 = s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1397, 4538, 894])).
% 1.43/1.67 tff(4540,plain,
% 1.43/1.67 (~(s(z) = elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1221, 4539])).
% 1.43/1.67 tff(4541,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4542,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4543,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 1.43/1.67 tff(4544,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4543, 121, 3505, 412, 4311])).
% 1.43/1.67 tff(4545,plain,
% 1.43/1.67 (s(s(s(z))) = s(elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1816, 4544, 3506])).
% 1.43/1.67 tff(4546,plain,
% 1.43/1.67 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4545])).
% 1.43/1.67 tff(4547,plain,
% 1.43/1.67 ((s(s(s(z))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4546, 345])).
% 1.43/1.67 tff(4548,plain,
% 1.43/1.67 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4547, 4396])).
% 1.43/1.67 tff(4549,plain,
% 1.43/1.67 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4548])).
% 1.43/1.67 tff(4550,plain,
% 1.43/1.67 (~(s(elem!1) = s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[97, 4549])).
% 1.43/1.67 tff(4551,plain,
% 1.43/1.67 (~(s(s(s(elem!1))) = elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2596, 4545])).
% 1.43/1.67 tff(4552,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[486, 4551, 479])).
% 1.43/1.67 tff(4553,plain,
% 1.43/1.67 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4334, 4545, 3499])).
% 1.43/1.67 tff(4554,plain,
% 1.43/1.67 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4545])).
% 1.43/1.67 tff(4555,plain,
% 1.43/1.67 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4554])).
% 1.43/1.67 tff(4556,plain,
% 1.43/1.67 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4555])).
% 1.43/1.67 tff(4557,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4556])).
% 1.43/1.67 tff(4558,plain,
% 1.43/1.67 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4557])).
% 1.43/1.67 tff(4559,plain,
% 1.43/1.67 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4558])).
% 1.43/1.67 tff(4560,plain,
% 1.43/1.67 (s(elem!1) = s(s(s(z)))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4545])).
% 1.43/1.67 tff(4561,plain,
% 1.43/1.67 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4560])).
% 1.43/1.67 tff(4562,plain,
% 1.43/1.67 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4561, 1487])).
% 1.43/1.67 tff(4563,plain,
% 1.43/1.67 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4562])).
% 1.43/1.67 tff(4564,plain,
% 1.43/1.67 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4563])).
% 1.43/1.67 tff(4565,plain,
% 1.43/1.67 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1489, 4564])).
% 1.43/1.67 tff(4566,plain,
% 1.43/1.67 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4565, 4559])).
% 1.43/1.67 tff(4567,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[679, 21, 4566, 4553])).
% 1.43/1.67 tff(4568,plain,
% 1.43/1.67 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4545])).
% 1.43/1.67 tff(4569,plain,
% 1.43/1.67 (s(s(z)) = elem!1),
% 1.43/1.67 inference(transitivity,[status(thm)],[92, 4568, 70])).
% 1.43/1.67 tff(4570,plain,
% 1.43/1.67 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4569])).
% 1.43/1.67 tff(4571,plain,
% 1.43/1.67 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.43/1.67 inference(transitivity,[status(thm)],[4570, 360])).
% 1.43/1.67 tff(4572,plain,
% 1.43/1.67 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4571])).
% 1.43/1.67 tff(4573,plain,
% 1.43/1.67 (~(z = elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[95, 4572])).
% 1.43/1.67 tff(4574,plain,
% 1.43/1.67 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4555])).
% 1.43/1.67 tff(4575,plain,
% 1.43/1.67 (b(z, s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1639, 4574])).
% 1.43/1.67 tff(4576,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4556])).
% 1.43/1.67 tff(4577,plain,
% 1.43/1.67 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.43/1.67 inference(symmetry,[status(thm)],[4576])).
% 1.43/1.67 tff(4578,plain,
% 1.43/1.67 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4577, 654])).
% 1.43/1.67 tff(4579,plain,
% 1.43/1.67 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4578])).
% 1.43/1.67 tff(4580,plain,
% 1.43/1.67 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4569])).
% 1.43/1.67 tff(4581,plain,
% 1.43/1.67 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4580])).
% 1.43/1.67 tff(4582,plain,
% 1.43/1.67 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[877, 4581])).
% 1.43/1.67 tff(4583,plain,
% 1.43/1.67 (~(elem!1 = s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4582, 4579])).
% 1.43/1.67 tff(4584,plain,
% 1.43/1.67 (~r(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4393, 4583, 412, 4575, 4573, 4567, 4551])).
% 1.43/1.67 tff(4585,plain,
% 1.43/1.67 (b(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[392, 4584, 377])).
% 1.43/1.67 tff(4586,plain,
% 1.43/1.67 (~b(elem!1, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1290, 1281, 307, 447])).
% 1.43/1.67 tff(4587,plain,
% 1.43/1.67 (r(elem!1, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[299, 4586, 258])).
% 1.43/1.67 tff(4588,plain,
% 1.43/1.67 (~r(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3888, 4587, 684, 139])).
% 1.43/1.67 tff(4589,plain,
% 1.43/1.67 (b(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2243, 4588, 2564])).
% 1.43/1.67 tff(4590,plain,
% 1.43/1.67 (~b(s(z), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2585, 271, 307, 2618, 260])).
% 1.43/1.67 tff(4591,plain,
% 1.43/1.67 (r(s(z), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[442, 21, 348, 4590])).
% 1.43/1.67 tff(4592,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4593,plain,
% 1.43/1.67 (((~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), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4594,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4593])).
% 1.43/1.67 tff(4595,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4594, 4592])).
% 1.43/1.67 tff(4596,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4597,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4596, 4595])).
% 1.43/1.67 tff(4598,plain,
% 1.43/1.67 ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4597, 271])).
% 1.43/1.67 tff(4599,plain,
% 1.43/1.67 (~b(s(elem!1), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4598, 1326, 307, 2618])).
% 1.43/1.67 tff(4600,plain,
% 1.43/1.67 (r(s(elem!1), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[408, 21, 405, 4599])).
% 1.43/1.67 tff(4601,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4602,plain,
% 1.43/1.67 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4603,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4602])).
% 1.43/1.67 tff(4604,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4603, 4601])).
% 1.43/1.67 tff(4605,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4606,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4605, 4604])).
% 1.43/1.67 tff(4607,plain,
% 1.43/1.67 (~b(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4606, 271, 307, 2618, 1326])).
% 1.43/1.67 tff(4608,plain,
% 1.43/1.67 (r(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1437, 21, 1433, 4607])).
% 1.43/1.67 tff(4609,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4610,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4611,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4610, 4609])).
% 1.43/1.67 tff(4612,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4611, 121, 4608, 4086, 4600, 4591])).
% 1.43/1.67 tff(4613,plain,((~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(4614,plain,
% 1.43/1.67 (~b(s(z), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4613, 4589, 1326, 307, 348])).
% 1.43/1.67 tff(4615,plain,
% 1.43/1.67 (r(s(z), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[236, 4614, 1257])).
% 1.43/1.67 tff(4616,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4617,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4618,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4617, 4616])).
% 1.43/1.67 tff(4619,plain,
% 1.43/1.67 (~r(s(s(s(elem!1))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4618, 121, 4615, 139, 4587])).
% 1.43/1.67 tff(4620,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[66, 21, 4619, 63])).
% 1.43/1.67 tff(4621,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4622,plain,
% 1.43/1.67 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4623,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4622])).
% 1.43/1.67 tff(4624,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4623, 4621])).
% 1.43/1.67 tff(4625,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4626,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4625, 4624])).
% 1.43/1.67 tff(4627,plain,
% 1.43/1.67 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4626, 121, 4615, 139, 4587])).
% 1.43/1.67 tff(4628,plain,
% 1.43/1.67 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[760, 4627])).
% 1.43/1.67 tff(4629,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4630,plain,
% 1.43/1.67 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4631,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4630])).
% 1.43/1.67 tff(4632,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4631, 4629])).
% 1.43/1.67 tff(4633,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4634,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4633, 4632])).
% 1.43/1.67 tff(4635,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4634, 271, 4628, 1281, 3407, 4620])).
% 1.43/1.67 tff(4636,plain,((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(4637,plain,
% 1.43/1.67 (~b(s(z), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4636, 447, 139, 1326, 307, 4327, 2564, 684, 258, 3407])).
% 1.43/1.67 tff(4638,plain,
% 1.43/1.67 (r(s(z), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[25, 4637])).
% 1.43/1.67 tff(4639,plain,
% 1.43/1.67 (r(z, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1439, 4123])).
% 1.43/1.67 tff(4640,plain,
% 1.43/1.67 (~r(s(s(s(elem!1))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2960, 121, 684, 4639, 412])).
% 1.43/1.67 tff(4641,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1904, 21, 30, 4640])).
% 1.43/1.67 tff(4642,plain,
% 1.43/1.67 (~r(s(z), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1300, 4638, 412, 909])).
% 1.43/1.67 tff(4643,plain,
% 1.43/1.67 (b(s(z), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[444, 4642, 4327])).
% 1.43/1.67 tff(4644,plain,
% 1.43/1.67 (~b(elem!1, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[456, 4643, 447, 307])).
% 1.43/1.67 tff(4645,plain,
% 1.43/1.67 (r(elem!1, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[299, 4644, 258])).
% 1.43/1.67 tff(4646,plain,
% 1.43/1.67 (~b(s(z), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4096, 4643, 1326, 4399, 909, 412, 307])).
% 1.43/1.67 tff(4647,plain,
% 1.43/1.67 (r(s(z), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[236, 4646, 1257])).
% 1.43/1.67 tff(4648,plain,
% 1.43/1.67 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4626, 121, 4647, 139, 4645])).
% 1.43/1.67 tff(4649,plain,
% 1.43/1.67 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[760, 4648])).
% 1.43/1.67 tff(4650,plain,
% 1.43/1.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3895, 4328])).
% 1.43/1.67 tff(4651,plain,
% 1.43/1.67 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4329])).
% 1.43/1.67 tff(4652,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1997])).
% 1.43/1.67 tff(4653,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[4652, 4651])).
% 1.43/1.67 tff(4654,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1997, 4329])).
% 1.43/1.67 tff(4655,plain,
% 1.43/1.67 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4654])).
% 1.43/1.67 tff(4656,plain,
% 1.43/1.67 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4655])).
% 1.43/1.67 tff(4657,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4313])).
% 1.43/1.67 tff(4658,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4657])).
% 1.43/1.67 tff(4659,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), s(s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[139, 4658])).
% 1.43/1.67 tff(4660,plain,
% 1.43/1.67 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4313])).
% 1.43/1.67 tff(4661,plain,
% 1.43/1.67 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.43/1.67 inference(symmetry,[status(thm)],[4660])).
% 1.43/1.67 tff(4662,plain,
% 1.43/1.67 ((~b(elem!1, s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[4661])).
% 1.43/1.67 tff(4663,plain,
% 1.43/1.67 (~b(s(s(z)), s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4644, 4662])).
% 1.43/1.67 tff(4664,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.43/1.67 tff(4665,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.43/1.67 tff(4666,plain,
% 1.43/1.67 (((~![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)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(4667,plain,
% 1.43/1.67 ((~![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)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(4668,plain,
% 1.43/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[4667, 4666])).
% 1.43/1.67 tff(4669,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4668, 21, 3595, 4665, 4664])).
% 1.43/1.67 tff(4670,plain,(b(s(s(z)), s(z)) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(4671,plain,
% 1.43/1.67 (r(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4670, 4663])).
% 1.43/1.67 tff(4672,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4673,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4674,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 1.43/1.68 tff(4675,plain,
% 1.43/1.68 ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4674, 121])).
% 1.43/1.68 tff(4676,plain,
% 1.43/1.68 (~r(s(s(s(elem!1))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4675, 4671, 4638, 4659])).
% 1.43/1.68 tff(4677,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[66, 21, 4676, 63])).
% 1.43/1.68 tff(4678,plain,
% 1.43/1.68 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2289, 271, 447, 4643, 4677])).
% 1.43/1.68 tff(4679,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4678, 4656])).
% 1.43/1.68 tff(4680,plain,
% 1.43/1.68 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1494, 4679])).
% 1.43/1.68 tff(4681,plain,
% 1.43/1.68 (r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4680, 4653])).
% 1.43/1.68 tff(4682,plain,
% 1.43/1.68 (~(s(elem!1) = s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[210, 4650])).
% 1.43/1.68 tff(4683,plain,
% 1.43/1.68 (~(s(s(elem!1)) = s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[620, 4682])).
% 1.43/1.68 tff(4684,plain,
% 1.43/1.68 (~(elem!1 = z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4317, 2885])).
% 1.43/1.68 tff(4685,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4686,plain,
% 1.43/1.68 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4687,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4686])).
% 1.43/1.68 tff(4688,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4687, 4685])).
% 1.43/1.68 tff(4689,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4690,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4689, 4688])).
% 1.43/1.68 tff(4691,plain,
% 1.43/1.68 (~r(elem!1, z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4690, 121, 4647, 909, 4645])).
% 1.43/1.68 tff(4692,plain,
% 1.43/1.68 ((elem!1 = z) | b(elem!1, z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[282, 21, 4691])).
% 1.43/1.68 tff(4693,plain,
% 1.43/1.68 (b(elem!1, z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4692, 4684])).
% 1.43/1.68 tff(4694,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4695,plain,
% 1.43/1.68 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4696,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4695])).
% 1.43/1.68 tff(4697,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4696, 4694])).
% 1.43/1.68 tff(4698,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4699,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4698, 4697])).
% 1.43/1.68 tff(4700,plain,
% 1.43/1.68 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4699, 271, 1326, 4693, 4641])).
% 1.43/1.68 tff(4701,plain,
% 1.43/1.68 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[660, 21, 4357, 4700])).
% 1.43/1.68 tff(4702,plain,
% 1.43/1.68 (~(s(s(elem!1)) = elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[197, 4405])).
% 1.43/1.68 tff(4703,plain,
% 1.43/1.68 (~r(s(elem!1), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3888, 4645, 684, 139])).
% 1.43/1.68 tff(4704,plain,
% 1.43/1.68 (b(s(elem!1), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2243, 4703, 2564])).
% 1.43/1.68 tff(4705,plain,
% 1.43/1.68 (~r(s(s(elem!1)), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3132, 623, 684, 798])).
% 1.43/1.68 tff(4706,plain,
% 1.43/1.68 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[701, 4705, 694])).
% 1.43/1.68 tff(4707,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4708,plain,
% 1.43/1.68 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4709,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4708])).
% 1.43/1.68 tff(4710,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4709, 4707])).
% 1.43/1.68 tff(4711,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4712,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 1.43/1.68 tff(4713,plain,
% 1.43/1.68 (~r(s(s(elem!1)), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4712, 121, 623, 684, 727])).
% 1.43/1.68 tff(4714,plain,
% 1.43/1.68 (b(s(s(elem!1)), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[862, 4713, 851])).
% 1.43/1.68 tff(4715,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4716,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4717,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4716, 4715])).
% 1.43/1.68 tff(4718,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4717, 271, 307, 2618, 4714, 4706])).
% 1.43/1.68 tff(4719,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(4720,plain,
% 1.43/1.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4719, 4704, 307, 4702, 684, 4701, 4683, 4681])).
% 1.43/1.68 tff(4721,plain,
% 1.43/1.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[556, 4720, 4650])).
% 1.43/1.68 tff(4722,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4723,plain,
% 1.43/1.68 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4724,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4723])).
% 1.43/1.68 tff(4725,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4724, 4722])).
% 1.43/1.68 tff(4726,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4727,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4726, 4725])).
% 1.43/1.68 tff(4728,plain,
% 1.43/1.68 (~b(s(s(elem!1)), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4727, 271, 4721, 4649, 4641])).
% 1.43/1.68 tff(4729,plain,
% 1.43/1.68 (r(s(s(elem!1)), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2143, 4728])).
% 1.43/1.68 tff(4730,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4731,plain,
% 1.43/1.68 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4732,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4731])).
% 1.43/1.68 tff(4733,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4732, 4730])).
% 1.43/1.68 tff(4734,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4735,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 1.43/1.68 tff(4736,plain,
% 1.43/1.68 (~b(s(s(elem!1)), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4735, 271, 4721, 3407, 4641])).
% 1.43/1.68 tff(4737,plain,
% 1.43/1.68 (r(s(s(elem!1)), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2430, 4736])).
% 1.43/1.68 tff(4738,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2422, 4737, 4729, 909, 4638])).
% 1.43/1.68 tff(4739,plain,((~b(s(elem!1), s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~(s(s(s(z))) = s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(4740,plain,
% 1.43/1.68 (~b(s(elem!1), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4739, 4575, 3505, 4585, 4567, 4538, 4545, 412, 4552, 3500, 4539])).
% 1.43/1.68 tff(4741,plain,
% 1.43/1.68 (r(s(elem!1), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[429, 4740, 4550])).
% 1.43/1.68 tff(4742,plain,
% 1.43/1.68 (~r(s(z), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1254, 4741, 3505, 412])).
% 1.43/1.68 tff(4743,plain,
% 1.43/1.68 (b(s(z), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[236, 4742, 4540])).
% 1.43/1.68 tff(4744,plain,
% 1.43/1.68 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4547])).
% 1.43/1.68 tff(4745,plain,
% 1.43/1.68 (~(s(z) = s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[97, 4744])).
% 1.43/1.68 tff(4746,plain,
% 1.43/1.68 (~b(s(z), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4096, 4743, 4538, 4550, 3505, 412, 4585])).
% 1.43/1.68 tff(4747,plain,
% 1.43/1.68 (r(s(z), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[444, 4746, 4745])).
% 1.43/1.68 tff(4748,plain,
% 1.43/1.68 (~r(s(z), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1300, 4747, 412, 3505])).
% 1.43/1.68 tff(4749,plain,
% 1.43/1.68 (b(s(z), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[25, 4748])).
% 1.43/1.68 tff(4750,plain,
% 1.43/1.68 (~b(s(elem!1), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4613, 4743, 4538, 4585, 4745])).
% 1.43/1.68 tff(4751,plain,
% 1.43/1.68 (r(s(elem!1), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2243, 4750, 3500])).
% 1.43/1.68 tff(4752,plain,
% 1.43/1.68 (~r(elem!1, s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3888, 4751, 4567, 4552])).
% 1.43/1.68 tff(4753,plain,
% 1.43/1.68 (b(elem!1, s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[299, 4752, 4539])).
% 1.43/1.68 tff(4754,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4755,plain,
% 1.43/1.68 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4756,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4755])).
% 1.43/1.68 tff(4757,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4756, 4754])).
% 1.43/1.68 tff(4758,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4759,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4758, 4757])).
% 1.43/1.68 tff(4760,plain,
% 1.43/1.68 ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4759, 271])).
% 1.43/1.68 tff(4761,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4760, 4753, 4749, 4538, 4743])).
% 1.43/1.68 tff(4762,plain,((~b(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(z))), s(elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(4763,plain,
% 1.43/1.68 (~b(z, s(s(s(s(s(z))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4762, 3506, 377, 479, 3499, 412, 894])).
% 1.43/1.68 tff(4764,plain,
% 1.43/1.68 (r(z, s(s(s(s(s(z))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1658, 4763])).
% 1.43/1.68 tff(4765,plain,
% 1.43/1.68 (~(elem!1 = z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3524, 2885])).
% 1.43/1.68 tff(4766,plain,
% 1.43/1.68 (~r(elem!1, z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1417, 3502, 3505, 412])).
% 1.43/1.68 tff(4767,plain,
% 1.43/1.68 ((elem!1 = z) | b(elem!1, z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[282, 21, 4766])).
% 1.43/1.68 tff(4768,plain,
% 1.43/1.68 (b(elem!1, z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4767, 4765])).
% 1.43/1.68 tff(4769,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4770,plain,
% 1.43/1.68 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(4771,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4770])).
% 1.43/1.68 tff(4772,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4771, 4769])).
% 1.43/1.68 tff(4773,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(4774,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4773, 4772])).
% 1.43/1.69 tff(4775,plain,
% 1.43/1.69 ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4774, 271])).
% 1.43/1.69 tff(4776,plain,
% 1.43/1.69 (~b(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4775, 3725, 4768, 3995])).
% 1.43/1.69 tff(4777,plain,
% 1.43/1.69 (r(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[25, 4776])).
% 1.43/1.69 tff(4778,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4779,plain,
% 1.43/1.69 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4780,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4779])).
% 1.43/1.69 tff(4781,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4780, 4778])).
% 1.43/1.69 tff(4782,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4783,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4782, 4781])).
% 1.43/1.69 tff(4784,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4783, 121, 110, 412, 431, 1661])).
% 1.43/1.69 tff(4785,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4786,plain,
% 1.43/1.69 (~r(s(z), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4785, 4777, 412, 4764])).
% 1.43/1.69 tff(4787,plain,
% 1.43/1.69 (b(s(z), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[444, 4786, 3998])).
% 1.43/1.69 tff(4788,plain,
% 1.43/1.69 (~b(s(elem!1), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3830, 4787, 3725, 412, 3502, 3505, 479, 3997, 3506])).
% 1.43/1.69 tff(4789,plain,
% 1.43/1.69 (r(s(elem!1), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2243, 4788, 3500])).
% 1.43/1.69 tff(4790,plain,
% 1.43/1.69 (~(s(s(s(elem!1))) = elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3881, 4789, 3505, 412, 3725, 3502, 4787, 3524, 3506])).
% 1.43/1.69 tff(4791,plain,
% 1.43/1.69 (r(s(s(s(elem!1))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[486, 4790, 479])).
% 1.43/1.69 tff(4792,plain,
% 1.43/1.69 (~(s(elem!1) = s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[350, 3998])).
% 1.43/1.69 tff(4793,plain,
% 1.43/1.69 (~(s(s(z)) = s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[960, 3997])).
% 1.43/1.69 tff(4794,plain,
% 1.43/1.69 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[953, 4793])).
% 1.43/1.69 tff(4795,plain,
% 1.43/1.69 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3895, 4790])).
% 1.43/1.69 tff(4796,plain,
% 1.43/1.69 (~(s(elem!1) = s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[210, 4795])).
% 1.43/1.69 tff(4797,plain,
% 1.43/1.69 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3952, 4796, 3505, 412, 4794, 3725, 3502, 3524, 4787, 3506, 4788])).
% 1.43/1.69 tff(4798,plain,
% 1.43/1.69 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[78, 4797])).
% 1.43/1.69 tff(4799,plain,
% 1.43/1.69 (~r(s(z), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3826, 4798, 412, 3502, 4792, 4791, 3505])).
% 1.43/1.69 tff(4800,plain,
% 1.43/1.69 (b(s(z), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[236, 4799, 3997])).
% 1.43/1.69 tff(4801,plain,
% 1.43/1.69 (~b(s(s(s(z))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[303, 271, 260, 448, 257])).
% 1.43/1.69 tff(4802,plain,
% 1.43/1.69 (r(s(s(s(z))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2323, 21, 4801, 97])).
% 1.43/1.69 tff(4803,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4804,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4805,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4804, 4803])).
% 1.43/1.69 tff(4806,plain,
% 1.43/1.69 (~b(s(s(s(z))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4805, 271, 1326, 448, 257])).
% 1.43/1.69 tff(4807,plain,
% 1.43/1.69 (r(s(s(s(z))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1153, 21, 166, 4806])).
% 1.43/1.69 tff(4808,plain,
% 1.43/1.69 ((s(z) = z) <=> (z = s(z))),
% 1.43/1.69 inference(symmetry,[status(thm)],[3541])).
% 1.43/1.69 tff(4809,plain,
% 1.43/1.69 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4808])).
% 1.43/1.69 tff(4810,plain,
% 1.43/1.69 (~(z = s(z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[11, 4809])).
% 1.43/1.69 tff(4811,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4812,plain,
% 1.43/1.69 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4813,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4812])).
% 1.43/1.69 tff(4814,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4813, 4811])).
% 1.43/1.69 tff(4815,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4816,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 1.43/1.69 tff(4817,plain,
% 1.43/1.69 ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4816, 271])).
% 1.43/1.69 tff(4818,plain,
% 1.43/1.69 (~b(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4817, 1326, 448, 260])).
% 1.43/1.69 tff(4819,plain,
% 1.43/1.69 ((z = s(z)) | r(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[902, 21, 4818])).
% 1.43/1.69 tff(4820,plain,
% 1.43/1.69 (r(z, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4819, 4810])).
% 1.43/1.69 tff(4821,plain,
% 1.43/1.69 (~b(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4760, 1326, 448, 260])).
% 1.43/1.69 tff(4822,plain,
% 1.43/1.69 (r(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[25, 4821])).
% 1.43/1.69 tff(4823,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4824,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4825,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4824, 4823])).
% 1.43/1.69 tff(4826,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4825, 121, 4822, 4820, 4807, 4802])).
% 1.43/1.69 tff(4827,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4828,plain,
% 1.43/1.69 (~b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4827, 4800, 3995, 3725])).
% 1.43/1.69 tff(4829,plain,
% 1.43/1.69 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3520, 121, 3502, 4789, 4791])).
% 1.43/1.69 tff(4830,plain,
% 1.43/1.69 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[681, 4829, 4798])).
% 1.43/1.69 tff(4831,plain,
% 1.43/1.69 (~(s(s(s(z))) = s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4334, 4830, 3499])).
% 1.43/1.69 tff(4832,plain,
% 1.43/1.69 (r(s(s(s(z))), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1816, 4831, 3506])).
% 1.43/1.69 tff(4833,plain,
% 1.43/1.69 (~r(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3838, 121, 3502, 4789, 4832])).
% 1.43/1.69 tff(4834,plain,
% 1.43/1.69 (s(s(s(z))) = elem!1),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[255, 4833, 4828])).
% 1.43/1.69 tff(4835,plain,
% 1.43/1.69 (s(elem!1) = s(s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2605, 4834])).
% 1.43/1.69 tff(4836,plain,
% 1.43/1.69 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4835])).
% 1.43/1.69 tff(4837,plain,
% 1.43/1.69 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4836])).
% 1.43/1.69 tff(4838,plain,
% 1.43/1.69 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(symmetry,[status(thm)],[4837])).
% 1.43/1.69 tff(4839,plain,
% 1.43/1.69 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4834])).
% 1.43/1.69 tff(4840,plain,
% 1.43/1.69 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.69 inference(transitivity,[status(thm)],[4839, 1836])).
% 1.43/1.69 tff(4841,plain,
% 1.43/1.69 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4840])).
% 1.43/1.69 tff(4842,plain,
% 1.43/1.69 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[1489, 4841])).
% 1.43/1.69 tff(4843,plain,
% 1.43/1.69 (s(s(s(s(z)))) = s(elem!1)),
% 1.43/1.69 inference(symmetry,[status(thm)],[4835])).
% 1.43/1.69 tff(4844,plain,
% 1.43/1.69 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4843])).
% 1.43/1.69 tff(4845,plain,
% 1.43/1.69 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4844])).
% 1.43/1.69 tff(4846,plain,
% 1.43/1.69 (r(elem!1, s(s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[3502, 4845])).
% 1.43/1.69 tff(4847,plain,
% 1.43/1.69 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4843])).
% 1.43/1.69 tff(4848,plain,
% 1.43/1.69 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.43/1.69 inference(symmetry,[status(thm)],[4847])).
% 1.43/1.69 tff(4849,plain,
% 1.43/1.69 (r(s(s(s(s(z)))), elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4789, 4848])).
% 1.43/1.69 tff(4850,plain,
% 1.43/1.69 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4835])).
% 1.43/1.69 tff(4851,plain,
% 1.43/1.69 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4850])).
% 1.43/1.69 tff(4852,plain,
% 1.43/1.69 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[3499, 4851])).
% 1.43/1.69 tff(4853,plain,
% 1.43/1.69 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4045, 4852, 4038])).
% 1.43/1.69 tff(4854,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4855,plain,
% 1.43/1.69 (((~r(s(s(s(s(z)))), elem!1)) | (~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))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4856,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4855])).
% 1.43/1.69 tff(4857,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4856, 4854])).
% 1.43/1.69 tff(4858,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~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)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4859,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4858, 4857])).
% 1.43/1.69 tff(4860,plain,
% 1.43/1.69 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4859, 121, 4853])).
% 1.43/1.69 tff(4861,plain,
% 1.43/1.69 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4860, 4849, 4846])).
% 1.43/1.69 tff(4862,plain,
% 1.43/1.69 (b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[840, 4861, 4842])).
% 1.43/1.69 tff(4863,plain,
% 1.43/1.69 (b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4862, 4838])).
% 1.43/1.69 tff(4864,plain,
% 1.43/1.69 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4836])).
% 1.43/1.69 tff(4865,plain,
% 1.43/1.69 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4864])).
% 1.43/1.69 tff(4866,plain,
% 1.43/1.69 (r(z, s(s(elem!1)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4764, 4865])).
% 1.43/1.69 tff(4867,plain,
% 1.43/1.69 (~(s(s(elem!1)) = s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[620, 4796])).
% 1.43/1.69 tff(4868,plain,
% 1.43/1.69 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4836, 4835])).
% 1.43/1.69 tff(4869,plain,
% 1.43/1.69 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4868])).
% 1.43/1.69 tff(4870,plain,
% 1.43/1.69 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4869])).
% 1.43/1.69 tff(4871,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(elem!1))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4852, 4870])).
% 1.43/1.69 tff(4872,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[701, 4871, 4867])).
% 1.43/1.69 tff(4873,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4874,plain,
% 1.43/1.69 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4875,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4874])).
% 1.43/1.69 tff(4876,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4875, 4873])).
% 1.43/1.69 tff(4877,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4878,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4877, 4876])).
% 1.43/1.69 tff(4879,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4878, 121, 2088, 412, 683, 2417])).
% 1.43/1.69 tff(4880,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4881,plain,
% 1.43/1.69 (~r(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4880, 412, 2088, 683])).
% 1.43/1.69 tff(4882,plain,
% 1.43/1.69 (b(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2430, 4881])).
% 1.43/1.69 tff(4883,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4884,plain,
% 1.43/1.69 (((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4885,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4884])).
% 1.43/1.69 tff(4886,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4885, 4883])).
% 1.43/1.69 tff(4887,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4888,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4887, 4886])).
% 1.43/1.69 tff(4889,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4888, 121, 622, 2088, 1409, 412])).
% 1.43/1.69 tff(4890,plain,((~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4891,plain,
% 1.43/1.69 (~r(elem!1, z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4890, 412, 622, 2088])).
% 1.43/1.69 tff(4892,plain,
% 1.43/1.69 ((elem!1 = z) | b(elem!1, z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[282, 21, 4891])).
% 1.43/1.69 tff(4893,plain,
% 1.43/1.69 (b(elem!1, z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4892, 2886])).
% 1.43/1.69 tff(4894,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4895,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4896,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4895, 4894])).
% 1.43/1.69 tff(4897,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4896, 271, 1326, 4893, 4882, 542])).
% 1.43/1.69 tff(4898,plain,((~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (z = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4899,plain,
% 1.43/1.69 (~b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4898, 4872, 3725, 4866, 3524, 412, 4789])).
% 1.43/1.69 tff(4900,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4899, 4863])).
% 1.43/1.70 tff(4901,plain,(b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(z))), s(elem!1)) | b(s(s(s(elem!1))), elem!1) | b(z, s(z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(4902,plain,
% 1.43/1.70 (b(elem!1, s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4901, 3506, 3499, 412, 479, 894, 377])).
% 1.43/1.70 tff(4903,plain,
% 1.43/1.70 (~(z = elem!1)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1543, 4902, 894])).
% 1.43/1.70 tff(4904,plain,
% 1.43/1.70 (~(s(z) = s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[343, 4903])).
% 1.43/1.70 tff(4905,plain,
% 1.43/1.70 (b(s(s(s(z))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[244])).
% 1.43/1.70 tff(4906,plain,
% 1.43/1.70 (b(elem!1, s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.43/1.70 inference(symmetry,[status(thm)],[4905])).
% 1.43/1.70 tff(4907,plain,
% 1.43/1.70 (b(s(s(s(z))), s(elem!1))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[307, 4906])).
% 1.43/1.70 tff(4908,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[3506, 4907])).
% 1.43/1.70 tff(4909,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(4910,plain,
% 1.43/1.70 (~(s(s(s(z))) = elem!1)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4909, 3506, 4902])).
% 1.43/1.70 tff(4911,plain,
% 1.43/1.70 (~(s(elem!1) = s(z))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[350, 4904])).
% 1.43/1.70 tff(4912,plain,
% 1.43/1.70 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[2063, 4904])).
% 1.43/1.70 tff(4913,plain,
% 1.43/1.70 (b(z, elem!1)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1303, 439, 909, 307, 331, 412, 1242])).
% 1.43/1.70 tff(4914,plain,
% 1.43/1.70 (r(s(z), s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[444, 439, 344])).
% 1.43/1.70 tff(4915,plain,
% 1.43/1.70 (r(s(z), elem!1)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[236, 1277, 1242])).
% 1.43/1.70 tff(4916,plain,
% 1.43/1.70 (~r(s(elem!1), s(z))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1254, 4915, 909, 412])).
% 1.43/1.70 tff(4917,plain,
% 1.43/1.70 (b(s(elem!1), s(z))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[429, 4916, 351])).
% 1.43/1.70 tff(4918,plain,
% 1.43/1.70 (~b(z, s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4122, 4917, 307, 4913])).
% 1.43/1.70 tff(4919,plain,
% 1.43/1.70 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[1997])).
% 1.43/1.70 tff(4920,plain,
% 1.43/1.70 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.43/1.70 inference(symmetry,[status(thm)],[4919])).
% 1.43/1.70 tff(4921,plain,
% 1.43/1.70 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[4920])).
% 1.43/1.70 tff(4922,plain,
% 1.43/1.70 (~b(z, s(s(s(z))))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[1429, 4921])).
% 1.43/1.70 tff(4923,plain,
% 1.43/1.70 (r(s(s(s(z))), z)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4006, 1997, 412])).
% 1.43/1.70 tff(4924,plain,
% 1.43/1.70 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[1997])).
% 1.43/1.70 tff(4925,plain,
% 1.43/1.70 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 1.43/1.70 inference(symmetry,[status(thm)],[4924])).
% 1.43/1.70 tff(4926,plain,
% 1.43/1.70 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[4925])).
% 1.43/1.70 tff(4927,plain,
% 1.43/1.70 (~b(s(z), s(s(s(z))))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[439, 4926])).
% 1.43/1.70 tff(4928,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[3871, 4927])).
% 1.43/1.70 tff(4929,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(s(z), s(s(s(z))))) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(4930,plain,
% 1.43/1.70 (~b(s(z), s(s(s(z))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4929, 1997, 439])).
% 1.43/1.70 tff(4931,plain,
% 1.43/1.70 (r(s(z), s(s(s(z))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[105, 4930])).
% 1.43/1.70 tff(4932,plain,
% 1.43/1.70 (~r(z, s(s(s(z))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1148, 4931, 4923, 909])).
% 1.43/1.70 tff(4933,plain,
% 1.43/1.70 (b(z, s(s(s(z))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1214, 4932])).
% 1.43/1.70 tff(4934,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4933, 4922])).
% 1.43/1.70 tff(4935,plain,((~(s(s(s(z))) = s(elem!1))) | b(z, s(elem!1)) | (~r(z, s(z))) | b(s(z), s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(4936,plain,
% 1.43/1.70 (~(s(s(s(z))) = s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4935, 4918, 909, 439, 412])).
% 1.53/1.70 tff(4937,plain,
% 1.53/1.70 (r(s(s(s(z))), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1816, 4936, 3506])).
% 1.53/1.70 tff(4938,plain,
% 1.53/1.70 (~b(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4021, 4937, 4914, 412, 4913, 909])).
% 1.53/1.70 tff(4939,plain,
% 1.53/1.70 (r(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1155, 4938])).
% 1.53/1.70 tff(4940,plain,
% 1.53/1.70 (r(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1439, 4918])).
% 1.53/1.70 tff(4941,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2658, 121, 4940, 412, 4937, 4939])).
% 1.53/1.70 tff(4942,plain,(b(s(z), s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(s(s(s(z))), s(elem!1)) | (~b(elem!1, s(elem!1))) | b(s(z), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(4943,plain,
% 1.53/1.70 (b(s(z), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4942, 1242, 3505, 3506, 4902, 412, 4903])).
% 1.53/1.70 tff(4944,plain,
% 1.53/1.70 (s(z) = elem!1),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1270, 378, 307, 446, 909, 412, 1242, 422])).
% 1.53/1.70 tff(4945,plain,
% 1.53/1.70 (s(s(z)) = s(elem!1)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4944])).
% 1.53/1.70 tff(4946,plain,
% 1.53/1.70 (~(s(s(s(z))) = elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4909, 3506, 307])).
% 1.53/1.70 tff(4947,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[223])).
% 1.53/1.70 tff(4948,plain,
% 1.53/1.70 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 1.53/1.70 inference(symmetry,[status(thm)],[4947])).
% 1.53/1.70 tff(4949,plain,
% 1.53/1.70 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1037])).
% 1.53/1.70 tff(4950,plain,
% 1.53/1.70 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), s(z))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4949, 4948])).
% 1.53/1.70 tff(4951,plain,
% 1.53/1.70 (s(s(elem!1)) = s(s(s(z)))),
% 1.53/1.70 inference(symmetry,[status(thm)],[1037])).
% 1.53/1.70 tff(4952,plain,
% 1.53/1.70 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3057, 4951])).
% 1.53/1.70 tff(4953,plain,
% 1.53/1.70 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4952])).
% 1.53/1.70 tff(4954,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3056])).
% 1.53/1.70 tff(4955,plain,
% 1.53/1.70 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4954])).
% 1.53/1.70 tff(4956,plain,
% 1.53/1.70 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[3499, 4955])).
% 1.53/1.70 tff(4957,plain,
% 1.53/1.70 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3057])).
% 1.53/1.70 tff(4958,plain,
% 1.53/1.70 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[4957])).
% 1.53/1.70 tff(4959,plain,
% 1.53/1.70 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4958])).
% 1.53/1.70 tff(4960,plain,
% 1.53/1.70 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1036])).
% 1.53/1.70 tff(4961,plain,
% 1.53/1.70 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4960])).
% 1.53/1.70 tff(4962,plain,
% 1.53/1.70 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[877, 4961])).
% 1.53/1.70 tff(4963,plain,
% 1.53/1.70 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4962, 4959])).
% 1.53/1.70 tff(4964,plain,
% 1.53/1.70 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[3112, 21, 4963, 4956])).
% 1.53/1.70 tff(4965,plain,
% 1.53/1.70 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1037])).
% 1.53/1.70 tff(4966,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1500, 4965])).
% 1.53/1.70 tff(4967,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~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)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4968,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(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)))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4969,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4968, 4967])).
% 1.53/1.70 tff(4970,plain,
% 1.53/1.70 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4969, 121, 412, 4966, 4964])).
% 1.53/1.70 tff(4971,plain,
% 1.53/1.70 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4970, 4953])).
% 1.53/1.70 tff(4972,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1733, 4971])).
% 1.53/1.70 tff(4973,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3042])).
% 1.53/1.70 tff(4974,plain,
% 1.53/1.70 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[4973])).
% 1.53/1.70 tff(4975,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[307, 4974])).
% 1.53/1.70 tff(4976,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[3499, 4975])).
% 1.53/1.70 tff(4977,plain,((~(s(s(s(s(s(z))))) = elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(4978,plain,
% 1.53/1.70 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4977, 307, 3499])).
% 1.53/1.70 tff(4979,plain,
% 1.53/1.70 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3057])).
% 1.53/1.70 tff(4980,plain,
% 1.53/1.70 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[4979])).
% 1.53/1.70 tff(4981,plain,
% 1.53/1.70 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1037])).
% 1.53/1.70 tff(4982,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4951, 3057])).
% 1.53/1.70 tff(4983,plain,
% 1.53/1.70 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4982])).
% 1.53/1.70 tff(4984,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4985,plain,
% 1.53/1.70 (((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4986,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4985])).
% 1.53/1.70 tff(4987,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4986, 4984])).
% 1.53/1.70 tff(4988,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4989,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 1.53/1.70 tff(4990,plain,
% 1.53/1.70 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4989, 121, 412, 4966, 4964])).
% 1.53/1.70 tff(4991,plain,
% 1.53/1.70 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4990, 4983])).
% 1.53/1.70 tff(4992,plain,
% 1.53/1.70 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1494, 4991])).
% 1.53/1.70 tff(4993,plain,
% 1.53/1.70 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4992, 4981])).
% 1.53/1.70 tff(4994,plain,
% 1.53/1.70 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4993, 4980])).
% 1.53/1.70 tff(4995,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3057])).
% 1.53/1.70 tff(4996,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[4995])).
% 1.53/1.70 tff(4997,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.53/1.70 tff(4998,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.70 tff(4999,plain,
% 1.53/1.70 (s(s(s(s(s(z))))) = elem!1),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4998, 1836])).
% 1.53/1.70 tff(5000,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4997, 4999])).
% 1.53/1.70 tff(5001,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(5002,plain,
% 1.53/1.70 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5001, 4997])).
% 1.53/1.70 tff(5003,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(5004,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(5005,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5004, 5003])).
% 1.53/1.70 tff(5006,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5005, 271, 307, 831, 257, 1723])).
% 1.53/1.70 tff(5007,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(5008,plain,
% 1.53/1.70 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5007, 257, 307, 1723])).
% 1.53/1.70 tff(5009,plain,
% 1.53/1.70 (r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[840, 5008, 4997])).
% 1.53/1.70 tff(5010,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(5011,plain,
% 1.53/1.70 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(5012,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5011])).
% 1.53/1.70 tff(5013,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[5012, 5010])).
% 1.53/1.70 tff(5014,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(5015,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 1.53/1.70 tff(5016,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5015, 121, 378, 3061, 1826, 1661])).
% 1.53/1.70 tff(5017,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(5018,plain,
% 1.53/1.70 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5017, 5009, 1661, 378])).
% 1.53/1.70 tff(5019,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1847, 5018, 5002])).
% 1.53/1.70 tff(5020,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5019, 4996])).
% 1.53/1.70 tff(5021,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.70 tff(5022,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1723, 3060])).
% 1.53/1.70 tff(5023,plain,
% 1.53/1.70 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5022, 3059])).
% 1.53/1.70 tff(5024,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(5025,plain,
% 1.53/1.70 (((~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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(5026,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5025])).
% 1.53/1.70 tff(5027,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[5026, 5024])).
% 1.53/1.70 tff(5028,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(5029,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5028, 5027])).
% 1.53/1.70 tff(5030,plain,
% 1.53/1.70 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5029, 271, 1383, 5023, 5021])).
% 1.53/1.70 tff(5031,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5030, 5020])).
% 1.53/1.70 tff(5032,plain,((~b(s(s(s(z))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(5033,plain,
% 1.53/1.70 (~b(s(s(s(z))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5032, 223, 4994, 1661, 378, 4978, 307, 4972])).
% 1.53/1.70 tff(5034,plain,
% 1.53/1.70 (r(s(s(s(z))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[255, 5033, 907])).
% 1.53/1.70 tff(5035,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5034, 4950])).
% 1.53/1.70 tff(5036,plain,
% 1.53/1.70 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[223])).
% 1.53/1.70 tff(5037,plain,
% 1.53/1.70 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5036])).
% 1.53/1.70 tff(5038,plain,
% 1.53/1.70 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2137, 5037])).
% 1.53/1.70 tff(5039,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4972, 3060])).
% 1.53/1.70 tff(5040,plain,
% 1.53/1.70 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[5039, 3059])).
% 1.53/1.70 tff(5041,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[3056])).
% 1.53/1.70 tff(5042,plain,
% 1.53/1.70 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.70 inference(symmetry,[status(thm)],[5041])).
% 1.53/1.70 tff(5043,plain,
% 1.53/1.70 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5042])).
% 1.53/1.70 tff(5044,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.53/1.71 tff(5045,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(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)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5046,plain,
% 1.53/1.71 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5047,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(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))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5046])).
% 1.53/1.71 tff(5048,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(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)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5047, 5045])).
% 1.53/1.71 tff(5049,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5050,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(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))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5049, 5048])).
% 1.53/1.71 tff(5051,plain,
% 1.53/1.71 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5050, 271, 588, 5044, 5021])).
% 1.53/1.71 tff(5052,plain,
% 1.53/1.71 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5051, 5043])).
% 1.53/1.71 tff(5053,plain,
% 1.53/1.71 (r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[840, 5052, 4997])).
% 1.53/1.71 tff(5054,plain,
% 1.53/1.71 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4995])).
% 1.53/1.71 tff(5055,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5056,plain,
% 1.53/1.71 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, 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(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5057,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5056])).
% 1.53/1.71 tff(5058,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5057, 5055])).
% 1.53/1.71 tff(5059,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5060,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5059, 5058])).
% 1.53/1.71 tff(5061,plain,
% 1.53/1.71 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5060, 271, 588, 5044, 5021])).
% 1.53/1.71 tff(5062,plain,
% 1.53/1.71 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5061, 5054])).
% 1.53/1.71 tff(5063,plain,
% 1.53/1.71 (r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1847, 5062, 5002])).
% 1.53/1.71 tff(5064,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5017, 5063, 5053, 1661, 378])).
% 1.53/1.71 tff(5065,plain,((~b(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~(s(z) = elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5066,plain,
% 1.53/1.71 (~b(elem!1, s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5065, 223, 378, 4978, 1661, 5040, 4994])).
% 1.53/1.71 tff(5067,plain,
% 1.53/1.71 (r(elem!1, s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[599, 5066, 5038])).
% 1.53/1.71 tff(5068,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5069,plain,
% 1.53/1.71 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5070,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5069])).
% 1.53/1.71 tff(5071,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5070, 5068])).
% 1.53/1.71 tff(5072,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5073,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5072, 5071])).
% 1.53/1.71 tff(5074,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5073, 121, 378, 2088, 624, 2117])).
% 1.53/1.71 tff(5075,plain,((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5076,plain,
% 1.53/1.71 (~r(z, s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5075, 5067, 378, 5035])).
% 1.53/1.71 tff(5077,plain,
% 1.53/1.71 (b(z, s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2106, 5076])).
% 1.53/1.71 tff(5078,plain,
% 1.53/1.71 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.71 inference(symmetry,[status(thm)],[558])).
% 1.53/1.71 tff(5079,plain,
% 1.53/1.71 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1037])).
% 1.53/1.71 tff(5080,plain,
% 1.53/1.71 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5079, 5078])).
% 1.53/1.71 tff(5081,plain,
% 1.53/1.71 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5080])).
% 1.53/1.71 tff(5082,plain,
% 1.53/1.71 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2065, 5081])).
% 1.53/1.71 tff(5083,plain,
% 1.53/1.71 (r(s(s(elem!1)), elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5034, 4949])).
% 1.53/1.71 tff(5084,plain,
% 1.53/1.71 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[223])).
% 1.53/1.71 tff(5085,plain,
% 1.53/1.71 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.53/1.71 inference(transitivity,[status(thm)],[5084, 653])).
% 1.53/1.71 tff(5086,plain,
% 1.53/1.71 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5085])).
% 1.53/1.71 tff(5087,plain,
% 1.53/1.71 (~(s(s(s(elem!1))) = elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[61, 5086])).
% 1.53/1.71 tff(5088,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[486, 5087, 479])).
% 1.53/1.71 tff(5089,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5090,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5091,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5090, 5089])).
% 1.53/1.71 tff(5092,plain,
% 1.53/1.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5091, 121, 5067, 5088, 5083])).
% 1.53/1.71 tff(5093,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[586, 5092, 5082])).
% 1.53/1.71 tff(5094,plain,
% 1.53/1.71 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5079])).
% 1.53/1.71 tff(5095,plain,
% 1.53/1.71 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2065, 5094])).
% 1.53/1.71 tff(5096,plain,
% 1.53/1.71 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2670, 5067, 5088, 5083])).
% 1.53/1.71 tff(5097,plain,
% 1.53/1.71 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[556, 5096, 5095])).
% 1.53/1.71 tff(5098,plain,
% 1.53/1.71 (~b(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1900, 271, 5097, 5093, 5077])).
% 1.53/1.71 tff(5099,plain,
% 1.53/1.71 (~r(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2678, 121, 378, 5067, 5088])).
% 1.53/1.71 tff(5100,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1904, 21, 30, 5099, 5098])).
% 1.53/1.71 tff(5101,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5102,plain,
% 1.53/1.71 (~r(s(s(s(z))), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5101, 4944, 1661, 4946, 307, 412, 479, 3499, 2065, 378])).
% 1.53/1.71 tff(5103,plain,
% 1.53/1.71 (s(s(s(z))) = s(elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1816, 5102, 3506])).
% 1.53/1.71 tff(5104,plain,
% 1.53/1.71 (s(elem!1) = s(s(s(z)))),
% 1.53/1.71 inference(symmetry,[status(thm)],[5103])).
% 1.53/1.71 tff(5105,plain,
% 1.53/1.71 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5104])).
% 1.53/1.71 tff(5106,plain,
% 1.53/1.71 (elem!1 = s(elem!1)),
% 1.53/1.71 inference(transitivity,[status(thm)],[75, 5105, 91, 4945])).
% 1.53/1.71 tff(5107,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[377, 5106])).
% 1.53/1.71 tff(5108,plain,((~r(z, elem!1)) | (elem!1 = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~r(z, s(z))) | b(s(z), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5109,plain,
% 1.53/1.71 (~r(z, elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5108, 4943, 3506, 4764, 4902, 412, 479, 3499, 4912, 377, 3505, 1242, 4911])).
% 1.53/1.71 tff(5110,plain,
% 1.53/1.71 (b(z, elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[355, 5109, 4903])).
% 1.53/1.71 tff(5111,plain,
% 1.53/1.71 (~(elem!1 = s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1397, 5110, 894])).
% 1.53/1.71 tff(5112,plain,
% 1.53/1.71 (~(s(z) = elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1221, 5111])).
% 1.53/1.71 tff(5113,plain,
% 1.53/1.71 (r(s(z), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[236, 5112, 1242])).
% 1.53/1.71 tff(5114,plain,
% 1.53/1.71 (~r(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1254, 5113, 3505, 412])).
% 1.53/1.71 tff(5115,plain,
% 1.53/1.71 (b(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[429, 5114, 4911])).
% 1.53/1.71 tff(5116,plain,
% 1.53/1.71 (~b(elem!1, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[456, 5115, 4902, 4943])).
% 1.53/1.71 tff(5117,plain,
% 1.53/1.71 (r(elem!1, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[299, 5116, 5111])).
% 1.53/1.71 tff(5118,plain,
% 1.53/1.71 (~r(s(s(s(elem!1))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4618, 121, 357, 4406, 3456])).
% 1.53/1.71 tff(5119,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[66, 21, 5118, 63])).
% 1.53/1.71 tff(5120,plain,
% 1.53/1.71 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1997])).
% 1.53/1.71 tff(5121,plain,
% 1.53/1.71 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[5120])).
% 1.53/1.71 tff(5122,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4336])).
% 1.53/1.71 tff(5123,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5122, 5121])).
% 1.53/1.71 tff(5124,plain,
% 1.53/1.71 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[3917, 1997, 348])).
% 1.53/1.71 tff(5125,plain,
% 1.53/1.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[78, 5124])).
% 1.53/1.71 tff(5126,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[681, 5125, 4335])).
% 1.53/1.71 tff(5127,plain,
% 1.53/1.71 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5126, 5123])).
% 1.53/1.71 tff(5128,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5129,plain,
% 1.53/1.71 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5130,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5129])).
% 1.53/1.71 tff(5131,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5130, 5128])).
% 1.53/1.71 tff(5132,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5133,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5132, 5131])).
% 1.53/1.71 tff(5134,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5133, 121, 1661, 1477, 1736, 109])).
% 1.53/1.71 tff(5135,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5136,plain,
% 1.53/1.71 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5135, 5127, 1661, 4923])).
% 1.53/1.71 tff(5137,plain,
% 1.53/1.71 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1494, 5136])).
% 1.53/1.71 tff(5138,plain,
% 1.53/1.71 (b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5137, 4654])).
% 1.53/1.71 tff(5139,plain,
% 1.53/1.71 (~r(s(z), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4626, 121, 357, 4406, 3456])).
% 1.53/1.71 tff(5140,plain,
% 1.53/1.71 (b(s(z), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[760, 5139])).
% 1.53/1.71 tff(5141,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5142,plain,
% 1.53/1.71 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5143,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5142])).
% 1.53/1.71 tff(5144,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5143, 5141])).
% 1.53/1.71 tff(5145,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5146,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5145, 5144])).
% 1.53/1.71 tff(5147,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5146, 271, 5140, 447, 5138, 5119])).
% 1.53/1.71 tff(5148,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5149,plain,
% 1.53/1.71 (~(s(s(s(z))) = s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5148, 5115, 4764, 5113, 5117, 479, 4904, 3499, 412])).
% 1.53/1.71 tff(5150,plain,
% 1.53/1.71 (~(s(elem!1) = s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2035, 5149])).
% 1.53/1.71 tff(5151,plain,
% 1.53/1.71 (~(s(s(z)) = s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[960, 5112])).
% 1.53/1.71 tff(5152,plain,
% 1.53/1.71 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[953, 5151])).
% 1.53/1.71 tff(5153,plain,
% 1.53/1.71 (r(s(s(s(z))), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1816, 5149, 3506])).
% 1.53/1.71 tff(5154,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4543, 121, 909, 412, 1500, 109])).
% 1.53/1.71 tff(5155,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(5156,plain,
% 1.53/1.71 (~r(s(s(s(z))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5155, 5153, 412, 3505])).
% 1.53/1.71 tff(5157,plain,
% 1.53/1.71 (b(s(s(s(z))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1155, 5156])).
% 1.53/1.71 tff(5158,plain,
% 1.53/1.71 (~b(s(s(s(z))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1940, 5157, 5110, 4902])).
% 1.53/1.71 tff(5159,plain,
% 1.53/1.71 (r(s(s(s(z))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[255, 5158, 4910])).
% 1.53/1.71 tff(5160,plain,
% 1.53/1.71 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[159])).
% 1.53/1.71 tff(5161,plain,
% 1.53/1.71 (~(elem!1 = s(s(s(z))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4910, 5160])).
% 1.53/1.71 tff(5162,plain,
% 1.53/1.71 (~(elem!1 = z)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4903, 2885])).
% 1.53/1.71 tff(5163,plain,
% 1.53/1.71 (~r(elem!1, z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4690, 121, 5113, 3505, 5117])).
% 1.53/1.71 tff(5164,plain,
% 1.53/1.71 ((elem!1 = z) | b(elem!1, z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[282, 21, 5163])).
% 1.53/1.71 tff(5165,plain,
% 1.53/1.71 (b(elem!1, z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5164, 5162])).
% 1.53/1.71 tff(5166,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5167,plain,
% 1.53/1.71 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5168,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5167])).
% 1.53/1.71 tff(5169,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[5168, 5166])).
% 1.53/1.71 tff(5170,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(5171,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[5170, 5169])).
% 1.53/1.71 tff(5172,plain,
% 1.53/1.71 (~b(elem!1, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5171, 271, 5110, 5165, 5157])).
% 1.53/1.71 tff(5173,plain,
% 1.53/1.71 (r(elem!1, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1192, 5172, 5161])).
% 1.53/1.71 tff(5174,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5175,plain,
% 1.53/1.71 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(5176,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5175])).
% 1.53/1.72 tff(5177,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5176, 5174])).
% 1.53/1.72 tff(5178,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5179,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5178, 5177])).
% 1.53/1.72 tff(5180,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5179, 121, 622, 1184, 145, 1500])).
% 1.53/1.72 tff(5181,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(5182,plain,
% 1.53/1.72 (~r(s(elem!1), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5181, 5173, 5159, 5153])).
% 1.53/1.72 tff(5183,plain,
% 1.53/1.72 (b(s(elem!1), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2243, 5182, 3500])).
% 1.53/1.72 tff(5184,plain,
% 1.53/1.72 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3790, 5183, 479])).
% 1.53/1.72 tff(5185,plain,
% 1.53/1.72 (~(s(s(elem!1)) = elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[197, 5184])).
% 1.53/1.72 tff(5186,plain,
% 1.53/1.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[78, 5184])).
% 1.53/1.72 tff(5187,plain,
% 1.53/1.72 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[614, 5186])).
% 1.53/1.72 tff(5188,plain,
% 1.53/1.72 (~b(s(s(s(z))), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1940, 1935, 1326, 307])).
% 1.53/1.72 tff(5189,plain,
% 1.53/1.72 (r(s(s(s(z))), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[255, 5188, 907])).
% 1.53/1.72 tff(5190,plain,
% 1.53/1.72 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2505])).
% 1.53/1.72 tff(5191,plain,
% 1.53/1.72 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(elem!1), elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5190])).
% 1.53/1.72 tff(5192,plain,
% 1.53/1.72 (~r(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4112, 5189, 3456, 357])).
% 1.53/1.72 tff(5193,plain,
% 1.53/1.72 (b(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[105, 5192])).
% 1.53/1.72 tff(5194,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5195,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5194, 4169])).
% 1.53/1.72 tff(5196,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5195, 121, 357, 3456, 5189])).
% 1.53/1.72 tff(5197,plain,
% 1.53/1.72 (b(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2325, 5196])).
% 1.53/1.72 tff(5198,plain,
% 1.53/1.72 (~b(s(elem!1), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3622, 5197, 447, 5193])).
% 1.53/1.72 tff(5199,plain,
% 1.53/1.72 (r(s(elem!1), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2044, 5198, 2037])).
% 1.53/1.72 tff(5200,plain,
% 1.53/1.72 (~r(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3865, 5199, 1500, 412])).
% 1.53/1.72 tff(5201,plain,
% 1.53/1.72 (b(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1214, 5200])).
% 1.53/1.72 tff(5202,plain,
% 1.53/1.72 (~(elem!1 = s(s(s(z))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[907, 5160])).
% 1.53/1.72 tff(5203,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5204,plain,
% 1.53/1.72 (((~b(z, s(s(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(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5205,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z)))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5204])).
% 1.53/1.72 tff(5206,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5205, 5203])).
% 1.53/1.72 tff(5207,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5208,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5207, 5206])).
% 1.53/1.72 tff(5209,plain,
% 1.53/1.72 (~b(elem!1, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5208, 271, 261, 1307, 1935])).
% 1.53/1.72 tff(5210,plain,
% 1.53/1.72 (r(elem!1, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1192, 5209, 1102])).
% 1.53/1.72 tff(5211,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5212,plain,
% 1.53/1.72 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5213,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5212])).
% 1.53/1.72 tff(5214,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5213, 5211])).
% 1.53/1.72 tff(5215,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5216,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5215, 5214])).
% 1.53/1.72 tff(5217,plain,
% 1.53/1.72 (~r(s(s(elem!1)), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5216, 121, 357, 1184, 1624])).
% 1.53/1.72 tff(5218,plain,
% 1.53/1.72 (b(s(s(elem!1)), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2143, 5217])).
% 1.53/1.72 tff(5219,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5220,plain,
% 1.53/1.72 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5221,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5220])).
% 1.53/1.72 tff(5222,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5221, 5219])).
% 1.53/1.72 tff(5223,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5224,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 1.53/1.72 tff(5225,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5224, 121, 1184, 145, 1624])).
% 1.53/1.72 tff(5226,plain,
% 1.53/1.72 (b(s(s(s(z))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2462, 21, 5225, 944])).
% 1.53/1.72 tff(5227,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5228,plain,
% 1.53/1.72 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5229,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5228])).
% 1.53/1.72 tff(5230,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5229, 5227])).
% 1.53/1.72 tff(5231,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5232,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5231, 5230])).
% 1.53/1.72 tff(5233,plain,
% 1.53/1.72 (~r(s(z), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5232, 121, 357, 1184, 1624])).
% 1.53/1.72 tff(5234,plain,
% 1.53/1.72 (b(s(z), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2167, 5233])).
% 1.53/1.72 tff(5235,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5236,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5237,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5236, 5235])).
% 1.53/1.72 tff(5238,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5237, 271, 5234, 222, 5226, 5218])).
% 1.53/1.72 tff(5239,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(5240,plain,
% 1.53/1.72 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5239, 5210, 944, 222, 145, 357])).
% 1.53/1.72 tff(5241,plain,
% 1.53/1.72 (b(s(s(elem!1)), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[862, 5240, 851])).
% 1.53/1.72 tff(5242,plain,
% 1.53/1.72 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2505])).
% 1.53/1.72 tff(5243,plain,
% 1.53/1.72 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.72 inference(symmetry,[status(thm)],[5242])).
% 1.53/1.72 tff(5244,plain,
% 1.53/1.72 (b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[307, 5243])).
% 1.53/1.72 tff(5245,plain,
% 1.53/1.72 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2511, 5240, 2505])).
% 1.53/1.72 tff(5246,plain,
% 1.53/1.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[556, 5245, 1])).
% 1.53/1.72 tff(5247,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5248,plain,
% 1.53/1.72 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(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(elem!1))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5249,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5248])).
% 1.53/1.72 tff(5250,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5249, 5247])).
% 1.53/1.72 tff(5251,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5252,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5251, 5250])).
% 1.53/1.72 tff(5253,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5252, 271, 543, 739, 638, 2494])).
% 1.53/1.72 tff(5254,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(5255,plain,
% 1.53/1.72 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5254, 5246, 739, 5244])).
% 1.53/1.72 tff(5256,plain,
% 1.53/1.72 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[701, 5255, 3313])).
% 1.53/1.72 tff(5257,plain,
% 1.53/1.72 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2505])).
% 1.53/1.72 tff(5258,plain,
% 1.53/1.72 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[5257])).
% 1.53/1.72 tff(5259,plain,
% 1.53/1.72 (b(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1326, 5258])).
% 1.53/1.72 tff(5260,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(elem!1)), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5261,plain,
% 1.53/1.72 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(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(s(s(elem!1)), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5262,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(elem!1)), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5261])).
% 1.53/1.72 tff(5263,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(elem!1)), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[5262, 5260])).
% 1.53/1.72 tff(5264,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(5265,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[5264, 5263])).
% 1.53/1.72 tff(5266,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5265, 271, 543, 3407, 638, 2449])).
% 1.53/1.72 tff(5267,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(5268,plain,
% 1.53/1.72 (~b(s(s(elem!1)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5267, 5246, 5259, 5244])).
% 1.53/1.72 tff(5269,plain,
% 1.53/1.72 (r(s(s(elem!1)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2430, 5268])).
% 1.53/1.72 tff(5270,plain,
% 1.53/1.72 (~r(z, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4880, 5269, 412, 5256])).
% 1.53/1.72 tff(5271,plain,
% 1.53/1.72 (b(z, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2106, 5270])).
% 1.53/1.72 tff(5272,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5273,plain,
% 1.53/1.72 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(5274,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5273])).
% 1.53/1.72 tff(5275,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[5274, 5272])).
% 1.53/1.73 tff(5276,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5277,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5276, 5275])).
% 1.53/1.73 tff(5278,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5277, 271, 307, 1326, 5271, 5241])).
% 1.53/1.73 tff(5279,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5280,plain,
% 1.53/1.73 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5279, 5197, 1326, 412, 1, 851, 2505, 944, 307, 5189, 357, 5202, 261, 5201, 1935])).
% 1.53/1.73 tff(5281,plain,
% 1.53/1.73 (~b(s(elem!1), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5280, 5191])).
% 1.53/1.73 tff(5282,plain,
% 1.53/1.73 (r(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2243, 5281, 2564])).
% 1.53/1.73 tff(5283,plain,
% 1.53/1.73 (~b(elem!1, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5208, 271, 261, 5201, 1935])).
% 1.53/1.73 tff(5284,plain,
% 1.53/1.73 (r(elem!1, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1192, 5283, 5202])).
% 1.53/1.73 tff(5285,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5181, 5284, 5282, 5189, 1500])).
% 1.53/1.73 tff(5286,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5287,plain,
% 1.53/1.73 (~(s(s(s(elem!1))) = elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5286, 5187, 3500, 5165, 5153, 5110, 412, 5157, 5185, 5152, 4902, 5113, 5150, 5115, 5117, 4910])).
% 1.53/1.73 tff(5288,plain,
% 1.53/1.73 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[486, 5287, 479])).
% 1.53/1.73 tff(5289,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5290,plain,
% 1.53/1.73 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5291,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5290])).
% 1.53/1.73 tff(5292,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[5291, 5289])).
% 1.53/1.73 tff(5293,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5294,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5293, 5292])).
% 1.53/1.73 tff(5295,plain,
% 1.53/1.73 (~r(s(s(s(elem!1))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5294, 121, 5113, 5173, 5288])).
% 1.53/1.73 tff(5296,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[66, 21, 5295, 63])).
% 1.53/1.73 tff(5297,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5195, 121, 5113, 5117, 5159])).
% 1.53/1.73 tff(5298,plain,
% 1.53/1.73 (b(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2325, 5297])).
% 1.53/1.73 tff(5299,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~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))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5300,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~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))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5301,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~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)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5300, 5299])).
% 1.53/1.73 tff(5302,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5301, 121, 5173, 5288, 5159])).
% 1.53/1.73 tff(5303,plain,
% 1.53/1.73 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2069, 21, 4912, 5302])).
% 1.53/1.73 tff(5304,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5305,plain,
% 1.53/1.73 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5306,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5305])).
% 1.53/1.73 tff(5307,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[5306, 5304])).
% 1.53/1.73 tff(5308,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5309,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5308, 5307])).
% 1.53/1.73 tff(5310,plain,
% 1.53/1.73 (~r(s(z), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5309, 121, 5113, 5173, 5288])).
% 1.53/1.73 tff(5311,plain,
% 1.53/1.73 (b(s(z), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[760, 5310])).
% 1.53/1.73 tff(5312,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5313,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5314,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5313, 5312])).
% 1.53/1.73 tff(5315,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5314, 271, 5311, 5303, 5298, 5296])).
% 1.53/1.73 tff(5316,plain,(b(s(z), elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), z)) | b(s(s(s(z))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | b(z, s(z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5317,plain,
% 1.53/1.73 (b(s(z), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5316, 3506, 412, 479, 3499, 894, 377])).
% 1.53/1.73 tff(5318,plain,
% 1.53/1.73 (~b(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4096, 1326, 307, 2282, 909, 412, 260])).
% 1.53/1.73 tff(5319,plain,
% 1.53/1.73 (r(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[444, 5318, 348])).
% 1.53/1.73 tff(5320,plain,
% 1.53/1.73 (~r(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1300, 5319, 412, 909])).
% 1.53/1.73 tff(5321,plain,
% 1.53/1.73 (b(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[25, 5320])).
% 1.53/1.73 tff(5322,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4084, 271, 307, 1326, 260, 5321])).
% 1.53/1.73 tff(5323,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5324,plain,
% 1.53/1.73 (~b(z, elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5323, 4902, 5317, 412, 3505, 4904])).
% 1.53/1.73 tff(5325,plain,
% 1.53/1.73 (r(z, elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[355, 5324, 4903])).
% 1.53/1.73 tff(5326,plain,
% 1.53/1.73 (~(elem!1 = z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[333, 4903])).
% 1.53/1.73 tff(5327,plain,
% 1.53/1.73 (r(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[444, 439, 348])).
% 1.53/1.73 tff(5328,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3488, 121, 909, 412, 431, 411])).
% 1.53/1.73 tff(5329,plain,((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5330,plain,
% 1.53/1.73 (~r(s(elem!1), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5329, 5327, 412, 909])).
% 1.53/1.73 tff(5331,plain,
% 1.53/1.73 (b(s(elem!1), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[429, 5330, 2282])).
% 1.53/1.73 tff(5332,plain,
% 1.53/1.73 (~r(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1300, 5327, 412, 909])).
% 1.53/1.73 tff(5333,plain,
% 1.53/1.73 (b(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[25, 5332])).
% 1.53/1.73 tff(5334,plain,
% 1.53/1.73 (~b(elem!1, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1290, 5331, 307, 5333])).
% 1.53/1.73 tff(5335,plain,
% 1.53/1.73 (r(elem!1, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[299, 5334, 1278])).
% 1.53/1.73 tff(5336,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5337,plain,
% 1.53/1.73 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5338,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5337])).
% 1.53/1.73 tff(5339,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[5338, 5336])).
% 1.53/1.73 tff(5340,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5341,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5340, 5339])).
% 1.53/1.73 tff(5342,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5341, 121, 622, 378, 3456, 412])).
% 1.53/1.73 tff(5343,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5344,plain,
% 1.53/1.73 (~r(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5343, 5335, 378, 412])).
% 1.53/1.73 tff(5345,plain,
% 1.53/1.73 (b(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2243, 5344, 2564])).
% 1.53/1.73 tff(5346,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3247, 271, 307, 5345, 260, 5331])).
% 1.53/1.73 tff(5347,plain,(b(s(z), s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5348,plain,
% 1.53/1.73 (b(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5347, 4902, 5317, 3500, 5325, 412, 3505, 4904])).
% 1.53/1.73 tff(5349,plain,
% 1.53/1.73 (~b(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3435, 5348, 4902, 5317])).
% 1.53/1.73 tff(5350,plain,
% 1.53/1.73 (r(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2243, 5349, 3500])).
% 1.53/1.73 tff(5351,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5352,plain,
% 1.53/1.73 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5353,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5352])).
% 1.53/1.73 tff(5354,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[5353, 5351])).
% 1.53/1.73 tff(5355,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5356,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5355, 5354])).
% 1.53/1.73 tff(5357,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5356, 121, 622, 378, 1409, 412])).
% 1.53/1.73 tff(5358,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5359,plain,
% 1.53/1.73 (~r(elem!1, z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5358, 5350, 5325, 412])).
% 1.53/1.73 tff(5360,plain,
% 1.53/1.73 (b(elem!1, z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[284, 5359, 5326])).
% 1.53/1.73 tff(5361,plain,
% 1.53/1.73 (b(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5347, 307, 260, 2564, 378, 412, 909, 348])).
% 1.53/1.73 tff(5362,plain,
% 1.53/1.73 (~b(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3435, 5361, 307, 260])).
% 1.53/1.73 tff(5363,plain,
% 1.53/1.73 (r(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2243, 5362, 2564])).
% 1.53/1.73 tff(5364,plain,
% 1.53/1.73 (~r(elem!1, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5343, 5363, 378, 412])).
% 1.53/1.73 tff(5365,plain,
% 1.53/1.73 (b(elem!1, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[299, 243, 5364])).
% 1.53/1.73 tff(5366,plain,
% 1.53/1.73 (~b(s(elem!1), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[456, 5365, 307, 5361])).
% 1.53/1.73 tff(5367,plain,
% 1.53/1.73 (r(s(elem!1), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[429, 5366, 2282])).
% 1.53/1.73 tff(5368,plain,
% 1.53/1.73 (s(s(s(elem!1))) = s(elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4508, 4335, 378, 412, 909, 446, 307, 243, 4406, 5124, 4328, 411, 2564, 231])).
% 1.53/1.73 tff(5369,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[78, 5368, 5124])).
% 1.53/1.73 tff(5370,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (s(elem!1) = elem!1) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5371,plain,
% 1.53/1.73 (~(s(s(s(z))) = s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5370, 5367, 412, 909, 5361, 307, 378, 2564, 231, 479, 348, 3499])).
% 1.53/1.73 tff(5372,plain,
% 1.53/1.73 (r(s(s(s(z))), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1816, 5371, 3506])).
% 1.53/1.73 tff(5373,plain,
% 1.53/1.73 (~r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5155, 5372, 412, 909])).
% 1.53/1.73 tff(5374,plain,
% 1.53/1.73 (b(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1155, 5373])).
% 1.53/1.73 tff(5375,plain,
% 1.53/1.73 (~r(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3490, 243, 412, 909, 307, 348, 2282, 378])).
% 1.53/1.73 tff(5376,plain,
% 1.53/1.73 (b(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[105, 5375])).
% 1.53/1.73 tff(5377,plain,
% 1.53/1.73 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.53/1.73 inference(commutativity,[status(thm)],[])).
% 1.53/1.73 tff(5378,plain,
% 1.53/1.73 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[5377])).
% 1.53/1.73 tff(5379,plain,
% 1.53/1.73 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5378])).
% 1.53/1.73 tff(5380,plain,
% 1.53/1.73 (~(s(z) = s(s(s(s(s(z))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1677, 5379])).
% 1.53/1.73 tff(5381,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.73 tff(5382,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5383,plain,
% 1.53/1.73 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(5384,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5383])).
% 1.53/1.73 tff(5385,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[5384, 5382])).
% 1.53/1.73 tff(5386,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(5387,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5386, 5385])).
% 1.53/1.73 tff(5388,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5387, 271, 307, 260, 831, 5381])).
% 1.53/1.73 tff(5389,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(5390,plain,
% 1.53/1.73 (~b(s(z), s(s(s(s(s(z))))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5389, 831, 260, 307])).
% 1.53/1.73 tff(5391,plain,
% 1.53/1.73 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1754, 21, 5390])).
% 1.53/1.74 tff(5392,plain,
% 1.53/1.74 (r(s(z), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5391, 5380])).
% 1.53/1.74 tff(5393,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.53/1.74 tff(5394,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5395,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5396,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5395, 5394])).
% 1.53/1.74 tff(5397,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5396, 271, 307, 260, 831, 5393])).
% 1.53/1.74 tff(5398,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5399,plain,
% 1.53/1.74 (~b(s(s(s(s(s(z))))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5398, 831, 307, 260])).
% 1.53/1.74 tff(5400,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1682, 5399])).
% 1.53/1.74 tff(5401,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5402,plain,
% 1.53/1.74 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5403,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5402])).
% 1.53/1.74 tff(5404,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[5403, 5401])).
% 1.53/1.74 tff(5405,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5406,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5405, 5404])).
% 1.53/1.74 tff(5407,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5406, 121, 909, 1661, 5400, 5392])).
% 1.53/1.74 tff(5408,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5409,plain,
% 1.53/1.74 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5408, 1661, 909, 260, 307])).
% 1.53/1.74 tff(5410,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[840, 5409, 4978])).
% 1.53/1.74 tff(5411,plain,
% 1.53/1.74 (~r(s(z), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[420, 5367, 412, 378])).
% 1.53/1.74 tff(5412,plain,
% 1.53/1.74 (b(s(z), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[25, 5411])).
% 1.53/1.74 tff(5413,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5414,plain,
% 1.53/1.74 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5415,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5414])).
% 1.53/1.74 tff(5416,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[5415, 5413])).
% 1.53/1.74 tff(5417,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5418,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5417, 5416])).
% 1.53/1.74 tff(5419,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5418, 271, 1894, 1281, 261, 448])).
% 1.53/1.74 tff(5420,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5421,plain,
% 1.53/1.74 (~b(z, s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5420, 5412, 261, 5365])).
% 1.53/1.74 tff(5422,plain,
% 1.53/1.74 (r(z, s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2106, 5421])).
% 1.53/1.74 tff(5423,plain,
% 1.53/1.74 (~b(s(elem!1), s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4497, 5361, 307, 260])).
% 1.53/1.74 tff(5424,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5425,plain,
% 1.53/1.74 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5426,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5425])).
% 1.53/1.74 tff(5427,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[5426, 5424])).
% 1.53/1.74 tff(5428,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5429,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5428, 5427])).
% 1.53/1.74 tff(5430,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5429, 121, 627, 2088, 2117, 412])).
% 1.53/1.74 tff(5431,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5432,plain,
% 1.53/1.74 (~r(s(s(elem!1)), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5431, 627, 412, 2088])).
% 1.53/1.74 tff(5433,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2143, 5432])).
% 1.53/1.74 tff(5434,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5435,plain,
% 1.53/1.74 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5436,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5435])).
% 1.53/1.74 tff(5437,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[5436, 5434])).
% 1.53/1.74 tff(5438,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5439,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5438, 5437])).
% 1.53/1.74 tff(5440,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5439, 271, 260, 448, 542, 981])).
% 1.53/1.74 tff(5441,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5442,plain,
% 1.53/1.74 (~b(s(s(elem!1)), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5441, 5433, 448, 260])).
% 1.53/1.74 tff(5443,plain,
% 1.53/1.74 (r(s(s(elem!1)), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[862, 5442, 851])).
% 1.53/1.74 tff(5444,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5445,plain,
% 1.53/1.74 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5446,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5445])).
% 1.53/1.74 tff(5447,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[5446, 5444])).
% 1.53/1.74 tff(5448,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5449,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 1.53/1.74 tff(5450,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5449, 121, 627, 2088, 412, 5443])).
% 1.53/1.74 tff(5451,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5452,plain,
% 1.53/1.74 (~r(s(elem!1), s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5451, 198, 412, 448, 2088, 260])).
% 1.53/1.74 tff(5453,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[526, 2209, 5452, 3784])).
% 1.53/1.74 tff(5454,plain,((elem!1 = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | (~r(s(elem!1), z)) | (~b(elem!1, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5455,plain,
% 1.53/1.74 (elem!1 = s(s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5454, 5365, 412, 5423, 5422, 260])).
% 1.53/1.74 tff(5456,plain,
% 1.53/1.74 (s(s(elem!1)) = elem!1),
% 1.53/1.74 inference(symmetry,[status(thm)],[2470])).
% 1.53/1.74 tff(5457,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5456])).
% 1.53/1.74 tff(5458,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.53/1.74 inference(symmetry,[status(thm)],[5457])).
% 1.53/1.74 tff(5459,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3061, 5458])).
% 1.53/1.74 tff(5460,assumption,(~r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 1.53/1.74 tff(5461,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5460, 5459])).
% 1.53/1.74 tff(5462,plain,(r(s(s(s(s(s(z))))), s(s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5463,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5462, 5455, 5410])).
% 1.53/1.74 tff(5464,plain,
% 1.53/1.74 (~(elem!1 = s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4946, 5160])).
% 1.53/1.74 tff(5465,plain,
% 1.53/1.74 (~b(z, elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5323, 307, 260, 412, 909, 348])).
% 1.53/1.74 tff(5466,plain,
% 1.53/1.74 (~(s(elem!1) = s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2035, 5371])).
% 1.53/1.74 tff(5467,plain,
% 1.53/1.74 (~b(z, s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4220, 221, 1281, 3871, 199])).
% 1.53/1.74 tff(5468,plain,
% 1.53/1.74 (r(z, s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1214, 5467])).
% 1.53/1.74 tff(5469,plain,
% 1.53/1.74 (b(s(s(s(z))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[255, 221, 907])).
% 1.53/1.74 tff(5470,plain,
% 1.53/1.74 (~b(s(elem!1), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3879, 5469, 446, 3871])).
% 1.53/1.74 tff(5471,plain,
% 1.53/1.74 (r(s(elem!1), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2044, 5470, 2037])).
% 1.53/1.74 tff(5472,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3865, 5471, 5468, 1500, 412])).
% 1.53/1.74 tff(5473,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | b(z, elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5474,plain,
% 1.53/1.74 (r(s(s(s(z))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5473, 5372, 412, 5466, 5361, 5376, 5412, 5465, 4946])).
% 1.53/1.74 tff(5475,plain,
% 1.53/1.74 (~r(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5181, 5474, 5363, 5372])).
% 1.53/1.74 tff(5476,plain,
% 1.53/1.74 (b(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1192, 5475, 5464])).
% 1.53/1.74 tff(5477,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5456])).
% 1.53/1.74 tff(5478,plain,
% 1.53/1.74 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[5477])).
% 1.53/1.74 tff(5479,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1195, 5478])).
% 1.53/1.74 tff(5480,assumption,(~b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.53/1.74 tff(5481,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5480, 5479])).
% 1.53/1.74 tff(5482,plain,(b(s(s(elem!1)), s(s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5483,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5482, 5455, 5476])).
% 1.53/1.74 tff(5484,plain,
% 1.53/1.74 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5455])).
% 1.53/1.74 tff(5485,plain,
% 1.53/1.74 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5001, 4978])).
% 1.53/1.74 tff(5486,plain,
% 1.53/1.74 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5017, 5410, 1661, 378])).
% 1.53/1.74 tff(5487,plain,
% 1.53/1.74 (b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1847, 5486, 5485])).
% 1.53/1.74 tff(5488,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5487, 5484])).
% 1.53/1.74 tff(5489,plain,
% 1.53/1.74 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5455])).
% 1.53/1.74 tff(5490,plain,
% 1.53/1.74 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5489])).
% 1.53/1.74 tff(5491,plain,
% 1.53/1.74 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5372, 5490])).
% 1.53/1.74 tff(5492,plain,
% 1.53/1.74 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5489])).
% 1.53/1.74 tff(5493,plain,
% 1.53/1.74 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5455])).
% 1.53/1.74 tff(5494,plain,
% 1.53/1.74 (r(s(elem!1), s(s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5363, 5493])).
% 1.53/1.74 tff(5495,plain,
% 1.53/1.74 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5494, 5492])).
% 1.53/1.74 tff(5496,plain,
% 1.53/1.74 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5489])).
% 1.53/1.74 tff(5497,plain,
% 1.53/1.74 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5496])).
% 1.53/1.74 tff(5498,plain,
% 1.53/1.74 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3506, 5497])).
% 1.53/1.74 tff(5499,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.53/1.74 tff(5500,plain,
% 1.53/1.74 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1731, 1519, 1722, 1721])).
% 1.53/1.74 tff(5501,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1733, 5500])).
% 1.53/1.74 tff(5502,plain,
% 1.53/1.74 (s(s(s(elem!1))) = s(elem!1)),
% 1.53/1.74 inference(symmetry,[status(thm)],[2471])).
% 1.53/1.74 tff(5503,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5502])).
% 1.53/1.74 tff(5504,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[5503])).
% 1.53/1.74 tff(5505,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4266, 5504])).
% 1.53/1.74 tff(5506,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(5507,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(5508,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[5507, 5506])).
% 1.53/1.74 tff(5509,plain,
% 1.53/1.74 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5508, 121, 573, 1736, 5499])).
% 1.53/1.74 tff(5510,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5509, 5505])).
% 1.53/1.74 tff(5511,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(5512,plain,
% 1.53/1.74 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5511, 5501, 573, 2470, 5499])).
% 1.53/1.74 tff(5513,plain,
% 1.53/1.74 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4138, 5512, 3499])).
% 1.53/1.74 tff(5514,plain,
% 1.53/1.74 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[5513, 2471])).
% 1.53/1.74 tff(5515,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5514])).
% 1.53/1.74 tff(5516,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[5515])).
% 1.53/1.75 tff(5517,plain,
% 1.53/1.75 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5516])).
% 1.53/1.75 tff(5518,plain,
% 1.53/1.75 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2066, 5517])).
% 1.53/1.75 tff(5519,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1519, 5518])).
% 1.53/1.75 tff(5520,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(5521,plain,
% 1.53/1.75 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5520, 5498, 5455, 3499, 5495, 5491, 5488, 5483])).
% 1.53/1.75 tff(5522,plain,
% 1.53/1.75 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1494, 5521])).
% 1.53/1.75 tff(5523,assumption,(r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 1.53/1.75 tff(5524,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5525,plain,
% 1.53/1.75 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5526,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5525])).
% 1.53/1.75 tff(5527,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[5526, 5524])).
% 1.53/1.75 tff(5528,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(5529,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5528, 5527])).
% 1.53/1.75 tff(5530,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5529, 121, 1661, 1477, 1140, 5523])).
% 1.53/1.75 tff(5531,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(5532,plain,
% 1.53/1.75 (~r(z, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5531, 5522, 5463, 1661])).
% 1.53/1.75 tff(5533,plain,
% 1.53/1.75 (b(z, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1214, 5532])).
% 1.53/1.75 tff(5534,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5535,plain,
% 1.53/1.75 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5536,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5535])).
% 1.53/1.75 tff(5537,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[5536, 5534])).
% 1.53/1.75 tff(5538,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(5539,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5538, 5537])).
% 1.53/1.75 tff(5540,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5539, 271, 5412, 5533, 5376, 5374])).
% 1.53/1.75 tff(5541,plain,((s(z) = elem!1) | (~r(z, s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(z))), s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(5542,plain,
% 1.53/1.75 (s(z) = elem!1),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5541, 4764, 3499, 3506, 412, 5317, 3505, 5360, 4902, 5325, 3500, 479, 4904])).
% 1.53/1.75 tff(5543,plain,
% 1.53/1.75 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5542])).
% 1.53/1.75 tff(5544,plain,
% 1.53/1.75 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.53/1.75 inference(symmetry,[status(thm)],[5543])).
% 1.53/1.75 tff(5545,plain,
% 1.53/1.75 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5544])).
% 1.53/1.75 tff(5546,plain,
% 1.53/1.75 (~b(s(z), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[192, 5545])).
% 1.53/1.75 tff(5547,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5317, 5546])).
% 1.53/1.75 tff(5548,plain,(b(s(s(s(z))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | b(z, s(z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(5549,plain,
% 1.53/1.75 (b(s(s(s(z))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5548, 479, 3501, 3499, 894, 377])).
% 1.53/1.75 tff(5550,plain,
% 1.53/1.75 (~r(s(z), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3673, 378, 379, 909])).
% 1.53/1.75 tff(5551,plain,
% 1.53/1.75 (s(z) = elem!1),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[236, 5550, 1242])).
% 1.53/1.75 tff(5552,plain,
% 1.53/1.75 (s(s(z)) = s(elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5551])).
% 1.53/1.75 tff(5553,plain,
% 1.53/1.75 (s(s(s(z))) = s(s(elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5552])).
% 1.53/1.75 tff(5554,plain,
% 1.53/1.75 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5553])).
% 1.53/1.75 tff(5555,plain,
% 1.53/1.75 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5554])).
% 1.53/1.75 tff(5556,plain,
% 1.53/1.75 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[5555])).
% 1.53/1.75 tff(5557,plain,
% 1.53/1.75 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5556])).
% 1.53/1.75 tff(5558,plain,
% 1.53/1.75 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[5557])).
% 1.53/1.75 tff(5559,plain,
% 1.53/1.75 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3049, 5551])).
% 1.53/1.75 tff(5560,plain,
% 1.53/1.75 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5001, 5559])).
% 1.53/1.75 tff(5561,plain,
% 1.53/1.75 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5556])).
% 1.53/1.75 tff(5562,plain,
% 1.53/1.75 ((~r(elem!1, s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5561])).
% 1.53/1.75 tff(5563,plain,
% 1.53/1.75 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5555])).
% 1.53/1.75 tff(5564,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5563])).
% 1.53/1.75 tff(5565,plain,
% 1.53/1.75 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3499, 5564])).
% 1.53/1.75 tff(5566,plain,
% 1.53/1.75 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5556])).
% 1.53/1.75 tff(5567,plain,
% 1.53/1.75 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.75 inference(symmetry,[status(thm)],[5566])).
% 1.53/1.75 tff(5568,plain,
% 1.53/1.75 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5567])).
% 1.53/1.75 tff(5569,plain,
% 1.53/1.75 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5552])).
% 1.53/1.75 tff(5570,plain,
% 1.53/1.75 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5569])).
% 1.53/1.75 tff(5571,plain,
% 1.53/1.75 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[877, 5570])).
% 1.53/1.75 tff(5572,plain,
% 1.53/1.75 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5571, 5568])).
% 1.53/1.75 tff(5573,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3112, 21, 5572, 5565])).
% 1.53/1.75 tff(5574,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5575,plain,
% 1.53/1.75 (((~r(s(elem!1), z)) | (~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(elem!1), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5576,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5575])).
% 1.53/1.75 tff(5577,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[5576, 5574])).
% 1.53/1.75 tff(5578,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(5579,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5578, 5577])).
% 1.53/1.75 tff(5580,plain,
% 1.53/1.75 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5579, 121, 379, 412, 5573])).
% 1.53/1.75 tff(5581,plain,
% 1.53/1.75 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5580, 5562])).
% 1.53/1.75 tff(5582,plain,
% 1.53/1.75 (b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1847, 5581, 5560])).
% 1.53/1.75 tff(5583,plain,
% 1.53/1.75 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5555])).
% 1.53/1.75 tff(5584,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5556])).
% 1.53/1.75 tff(5585,plain,
% 1.53/1.75 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5584])).
% 1.53/1.75 tff(5586,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5587,plain,
% 1.53/1.75 (((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5588,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5587])).
% 1.53/1.75 tff(5589,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[5588, 5586])).
% 1.53/1.75 tff(5590,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(5591,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5590, 5589])).
% 1.53/1.75 tff(5592,plain,
% 1.53/1.75 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5591, 121, 379, 412, 5573])).
% 1.53/1.75 tff(5593,plain,
% 1.53/1.75 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5592, 5585])).
% 1.53/1.75 tff(5594,plain,
% 1.53/1.75 (b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[840, 5593, 5559])).
% 1.53/1.75 tff(5595,plain,
% 1.53/1.75 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5594, 5583])).
% 1.53/1.75 tff(5596,plain,
% 1.53/1.75 ((s(z) = z) <=> (elem!1 = z)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5551])).
% 1.53/1.75 tff(5597,plain,
% 1.53/1.75 ((s(z) = z) <=> (z = elem!1)),
% 1.53/1.75 inference(transitivity,[status(thm)],[5596, 360])).
% 1.53/1.75 tff(5598,plain,
% 1.53/1.75 ((s(z) = z) <=> (elem!1 = z)),
% 1.53/1.75 inference(transitivity,[status(thm)],[5597, 361])).
% 1.53/1.75 tff(5599,plain,
% 1.53/1.75 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5598])).
% 1.53/1.75 tff(5600,plain,
% 1.53/1.75 (~(elem!1 = z)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[11, 5599])).
% 1.53/1.75 tff(5601,plain,
% 1.53/1.75 (b(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[284, 5600, 3712])).
% 1.53/1.75 tff(5602,plain,
% 1.53/1.75 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1849, 4996])).
% 1.53/1.75 tff(5603,plain,
% 1.53/1.75 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3057])).
% 1.53/1.75 tff(5604,plain,
% 1.53/1.75 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[5603])).
% 1.53/1.75 tff(5605,plain,
% 1.53/1.75 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1639, 5604])).
% 1.53/1.75 tff(5606,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.53/1.75 tff(5607,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5608,plain,
% 1.53/1.75 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5609,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5608])).
% 1.53/1.75 tff(5610,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[5609, 5607])).
% 1.53/1.75 tff(5611,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(5612,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5611, 5610])).
% 1.53/1.75 tff(5613,plain,
% 1.53/1.75 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5612, 271, 261, 5606])).
% 1.53/1.75 tff(5614,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5613, 5605, 5602])).
% 1.53/1.75 tff(5615,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(5616,plain,
% 1.53/1.75 (~b(z, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5615, 5601, 5595, 5551, 5582])).
% 1.53/1.75 tff(5617,plain,
% 1.53/1.75 (r(z, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1658, 5616])).
% 1.53/1.75 tff(5618,plain,
% 1.53/1.75 (r(z, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5617, 5558])).
% 1.53/1.75 tff(5619,plain,
% 1.53/1.75 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.75 inference(commutativity,[status(thm)],[])).
% 1.53/1.75 tff(5620,plain,
% 1.53/1.75 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[5619])).
% 1.53/1.75 tff(5621,plain,
% 1.53/1.75 ((~(s(s(s(s(elem!1)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5620])).
% 1.53/1.75 tff(5622,plain,
% 1.53/1.75 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5572, 5621])).
% 1.53/1.75 tff(5623,plain,
% 1.53/1.75 (~r(s(elem!1), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3683, 378, 379, 412])).
% 1.53/1.75 tff(5624,plain,
% 1.53/1.75 (b(s(elem!1), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2243, 5623, 2564])).
% 1.53/1.75 tff(5625,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5626,plain,
% 1.53/1.75 (((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(5627,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5626])).
% 1.53/1.75 tff(5628,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[5627, 5625])).
% 1.53/1.75 tff(5629,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(5630,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5629, 5628])).
% 1.53/1.75 tff(5631,plain,
% 1.53/1.75 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5630, 271, 5624, 5601, 5595])).
% 1.53/1.75 tff(5632,plain,
% 1.53/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5633,plain,
% 1.53/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5634,plain,
% 1.53/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 1.53/1.76 tff(5635,plain,
% 1.53/1.76 ((s(elem!1) = s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5634, 21, 5631])).
% 1.53/1.76 tff(5636,plain,
% 1.53/1.76 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5635, 5622])).
% 1.53/1.76 tff(5637,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5638,plain,
% 1.53/1.76 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5639,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5638])).
% 1.53/1.76 tff(5640,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5639, 5637])).
% 1.53/1.76 tff(5641,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5642,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 1.53/1.76 tff(5643,plain,
% 1.53/1.76 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5642, 121, 412, 5573, 5636])).
% 1.53/1.76 tff(5644,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5643, 5618])).
% 1.53/1.76 tff(5645,plain,((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(elem!1) = elem!1) | b(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(5646,plain,
% 1.53/1.76 (~r(z, elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5645, 1242, 379, 3499, 2564, 412, 3505])).
% 1.53/1.76 tff(5647,plain,
% 1.53/1.76 (~(s(z) = elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1402, 5646, 894])).
% 1.53/1.76 tff(5648,plain,
% 1.53/1.76 (~(elem!1 = s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[242, 5647])).
% 1.53/1.76 tff(5649,plain,
% 1.53/1.76 (r(s(z), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[236, 5647, 1242])).
% 1.53/1.76 tff(5650,plain,
% 1.53/1.76 (~(s(s(z)) = s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[960, 5647])).
% 1.53/1.76 tff(5651,plain,
% 1.53/1.76 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[953, 5650])).
% 1.53/1.76 tff(5652,plain,
% 1.53/1.76 (b(s(elem!1), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[429, 351, 3793])).
% 1.53/1.76 tff(5653,plain,
% 1.53/1.76 (b(z, elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[355, 331, 1391])).
% 1.53/1.76 tff(5654,plain,
% 1.53/1.76 (b(elem!1, z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[284, 358, 3712])).
% 1.53/1.76 tff(5655,plain,
% 1.53/1.76 (b(s(z), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[25, 1301])).
% 1.53/1.76 tff(5656,plain,
% 1.53/1.76 (~r(elem!1, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3709, 1295, 379, 412])).
% 1.53/1.76 tff(5657,plain,
% 1.53/1.76 (b(elem!1, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[299, 5656, 258])).
% 1.53/1.76 tff(5658,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4775, 5657, 5655, 1326, 5654])).
% 1.53/1.76 tff(5659,plain,((z = elem!1) | (~b(z, elem!1)) | (elem!1 = s(z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(5660,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5659, 5653, 331, 258, 379, 412, 909, 439])).
% 1.53/1.76 tff(5661,plain,((z = elem!1) | (elem!1 = s(z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | b(s(z), s(elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(5662,plain,
% 1.53/1.76 (b(s(z), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5661, 331, 379, 412, 909, 258, 1391])).
% 1.53/1.76 tff(5663,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5664,plain,
% 1.53/1.76 (((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5665,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5664])).
% 1.53/1.76 tff(5666,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5665, 5663])).
% 1.53/1.76 tff(5667,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5668,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5667, 5666])).
% 1.53/1.76 tff(5669,plain,
% 1.53/1.76 (~b(s(z), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5668, 271, 1422, 447, 446])).
% 1.53/1.76 tff(5670,plain,
% 1.53/1.76 (r(s(z), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[105, 5669])).
% 1.53/1.76 tff(5671,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5672,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5673,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5672, 5671])).
% 1.53/1.76 tff(5674,plain,
% 1.53/1.76 (~b(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5673, 271, 1422, 447, 446])).
% 1.53/1.76 tff(5675,plain,
% 1.53/1.76 (r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2325, 5674])).
% 1.53/1.76 tff(5676,plain,
% 1.53/1.76 (~(elem!1 = s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2065, 3853])).
% 1.53/1.76 tff(5677,plain,
% 1.53/1.76 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2505])).
% 1.53/1.76 tff(5678,plain,
% 1.53/1.76 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5677])).
% 1.53/1.76 tff(5679,plain,
% 1.53/1.76 (~r(z, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2335, 5670, 909, 5675])).
% 1.53/1.76 tff(5680,plain,
% 1.53/1.76 (b(z, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1214, 5679])).
% 1.53/1.76 tff(5681,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5682,plain,
% 1.53/1.76 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5683,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5682])).
% 1.53/1.76 tff(5684,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5683, 5681])).
% 1.53/1.76 tff(5685,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5686,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5685, 5684])).
% 1.53/1.76 tff(5687,plain,
% 1.53/1.76 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5686, 271])).
% 1.53/1.76 tff(5688,plain,
% 1.53/1.76 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5687, 5680, 1422, 5259])).
% 1.53/1.76 tff(5689,plain,
% 1.53/1.76 (~b(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5688, 5678])).
% 1.53/1.76 tff(5690,plain,
% 1.53/1.76 (r(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1192, 5689, 5676])).
% 1.53/1.76 tff(5691,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5692,plain,
% 1.53/1.76 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5693,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5692])).
% 1.53/1.76 tff(5694,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5693, 5691])).
% 1.53/1.76 tff(5695,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5696,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 1.53/1.76 tff(5697,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5696, 121, 357, 5690, 5675, 5670])).
% 1.53/1.76 tff(5698,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(5699,plain,
% 1.53/1.76 (~(s(s(s(elem!1))) = elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5698, 5652, 1422, 909, 357, 5662, 2064, 5653])).
% 1.53/1.76 tff(5700,plain,
% 1.53/1.76 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[486, 5699, 479])).
% 1.53/1.76 tff(5701,plain,
% 1.53/1.76 (s(s(s(elem!1))) = s(elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3823, 5700, 412, 379, 357, 5652])).
% 1.53/1.76 tff(5702,plain,
% 1.53/1.76 (elem!1 = s(s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[78, 5701])).
% 1.53/1.76 tff(5703,plain,
% 1.53/1.76 (s(s(elem!1)) = elem!1),
% 1.53/1.76 inference(symmetry,[status(thm)],[5702])).
% 1.53/1.76 tff(5704,plain,
% 1.53/1.76 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5703])).
% 1.53/1.76 tff(5705,plain,
% 1.53/1.76 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.76 inference(symmetry,[status(thm)],[5704])).
% 1.53/1.76 tff(5706,plain,
% 1.53/1.76 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5703])).
% 1.53/1.76 tff(5707,plain,
% 1.53/1.76 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5706, 159])).
% 1.53/1.76 tff(5708,plain,
% 1.53/1.76 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5707])).
% 1.53/1.76 tff(5709,plain,
% 1.53/1.76 (~(elem!1 = s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[944, 5708])).
% 1.53/1.76 tff(5710,plain,
% 1.53/1.76 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5702])).
% 1.53/1.76 tff(5711,plain,
% 1.53/1.76 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5710])).
% 1.53/1.76 tff(5712,plain,
% 1.53/1.76 (b(s(s(s(elem!1))), s(z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5652, 5711])).
% 1.53/1.76 tff(5713,plain,
% 1.53/1.76 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5710])).
% 1.53/1.76 tff(5714,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1422, 5713])).
% 1.53/1.76 tff(5715,plain,
% 1.53/1.76 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5710])).
% 1.53/1.76 tff(5716,plain,
% 1.53/1.76 (b(s(z), s(s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5662, 5715])).
% 1.53/1.76 tff(5717,plain,
% 1.53/1.76 (~b(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2079, 271, 5716, 5714, 5712])).
% 1.53/1.76 tff(5718,plain,
% 1.53/1.76 (r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2325, 5717])).
% 1.53/1.76 tff(5719,plain,
% 1.53/1.76 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5702])).
% 1.53/1.76 tff(5720,plain,
% 1.53/1.76 (r(s(z), s(s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[357, 5719])).
% 1.53/1.76 tff(5721,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5722,plain,
% 1.53/1.76 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5723,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5722])).
% 1.53/1.76 tff(5724,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5723, 5721])).
% 1.53/1.76 tff(5725,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5726,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5725, 5724])).
% 1.53/1.76 tff(5727,plain,
% 1.53/1.76 (~r(s(s(s(z))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5726, 121, 5720, 909, 5718])).
% 1.53/1.76 tff(5728,plain,
% 1.53/1.76 (b(s(s(s(z))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1155, 5727])).
% 1.53/1.76 tff(5729,plain,
% 1.53/1.76 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5702])).
% 1.53/1.76 tff(5730,plain,
% 1.53/1.76 (b(s(s(elem!1)), z)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5654, 5729])).
% 1.53/1.76 tff(5731,plain,
% 1.53/1.76 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5702])).
% 1.53/1.76 tff(5732,plain,
% 1.53/1.76 (b(z, s(s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5653, 5731])).
% 1.53/1.76 tff(5733,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5734,plain,
% 1.53/1.76 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5735,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5734])).
% 1.53/1.76 tff(5736,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5735, 5733])).
% 1.53/1.76 tff(5737,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(5738,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5737, 5736])).
% 1.53/1.76 tff(5739,plain,
% 1.53/1.76 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5738, 271, 5732, 5730, 5728])).
% 1.53/1.76 tff(5740,plain,
% 1.53/1.76 (~b(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5482, 5739, 5702])).
% 1.53/1.76 tff(5741,plain,
% 1.53/1.76 (r(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1192, 5740, 5709])).
% 1.53/1.76 tff(5742,plain,
% 1.53/1.76 (r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[5741, 5705])).
% 1.53/1.76 tff(5743,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(5744,plain,
% 1.53/1.76 (((~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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5745,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5744])).
% 1.53/1.77 tff(5746,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5745, 5743])).
% 1.53/1.77 tff(5747,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5748,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5747, 5746])).
% 1.53/1.77 tff(5749,plain,
% 1.53/1.77 (~b(s(z), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5748, 271, 5716, 5714, 5712])).
% 1.53/1.77 tff(5750,plain,
% 1.53/1.77 (r(s(z), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[105, 5749])).
% 1.53/1.77 tff(5751,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5752,plain,
% 1.53/1.77 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5753,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5752])).
% 1.53/1.77 tff(5754,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5753, 5751])).
% 1.53/1.77 tff(5755,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5756,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5755, 5754])).
% 1.53/1.77 tff(5757,plain,
% 1.53/1.77 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5756, 121, 5720, 5718, 5750])).
% 1.53/1.77 tff(5758,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5757, 5742])).
% 1.53/1.77 tff(5759,plain,((z = elem!1) | (~r(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(5760,plain,
% 1.53/1.77 (z = elem!1),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5759, 5651, 1422, 3505, 5649, 412, 379, 479, 5648, 5646])).
% 1.53/1.77 tff(5761,plain,
% 1.53/1.77 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5760])).
% 1.53/1.77 tff(5762,plain,
% 1.53/1.77 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5761, 2211])).
% 1.53/1.77 tff(5763,plain,
% 1.53/1.77 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5762])).
% 1.53/1.77 tff(5764,plain,
% 1.53/1.77 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[59, 5763])).
% 1.53/1.77 tff(5765,plain,
% 1.53/1.77 (s(z) = s(elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5760])).
% 1.53/1.77 tff(5766,plain,
% 1.53/1.77 (b(s(z), s(elem!1)) <=> b(s(elem!1), s(elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5765])).
% 1.53/1.77 tff(5767,plain,
% 1.53/1.77 (b(s(elem!1), s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5766])).
% 1.53/1.77 tff(5768,plain,
% 1.53/1.77 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(z), s(elem!1)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5767])).
% 1.53/1.77 tff(5769,plain,
% 1.53/1.77 ((~![X: $i] : (~b(X, X))) | (~b(s(elem!1), s(elem!1)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5770,plain,
% 1.53/1.77 (~b(s(elem!1), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5769, 190])).
% 1.53/1.77 tff(5771,plain,
% 1.53/1.77 (~b(s(z), s(elem!1))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5770, 5768])).
% 1.53/1.77 tff(5772,plain,
% 1.53/1.77 (~(s(z) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1402, 1391, 894])).
% 1.53/1.77 tff(5773,plain,
% 1.53/1.77 (~(elem!1 = s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[242, 5772])).
% 1.53/1.77 tff(5774,plain,
% 1.53/1.77 (z = elem!1),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5661, 5773, 379, 412, 3505, 439, 1391])).
% 1.53/1.77 tff(5775,plain,
% 1.53/1.77 (s(z) = s(elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5774])).
% 1.53/1.77 tff(5776,plain,
% 1.53/1.77 (s(s(z)) = s(s(elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5775])).
% 1.53/1.77 tff(5777,plain,
% 1.53/1.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5776])).
% 1.53/1.77 tff(5778,plain,
% 1.53/1.77 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5777])).
% 1.53/1.77 tff(5779,plain,
% 1.53/1.77 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5778])).
% 1.53/1.77 tff(5780,plain,
% 1.53/1.77 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5779])).
% 1.53/1.77 tff(5781,plain,
% 1.53/1.77 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5780])).
% 1.53/1.77 tff(5782,plain,
% 1.53/1.77 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5781])).
% 1.53/1.77 tff(5783,plain,
% 1.53/1.77 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5774])).
% 1.53/1.77 tff(5784,plain,
% 1.53/1.77 (z = elem!1),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[355, 199, 1391])).
% 1.53/1.77 tff(5785,plain,
% 1.53/1.77 (s(z) = s(elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5784])).
% 1.53/1.77 tff(5786,plain,
% 1.53/1.77 (s(s(z)) = s(s(elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5785])).
% 1.53/1.77 tff(5787,plain,
% 1.53/1.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5786])).
% 1.53/1.77 tff(5788,plain,
% 1.53/1.77 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5787])).
% 1.53/1.77 tff(5789,plain,
% 1.53/1.77 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5788])).
% 1.53/1.77 tff(5790,plain,
% 1.53/1.77 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5789])).
% 1.53/1.77 tff(5791,plain,
% 1.53/1.77 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5788])).
% 1.53/1.77 tff(5792,plain,
% 1.53/1.77 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5791, 5790])).
% 1.53/1.77 tff(5793,plain,
% 1.53/1.77 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5792])).
% 1.53/1.77 tff(5794,plain,
% 1.53/1.77 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5784])).
% 1.53/1.77 tff(5795,plain,
% 1.53/1.77 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5794])).
% 1.53/1.77 tff(5796,plain,
% 1.53/1.77 (~(s(s(s(elem!1))) = elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[30, 5795])).
% 1.53/1.77 tff(5797,plain,
% 1.53/1.77 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2837, 5796])).
% 1.53/1.77 tff(5798,plain,
% 1.53/1.77 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5784])).
% 1.53/1.77 tff(5799,plain,
% 1.53/1.77 (r(s(elem!1), elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[412, 5798])).
% 1.53/1.77 tff(5800,plain,
% 1.53/1.77 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5787])).
% 1.53/1.77 tff(5801,plain,
% 1.53/1.77 (b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[1422, 5800])).
% 1.53/1.77 tff(5802,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5787])).
% 1.53/1.77 tff(5803,plain,
% 1.53/1.77 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5785])).
% 1.53/1.77 tff(5804,plain,
% 1.53/1.77 (r(elem!1, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3700, 199, 412, 2564, 379, 258, 317, 909])).
% 1.53/1.77 tff(5805,plain,
% 1.53/1.77 (r(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[490, 5784, 479])).
% 1.53/1.77 tff(5806,plain,
% 1.53/1.77 (r(s(s(s(z))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[475, 5784, 5805])).
% 1.53/1.77 tff(5807,plain,
% 1.53/1.77 (~r(s(z), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4112, 5806, 5804, 357])).
% 1.53/1.77 tff(5808,plain,
% 1.53/1.77 (b(s(z), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[105, 5807])).
% 1.53/1.77 tff(5809,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5808, 5803])).
% 1.53/1.77 tff(5810,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5809, 5802])).
% 1.53/1.77 tff(5811,plain,
% 1.53/1.77 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[149, 5806, 5784])).
% 1.53/1.77 tff(5812,plain,
% 1.53/1.77 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1576, 2208])).
% 1.53/1.77 tff(5813,plain,
% 1.53/1.77 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5785])).
% 1.53/1.77 tff(5814,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5813])).
% 1.53/1.77 tff(5815,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5802, 5814])).
% 1.53/1.77 tff(5816,plain,
% 1.53/1.77 (b(s(z), s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5809, 5815])).
% 1.53/1.77 tff(5817,plain,
% 1.53/1.77 (~r(s(z), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1633, 357, 379, 1624])).
% 1.53/1.77 tff(5818,plain,
% 1.53/1.77 (b(s(z), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2167, 5817])).
% 1.53/1.77 tff(5819,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(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))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5820,plain,
% 1.53/1.77 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(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))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5821,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5820])).
% 1.53/1.77 tff(5822,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5821, 5819])).
% 1.53/1.77 tff(5823,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5824,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 1.53/1.77 tff(5825,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5824, 271, 543, 5818, 3807, 638])).
% 1.53/1.77 tff(5826,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(5827,plain,
% 1.53/1.77 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5826, 543, 379, 357, 139, 638])).
% 1.53/1.77 tff(5828,plain,
% 1.53/1.77 (b(s(s(elem!1)), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[862, 5827, 198])).
% 1.53/1.77 tff(5829,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.53/1.77 tff(5830,plain,
% 1.53/1.77 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5829])).
% 1.53/1.77 tff(5831,plain,
% 1.53/1.77 (s(s(s(elem!1))) = s(elem!1)),
% 1.53/1.77 inference(transitivity,[status(thm)],[2834, 5830, 604])).
% 1.53/1.77 tff(5832,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[82, 5831])).
% 1.53/1.77 tff(5833,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(5834,plain,
% 1.53/1.77 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5833, 79])).
% 1.53/1.77 tff(5835,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5836,plain,
% 1.53/1.77 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5837,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5836])).
% 1.53/1.77 tff(5838,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5837, 5835])).
% 1.53/1.77 tff(5839,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5840,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5839, 5838])).
% 1.53/1.77 tff(5841,plain,
% 1.53/1.77 (~b(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5840, 271, 543, 750, 638])).
% 1.53/1.77 tff(5842,plain,
% 1.53/1.77 (r(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 5841])).
% 1.53/1.77 tff(5843,plain,
% 1.53/1.77 (~b(s(z), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5824, 271, 543, 750, 638])).
% 1.53/1.77 tff(5844,plain,
% 1.53/1.77 (r(s(z), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2167, 5843])).
% 1.53/1.77 tff(5845,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5846,plain,
% 1.53/1.77 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5847,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5846])).
% 1.53/1.77 tff(5848,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[5847, 5845])).
% 1.53/1.77 tff(5849,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5850,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5849, 5848])).
% 1.53/1.77 tff(5851,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5850, 121, 5844, 624, 5842, 3456])).
% 1.53/1.77 tff(5852,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(5853,plain,
% 1.53/1.77 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5852, 543, 3456, 750, 638])).
% 1.53/1.77 tff(5854,plain,
% 1.53/1.77 (b(elem!1, s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[599, 5853, 68])).
% 1.53/1.77 tff(5855,plain,
% 1.53/1.77 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5254, 543, 739, 638])).
% 1.53/1.77 tff(5856,plain,
% 1.53/1.77 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[701, 5855, 2210])).
% 1.53/1.77 tff(5857,plain,
% 1.53/1.77 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1578])).
% 1.53/1.77 tff(5858,plain,
% 1.53/1.77 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[5857])).
% 1.53/1.77 tff(5859,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1578, 5857])).
% 1.53/1.77 tff(5860,plain,
% 1.53/1.77 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5859])).
% 1.53/1.77 tff(5861,plain,
% 1.53/1.77 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2837, 481])).
% 1.53/1.77 tff(5862,plain,
% 1.53/1.77 ((~b(z, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1179])).
% 1.53/1.77 tff(5863,plain,
% 1.53/1.77 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[107])).
% 1.53/1.77 tff(5864,plain,
% 1.53/1.77 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.53/1.77 inference(symmetry,[status(thm)],[5863])).
% 1.53/1.77 tff(5865,plain,
% 1.53/1.77 (b(s(s(elem!1)), z)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[542, 5864])).
% 1.53/1.77 tff(5866,plain,
% 1.53/1.77 (~b(z, s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5267, 5865, 543, 638])).
% 1.53/1.77 tff(5867,plain,
% 1.53/1.77 (~b(elem!1, s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5866, 5862])).
% 1.53/1.77 tff(5868,plain,
% 1.53/1.77 (r(elem!1, s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[660, 21, 656, 5867])).
% 1.53/1.77 tff(5869,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.53/1.77 tff(5870,plain,
% 1.53/1.77 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3112, 21, 3109, 1564])).
% 1.53/1.77 tff(5871,plain,
% 1.53/1.77 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[804])).
% 1.53/1.77 tff(5872,plain,
% 1.53/1.77 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.77 inference(symmetry,[status(thm)],[5871])).
% 1.53/1.77 tff(5873,plain,
% 1.53/1.77 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5872])).
% 1.53/1.77 tff(5874,plain,
% 1.53/1.77 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[812, 5873])).
% 1.53/1.77 tff(5875,plain,
% 1.53/1.77 (((~![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))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5876,plain,
% 1.53/1.77 ((~![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))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(5877,plain,
% 1.53/1.77 ((~![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)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[5876, 5875])).
% 1.53/1.77 tff(5878,plain,
% 1.53/1.77 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5877, 21, 5869])).
% 1.53/1.77 tff(5879,plain,
% 1.53/1.77 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5878, 5874])).
% 1.53/1.77 tff(5880,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(5881,plain,
% 1.53/1.77 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5882,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5881])).
% 1.53/1.78 tff(5883,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[5882, 5880])).
% 1.53/1.78 tff(5884,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5885,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 1.53/1.78 tff(5886,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5885, 121, 379, 622, 5879, 5870])).
% 1.53/1.78 tff(5887,plain,(b(s(s(s(s(elem!1)))), s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | b(s(s(s(s(elem!1)))), elem!1) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(5888,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5887, 5869, 622, 379, 3109, 107])).
% 1.53/1.78 tff(5889,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5890,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5891,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5890, 5889])).
% 1.53/1.78 tff(5892,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5891, 271, 739, 638, 5888])).
% 1.53/1.78 tff(5893,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1594, 21, 1591, 5892])).
% 1.53/1.78 tff(5894,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5895,plain,
% 1.53/1.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5896,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5895])).
% 1.53/1.78 tff(5897,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[5896, 5894])).
% 1.53/1.78 tff(5898,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5899,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5898, 5897])).
% 1.53/1.78 tff(5900,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5899, 121, 139, 727, 5879, 5893])).
% 1.53/1.78 tff(5901,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(5902,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5901, 5868, 139, 1591, 107, 739, 638, 622, 379, 5861])).
% 1.53/1.78 tff(5903,plain,
% 1.53/1.78 (r(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[143, 107, 139])).
% 1.53/1.78 tff(5904,plain,
% 1.53/1.78 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3061, 707])).
% 1.53/1.78 tff(5905,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5906,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5907,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5906, 5905])).
% 1.53/1.78 tff(5908,plain,
% 1.53/1.78 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5907, 121, 379, 622, 5904])).
% 1.53/1.78 tff(5909,plain,
% 1.53/1.78 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[818, 21, 815, 5908])).
% 1.53/1.78 tff(5910,plain,
% 1.53/1.78 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[704, 135])).
% 1.53/1.78 tff(5911,plain,
% 1.53/1.78 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[107])).
% 1.53/1.78 tff(5912,plain,
% 1.53/1.78 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.53/1.78 inference(symmetry,[status(thm)],[5911])).
% 1.53/1.78 tff(5913,plain,
% 1.53/1.78 (r(z, s(elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[379, 5912])).
% 1.53/1.78 tff(5914,plain,
% 1.53/1.78 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[107])).
% 1.53/1.78 tff(5915,plain,
% 1.53/1.78 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.53/1.78 inference(symmetry,[status(thm)],[5914])).
% 1.53/1.78 tff(5916,plain,
% 1.53/1.78 (r(s(s(s(s(s(z))))), z)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3061, 5915])).
% 1.53/1.78 tff(5917,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.53/1.78 tff(5918,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~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))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5919,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5920,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 1.53/1.78 tff(5921,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5920, 121, 1441, 1736, 5917, 109])).
% 1.53/1.78 tff(5922,plain,((~r(s(s(s(z))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(5923,plain,
% 1.53/1.78 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5922, 5916, 5913, 109])).
% 1.53/1.78 tff(5924,plain,
% 1.53/1.78 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1733, 5923])).
% 1.53/1.78 tff(5925,plain,
% 1.53/1.78 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5924, 5910])).
% 1.53/1.78 tff(5926,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5927,plain,
% 1.53/1.78 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5928,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5927])).
% 1.53/1.78 tff(5929,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[5928, 5926])).
% 1.53/1.78 tff(5930,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5931,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5930, 5929])).
% 1.53/1.78 tff(5932,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5931, 271, 739, 638, 5925, 5909])).
% 1.53/1.78 tff(5933,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(5934,plain,
% 1.53/1.78 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5933, 107, 638, 739, 5903, 379, 622])).
% 1.53/1.78 tff(5935,plain,
% 1.53/1.78 (b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[840, 5934, 712])).
% 1.53/1.78 tff(5936,plain,
% 1.53/1.78 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[835, 5935, 107])).
% 1.53/1.78 tff(5937,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5938,plain,
% 1.53/1.78 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5939,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5938])).
% 1.53/1.78 tff(5940,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[5939, 5937])).
% 1.53/1.78 tff(5941,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1))))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5942,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5941, 5940])).
% 1.53/1.78 tff(5943,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5942, 271, 588, 5936, 5902])).
% 1.53/1.78 tff(5944,plain,
% 1.53/1.78 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5943, 5860])).
% 1.53/1.78 tff(5945,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[1578, 5857])).
% 1.53/1.78 tff(5946,plain,
% 1.53/1.78 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5945])).
% 1.53/1.78 tff(5947,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5948,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5949,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5948, 5947])).
% 1.53/1.78 tff(5950,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5949, 271, 588, 5902, 542])).
% 1.53/1.78 tff(5951,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.53/1.78 tff(5952,plain,
% 1.53/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5953,plain,
% 1.53/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5954,plain,
% 1.53/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5953, 5952])).
% 1.53/1.78 tff(5955,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 5950])).
% 1.53/1.78 tff(5956,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(5957,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(5958,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[5957, 5956])).
% 1.53/1.78 tff(5959,plain,
% 1.53/1.78 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5958, 271, 588, 5936, 542])).
% 1.53/1.78 tff(5960,assumption,(s(s(s(s(s(elem!1))))) = s(s(elem!1))), introduced(assumption)).
% 1.53/1.78 tff(5961,plain,
% 1.53/1.78 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5960])).
% 1.53/1.78 tff(5962,plain,
% 1.53/1.78 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.53/1.78 inference(symmetry,[status(thm)],[5961])).
% 1.53/1.78 tff(5963,plain,
% 1.53/1.78 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[605, 5962, 808])).
% 1.53/1.78 tff(5964,plain,
% 1.53/1.78 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5963])).
% 1.53/1.78 tff(5965,plain,
% 1.53/1.78 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.53/1.78 inference(symmetry,[status(thm)],[5964])).
% 1.53/1.78 tff(5966,plain,
% 1.53/1.78 (s(s(s(elem!1))) = elem!1),
% 1.53/1.78 inference(transitivity,[status(thm)],[2834, 5965, 70])).
% 1.53/1.78 tff(5967,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[481, 5966])).
% 1.53/1.78 tff(5968,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(5969,plain,
% 1.53/1.78 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5968, 481])).
% 1.53/1.78 tff(5970,plain,
% 1.53/1.78 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[881, 21, 5969, 5959])).
% 1.53/1.78 tff(5971,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5972,plain,
% 1.53/1.79 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5973,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5972])).
% 1.53/1.79 tff(5974,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[5973, 5971])).
% 1.53/1.79 tff(5975,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(5976,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5975, 5974])).
% 1.53/1.79 tff(5977,plain,
% 1.53/1.79 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5976, 121, 5970, 683, 5955])).
% 1.53/1.79 tff(5978,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5977, 5946])).
% 1.53/1.79 tff(5979,plain,
% 1.53/1.79 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1776, 5978, 5944])).
% 1.53/1.79 tff(5980,plain,
% 1.53/1.79 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[1578, 5979, 5858])).
% 1.53/1.79 tff(5981,plain,
% 1.53/1.79 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5980])).
% 1.53/1.79 tff(5982,plain,
% 1.53/1.79 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[5981])).
% 1.53/1.79 tff(5983,plain,
% 1.53/1.79 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[809, 5982, 1570])).
% 1.53/1.79 tff(5984,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1591, 5983])).
% 1.53/1.79 tff(5985,plain,((~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(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))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(5986,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5985, 5856, 5854, 107, 5834, 543, 5828, 139, 739, 638, 622, 379, 626, 5812])).
% 1.53/1.79 tff(5987,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(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))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(5988,plain,
% 1.53/1.79 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5987, 5784, 5811, 5810, 5801, 5799, 379, 68, 357, 5804, 5816])).
% 1.53/1.79 tff(5989,plain,
% 1.53/1.79 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[556, 5988, 2208])).
% 1.53/1.79 tff(5990,plain,
% 1.53/1.79 (b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5790])).
% 1.53/1.79 tff(5991,plain,
% 1.53/1.79 ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5990])).
% 1.53/1.79 tff(5992,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5790])).
% 1.53/1.79 tff(5993,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[5992])).
% 1.53/1.79 tff(5994,plain,
% 1.53/1.79 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5784])).
% 1.53/1.79 tff(5995,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[1639, 5994])).
% 1.53/1.79 tff(5996,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5995, 5993])).
% 1.53/1.79 tff(5997,plain,
% 1.53/1.79 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5784])).
% 1.53/1.79 tff(5998,plain,
% 1.53/1.79 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5997])).
% 1.53/1.79 tff(5999,plain,
% 1.53/1.79 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[711, 5998])).
% 1.53/1.79 tff(6000,plain,
% 1.53/1.79 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5933, 5801, 5784, 5810, 5805, 379, 5799])).
% 1.53/1.79 tff(6001,plain,
% 1.53/1.79 (b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[840, 6000, 5999])).
% 1.53/1.79 tff(6002,plain,
% 1.53/1.79 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[835, 6001, 5784])).
% 1.53/1.79 tff(6003,assumption,(b(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.53/1.79 tff(6004,assumption,(b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.53/1.79 tff(6005,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6006,plain,
% 1.53/1.79 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6007,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6006])).
% 1.53/1.79 tff(6008,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6007, 6005])).
% 1.53/1.79 tff(6009,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(6010,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6009, 6008])).
% 1.53/1.79 tff(6011,plain,
% 1.53/1.79 (~b(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6010, 271, 785, 6004, 6003])).
% 1.53/1.79 tff(6012,plain,
% 1.53/1.79 (r(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[862, 6011, 198])).
% 1.53/1.79 tff(6013,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6014,plain,
% 1.53/1.79 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6015,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6014])).
% 1.53/1.79 tff(6016,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6015, 6013])).
% 1.53/1.79 tff(6017,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(6018,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6017, 6016])).
% 1.53/1.79 tff(6019,plain,
% 1.53/1.79 (~b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6018, 271, 785, 6004, 6003])).
% 1.53/1.79 tff(6020,plain,
% 1.53/1.79 (r(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[599, 6019, 68])).
% 1.53/1.79 tff(6021,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2670, 6020, 6012, 139, 623])).
% 1.53/1.79 tff(6022,plain,((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(6023,plain,
% 1.53/1.79 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6022, 5989, 5811, 68, 6002, 5996])).
% 1.53/1.79 tff(6024,plain,
% 1.53/1.79 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6023, 5991])).
% 1.53/1.79 tff(6025,plain,
% 1.53/1.79 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1719, 6024, 5784])).
% 1.53/1.79 tff(6026,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.53/1.79 tff(6027,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6028,plain,
% 1.53/1.79 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6029,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6028])).
% 1.53/1.79 tff(6030,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6029, 6027])).
% 1.53/1.79 tff(6031,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(elem!1))))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(6032,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6031, 6030])).
% 1.53/1.79 tff(6033,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6032, 121, 623, 139, 1694, 6026])).
% 1.53/1.79 tff(6034,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(6035,plain,
% 1.53/1.79 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6034, 6025, 5989, 5811])).
% 1.53/1.79 tff(6036,plain,
% 1.53/1.79 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[1736, 781])).
% 1.53/1.79 tff(6037,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.53/1.79 tff(6038,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6037, 6036])).
% 1.53/1.79 tff(6039,plain,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(6040,plain,
% 1.53/1.79 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6039, 6035, 5784])).
% 1.53/1.79 tff(6041,plain,
% 1.53/1.79 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1733, 6040])).
% 1.53/1.79 tff(6042,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6043,plain,
% 1.53/1.79 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6044,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6043])).
% 1.53/1.79 tff(6045,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6044, 6042])).
% 1.53/1.79 tff(6046,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(6047,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6046, 6045])).
% 1.53/1.79 tff(6048,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6047, 271, 1422, 1307, 1639, 1723])).
% 1.53/1.79 tff(6049,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(6050,plain,
% 1.53/1.79 (~b(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6049, 6041, 1422, 1639])).
% 1.53/1.79 tff(6051,plain,
% 1.53/1.79 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[107])).
% 1.53/1.79 tff(6052,plain,
% 1.53/1.79 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[6051])).
% 1.53/1.79 tff(6053,plain,
% 1.53/1.79 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[1194])).
% 1.53/1.79 tff(6054,plain,
% 1.53/1.79 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6053, 6052])).
% 1.53/1.79 tff(6055,plain,
% 1.53/1.79 (b(z, s(s(s(z))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[738, 6054])).
% 1.53/1.79 tff(6056,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1209, 6055])).
% 1.53/1.79 tff(6057,plain,((~b(elem!1, s(s(s(elem!1))))) | b(z, s(s(s(z)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(6058,plain,
% 1.53/1.79 (~b(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6057, 6050, 5784])).
% 1.53/1.79 tff(6059,plain,
% 1.53/1.79 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[5794, 654])).
% 1.53/1.79 tff(6060,plain,
% 1.53/1.79 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6059])).
% 1.53/1.79 tff(6061,plain,
% 1.53/1.79 (~(elem!1 = s(s(s(elem!1))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[30, 6060])).
% 1.53/1.79 tff(6062,plain,
% 1.53/1.79 (r(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[660, 21, 6061, 6058])).
% 1.53/1.79 tff(6063,plain,
% 1.53/1.79 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5901, 6062, 5812, 5784, 5811, 5810, 5801, 5799, 379, 5797])).
% 1.53/1.79 tff(6064,plain,
% 1.53/1.79 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[671, 6058, 5796, 479, 5989])).
% 1.53/1.79 tff(6065,plain,
% 1.53/1.79 (b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[599, 6064, 68])).
% 1.53/1.79 tff(6066,plain,
% 1.53/1.79 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[1578, 705])).
% 1.53/1.79 tff(6067,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[6066])).
% 1.53/1.79 tff(6068,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.79 tff(6069,plain,
% 1.53/1.79 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6068, 6067])).
% 1.53/1.79 tff(6070,plain,
% 1.53/1.79 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5942, 271, 588, 785, 5606])).
% 1.53/1.79 tff(6071,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6070, 6069])).
% 1.53/1.79 tff(6072,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(z = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(6073,plain,
% 1.53/1.79 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6072, 5784, 6065, 6002, 6063])).
% 1.53/1.79 tff(6074,plain,
% 1.53/1.79 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1776, 6073, 1772])).
% 1.53/1.79 tff(6075,plain,
% 1.53/1.79 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6074, 5793])).
% 1.53/1.79 tff(6076,plain,
% 1.53/1.79 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5785])).
% 1.53/1.79 tff(6077,plain,
% 1.53/1.79 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.53/1.79 inference(symmetry,[status(thm)],[6076])).
% 1.53/1.79 tff(6078,plain,
% 1.53/1.79 (b(s(s(s(z))), s(z))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[1422, 6077])).
% 1.53/1.79 tff(6079,plain,
% 1.53/1.79 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5784])).
% 1.53/1.79 tff(6080,plain,
% 1.53/1.79 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6079, 159])).
% 1.53/1.79 tff(6081,plain,
% 1.53/1.79 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6080])).
% 1.53/1.79 tff(6082,plain,
% 1.53/1.79 (~(elem!1 = s(s(s(z))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[166, 6081])).
% 1.53/1.79 tff(6083,plain,
% 1.53/1.79 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5787])).
% 1.53/1.79 tff(6084,plain,
% 1.53/1.79 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[6083])).
% 1.53/1.79 tff(6085,plain,
% 1.53/1.79 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6084])).
% 1.53/1.79 tff(6086,plain,
% 1.53/1.79 (~b(elem!1, s(s(s(z))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[6058, 6085])).
% 1.53/1.79 tff(6087,plain,
% 1.53/1.79 (r(elem!1, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1192, 6086, 6082])).
% 1.53/1.79 tff(6088,plain,
% 1.53/1.79 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5239, 6087, 944, 6078, 5806, 357])).
% 1.53/1.79 tff(6089,plain,
% 1.53/1.79 (b(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[862, 6088, 198])).
% 1.53/1.79 tff(6090,plain,
% 1.53/1.79 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5949, 271, 6065, 6063, 6089])).
% 1.53/1.79 tff(6091,plain,
% 1.53/1.79 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5954, 21, 5834, 6090])).
% 1.53/1.79 tff(6092,plain,
% 1.53/1.79 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5958, 271, 6065, 6002, 6089])).
% 1.53/1.79 tff(6093,plain,
% 1.53/1.79 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5789, 5786])).
% 1.53/1.79 tff(6094,plain,
% 1.53/1.79 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6093])).
% 1.53/1.79 tff(6095,plain,
% 1.53/1.79 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[877, 6094])).
% 1.53/1.79 tff(6096,plain,
% 1.53/1.79 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[881, 21, 6095, 6092])).
% 1.53/1.79 tff(6097,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6098,plain,
% 1.53/1.79 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(6099,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[6098])).
% 1.53/1.79 tff(6100,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[6099, 6097])).
% 1.53/1.79 tff(6101,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.80 inference(quant_inst,[status(thm)],[])).
% 1.53/1.80 tff(6102,plain,
% 1.53/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[6101, 6100])).
% 1.53/1.80 tff(6103,plain,
% 1.53/1.80 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[6102, 121, 6096, 6025])).
% 1.53/1.80 tff(6104,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[6103, 6091, 6075])).
% 1.53/1.80 tff(6105,plain,(b(z, elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | (elem!1 = s(z)) | b(elem!1, s(elem!1)) | (~r(z, s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.80 tff(6106,plain,
% 1.53/1.80 (b(z, elem!1)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[6105, 3504, 1244, 379, 68, 479, 1422, 1639, 412, 2564, 243, 317, 909, 1391])).
% 1.53/1.80 tff(6107,plain,
% 1.53/1.80 (z = elem!1),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[5659, 6106, 243, 379, 412, 909, 439])).
% 1.53/1.80 tff(6108,plain,
% 1.53/1.80 (r(s(s(s(z))), z)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[490, 6107, 479])).
% 1.53/1.80 tff(6109,plain,
% 1.53/1.80 (r(s(s(s(z))), elem!1)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[475, 6107, 6108])).
% 1.53/1.80 tff(6110,plain,
% 1.53/1.80 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[149, 6109, 6107])).
% 1.53/1.80 tff(6111,plain,
% 1.53/1.80 (s(elem!1) = s(z)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3826, 6110, 412, 379, 79, 1244, 909])).
% 1.53/1.80 tff(6112,plain,
% 1.53/1.80 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[6111])).
% 1.53/1.80 tff(6113,plain,
% 1.53/1.80 (elem!1 = z),
% 1.53/1.80 inference(transitivity,[status(thm)],[75, 6112, 50])).
% 1.53/1.80 tff(6114,plain,
% 1.53/1.80 (b(z, elem!1) <=> b(z, z)),
% 1.53/1.80 inference(monotonicity,[status(thm)],[6113])).
% 1.53/1.80 tff(6115,plain,
% 1.53/1.80 (b(z, z) <=> b(z, elem!1)),
% 1.53/1.80 inference(symmetry,[status(thm)],[6114])).
% 1.53/1.80 tff(6116,plain,
% 1.53/1.80 ((~b(z, z)) <=> (~b(z, elem!1))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[6115])).
% 1.53/1.80 tff(6117,plain,
% 1.53/1.80 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 1.53/1.80 inference(quant_inst,[status(thm)],[])).
% 1.53/1.80 tff(6118,plain,
% 1.53/1.80 (~b(z, z)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[6117, 190])).
% 1.53/1.80 tff(6119,plain,
% 1.53/1.80 (~b(z, elem!1)),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[6118, 6116])).
% 1.53/1.80 tff(6120,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[6106, 6119])).
% 1.53/1.80 tff(6121,plain,((s(z) = elem!1) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | b(s(s(s(elem!1))), elem!1) | b(s(z), s(elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (s(elem!1) = elem!1) | b(elem!1, s(elem!1)) | r(z, elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.80 tff(6122,plain,
% 1.53/1.80 (~b(z, s(s(s(s(s(z))))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[6121, 5772, 379, 3505, 479, 439, 68, 1422, 412, 2564, 317, 1391, 1242])).
% 1.53/1.80 tff(6123,plain,
% 1.53/1.80 (r(z, s(s(s(s(s(z))))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[1658, 6122])).
% 1.53/1.80 tff(6124,plain,
% 1.53/1.80 (r(elem!1, s(s(s(s(s(z))))))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[6123, 5783])).
% 1.53/1.80 tff(6125,plain,
% 1.53/1.80 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[6124, 5782])).
% 1.53/1.80 tff(6126,plain,
% 1.53/1.80 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[5780])).
% 1.53/1.80 tff(6127,plain,
% 1.53/1.80 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.53/1.80 inference(symmetry,[status(thm)],[6126])).
% 1.53/1.80 tff(6128,plain,
% 1.53/1.80 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6127])).
% 1.63/1.80 tff(6129,plain,
% 1.63/1.80 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3499, 6128])).
% 1.63/1.80 tff(6130,plain,
% 1.63/1.80 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[814, 5774])).
% 1.63/1.80 tff(6131,plain,
% 1.63/1.80 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[818, 21, 6130, 6129])).
% 1.63/1.80 tff(6132,plain,
% 1.63/1.80 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5774])).
% 1.63/1.80 tff(6133,plain,
% 1.63/1.80 (r(s(elem!1), elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[412, 6132])).
% 1.63/1.80 tff(6134,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6135,plain,
% 1.63/1.80 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6136,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6135])).
% 1.63/1.80 tff(6137,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[6136, 6134])).
% 1.63/1.80 tff(6138,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(6139,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[6138, 6137])).
% 1.63/1.80 tff(6140,plain,
% 1.63/1.80 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6139, 121, 379, 6133, 6131])).
% 1.63/1.80 tff(6141,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6140, 6125])).
% 1.63/1.80 tff(6142,plain,(r(z, elem!1) | (~r(elem!1, s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z)) | b(s(z), s(elem!1)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (s(elem!1) = elem!1) | b(elem!1, s(elem!1)) | b(s(z), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(6143,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6142, 5771, 5764, 3499, 412, 379, 479, 5646, 1422, 2564, 317, 1242, 894])).
% 1.63/1.80 tff(6144,plain,(b(s(z), elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(elem!1))) | (s(elem!1) = elem!1) | b(elem!1, s(elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(6145,plain,
% 1.63/1.80 (b(s(z), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6144, 3502, 3501, 3499, 479, 5549, 3500, 317, 894])).
% 1.63/1.80 tff(6146,plain,
% 1.63/1.80 (~r(s(elem!1), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5329, 431, 412, 909])).
% 1.63/1.80 tff(6147,plain,
% 1.63/1.80 (b(s(elem!1), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[429, 6146, 351])).
% 1.63/1.80 tff(6148,plain,
% 1.63/1.80 (~b(z, elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3964, 4016, 260, 5654])).
% 1.63/1.80 tff(6149,plain,
% 1.63/1.80 (r(z, elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[355, 6148, 331])).
% 1.63/1.80 tff(6150,plain,
% 1.63/1.80 (~r(s(elem!1), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3683, 6149, 379, 412])).
% 1.63/1.80 tff(6151,plain,
% 1.63/1.80 (b(s(elem!1), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2243, 6150, 2564])).
% 1.63/1.80 tff(6152,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6153,plain,
% 1.63/1.80 (((~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(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6154,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6153])).
% 1.63/1.80 tff(6155,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[6154, 6152])).
% 1.63/1.80 tff(6156,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(6157,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[6156, 6155])).
% 1.63/1.80 tff(6158,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6157, 271, 6151, 260, 5654, 6147])).
% 1.63/1.80 tff(6159,plain,((~r(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (z = elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(6160,plain,
% 1.63/1.80 (~r(s(z), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6159, 331, 2564, 379, 412, 260, 909])).
% 1.63/1.80 tff(6161,plain,
% 1.63/1.80 (b(s(z), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[444, 6160, 344])).
% 1.63/1.80 tff(6162,plain,
% 1.63/1.80 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[4906])).
% 1.63/1.80 tff(6163,plain,
% 1.63/1.80 (~b(s(s(s(z))), s(elem!1))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[317, 6162])).
% 1.63/1.80 tff(6164,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1422, 6163])).
% 1.63/1.80 tff(6165,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(elem!1))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(6166,plain,
% 1.63/1.80 (~(s(s(s(z))) = elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6165, 317, 1422])).
% 1.63/1.80 tff(6167,plain,
% 1.63/1.80 (~(elem!1 = s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3576, 6161, 317])).
% 1.63/1.80 tff(6168,plain,
% 1.63/1.80 (~(s(z) = elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1221, 6167])).
% 1.63/1.80 tff(6169,plain,
% 1.63/1.80 (~(s(s(z)) = s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[960, 6168])).
% 1.63/1.80 tff(6170,plain,
% 1.63/1.80 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[953, 6169])).
% 1.63/1.80 tff(6171,plain,
% 1.63/1.80 (~b(s(z), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3964, 1326, 260, 261])).
% 1.63/1.80 tff(6172,plain,
% 1.63/1.80 (r(s(z), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[25, 6171])).
% 1.63/1.80 tff(6173,plain,
% 1.63/1.80 (~r(s(elem!1), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3972, 121, 6172, 909, 412])).
% 1.63/1.80 tff(6174,plain,
% 1.63/1.80 (b(s(elem!1), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[429, 6173, 422])).
% 1.63/1.80 tff(6175,plain,
% 1.63/1.80 (~b(s(s(s(z))), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5673, 271, 1422, 6174, 446])).
% 1.63/1.80 tff(6176,plain,
% 1.63/1.80 (r(s(s(s(z))), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2325, 6175])).
% 1.63/1.80 tff(6177,plain,
% 1.63/1.80 (~b(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5668, 271, 1422, 6174, 446])).
% 1.63/1.80 tff(6178,plain,
% 1.63/1.80 (r(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[105, 6177])).
% 1.63/1.80 tff(6179,plain,
% 1.63/1.80 (~r(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2335, 6178, 909, 6176])).
% 1.63/1.80 tff(6180,plain,
% 1.63/1.80 (b(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1214, 6179])).
% 1.63/1.80 tff(6181,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6182,plain,
% 1.63/1.80 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6183,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6182])).
% 1.63/1.80 tff(6184,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[6183, 6181])).
% 1.63/1.80 tff(6185,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(6186,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 1.63/1.80 tff(6187,plain,
% 1.63/1.80 (~r(s(s(s(z))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6186, 121, 909, 6176, 6178])).
% 1.63/1.80 tff(6188,plain,
% 1.63/1.80 (b(s(s(s(z))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1155, 6187])).
% 1.63/1.80 tff(6189,plain,
% 1.63/1.80 (~b(s(s(s(z))), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3764, 271, 1326, 261, 6188])).
% 1.63/1.80 tff(6190,plain,
% 1.63/1.80 (r(s(s(s(z))), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[255, 6189, 907])).
% 1.63/1.80 tff(6191,plain,
% 1.63/1.80 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[1997])).
% 1.63/1.80 tff(6192,plain,
% 1.63/1.80 ((~b(s(s(s(z))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6191])).
% 1.63/1.80 tff(6193,plain,
% 1.63/1.80 (~b(s(elem!1), s(z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2319, 6192])).
% 1.63/1.80 tff(6194,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[447, 6193])).
% 1.63/1.80 tff(6195,plain,(b(s(s(s(z))), s(z)) | (~b(s(elem!1), s(z))) | (~(s(s(s(z))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(6196,plain,
% 1.63/1.80 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6195, 6175, 6174])).
% 1.63/1.80 tff(6197,plain,
% 1.63/1.80 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.63/1.80 inference(commutativity,[status(thm)],[])).
% 1.63/1.80 tff(6198,plain,
% 1.63/1.80 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.63/1.80 inference(symmetry,[status(thm)],[6197])).
% 1.63/1.80 tff(6199,plain,
% 1.63/1.80 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6198])).
% 1.63/1.80 tff(6200,plain,
% 1.63/1.80 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2065, 6199])).
% 1.63/1.80 tff(6201,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.80 tff(6202,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.63/1.80 tff(6203,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6204,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(6205,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[6204, 6203])).
% 1.63/1.80 tff(6206,plain,
% 1.63/1.80 (~b(s(s(s(elem!1))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6205, 271, 1422, 1307, 6202])).
% 1.63/1.80 tff(6207,plain,
% 1.63/1.80 (r(s(s(s(elem!1))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1904, 21, 30, 6206])).
% 1.63/1.80 tff(6208,plain,
% 1.63/1.80 (~b(z, s(s(s(elem!1))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5687, 6202, 1422, 1307])).
% 1.63/1.80 tff(6209,plain,
% 1.63/1.80 (r(z, s(s(s(elem!1))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[36, 21, 6208, 32])).
% 1.63/1.80 tff(6210,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6211,plain,
% 1.63/1.80 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6212,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6211])).
% 1.63/1.80 tff(6213,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[6212, 6210])).
% 1.63/1.80 tff(6214,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(6215,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 1.63/1.80 tff(6216,plain,
% 1.63/1.80 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6215, 121, 6209, 412, 6207])).
% 1.63/1.80 tff(6217,plain,
% 1.63/1.80 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6218,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[6217])).
% 1.63/1.80 tff(6219,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[6218, 1914])).
% 1.63/1.80 tff(6220,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(6221,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[6220, 6219])).
% 1.63/1.80 tff(6222,plain,
% 1.63/1.80 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6221, 121, 6209, 110, 6207])).
% 1.63/1.80 tff(6223,plain,
% 1.63/1.80 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[760, 6222])).
% 1.63/1.80 tff(6224,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(6225,plain,
% 1.63/1.80 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6226,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6225])).
% 1.63/1.81 tff(6227,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6226, 6224])).
% 1.63/1.81 tff(6228,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6229,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6228, 6227])).
% 1.63/1.81 tff(6230,plain,
% 1.63/1.81 ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6229, 271])).
% 1.63/1.81 tff(6231,plain,
% 1.63/1.81 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6230, 6223, 447, 6202])).
% 1.63/1.81 tff(6232,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2293, 21, 6231, 6216, 6201])).
% 1.63/1.81 tff(6233,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(6234,plain,
% 1.63/1.81 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6233, 2280, 447, 412, 110, 1422, 1307])).
% 1.63/1.81 tff(6235,plain,
% 1.63/1.81 (((~![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)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6236,plain,
% 1.63/1.81 ((~![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)))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6237,plain,
% 1.63/1.81 ((~![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))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6236, 6235])).
% 1.63/1.81 tff(6238,plain,
% 1.63/1.81 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6237, 21, 6234])).
% 1.63/1.81 tff(6239,plain,
% 1.63/1.81 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6238, 6200])).
% 1.63/1.81 tff(6240,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6241,plain,
% 1.63/1.81 (((~r(s(s(s(z))), elem!1)) | (~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(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6242,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6241])).
% 1.63/1.81 tff(6243,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6242, 6240])).
% 1.63/1.81 tff(6244,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6245,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6244, 6243])).
% 1.63/1.81 tff(6246,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6245, 121, 145, 108, 6239])).
% 1.63/1.81 tff(6247,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[66, 21, 6246, 63])).
% 1.63/1.81 tff(6248,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6249,plain,
% 1.63/1.81 (((~b(s(z), 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(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6250,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6249])).
% 1.63/1.81 tff(6251,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6250, 6248])).
% 1.63/1.81 tff(6252,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6253,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6252, 6251])).
% 1.63/1.81 tff(6254,plain,
% 1.63/1.81 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6253, 271, 260, 447, 6247])).
% 1.63/1.81 tff(6255,plain,
% 1.63/1.81 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[681, 6254, 82])).
% 1.63/1.81 tff(6256,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3821, 121, 379, 6255, 412])).
% 1.63/1.81 tff(6257,plain,
% 1.63/1.81 (s(s(s(elem!1))) = elem!1),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[486, 6256, 479])).
% 1.63/1.81 tff(6258,plain,
% 1.63/1.81 (elem!1 = s(s(s(elem!1)))),
% 1.63/1.81 inference(symmetry,[status(thm)],[6257])).
% 1.63/1.81 tff(6259,plain,
% 1.63/1.81 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[4124])).
% 1.63/1.81 tff(6260,plain,
% 1.63/1.81 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[872, 6259, 70, 2590])).
% 1.63/1.81 tff(6261,plain,
% 1.63/1.81 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6260])).
% 1.63/1.81 tff(6262,plain,
% 1.63/1.81 (s(s(s(z))) = s(s(elem!1))),
% 1.63/1.81 inference(transitivity,[status(thm)],[775, 6261, 55])).
% 1.63/1.81 tff(6263,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[944, 6262])).
% 1.63/1.81 tff(6264,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(6265,plain,
% 1.63/1.81 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6264, 6257, 944])).
% 1.63/1.81 tff(6266,plain,
% 1.63/1.81 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4138, 6265, 3499])).
% 1.63/1.81 tff(6267,plain,
% 1.63/1.81 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6257])).
% 1.63/1.81 tff(6268,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6269,plain,
% 1.63/1.81 (((~b(s(z), 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(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6270,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6269])).
% 1.63/1.81 tff(6271,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6270, 6268])).
% 1.63/1.81 tff(6272,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6273,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6272, 6271])).
% 1.63/1.81 tff(6274,plain,
% 1.63/1.81 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6273, 271, 260, 447, 6247])).
% 1.63/1.81 tff(6275,plain,
% 1.63/1.81 (r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2293, 21, 6274, 2280])).
% 1.63/1.81 tff(6276,plain,
% 1.63/1.81 (r(s(elem!1), elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6275, 6267])).
% 1.63/1.81 tff(6277,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6278,plain,
% 1.63/1.81 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6279,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6278])).
% 1.63/1.81 tff(6280,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6279, 6277])).
% 1.63/1.81 tff(6281,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6282,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6281, 6280])).
% 1.63/1.81 tff(6283,plain,
% 1.63/1.81 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6282, 121, 379, 6276, 6266])).
% 1.63/1.81 tff(6284,plain,
% 1.63/1.81 (~(s(elem!1) = s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2035, 2033])).
% 1.63/1.81 tff(6285,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6286,plain,
% 1.63/1.81 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6287,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6286])).
% 1.63/1.81 tff(6288,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6287, 6285])).
% 1.63/1.81 tff(6289,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6290,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6289, 6288])).
% 1.63/1.81 tff(6291,plain,
% 1.63/1.81 (~r(s(elem!1), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6290, 121, 379, 6276, 145])).
% 1.63/1.81 tff(6292,plain,
% 1.63/1.81 (b(s(elem!1), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2044, 6291, 6284])).
% 1.63/1.81 tff(6293,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6294,plain,
% 1.63/1.81 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(6295,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[6294])).
% 1.63/1.81 tff(6296,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[6295, 6293])).
% 1.63/1.81 tff(6297,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(6298,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6297, 6296])).
% 1.63/1.82 tff(6299,plain,
% 1.63/1.82 (~b(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6298, 271, 1422, 1307, 6292])).
% 1.63/1.82 tff(6300,plain,
% 1.63/1.82 (r(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1439, 6299])).
% 1.63/1.82 tff(6301,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6302,plain,
% 1.63/1.82 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6303,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6302])).
% 1.63/1.82 tff(6304,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6303, 6301])).
% 1.63/1.82 tff(6305,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6306,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6305, 6304])).
% 1.63/1.82 tff(6307,plain,
% 1.63/1.82 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6306, 121, 6276, 6300, 6266])).
% 1.63/1.82 tff(6308,plain,
% 1.63/1.82 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1658, 6307])).
% 1.63/1.82 tff(6309,plain,
% 1.63/1.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6049, 6308, 1422, 1307])).
% 1.63/1.82 tff(6310,plain,
% 1.63/1.82 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1733, 6309])).
% 1.63/1.82 tff(6311,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~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))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6312,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6313,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~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)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6312, 6311])).
% 1.63/1.82 tff(6314,plain,
% 1.63/1.82 (~r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6313, 121, 145, 6310, 108])).
% 1.63/1.82 tff(6315,plain,
% 1.63/1.82 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1682, 6314])).
% 1.63/1.82 tff(6316,plain,
% 1.63/1.82 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6257])).
% 1.63/1.82 tff(6317,plain,
% 1.63/1.82 (b(elem!1, s(z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6247, 6316])).
% 1.63/1.82 tff(6318,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6319,plain,
% 1.63/1.82 (((~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))) <=> ((~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))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6320,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6319])).
% 1.63/1.82 tff(6321,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6320, 6318])).
% 1.63/1.82 tff(6322,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6323,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6322, 6321])).
% 1.63/1.82 tff(6324,plain,
% 1.63/1.82 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6323, 271, 260, 6317, 6315])).
% 1.63/1.82 tff(6325,plain,
% 1.63/1.82 (s(s(s(s(s(z))))) = elem!1),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[840, 6324, 6283])).
% 1.63/1.82 tff(6326,plain,
% 1.63/1.82 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6325, 6258])).
% 1.63/1.82 tff(6327,plain,
% 1.63/1.82 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6326])).
% 1.63/1.82 tff(6328,plain,
% 1.63/1.82 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.63/1.82 inference(transitivity,[status(thm)],[872, 6327, 55])).
% 1.63/1.82 tff(6329,plain,
% 1.63/1.82 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6328])).
% 1.63/1.82 tff(6330,plain,
% 1.63/1.82 (s(s(s(z))) = s(elem!1)),
% 1.63/1.82 inference(transitivity,[status(thm)],[775, 6329, 604])).
% 1.63/1.82 tff(6331,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2033, 6330])).
% 1.63/1.82 tff(6332,plain,((s(s(s(elem!1))) = s(elem!1)) | (s(s(s(z))) = s(elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~r(elem!1, s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(6333,plain,
% 1.63/1.82 (s(s(s(elem!1))) = s(elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6332, 6196, 260, 6190, 6178, 1422, 6180, 379, 3499, 944, 479, 412, 6174, 2065, 6172])).
% 1.63/1.82 tff(6334,plain,
% 1.63/1.82 (elem!1 = s(s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[78, 6333])).
% 1.63/1.82 tff(6335,plain,
% 1.63/1.82 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6334])).
% 1.63/1.82 tff(6336,plain,
% 1.63/1.82 (r(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6190, 6335])).
% 1.63/1.82 tff(6337,plain,
% 1.63/1.82 (~(s(elem!1) = s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2035, 6196])).
% 1.63/1.82 tff(6338,plain,
% 1.63/1.82 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6334])).
% 1.63/1.82 tff(6339,plain,
% 1.63/1.82 (r(s(s(elem!1)), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[379, 6338])).
% 1.63/1.82 tff(6340,plain,
% 1.63/1.82 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6334])).
% 1.63/1.82 tff(6341,plain,
% 1.63/1.82 (~b(s(elem!1), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3790, 6334, 479])).
% 1.63/1.82 tff(6342,plain,
% 1.63/1.82 (r(s(elem!1), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2243, 6341, 2564])).
% 1.63/1.82 tff(6343,plain,
% 1.63/1.82 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6342, 6340])).
% 1.63/1.82 tff(6344,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6345,plain,
% 1.63/1.82 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6346,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6345])).
% 1.63/1.82 tff(6347,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6346, 6344])).
% 1.63/1.82 tff(6348,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6349,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6348, 6347])).
% 1.63/1.82 tff(6350,plain,
% 1.63/1.82 (~r(s(elem!1), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6349, 121, 6343, 6336, 6339])).
% 1.63/1.82 tff(6351,plain,
% 1.63/1.82 (b(s(elem!1), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2044, 6350, 6337])).
% 1.63/1.82 tff(6352,plain,
% 1.63/1.82 (~b(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6298, 271, 1422, 6180, 6351])).
% 1.63/1.82 tff(6353,plain,
% 1.63/1.82 (r(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1439, 6352])).
% 1.63/1.82 tff(6354,plain,
% 1.63/1.82 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.63/1.82 inference(transitivity,[status(thm)],[872, 6259, 70, 2470])).
% 1.63/1.82 tff(6355,plain,
% 1.63/1.82 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6354])).
% 1.63/1.82 tff(6356,plain,
% 1.63/1.82 (s(s(s(z))) = s(elem!1)),
% 1.63/1.82 inference(transitivity,[status(thm)],[775, 6355, 604])).
% 1.63/1.82 tff(6357,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2033, 6356])).
% 1.63/1.82 tff(6358,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(6359,plain,
% 1.63/1.82 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6358, 6196, 6334])).
% 1.63/1.82 tff(6360,plain,
% 1.63/1.82 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4138, 6359, 3499])).
% 1.63/1.82 tff(6361,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6362,plain,
% 1.63/1.82 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6363,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6362])).
% 1.63/1.82 tff(6364,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6363, 6361])).
% 1.63/1.82 tff(6365,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6366,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6365, 6364])).
% 1.63/1.82 tff(6367,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6366, 121, 1441, 627, 1661, 4266])).
% 1.63/1.82 tff(6368,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(6369,plain,
% 1.63/1.82 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6368, 6360, 6343, 6353])).
% 1.63/1.82 tff(6370,plain,
% 1.63/1.82 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1658, 6369])).
% 1.63/1.82 tff(6371,plain,
% 1.63/1.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6049, 6370, 1422, 6180])).
% 1.63/1.82 tff(6372,plain,
% 1.63/1.82 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1733, 6371])).
% 1.63/1.82 tff(6373,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~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))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6374,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~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))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6375,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~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)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6374, 6373])).
% 1.63/1.82 tff(6376,plain,
% 1.63/1.82 (~r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6375, 121, 6372, 6336, 6178])).
% 1.63/1.82 tff(6377,plain,
% 1.63/1.82 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1682, 6376])).
% 1.63/1.82 tff(6378,plain,
% 1.63/1.82 (s(s(elem!1)) = elem!1),
% 1.63/1.82 inference(symmetry,[status(thm)],[6334])).
% 1.63/1.82 tff(6379,plain,
% 1.63/1.82 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6378])).
% 1.63/1.82 tff(6380,plain,
% 1.63/1.82 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.82 inference(symmetry,[status(thm)],[6379])).
% 1.63/1.82 tff(6381,plain,
% 1.63/1.82 (~b(elem!1, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5171, 271, 1326, 261, 6188])).
% 1.63/1.82 tff(6382,plain,
% 1.63/1.82 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6378])).
% 1.63/1.82 tff(6383,plain,
% 1.63/1.82 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6382, 159])).
% 1.63/1.82 tff(6384,plain,
% 1.63/1.82 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6383])).
% 1.63/1.82 tff(6385,plain,
% 1.63/1.82 (~(elem!1 = s(s(s(z))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[944, 6384])).
% 1.63/1.82 tff(6386,plain,
% 1.63/1.82 (r(elem!1, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1192, 6385, 6381])).
% 1.63/1.82 tff(6387,plain,
% 1.63/1.82 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6386, 6380])).
% 1.63/1.82 tff(6388,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6389,plain,
% 1.63/1.82 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6390,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6389])).
% 1.63/1.82 tff(6391,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[6390, 6388])).
% 1.63/1.82 tff(6392,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6393,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6392, 6391])).
% 1.63/1.82 tff(6394,plain,
% 1.63/1.82 (~r(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6393, 121, 6336, 6178, 6387])).
% 1.63/1.82 tff(6395,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2143, 6394])).
% 1.63/1.82 tff(6396,plain,
% 1.63/1.82 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[6334])).
% 1.63/1.82 tff(6397,plain,
% 1.63/1.82 (b(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[260, 6396])).
% 1.63/1.82 tff(6398,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6399,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6400,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[6399, 6398])).
% 1.63/1.82 tff(6401,plain,
% 1.63/1.82 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6400, 271, 6397, 6395, 6377])).
% 1.63/1.82 tff(6402,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(6403,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(6404,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6403, 6402])).
% 1.63/1.83 tff(6405,plain,
% 1.63/1.83 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6404, 121, 6343, 6339, 6360])).
% 1.63/1.83 tff(6406,plain,
% 1.63/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6407,plain,
% 1.63/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6408,plain,
% 1.63/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6407, 6406])).
% 1.63/1.83 tff(6409,plain,
% 1.63/1.83 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6408, 21, 6405])).
% 1.63/1.83 tff(6410,plain,
% 1.63/1.83 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6409, 6401])).
% 1.63/1.83 tff(6411,plain,
% 1.63/1.83 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6410])).
% 1.63/1.83 tff(6412,plain,
% 1.63/1.83 (s(s(s(s(z)))) = s(elem!1)),
% 1.63/1.83 inference(transitivity,[status(thm)],[872, 6411, 604])).
% 1.63/1.83 tff(6413,plain,
% 1.63/1.83 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6412])).
% 1.63/1.83 tff(6414,plain,
% 1.63/1.83 (s(s(s(z))) = s(s(elem!1))),
% 1.63/1.83 inference(transitivity,[status(thm)],[775, 6413, 70, 6334])).
% 1.63/1.83 tff(6415,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[944, 6414])).
% 1.63/1.83 tff(6416,plain,((~b(z, elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~r(z, s(z))) | (~b(s(z), s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6417,plain,
% 1.63/1.83 (~b(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6416, 6170, 1422, 3499, 260, 379, 2564, 479, 412, 2064, 6166, 5654, 909, 6161, 351])).
% 1.63/1.83 tff(6418,plain,
% 1.63/1.83 (r(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[355, 6417, 331])).
% 1.63/1.83 tff(6419,plain,
% 1.63/1.83 (r(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3700, 6417, 412, 2564, 379, 6167, 317, 909])).
% 1.63/1.83 tff(6420,plain,
% 1.63/1.83 (~r(s(z), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3464, 6419, 909, 6418])).
% 1.63/1.83 tff(6421,plain,
% 1.63/1.83 (b(s(z), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[105, 6420])).
% 1.63/1.83 tff(6422,plain,
% 1.63/1.83 (~r(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3683, 6418, 379, 412])).
% 1.63/1.83 tff(6423,plain,
% 1.63/1.83 (b(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2243, 6422, 2564])).
% 1.63/1.83 tff(6424,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6425,plain,
% 1.63/1.83 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6426,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6425])).
% 1.63/1.83 tff(6427,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[6426, 6424])).
% 1.63/1.83 tff(6428,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6429,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6428, 6427])).
% 1.63/1.83 tff(6430,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6429, 271, 6423, 1422, 6421, 6161])).
% 1.63/1.83 tff(6431,plain,((z = elem!1) | (~b(s(s(s(z))), s(elem!1))) | (s(elem!1) = elem!1) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | b(elem!1, s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(z), elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6432,plain,
% 1.63/1.83 (z = elem!1),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6431, 3502, 3500, 3505, 5549, 3501, 317, 3499, 6145, 479])).
% 1.63/1.83 tff(6433,plain,
% 1.63/1.83 (s(z) = s(elem!1)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6432])).
% 1.63/1.83 tff(6434,plain,
% 1.63/1.83 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6433])).
% 1.63/1.83 tff(6435,plain,
% 1.63/1.83 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.63/1.83 inference(symmetry,[status(thm)],[6434])).
% 1.63/1.83 tff(6436,plain,
% 1.63/1.83 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6435])).
% 1.63/1.83 tff(6437,plain,
% 1.63/1.83 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6432])).
% 1.63/1.83 tff(6438,plain,
% 1.63/1.83 ((~b(s(elem!1), z)) <=> (~b(s(elem!1), elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6437])).
% 1.63/1.83 tff(6439,plain,
% 1.63/1.83 (~b(s(elem!1), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3498, 6438])).
% 1.63/1.83 tff(6440,plain,
% 1.63/1.83 (~b(s(z), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6439, 6436])).
% 1.63/1.83 tff(6441,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6145, 6440])).
% 1.63/1.83 tff(6442,plain,(b(elem!1, s(elem!1)) | b(s(elem!1), z) | b(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(elem!1))), elem!1) | b(z, s(z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6443,plain,
% 1.63/1.83 (b(elem!1, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6442, 479, 3499, 3498, 894, 377])).
% 1.63/1.83 tff(6444,plain,
% 1.63/1.83 (~(z = elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1543, 6443, 894])).
% 1.63/1.83 tff(6445,plain,
% 1.63/1.83 (~b(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5323, 260, 307, 412, 909, 344])).
% 1.63/1.83 tff(6446,plain,
% 1.63/1.83 (r(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[355, 6445, 331])).
% 1.63/1.83 tff(6447,plain,
% 1.63/1.83 (b(s(z), s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5347, 6446, 307, 2564, 260, 412, 909, 344])).
% 1.63/1.83 tff(6448,plain,
% 1.63/1.83 (~b(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3435, 6447, 307, 260])).
% 1.63/1.83 tff(6449,plain,
% 1.63/1.83 (r(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2243, 6448, 2564])).
% 1.63/1.83 tff(6450,plain,
% 1.63/1.83 (~r(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5358, 6449, 6446, 412])).
% 1.63/1.83 tff(6451,plain,
% 1.63/1.83 (b(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[284, 6450, 358])).
% 1.63/1.83 tff(6452,plain,
% 1.63/1.83 (b(s(z), s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5347, 378, 307, 2564, 260, 412, 909, 348])).
% 1.63/1.83 tff(6453,plain,
% 1.63/1.83 (~b(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3435, 6452, 307, 260])).
% 1.63/1.83 tff(6454,plain,
% 1.63/1.83 (r(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2243, 6453, 2564])).
% 1.63/1.83 tff(6455,plain,
% 1.63/1.83 (~r(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5343, 6454, 378, 412])).
% 1.63/1.83 tff(6456,plain,
% 1.63/1.83 (b(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[299, 243, 6455])).
% 1.63/1.83 tff(6457,plain,
% 1.63/1.83 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4497, 6452, 307, 260])).
% 1.63/1.83 tff(6458,plain,
% 1.63/1.83 (~b(s(elem!1), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[456, 6456, 307, 6452])).
% 1.63/1.83 tff(6459,plain,
% 1.63/1.83 (r(s(elem!1), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[429, 6458, 2282])).
% 1.63/1.83 tff(6460,plain,
% 1.63/1.83 (~r(s(z), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[420, 6459, 412, 378])).
% 1.63/1.83 tff(6461,plain,
% 1.63/1.83 (b(s(z), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[25, 6460])).
% 1.63/1.83 tff(6462,plain,
% 1.63/1.83 (~b(z, s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5420, 6461, 261, 6456])).
% 1.63/1.83 tff(6463,plain,
% 1.63/1.83 (r(z, s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2106, 6462])).
% 1.63/1.83 tff(6464,plain,
% 1.63/1.83 (elem!1 = s(s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5454, 6463, 412, 6457, 6456, 260])).
% 1.63/1.83 tff(6465,plain,
% 1.63/1.83 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6464])).
% 1.63/1.83 tff(6466,plain,
% 1.63/1.83 (b(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6456, 6465])).
% 1.63/1.83 tff(6467,plain,
% 1.63/1.83 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6464])).
% 1.63/1.83 tff(6468,plain,
% 1.63/1.83 (b(s(s(elem!1)), z)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[261, 6467])).
% 1.63/1.83 tff(6469,plain,
% 1.63/1.83 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5370, 6459, 412, 909, 307, 378, 6452, 2564, 231, 479, 348, 3499])).
% 1.63/1.83 tff(6470,plain,
% 1.63/1.83 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6358, 6464, 6469])).
% 1.63/1.83 tff(6471,plain,
% 1.63/1.83 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4138, 6470, 3499])).
% 1.63/1.83 tff(6472,plain,
% 1.63/1.83 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6464])).
% 1.63/1.83 tff(6473,plain,
% 1.63/1.83 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6454, 6472])).
% 1.63/1.83 tff(6474,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6475,plain,
% 1.63/1.83 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6476,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6475])).
% 1.63/1.83 tff(6477,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[6476, 6474])).
% 1.63/1.83 tff(6478,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6479,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6478, 6477])).
% 1.63/1.83 tff(6480,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6479, 271, 1281, 1639, 2449, 981])).
% 1.63/1.83 tff(6481,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6482,plain,
% 1.63/1.83 (~b(z, s(s(s(s(s(z))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6481, 6461, 6468, 6466])).
% 1.63/1.83 tff(6483,plain,
% 1.63/1.83 (r(z, s(s(s(s(s(z))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1658, 6482])).
% 1.63/1.83 tff(6484,plain,
% 1.63/1.83 (~r(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6368, 6483, 6473, 6471])).
% 1.63/1.83 tff(6485,plain,
% 1.63/1.83 (b(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1439, 6484])).
% 1.63/1.83 tff(6486,plain,
% 1.63/1.83 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[2471])).
% 1.63/1.83 tff(6487,plain,
% 1.63/1.83 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.63/1.83 inference(symmetry,[status(thm)],[6486])).
% 1.63/1.83 tff(6488,plain,
% 1.63/1.83 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, s(elem!1)))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6487])).
% 1.63/1.83 tff(6489,plain,
% 1.63/1.83 (~b(z, s(elem!1))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[33, 6488])).
% 1.63/1.83 tff(6490,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1421, 6489])).
% 1.63/1.83 tff(6491,plain,(b(z, s(s(s(elem!1)))) | (~b(z, s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6492,plain,
% 1.63/1.83 (b(z, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6491, 6485, 6464])).
% 1.63/1.83 tff(6493,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6494,plain,
% 1.63/1.83 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6495,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6494])).
% 1.63/1.83 tff(6496,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.83 inference(transitivity,[status(thm)],[6495, 6493])).
% 1.63/1.83 tff(6497,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6498,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6497, 6496])).
% 1.63/1.83 tff(6499,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6498, 271, 6461, 6492, 6468, 6466])).
% 1.63/1.83 tff(6500,plain,((s(z) = elem!1) | (~b(elem!1, z)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6501,plain,
% 1.63/1.83 (s(z) = elem!1),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6500, 6451, 3499, 412, 260, 909, 307, 6446, 2564, 479, 344])).
% 1.63/1.83 tff(6502,plain,
% 1.63/1.83 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6501])).
% 1.63/1.83 tff(6503,plain,
% 1.63/1.83 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.63/1.83 inference(symmetry,[status(thm)],[6502])).
% 1.63/1.83 tff(6504,plain,
% 1.63/1.83 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6503])).
% 1.63/1.83 tff(6505,plain,
% 1.63/1.83 (~b(s(z), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[192, 6504])).
% 1.63/1.83 tff(6506,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[260, 6505])).
% 1.63/1.83 tff(6507,plain,((~b(s(z), elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | b(s(s(s(elem!1))), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6508,plain,
% 1.63/1.83 (~b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6507, 6443, 3501, 3505, 3499, 3500, 479, 6444])).
% 1.63/1.83 tff(6509,plain,
% 1.63/1.83 (~(z = elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1543, 307, 894])).
% 1.63/1.83 tff(6510,plain,
% 1.63/1.83 (~(s(z) = s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[343, 6509])).
% 1.63/1.83 tff(6511,plain,
% 1.63/1.83 (~(s(elem!1) = s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[350, 6510])).
% 1.63/1.83 tff(6512,plain,
% 1.63/1.83 (r(s(z), s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[444, 439, 6510])).
% 1.63/1.83 tff(6513,plain,
% 1.63/1.83 (b(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1303, 439, 3505, 307, 6509, 412, 1242])).
% 1.63/1.83 tff(6514,plain,
% 1.63/1.83 (~(elem!1 = s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1397, 6513, 894])).
% 1.63/1.83 tff(6515,plain,
% 1.63/1.83 (~r(s(z), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1300, 6512, 412, 3505])).
% 1.63/1.83 tff(6516,plain,
% 1.63/1.83 (b(s(z), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[25, 6515])).
% 1.63/1.83 tff(6517,plain,
% 1.63/1.83 (~r(s(elem!1), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5329, 6512, 412, 3505])).
% 1.63/1.83 tff(6518,plain,
% 1.63/1.83 (b(s(elem!1), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[429, 6517, 6511])).
% 1.63/1.83 tff(6519,plain,
% 1.63/1.83 (~b(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1290, 6518, 307, 6516])).
% 1.63/1.83 tff(6520,plain,
% 1.63/1.83 (r(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[299, 6519, 6514])).
% 1.63/1.83 tff(6521,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6522,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6523,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6522, 6521])).
% 1.63/1.83 tff(6524,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6523, 121, 622, 357, 3456, 431])).
% 1.63/1.83 tff(6525,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6526,plain,
% 1.63/1.83 (~r(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6525, 4915, 6520, 6512])).
% 1.63/1.83 tff(6527,plain,
% 1.63/1.83 (b(s(elem!1), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2243, 6526, 2564])).
% 1.63/1.83 tff(6528,plain,
% 1.63/1.83 (~b(s(s(s(z))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2626, 271, 307, 6527, 1422])).
% 1.63/1.83 tff(6529,plain,
% 1.63/1.83 (~b(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4122, 6518, 307, 6513])).
% 1.63/1.83 tff(6530,plain,
% 1.63/1.83 (r(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1439, 6529])).
% 1.63/1.83 tff(6531,plain,
% 1.63/1.83 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4935, 6529, 3505, 439, 412])).
% 1.63/1.83 tff(6532,plain,
% 1.63/1.83 (~(s(elem!1) = s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2035, 6531])).
% 1.63/1.83 tff(6533,plain,
% 1.63/1.83 (r(z, s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1214, 1209])).
% 1.63/1.83 tff(6534,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6535,plain,
% 1.63/1.83 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6536,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6535])).
% 1.63/1.83 tff(6537,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[6536, 6534])).
% 1.63/1.83 tff(6538,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6539,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6538, 6537])).
% 1.63/1.83 tff(6540,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6539, 121, 357, 909, 2327, 1140])).
% 1.63/1.83 tff(6541,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6542,plain,
% 1.63/1.83 (~r(s(s(s(z))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6541, 6533, 909, 357])).
% 1.63/1.83 tff(6543,plain,
% 1.63/1.83 (b(s(s(s(z))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2325, 6542])).
% 1.63/1.83 tff(6544,plain,
% 1.63/1.83 (~b(s(elem!1), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3622, 6543, 447, 3871])).
% 1.63/1.83 tff(6545,plain,
% 1.63/1.83 (r(s(elem!1), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2044, 6544, 2037])).
% 1.63/1.83 tff(6546,plain,
% 1.63/1.83 (b(z, s(s(s(z))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[1326, 4206])).
% 1.63/1.83 tff(6547,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1209, 6546])).
% 1.63/1.83 tff(6548,plain,((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6549,plain,
% 1.63/1.83 (~(s(s(s(z))) = elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6548, 1209, 1326])).
% 1.63/1.83 tff(6550,plain,
% 1.63/1.83 (r(s(s(s(z))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[255, 6549, 2346])).
% 1.63/1.83 tff(6551,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6552,plain,
% 1.63/1.83 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6553,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[6552])).
% 1.63/1.83 tff(6554,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[6553, 6551])).
% 1.63/1.83 tff(6555,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(6556,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[6555, 6554])).
% 1.63/1.83 tff(6557,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6556, 121, 1441, 6550, 6533, 6545])).
% 1.63/1.83 tff(6558,plain,(b(z, s(s(s(z)))) | (~r(z, s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(6559,plain,
% 1.63/1.83 (b(z, s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6558, 3871, 2037, 447, 1441, 2346, 909, 357, 1326])).
% 1.63/1.83 tff(6560,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6561,plain,
% 1.63/1.83 (((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(6562,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6561])).
% 1.63/1.84 tff(6563,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6562, 6560])).
% 1.63/1.84 tff(6564,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6565,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6564, 6563])).
% 1.63/1.84 tff(6566,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6565, 271, 1281, 1422, 6559, 3871])).
% 1.63/1.84 tff(6567,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), s(z))) | (~r(z, s(elem!1))) | b(s(s(s(z))), elem!1) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(6568,plain,
% 1.63/1.84 (~b(s(z), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6567, 6516, 1422, 6532, 6518, 6530, 6528, 3505, 4915, 6513])).
% 1.63/1.84 tff(6569,plain,
% 1.63/1.84 (r(s(z), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[105, 6568])).
% 1.63/1.84 tff(6570,plain,
% 1.63/1.84 (~r(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4112, 6569, 4915, 6520])).
% 1.63/1.84 tff(6571,plain,
% 1.63/1.84 (s(s(s(z))) = elem!1),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[255, 6570, 6528])).
% 1.63/1.84 tff(6572,plain,
% 1.63/1.84 (s(elem!1) = s(s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2605, 6571])).
% 1.63/1.84 tff(6573,plain,
% 1.63/1.84 (s(s(s(s(z)))) = s(elem!1)),
% 1.63/1.84 inference(symmetry,[status(thm)],[6572])).
% 1.63/1.84 tff(6574,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6573])).
% 1.63/1.84 tff(6575,plain,
% 1.63/1.84 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 1.63/1.84 inference(symmetry,[status(thm)],[6574])).
% 1.63/1.84 tff(6576,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), z)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[412, 6575])).
% 1.63/1.84 tff(6577,plain,
% 1.63/1.84 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6572])).
% 1.63/1.84 tff(6578,plain,
% 1.63/1.84 (r(z, s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6530, 6577])).
% 1.63/1.84 tff(6579,plain,
% 1.63/1.84 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6572])).
% 1.63/1.84 tff(6580,plain,
% 1.63/1.84 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6579])).
% 1.63/1.84 tff(6581,plain,
% 1.63/1.84 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3499, 6580])).
% 1.63/1.84 tff(6582,plain,
% 1.63/1.84 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4045, 6581, 4038])).
% 1.63/1.84 tff(6583,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6584,plain,
% 1.63/1.84 (((~r(s(s(s(s(z)))), z)) | (~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))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6585,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6584])).
% 1.63/1.84 tff(6586,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6585, 6583])).
% 1.63/1.84 tff(6587,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6588,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6587, 6586])).
% 1.63/1.84 tff(6589,plain,
% 1.63/1.84 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6588, 121, 6582, 6578])).
% 1.63/1.84 tff(6590,plain,
% 1.63/1.84 (~r(s(s(s(s(s(z))))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6589, 6576])).
% 1.63/1.84 tff(6591,plain,
% 1.63/1.84 (((~![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))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6592,plain,
% 1.63/1.84 ((~![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))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6593,plain,
% 1.63/1.84 ((~![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)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6592, 6591])).
% 1.63/1.84 tff(6594,plain,
% 1.63/1.84 (b(s(s(s(s(s(z))))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6593, 21, 711, 6590])).
% 1.63/1.84 tff(6595,plain,
% 1.63/1.84 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6571])).
% 1.63/1.84 tff(6596,plain,
% 1.63/1.84 (b(z, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6548, 6571, 6513])).
% 1.63/1.84 tff(6597,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6598,plain,
% 1.63/1.84 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6599,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6598])).
% 1.63/1.84 tff(6600,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6599, 6597])).
% 1.63/1.84 tff(6601,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6602,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6601, 6600])).
% 1.63/1.84 tff(6603,plain,
% 1.63/1.84 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6602, 121, 6582, 6578])).
% 1.63/1.84 tff(6604,plain,
% 1.63/1.84 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6603, 6576])).
% 1.63/1.84 tff(6605,plain,
% 1.63/1.84 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1658, 6604])).
% 1.63/1.84 tff(6606,plain,
% 1.63/1.84 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6049, 6605, 1422, 6596])).
% 1.63/1.84 tff(6607,plain,
% 1.63/1.84 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1733, 6606])).
% 1.63/1.84 tff(6608,plain,
% 1.63/1.84 (r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6607, 6595])).
% 1.63/1.84 tff(6609,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6610,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6611,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6610, 6609])).
% 1.63/1.84 tff(6612,plain,
% 1.63/1.84 (~r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6611, 121, 4915, 6520, 6608])).
% 1.63/1.84 tff(6613,plain,
% 1.63/1.84 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1682, 6612])).
% 1.63/1.84 tff(6614,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6615,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6616,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 1.63/1.84 tff(6617,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6616, 271, 6513, 6516, 6613, 6594])).
% 1.63/1.84 tff(6618,plain,(b(s(z), s(elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | b(s(z), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(6619,plain,
% 1.63/1.84 (b(s(z), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6618, 1242, 412, 3499, 307, 2564, 1422, 894])).
% 1.63/1.84 tff(6620,plain,
% 1.63/1.84 (s(z) = elem!1),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1270, 1243, 307, 1242, 909, 412, 446, 351])).
% 1.63/1.84 tff(6621,plain,
% 1.63/1.84 (s(s(z)) = s(elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6620])).
% 1.63/1.84 tff(6622,plain,
% 1.63/1.84 (s(s(s(z))) = s(s(elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6621])).
% 1.63/1.84 tff(6623,plain,
% 1.63/1.84 (s(s(elem!1)) = s(s(s(z)))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6622])).
% 1.63/1.84 tff(6624,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6623])).
% 1.63/1.84 tff(6625,plain,
% 1.63/1.84 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6624])).
% 1.63/1.84 tff(6626,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1422, 6625])).
% 1.63/1.84 tff(6627,plain,
% 1.63/1.84 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6620])).
% 1.63/1.84 tff(6628,plain,
% 1.63/1.84 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.63/1.84 inference(transitivity,[status(thm)],[6627, 2212])).
% 1.63/1.84 tff(6629,plain,
% 1.63/1.84 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6628])).
% 1.63/1.84 tff(6630,plain,
% 1.63/1.84 (~(s(s(elem!1)) = elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[2137, 6629])).
% 1.63/1.84 tff(6631,plain,
% 1.63/1.84 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6622])).
% 1.63/1.84 tff(6632,plain,
% 1.63/1.84 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6631, 5078])).
% 1.63/1.84 tff(6633,plain,
% 1.63/1.84 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6632])).
% 1.63/1.84 tff(6634,plain,
% 1.63/1.84 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[2064, 6633])).
% 1.63/1.84 tff(6635,plain,
% 1.63/1.84 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6620])).
% 1.63/1.84 tff(6636,plain,
% 1.63/1.84 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.63/1.84 inference(transitivity,[status(thm)],[6635, 653])).
% 1.63/1.84 tff(6637,plain,
% 1.63/1.84 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6636])).
% 1.63/1.84 tff(6638,plain,
% 1.63/1.84 (~(s(s(s(elem!1))) = elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[61, 6637])).
% 1.63/1.84 tff(6639,plain,
% 1.63/1.84 (r(s(s(s(elem!1))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[486, 6638, 479])).
% 1.63/1.84 tff(6640,plain,
% 1.63/1.84 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6631])).
% 1.63/1.84 tff(6641,plain,
% 1.63/1.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[2064, 6640])).
% 1.63/1.84 tff(6642,plain,
% 1.63/1.84 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6622])).
% 1.63/1.84 tff(6643,plain,
% 1.63/1.84 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6620])).
% 1.63/1.84 tff(6644,plain,
% 1.63/1.84 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6643, 6642])).
% 1.63/1.84 tff(6645,plain,
% 1.63/1.84 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6621])).
% 1.63/1.84 tff(6646,plain,
% 1.63/1.84 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6645])).
% 1.63/1.84 tff(6647,plain,
% 1.63/1.84 (b(elem!1, s(s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[307, 6646])).
% 1.63/1.84 tff(6648,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6621])).
% 1.63/1.84 tff(6649,plain,
% 1.63/1.84 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6648])).
% 1.63/1.84 tff(6650,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1422, 6649])).
% 1.63/1.84 tff(6651,plain,
% 1.63/1.84 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[223])).
% 1.63/1.84 tff(6652,plain,
% 1.63/1.84 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6651, 159])).
% 1.63/1.84 tff(6653,plain,
% 1.63/1.84 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.63/1.84 inference(transitivity,[status(thm)],[6652, 160])).
% 1.63/1.84 tff(6654,plain,
% 1.63/1.84 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6653])).
% 1.63/1.84 tff(6655,plain,
% 1.63/1.84 (~(s(s(s(z))) = elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[97, 6654])).
% 1.63/1.84 tff(6656,plain,
% 1.63/1.84 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[78, 5038])).
% 1.63/1.84 tff(6657,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[1038, 223])).
% 1.63/1.84 tff(6658,plain,
% 1.63/1.84 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6657])).
% 1.63/1.84 tff(6659,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[139, 6658])).
% 1.63/1.84 tff(6660,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[1226])).
% 1.63/1.84 tff(6661,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6660])).
% 1.63/1.84 tff(6662,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[1224])).
% 1.63/1.84 tff(6663,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6662, 6661])).
% 1.63/1.84 tff(6664,plain,
% 1.63/1.84 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[2372])).
% 1.63/1.84 tff(6665,plain,
% 1.63/1.84 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6664])).
% 1.63/1.84 tff(6666,plain,
% 1.63/1.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[2064, 6665])).
% 1.63/1.84 tff(6667,plain,
% 1.63/1.84 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[239])).
% 1.63/1.84 tff(6668,plain,
% 1.63/1.84 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6667])).
% 1.63/1.84 tff(6669,plain,
% 1.63/1.84 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.63/1.84 inference(transitivity,[status(thm)],[6668, 2212])).
% 1.63/1.84 tff(6670,plain,
% 1.63/1.84 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6669])).
% 1.63/1.84 tff(6671,plain,
% 1.63/1.84 (~(s(s(elem!1)) = elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[2137, 6670])).
% 1.63/1.84 tff(6672,plain,
% 1.63/1.84 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6668])).
% 1.63/1.84 tff(6673,plain,
% 1.63/1.84 (~(elem!1 = s(s(elem!1)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[2137, 6672])).
% 1.63/1.84 tff(6674,plain,
% 1.63/1.84 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[1224])).
% 1.63/1.84 tff(6675,plain,
% 1.63/1.84 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[239])).
% 1.63/1.84 tff(6676,plain,
% 1.63/1.84 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6675, 6674])).
% 1.63/1.84 tff(6677,plain,
% 1.63/1.84 (b(s(z), s(s(s(z))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[588, 6676])).
% 1.63/1.84 tff(6678,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[71, 6677])).
% 1.63/1.84 tff(6679,plain,((~b(elem!1, s(s(elem!1)))) | b(s(z), s(s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(6680,plain,
% 1.63/1.84 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6679, 71, 239])).
% 1.63/1.84 tff(6681,plain,
% 1.63/1.84 (r(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[599, 6680, 6673])).
% 1.63/1.84 tff(6682,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3310, 6681, 199, 331, 6671, 2344, 82])).
% 1.63/1.84 tff(6683,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[556, 6682, 6666])).
% 1.63/1.84 tff(6684,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6683, 6663])).
% 1.63/1.84 tff(6685,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6686,plain,
% 1.63/1.84 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6687,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6686])).
% 1.63/1.84 tff(6688,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[6687, 6685])).
% 1.63/1.84 tff(6689,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(6690,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[6689, 6688])).
% 1.63/1.84 tff(6691,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6690, 121, 909, 911, 106])).
% 1.63/1.84 tff(6692,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1093, 21, 1090, 6691])).
% 1.63/1.84 tff(6693,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6694,plain,
% 1.63/1.84 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(6695,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6694])).
% 1.63/1.84 tff(6696,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6695, 6693])).
% 1.63/1.85 tff(6697,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(6698,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6697, 6696])).
% 1.63/1.85 tff(6699,plain,
% 1.63/1.85 (~r(z, s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6698, 121, 909, 911, 106])).
% 1.63/1.85 tff(6700,plain,
% 1.63/1.85 (b(z, s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1119, 21, 6699, 1114])).
% 1.63/1.85 tff(6701,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6702,plain,
% 1.63/1.85 (((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6703,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6702])).
% 1.63/1.85 tff(6704,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6703, 6701])).
% 1.63/1.85 tff(6705,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(6706,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6705, 6704])).
% 1.63/1.85 tff(6707,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6706, 271, 1307, 6700, 6692, 6684])).
% 1.63/1.85 tff(6708,plain,(b(s(z), s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | b(z, elem!1) | (z = elem!1) | r(elem!1, s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6709,plain,
% 1.63/1.85 (~b(z, s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6708, 71, 909, 2344, 1222, 199, 331, 6659, 6656])).
% 1.63/1.85 tff(6710,plain,
% 1.63/1.85 (r(z, s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1214, 6709])).
% 1.63/1.85 tff(6711,plain,
% 1.63/1.85 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1037])).
% 1.63/1.85 tff(6712,plain,
% 1.63/1.85 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6711])).
% 1.63/1.85 tff(6713,plain,
% 1.63/1.85 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6679, 71, 1222])).
% 1.63/1.85 tff(6714,plain,
% 1.63/1.85 (r(elem!1, s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[599, 6713, 5038])).
% 1.63/1.85 tff(6715,plain,
% 1.63/1.85 (r(elem!1, s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6714, 6712])).
% 1.63/1.85 tff(6716,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6717,plain,
% 1.63/1.85 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6718,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6717])).
% 1.63/1.85 tff(6719,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6718, 6716])).
% 1.63/1.85 tff(6720,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(6721,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6720, 6719])).
% 1.63/1.85 tff(6722,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6721, 121, 378, 1184, 145, 1140])).
% 1.63/1.85 tff(6723,plain,((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6724,plain,
% 1.63/1.85 (~r(s(s(s(z))), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6723, 6715, 1243, 6710])).
% 1.63/1.85 tff(6725,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.63/1.85 tff(6726,plain,
% 1.63/1.85 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[223])).
% 1.63/1.85 tff(6727,plain,
% 1.63/1.85 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6726])).
% 1.63/1.85 tff(6728,plain,
% 1.63/1.85 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1036])).
% 1.63/1.85 tff(6729,plain,
% 1.63/1.85 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.63/1.85 inference(symmetry,[status(thm)],[6728])).
% 1.63/1.85 tff(6730,plain,
% 1.63/1.85 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6729, 6727])).
% 1.63/1.85 tff(6731,plain,
% 1.63/1.85 (~r(s(elem!1), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2697, 6714, 1243, 139, 6656])).
% 1.63/1.85 tff(6732,plain,
% 1.63/1.85 (b(s(elem!1), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2243, 6731, 2564])).
% 1.63/1.85 tff(6733,plain,
% 1.63/1.85 (b(s(s(z)), s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6732, 6730])).
% 1.63/1.85 tff(6734,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6735,plain,
% 1.63/1.85 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6736,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6735])).
% 1.63/1.85 tff(6737,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6736, 6734])).
% 1.63/1.85 tff(6738,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(6739,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6738, 6737])).
% 1.63/1.85 tff(6740,plain,
% 1.63/1.85 ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6739, 271])).
% 1.63/1.85 tff(6741,plain,
% 1.63/1.85 (~b(s(s(s(z))), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6740, 6733, 1405, 6725])).
% 1.63/1.85 tff(6742,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[255, 6741, 6724, 6655])).
% 1.63/1.85 tff(6743,plain,(b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~(s(z) = elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | r(elem!1, s(elem!1)) | b(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6744,plain,
% 1.63/1.85 (b(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6743, 6650, 6647, 6620, 2564, 6639, 909, 2344, 199, 331])).
% 1.63/1.85 tff(6745,plain,
% 1.63/1.85 (b(elem!1, s(s(elem!1)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6744, 6644])).
% 1.63/1.85 tff(6746,plain,
% 1.63/1.85 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6623])).
% 1.63/1.85 tff(6747,plain,
% 1.63/1.85 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(z))) = s(elem!1))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6746, 3535])).
% 1.63/1.85 tff(6748,plain,
% 1.63/1.85 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6747])).
% 1.63/1.85 tff(6749,plain,
% 1.63/1.85 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6748])).
% 1.63/1.85 tff(6750,plain,
% 1.63/1.85 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6621])).
% 1.63/1.85 tff(6751,plain,
% 1.63/1.85 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6750, 3535])).
% 1.63/1.85 tff(6752,plain,
% 1.63/1.85 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6751])).
% 1.63/1.85 tff(6753,plain,
% 1.63/1.85 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[1136, 6752])).
% 1.63/1.85 tff(6754,plain,
% 1.63/1.85 (~(s(elem!1) = s(s(elem!1)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6753, 6749])).
% 1.63/1.85 tff(6755,plain,
% 1.63/1.85 (elem!1 = s(z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1221, 6620])).
% 1.63/1.85 tff(6756,plain,
% 1.63/1.85 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6620])).
% 1.63/1.85 tff(6757,plain,
% 1.63/1.85 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6756])).
% 1.63/1.85 tff(6758,plain,
% 1.63/1.85 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6646, 6757])).
% 1.63/1.85 tff(6759,plain,
% 1.63/1.85 (b(s(z), s(s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[307, 6758])).
% 1.63/1.85 tff(6760,plain,
% 1.63/1.85 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[2376])).
% 1.63/1.85 tff(6761,plain,
% 1.63/1.85 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6760])).
% 1.63/1.85 tff(6762,plain,
% 1.63/1.85 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3870, 6761])).
% 1.63/1.85 tff(6763,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.63/1.85 tff(6764,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6765,plain,
% 1.63/1.85 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6766,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6765])).
% 1.63/1.85 tff(6767,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6766, 6764])).
% 1.63/1.85 tff(6768,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(6769,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6768, 6767])).
% 1.63/1.85 tff(6770,plain,
% 1.63/1.85 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6769, 271, 3871, 6763])).
% 1.63/1.85 tff(6771,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6770, 6762, 1405])).
% 1.63/1.85 tff(6772,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6773,plain,
% 1.63/1.85 (~b(s(elem!1), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6772, 6744, 6755, 6650, 6759])).
% 1.63/1.85 tff(6774,plain,
% 1.63/1.85 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2369, 6773, 6755])).
% 1.63/1.85 tff(6775,plain,
% 1.63/1.85 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[526, 6774, 6754])).
% 1.63/1.85 tff(6776,plain,
% 1.63/1.85 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6622])).
% 1.63/1.85 tff(6777,plain,
% 1.63/1.85 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6776])).
% 1.63/1.85 tff(6778,plain,
% 1.63/1.85 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6777])).
% 1.63/1.85 tff(6779,plain,
% 1.63/1.85 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6778])).
% 1.63/1.85 tff(6780,plain,
% 1.63/1.85 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3499, 6779])).
% 1.63/1.85 tff(6781,plain,
% 1.63/1.85 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6777])).
% 1.63/1.85 tff(6782,plain,
% 1.63/1.85 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6781])).
% 1.63/1.85 tff(6783,plain,
% 1.63/1.85 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6782])).
% 1.63/1.85 tff(6784,plain,
% 1.63/1.85 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6783])).
% 1.63/1.85 tff(6785,plain,
% 1.63/1.85 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6621])).
% 1.63/1.85 tff(6786,plain,
% 1.63/1.85 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6785])).
% 1.63/1.85 tff(6787,plain,
% 1.63/1.85 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[877, 6786])).
% 1.63/1.85 tff(6788,plain,
% 1.63/1.85 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6787, 6784])).
% 1.63/1.85 tff(6789,plain,
% 1.63/1.85 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3112, 21, 6788, 6780])).
% 1.63/1.85 tff(6790,plain,
% 1.63/1.85 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1038])).
% 1.63/1.85 tff(6791,plain,
% 1.63/1.85 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6790])).
% 1.63/1.85 tff(6792,plain,
% 1.63/1.85 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[223])).
% 1.63/1.85 tff(6793,plain,
% 1.63/1.85 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6792, 6791])).
% 1.63/1.85 tff(6794,plain,
% 1.63/1.85 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.63/1.85 inference(transitivity,[status(thm)],[5036, 2212])).
% 1.63/1.85 tff(6795,plain,
% 1.63/1.85 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6794])).
% 1.63/1.85 tff(6796,plain,
% 1.63/1.85 (~(s(s(elem!1)) = elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[2137, 6795])).
% 1.63/1.85 tff(6797,plain,
% 1.63/1.85 (~r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5431, 2088, 412, 627])).
% 1.63/1.85 tff(6798,plain,
% 1.63/1.85 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[239])).
% 1.63/1.85 tff(6799,plain,
% 1.63/1.85 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(symmetry,[status(thm)],[6798])).
% 1.63/1.85 tff(6800,plain,
% 1.63/1.85 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(s(elem!1)), elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6799])).
% 1.63/1.85 tff(6801,plain,
% 1.63/1.85 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[2128, 6800])).
% 1.63/1.85 tff(6802,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1624, 6801])).
% 1.63/1.85 tff(6803,plain,((~(elem!1 = s(z))) | (~r(s(s(elem!1)), elem!1)) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6804,plain,
% 1.63/1.85 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6803, 6797, 1222])).
% 1.63/1.85 tff(6805,plain,
% 1.63/1.85 (b(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[862, 6804, 6796])).
% 1.63/1.85 tff(6806,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2702, 271, 307, 2618, 542, 2494])).
% 1.63/1.85 tff(6807,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6808,plain,
% 1.63/1.85 (~b(s(elem!1), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6807, 6805, 307, 2494])).
% 1.63/1.85 tff(6809,plain,
% 1.63/1.85 (r(s(elem!1), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2243, 6808, 2564])).
% 1.63/1.85 tff(6810,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6811,plain,
% 1.63/1.85 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(6812,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[6811])).
% 1.63/1.85 tff(6813,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[6812, 6810])).
% 1.63/1.85 tff(6814,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(6815,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6814, 6813])).
% 1.63/1.85 tff(6816,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6815, 121, 622, 378, 727, 412])).
% 1.63/1.85 tff(6817,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6818,plain,
% 1.63/1.85 (~r(elem!1, s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6817, 6809, 378, 412])).
% 1.63/1.85 tff(6819,plain,
% 1.63/1.85 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1045, 6818, 223])).
% 1.63/1.85 tff(6820,plain,
% 1.63/1.85 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[760, 6819])).
% 1.63/1.85 tff(6821,plain,
% 1.63/1.85 (b(elem!1, s(s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[6820, 6793])).
% 1.63/1.85 tff(6822,plain,
% 1.63/1.85 (r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[145, 4950])).
% 1.63/1.85 tff(6823,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2128, 6822])).
% 1.63/1.85 tff(6824,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(elem!1)), s(z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(6825,plain,
% 1.63/1.85 (~r(s(s(s(z))), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6824, 6797, 223])).
% 1.63/1.85 tff(6826,plain,
% 1.63/1.85 (b(s(s(s(z))), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[255, 6825, 6655])).
% 1.63/1.85 tff(6827,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1037, 1038])).
% 1.63/1.85 tff(6828,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[6827])).
% 1.63/1.85 tff(6829,plain,
% 1.63/1.86 (~r(elem!1, z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5358, 6809, 378, 412])).
% 1.63/1.86 tff(6830,plain,
% 1.63/1.86 (b(elem!1, z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[284, 6829, 259])).
% 1.63/1.86 tff(6831,plain,
% 1.63/1.86 (b(elem!1, s(s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6820, 6792])).
% 1.63/1.86 tff(6832,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6833,plain,
% 1.63/1.86 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6834,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6833])).
% 1.63/1.86 tff(6835,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6834, 6832])).
% 1.63/1.86 tff(6836,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6837,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6836, 6835])).
% 1.63/1.86 tff(6838,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6837, 271, 261, 1421, 1638, 738])).
% 1.63/1.86 tff(6839,plain,((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(6840,plain,
% 1.63/1.86 (~b(s(s(s(elem!1))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6839, 738, 1421, 261])).
% 1.63/1.86 tff(6841,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1904, 21, 30, 6840])).
% 1.63/1.86 tff(6842,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.63/1.86 tff(6843,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6844,plain,
% 1.63/1.86 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6845,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6844])).
% 1.63/1.86 tff(6846,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6845, 6843])).
% 1.63/1.86 tff(6847,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6848,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6847, 6846])).
% 1.63/1.86 tff(6849,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6848, 121, 684, 2088, 412, 6842])).
% 1.63/1.86 tff(6850,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(6851,plain,
% 1.63/1.86 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6850, 6841, 412, 2088])).
% 1.63/1.86 tff(6852,plain,
% 1.63/1.86 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[681, 6851, 82])).
% 1.63/1.86 tff(6853,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6854,plain,
% 1.63/1.86 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6855,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6854])).
% 1.63/1.86 tff(6856,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6855, 6853])).
% 1.63/1.86 tff(6857,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6858,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6857, 6856])).
% 1.63/1.86 tff(6859,plain,
% 1.63/1.86 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6858, 121, 378, 412, 6841])).
% 1.63/1.86 tff(6860,plain,
% 1.63/1.86 (b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2293, 21, 6859, 2280])).
% 1.63/1.86 tff(6861,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6862,plain,
% 1.63/1.86 (((~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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6863,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6862])).
% 1.63/1.86 tff(6864,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6863, 6861])).
% 1.63/1.86 tff(6865,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6866,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6865, 6864])).
% 1.63/1.86 tff(6867,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6866, 271, 307, 6860, 6852, 738])).
% 1.63/1.86 tff(6868,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(6869,plain,
% 1.63/1.86 (~b(z, s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6868, 6831, 378, 412, 6656, 2088, 307, 6830])).
% 1.63/1.86 tff(6870,plain,
% 1.63/1.86 (r(z, s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1439, 6869])).
% 1.63/1.86 tff(6871,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6872,plain,
% 1.63/1.86 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6873,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6872])).
% 1.63/1.86 tff(6874,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6873, 6871])).
% 1.63/1.86 tff(6875,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6876,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6875, 6874])).
% 1.63/1.86 tff(6877,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6876, 121, 623, 1441, 627, 2088])).
% 1.63/1.86 tff(6878,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(6879,plain,
% 1.63/1.86 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6878, 6870, 627, 2088])).
% 1.63/1.86 tff(6880,plain,
% 1.63/1.86 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[556, 6879, 1])).
% 1.63/1.86 tff(6881,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6880, 6828])).
% 1.63/1.86 tff(6882,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6883,plain,
% 1.63/1.86 (((~b(s(s(s(s(z)))), s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6884,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6883])).
% 1.63/1.86 tff(6885,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~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))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6884, 6882])).
% 1.63/1.86 tff(6886,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6887,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6886, 6885])).
% 1.63/1.86 tff(6888,plain,
% 1.63/1.86 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6887, 271])).
% 1.63/1.86 tff(6889,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6888, 6881, 6826, 6821])).
% 1.63/1.86 tff(6890,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1776, 6889, 1772])).
% 1.63/1.86 tff(6891,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[1373, 3057])).
% 1.63/1.86 tff(6892,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[6891])).
% 1.63/1.86 tff(6893,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[1758, 6892])).
% 1.63/1.86 tff(6894,assumption,(~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.86 tff(6895,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6894, 6893])).
% 1.63/1.86 tff(6896,plain,(r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(6897,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6896, 6890, 223])).
% 1.63/1.86 tff(6898,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.63/1.86 tff(6899,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6900,plain,
% 1.63/1.86 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(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))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6901,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(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)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6900])).
% 1.63/1.86 tff(6902,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6901, 6899])).
% 1.63/1.86 tff(6903,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6904,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6903, 6902])).
% 1.63/1.86 tff(6905,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6904, 271, 543, 588, 638, 738])).
% 1.63/1.86 tff(6906,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(6907,plain,
% 1.63/1.86 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6906, 6880, 588, 6831])).
% 1.63/1.86 tff(6908,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[681, 6907, 6656])).
% 1.63/1.86 tff(6909,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6910,plain,
% 1.63/1.86 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(6911,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[6910])).
% 1.63/1.86 tff(6912,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[6911, 6909])).
% 1.63/1.86 tff(6913,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(6914,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[6913, 6912])).
% 1.63/1.86 tff(6915,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6914, 121, 6809, 6908, 6898, 6897])).
% 1.63/1.87 tff(6916,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (elem!1 = z) | (s(elem!1) = elem!1) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(6917,plain,
% 1.63/1.87 (~r(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6916, 6789, 6745, 6620, 6641, 6775, 1243, 412, 307, 358, 2564, 6626])).
% 1.63/1.87 tff(6918,plain,
% 1.63/1.87 (b(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2106, 6917])).
% 1.63/1.87 tff(6919,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6920,plain,
% 1.63/1.87 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6921,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6920])).
% 1.63/1.87 tff(6922,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[6921, 6919])).
% 1.63/1.87 tff(6923,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(6924,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[6923, 6922])).
% 1.63/1.87 tff(6925,plain,
% 1.63/1.87 (~b(elem!1, z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6924, 271, 6918, 6745, 6626])).
% 1.63/1.87 tff(6926,plain,
% 1.63/1.87 (r(elem!1, z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[284, 6925, 358])).
% 1.63/1.87 tff(6927,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6928,plain,
% 1.63/1.87 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6929,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6928])).
% 1.63/1.87 tff(6930,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)))),
% 1.63/1.87 inference(transitivity,[status(thm)],[6929, 6927])).
% 1.63/1.87 tff(6931,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(6932,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[6931, 6930])).
% 1.63/1.87 tff(6933,plain,
% 1.63/1.87 (~r(z, s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6932, 121, 378, 1409, 139])).
% 1.63/1.87 tff(6934,plain,
% 1.63/1.87 (b(z, s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[36, 21, 6933, 32])).
% 1.63/1.87 tff(6935,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6936,plain,
% 1.63/1.87 (((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6937,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6936])).
% 1.63/1.87 tff(6938,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[6937, 6935])).
% 1.63/1.87 tff(6939,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(6940,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[6939, 6938])).
% 1.63/1.87 tff(6941,plain,
% 1.63/1.87 (~r(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6940, 121, 378, 1409, 1624])).
% 1.63/1.87 tff(6942,plain,
% 1.63/1.87 (b(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2106, 6941])).
% 1.63/1.87 tff(6943,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.63/1.87 tff(6944,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6945,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(6946,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[6945, 6944])).
% 1.63/1.87 tff(6947,plain,
% 1.63/1.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6946, 121, 1409, 139, 1624])).
% 1.63/1.87 tff(6948,plain,
% 1.63/1.87 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[586, 6947, 6943])).
% 1.63/1.87 tff(6949,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6950,plain,
% 1.63/1.87 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6951,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6950])).
% 1.63/1.87 tff(6952,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.87 inference(transitivity,[status(thm)],[6951, 6949])).
% 1.63/1.87 tff(6953,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(6954,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[6953, 6952])).
% 1.63/1.87 tff(6955,plain,
% 1.63/1.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6954, 121, 1409, 139, 1624])).
% 1.63/1.87 tff(6956,plain,
% 1.63/1.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[556, 6955, 1])).
% 1.63/1.87 tff(6957,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1911, 271, 6956, 6948, 6942, 6934])).
% 1.63/1.87 tff(6958,plain,((~r(elem!1, z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(6959,plain,
% 1.63/1.87 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6958, 6926, 6641, 6639, 6634, 1243])).
% 1.63/1.87 tff(6960,plain,
% 1.63/1.87 (b(s(s(elem!1)), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[862, 6959, 6630])).
% 1.63/1.87 tff(6961,plain,
% 1.63/1.87 (~r(s(elem!1), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5358, 6926, 1243, 412])).
% 1.63/1.87 tff(6962,plain,
% 1.63/1.87 (b(s(elem!1), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2243, 6961, 2564])).
% 1.63/1.87 tff(6963,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6807, 6962, 6960, 307, 6626])).
% 1.63/1.87 tff(6964,plain,(b(z, elem!1) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~r(z, s(z))) | r(elem!1, s(elem!1)) | (z = elem!1) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(s(z))), s(elem!1))) | b(s(z), elem!1) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(6965,plain,
% 1.63/1.87 (b(z, elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6964, 1242, 2564, 412, 3505, 2344, 6509, 479, 3499, 1422, 307, 6619])).
% 1.63/1.87 tff(6966,plain,
% 1.63/1.87 (~(elem!1 = s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1397, 6965, 894])).
% 1.63/1.87 tff(6967,plain,
% 1.63/1.87 (~(s(z) = elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1221, 6966])).
% 1.63/1.87 tff(6968,plain,
% 1.63/1.87 (r(s(z), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[236, 6967, 1242])).
% 1.63/1.87 tff(6969,plain,
% 1.63/1.87 (~r(s(elem!1), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1254, 6968, 3505, 412])).
% 1.63/1.87 tff(6970,plain,
% 1.63/1.87 (b(s(elem!1), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[429, 6969, 6511])).
% 1.63/1.87 tff(6971,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6972,plain,
% 1.63/1.87 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(6973,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6972])).
% 1.63/1.87 tff(6974,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.87 inference(transitivity,[status(thm)],[6973, 6971])).
% 1.63/1.87 tff(6975,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(6976,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[6975, 6974])).
% 1.63/1.87 tff(6977,plain,
% 1.63/1.87 (~b(s(s(s(z))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6976, 271, 307, 1422, 6970])).
% 1.63/1.87 tff(6978,plain,
% 1.63/1.87 (~b(elem!1, s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[456, 6970, 307, 6619])).
% 1.63/1.87 tff(6979,plain,
% 1.63/1.87 (r(elem!1, s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[299, 6978, 6966])).
% 1.63/1.87 tff(6980,plain,
% 1.63/1.87 (~b(s(z), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5668, 271, 1422, 6970, 6619])).
% 1.63/1.87 tff(6981,plain,
% 1.63/1.87 (r(s(z), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[105, 6980])).
% 1.63/1.87 tff(6982,plain,
% 1.63/1.87 (~r(s(s(s(z))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4112, 6981, 6968, 6979])).
% 1.63/1.87 tff(6983,plain,
% 1.63/1.87 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2063, 6510])).
% 1.63/1.87 tff(6984,plain,
% 1.63/1.87 (~(s(s(s(elem!1))) = elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5698, 6970, 1422, 3505, 6619, 6968, 6983, 6965])).
% 1.63/1.87 tff(6985,plain,
% 1.63/1.87 (r(s(s(s(elem!1))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[486, 6984, 479])).
% 1.63/1.87 tff(6986,plain,
% 1.63/1.87 (~b(z, s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4122, 6970, 307, 6965])).
% 1.63/1.87 tff(6987,plain,
% 1.63/1.87 (r(z, s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1439, 6986])).
% 1.63/1.87 tff(6988,plain,
% 1.63/1.87 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[3895, 6984])).
% 1.63/1.87 tff(6989,plain,
% 1.63/1.87 (~b(s(z), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6429, 271, 2618, 1422, 446])).
% 1.63/1.87 tff(6990,plain,
% 1.63/1.87 (r(s(z), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[105, 6989])).
% 1.63/1.87 tff(6991,plain,
% 1.63/1.87 (~r(s(s(s(z))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4112, 6990, 357, 3456])).
% 1.63/1.87 tff(6992,plain,
% 1.63/1.87 (s(s(s(z))) = elem!1),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[255, 6991, 2627])).
% 1.63/1.87 tff(6993,plain,
% 1.63/1.87 (s(elem!1) = s(s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2605, 6992])).
% 1.63/1.87 tff(6994,plain,
% 1.63/1.87 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6993])).
% 1.63/1.87 tff(6995,plain,
% 1.63/1.87 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.63/1.87 inference(symmetry,[status(thm)],[6994])).
% 1.63/1.87 tff(6996,plain,
% 1.63/1.87 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6995])).
% 1.63/1.87 tff(6997,plain,
% 1.63/1.87 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.63/1.87 inference(symmetry,[status(thm)],[6996])).
% 1.63/1.87 tff(6998,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6995])).
% 1.63/1.87 tff(6999,plain,
% 1.63/1.87 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6998])).
% 1.63/1.87 tff(7000,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6992])).
% 1.63/1.87 tff(7001,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(7002,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(7003,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[7002, 7001])).
% 1.63/1.87 tff(7004,plain,
% 1.63/1.87 (~b(s(s(s(z))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[7003, 271, 2618, 1422, 446])).
% 1.63/1.87 tff(7005,plain,
% 1.63/1.87 (r(s(s(s(z))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2325, 7004])).
% 1.63/1.87 tff(7006,plain,
% 1.63/1.87 (~r(z, s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6541, 7005, 909, 357])).
% 1.63/1.87 tff(7007,plain,
% 1.63/1.87 (b(z, s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1214, 7006])).
% 1.63/1.87 tff(7008,plain,
% 1.63/1.87 (s(s(s(s(z)))) = s(elem!1)),
% 1.63/1.87 inference(symmetry,[status(thm)],[6993])).
% 1.63/1.87 tff(7009,plain,
% 1.63/1.87 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 1.63/1.87 inference(monotonicity,[status(thm)],[7008])).
% 1.63/1.87 tff(7010,plain,
% 1.63/1.87 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 1.63/1.87 inference(symmetry,[status(thm)],[7009])).
% 1.63/1.87 tff(7011,plain,
% 1.63/1.87 (r(s(s(s(s(z)))), z)),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[412, 7010])).
% 1.63/1.87 tff(7012,plain,
% 1.63/1.87 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6993])).
% 1.63/1.87 tff(7013,plain,
% 1.63/1.87 (r(z, s(s(s(s(z)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[1441, 7012])).
% 1.63/1.87 tff(7014,plain,
% 1.63/1.87 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[6993])).
% 1.63/1.87 tff(7015,plain,
% 1.63/1.87 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[7014])).
% 1.63/1.87 tff(7016,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[3499, 7015])).
% 1.63/1.87 tff(7017,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4045, 7016, 4038])).
% 1.63/1.87 tff(7018,plain,
% 1.63/1.87 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6602, 121, 7017, 7013])).
% 1.63/1.87 tff(7019,plain,
% 1.63/1.87 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[7018, 7011])).
% 1.63/1.87 tff(7020,plain,
% 1.63/1.87 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1658, 7019])).
% 1.63/1.87 tff(7021,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6049, 7020, 1422, 7007])).
% 1.63/1.87 tff(7022,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1733, 7021])).
% 1.63/1.87 tff(7023,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[7022, 7000])).
% 1.63/1.87 tff(7024,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(7025,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(7026,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7025, 7024])).
% 1.63/1.88 tff(7027,plain,
% 1.63/1.88 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7026, 121, 139, 3456, 7023])).
% 1.63/1.88 tff(7028,plain,
% 1.63/1.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7027, 6999])).
% 1.63/1.88 tff(7029,plain,
% 1.63/1.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[556, 7028, 1])).
% 1.63/1.88 tff(7030,plain,
% 1.63/1.88 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7029, 6997])).
% 1.63/1.88 tff(7031,plain,
% 1.63/1.88 (~r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6611, 121, 357, 3456, 7023])).
% 1.63/1.88 tff(7032,plain,
% 1.63/1.88 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1682, 7031])).
% 1.63/1.88 tff(7033,plain,
% 1.63/1.88 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4618, 121, 357, 139, 3456])).
% 1.63/1.88 tff(7034,plain,
% 1.63/1.88 (b(s(s(s(elem!1))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[66, 21, 7033, 63])).
% 1.63/1.88 tff(7035,plain,
% 1.63/1.88 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4626, 121, 357, 139, 3456])).
% 1.63/1.88 tff(7036,plain,
% 1.63/1.88 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[760, 7035])).
% 1.63/1.88 tff(7037,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7038,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7039,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7038, 7037])).
% 1.63/1.88 tff(7040,plain,
% 1.63/1.88 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7039, 271, 7036, 7034, 7032])).
% 1.63/1.88 tff(7041,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7040, 7030])).
% 1.63/1.88 tff(7042,plain,((~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(7043,plain,
% 1.63/1.88 (~b(s(elem!1), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7042, 6988, 6985, 6979, 6968, 1422, 412, 3499, 6987, 3505, 6619, 307])).
% 1.63/1.88 tff(7044,plain,
% 1.63/1.88 (r(s(elem!1), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2243, 7043, 2564])).
% 1.63/1.88 tff(7045,plain,
% 1.63/1.88 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3888, 7044, 6979, 6985])).
% 1.63/1.88 tff(7046,plain,
% 1.63/1.88 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4618, 121, 6968, 6985, 6979])).
% 1.63/1.88 tff(7047,plain,
% 1.63/1.88 (b(s(s(s(elem!1))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[66, 21, 7046, 63])).
% 1.63/1.88 tff(7048,plain,
% 1.63/1.88 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4626, 121, 6968, 6985, 6979])).
% 1.63/1.88 tff(7049,plain,
% 1.63/1.88 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[760, 7048])).
% 1.63/1.88 tff(7050,plain,
% 1.63/1.88 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3813, 271, 7049, 6970, 7047])).
% 1.63/1.88 tff(7051,plain,
% 1.63/1.88 (s(s(s(elem!1))) = s(elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[681, 7050, 7045])).
% 1.63/1.88 tff(7052,plain,
% 1.63/1.88 (elem!1 = s(s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[78, 7051])).
% 1.63/1.88 tff(7053,plain,
% 1.63/1.88 (~(s(s(s(z))) = elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3906, 7052])).
% 1.63/1.88 tff(7054,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[255, 7053, 6982, 6977])).
% 1.63/1.88 tff(7055,plain,(b(s(z), elem!1) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(elem!1))), elem!1) | b(z, s(z)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(7056,plain,
% 1.63/1.88 (r(elem!1, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7055, 6508, 6443, 3500, 3501, 3499, 479, 894, 5549])).
% 1.63/1.88 tff(7057,plain,
% 1.63/1.88 (~r(z, elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5645, 7056, 6508, 3499, 3500, 3501, 3505])).
% 1.63/1.88 tff(7058,plain,
% 1.63/1.88 (~(s(z) = elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1402, 7057, 894])).
% 1.63/1.88 tff(7059,plain,
% 1.63/1.88 (~(elem!1 = s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[242, 7058])).
% 1.63/1.88 tff(7060,plain,
% 1.63/1.88 (r(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[236, 7058, 6508])).
% 1.63/1.88 tff(7061,plain,
% 1.63/1.88 (~(s(s(z)) = s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[960, 7058])).
% 1.63/1.88 tff(7062,plain,
% 1.63/1.88 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[953, 7061])).
% 1.63/1.88 tff(7063,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5759, 7062, 7060, 5549, 3505, 6444, 3501, 7056, 479, 7057, 7059])).
% 1.63/1.88 tff(7064,plain,(b(s(s(s(elem!1))), elem!1) | b(z, s(z)) | b(s(s(s(s(s(z))))), s(elem!1)) | b(s(elem!1), z) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(7065,plain,
% 1.63/1.88 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7064, 377, 3499, 3498, 894])).
% 1.63/1.88 tff(7066,plain,
% 1.63/1.88 (~r(elem!1, z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1417, 379, 3505, 3501])).
% 1.63/1.88 tff(7067,plain,
% 1.63/1.88 (b(s(elem!1), z)),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[2618, 2484])).
% 1.63/1.88 tff(7068,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3498, 7067])).
% 1.63/1.88 tff(7069,plain,((~(z = elem!1)) | b(s(elem!1), z) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(7070,plain,
% 1.63/1.88 (~(z = elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7069, 2618, 3498])).
% 1.63/1.88 tff(7071,plain,
% 1.63/1.88 (~(elem!1 = z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[333, 7070])).
% 1.63/1.88 tff(7072,plain,
% 1.63/1.88 (b(elem!1, z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[284, 7071, 7066])).
% 1.63/1.88 tff(7073,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7074,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7075,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7074, 7073])).
% 1.63/1.88 tff(7076,plain,
% 1.63/1.88 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7075, 271, 2618, 7072, 7065])).
% 1.63/1.88 tff(7077,plain,
% 1.63/1.88 (b(z, elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[355, 7070, 1391])).
% 1.63/1.88 tff(7078,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7079,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7080,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7079, 7078])).
% 1.63/1.88 tff(7081,plain,
% 1.63/1.88 (~b(s(s(s(elem!1))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7080, 271, 7077, 7072, 7065])).
% 1.63/1.88 tff(7082,plain,
% 1.63/1.88 (r(s(s(s(elem!1))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1904, 21, 30, 7081])).
% 1.63/1.88 tff(7083,plain,
% 1.63/1.88 (~b(z, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3747, 271, 2618, 7077, 7072])).
% 1.63/1.88 tff(7084,plain,
% 1.63/1.88 (r(z, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1439, 7083])).
% 1.63/1.88 tff(7085,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7086,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7087,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7086, 7085])).
% 1.63/1.88 tff(7088,plain,
% 1.63/1.88 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7087, 121, 7084, 3501, 7082])).
% 1.63/1.88 tff(7089,plain,
% 1.63/1.88 (s(s(s(elem!1))) = s(elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[681, 7088, 7076])).
% 1.63/1.88 tff(7090,plain,
% 1.63/1.88 (elem!1 = s(s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[78, 7089])).
% 1.63/1.88 tff(7091,plain,
% 1.63/1.88 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7090])).
% 1.63/1.88 tff(7092,plain,
% 1.63/1.88 (b(s(s(elem!1)), z)),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7072, 7091])).
% 1.63/1.88 tff(7093,plain,
% 1.63/1.88 (b(s(z), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5661, 7070, 379, 3501, 3505, 1391, 258])).
% 1.63/1.88 tff(7094,plain,
% 1.63/1.88 (b(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3787, 7090, 2618])).
% 1.63/1.88 tff(7095,plain,
% 1.63/1.88 (s(s(elem!1)) = elem!1),
% 1.63/1.88 inference(symmetry,[status(thm)],[7090])).
% 1.63/1.88 tff(7096,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7095])).
% 1.63/1.88 tff(7097,plain,
% 1.63/1.88 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.88 inference(symmetry,[status(thm)],[7096])).
% 1.63/1.88 tff(7098,plain,
% 1.63/1.88 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7095])).
% 1.63/1.88 tff(7099,plain,
% 1.63/1.88 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[7098, 159])).
% 1.63/1.88 tff(7100,plain,
% 1.63/1.88 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7099])).
% 1.63/1.88 tff(7101,plain,
% 1.63/1.88 (~(elem!1 = s(s(s(z))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[944, 7100])).
% 1.63/1.88 tff(7102,plain,
% 1.63/1.88 (~(s(z) = s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[343, 7070])).
% 1.63/1.88 tff(7103,plain,
% 1.63/1.88 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3917, 7090, 7102])).
% 1.63/1.88 tff(7104,plain,
% 1.63/1.88 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6358, 7090, 7103])).
% 1.63/1.88 tff(7105,plain,
% 1.63/1.88 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4138, 7104, 3499])).
% 1.63/1.88 tff(7106,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7107,plain,
% 1.63/1.88 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7108,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7107])).
% 1.63/1.88 tff(7109,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[7108, 7106])).
% 1.63/1.88 tff(7110,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7111,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7110, 7109])).
% 1.63/1.88 tff(7112,plain,
% 1.63/1.88 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7111, 121, 7084, 3501, 7105])).
% 1.63/1.88 tff(7113,plain,
% 1.63/1.88 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1658, 7112])).
% 1.63/1.88 tff(7114,plain,
% 1.63/1.88 (r(s(s(s(z))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1816, 3506, 2033])).
% 1.63/1.88 tff(7115,plain,
% 1.63/1.88 (~r(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5155, 7114, 412, 3505])).
% 1.63/1.88 tff(7116,plain,
% 1.63/1.88 (~b(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4176, 7114, 3499, 1639, 3506, 1326, 6284, 412, 377, 331, 894])).
% 1.63/1.88 tff(7117,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1155, 7116, 7115])).
% 1.63/1.88 tff(7118,plain,(b(s(s(s(z))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (z = elem!1) | b(z, s(z)) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(7119,plain,
% 1.63/1.88 (b(s(s(s(z))), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7118, 7113, 3499, 7077, 3501, 377, 7070, 894, 7103])).
% 1.63/1.88 tff(7120,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7121,plain,
% 1.63/1.88 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7122,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7121])).
% 1.63/1.88 tff(7123,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[7122, 7120])).
% 1.63/1.88 tff(7124,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7125,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 1.63/1.88 tff(7126,plain,
% 1.63/1.88 (~b(s(z), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7125, 271, 7094, 7119, 7093])).
% 1.63/1.88 tff(7127,plain,
% 1.63/1.88 (r(s(z), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[105, 7126])).
% 1.63/1.88 tff(7128,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7129,plain,
% 1.63/1.88 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7130,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7129])).
% 1.63/1.88 tff(7131,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[7130, 7128])).
% 1.63/1.88 tff(7132,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7133,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7132, 7131])).
% 1.63/1.88 tff(7134,plain,
% 1.63/1.88 (~b(s(s(s(z))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7133, 271, 7094, 7119, 7093])).
% 1.63/1.88 tff(7135,plain,
% 1.63/1.88 (r(s(s(s(z))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2325, 7134])).
% 1.63/1.88 tff(7136,plain,
% 1.63/1.88 (~r(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6186, 121, 3505, 7135, 7127])).
% 1.63/1.88 tff(7137,plain,
% 1.63/1.88 (b(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1155, 7136])).
% 1.63/1.88 tff(7138,plain,
% 1.63/1.88 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7090])).
% 1.63/1.88 tff(7139,plain,
% 1.63/1.88 (b(z, s(s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7077, 7138])).
% 1.63/1.88 tff(7140,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5738, 271, 7139, 7092, 7137])).
% 1.63/1.88 tff(7141,plain,
% 1.63/1.88 (~b(elem!1, s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5482, 7140, 7090])).
% 1.63/1.88 tff(7142,plain,
% 1.63/1.88 (r(elem!1, s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1192, 7141, 7101])).
% 1.63/1.88 tff(7143,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7142, 7097])).
% 1.63/1.88 tff(7144,plain,
% 1.63/1.88 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2454, 7137, 7092, 7139])).
% 1.63/1.88 tff(7145,plain,
% 1.63/1.88 (r(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2462, 21, 7144, 944])).
% 1.63/1.88 tff(7146,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7147,plain,
% 1.63/1.88 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7148,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[7147])).
% 1.63/1.88 tff(7149,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[7148, 7146])).
% 1.63/1.88 tff(7150,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(7151,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[7150, 7149])).
% 1.63/1.88 tff(7152,plain,
% 1.63/1.88 (~r(s(z), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[7151, 121, 7145, 7127, 7143])).
% 1.63/1.88 tff(7153,plain,
% 1.63/1.88 (b(s(z), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2167, 7152])).
% 1.63/1.88 tff(7154,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(7155,plain,
% 1.63/1.88 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7156,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7155])).
% 1.63/1.89 tff(7157,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.89 inference(transitivity,[status(thm)],[7156, 7154])).
% 1.63/1.89 tff(7158,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(7159,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7158, 7157])).
% 1.63/1.89 tff(7160,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7159, 271, 7153, 7094, 7093, 7092])).
% 1.63/1.89 tff(7161,plain,((~b(s(elem!1), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(elem!1)) | (elem!1 = s(elem!1)) | b(z, s(z)) | (~r(elem!1, s(elem!1))) | r(z, elem!1) | (elem!1 = s(z)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7162,plain,
% 1.63/1.89 (~b(s(elem!1), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7161, 1391, 3499, 377, 894, 3502, 3504, 243, 3498])).
% 1.63/1.89 tff(7163,plain,
% 1.63/1.89 (b(elem!1, z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[284, 358, 3956])).
% 1.63/1.89 tff(7164,plain,
% 1.63/1.89 (~b(s(s(s(elem!1))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7080, 271, 5653, 7163, 504])).
% 1.63/1.89 tff(7165,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1904, 21, 30, 7164])).
% 1.63/1.89 tff(7166,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7167,plain,
% 1.63/1.89 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7168,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7167])).
% 1.63/1.89 tff(7169,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.89 inference(transitivity,[status(thm)],[7168, 7166])).
% 1.63/1.89 tff(7170,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(7171,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7170, 7169])).
% 1.63/1.89 tff(7172,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7171, 271, 1326, 261, 3407, 504])).
% 1.63/1.89 tff(7173,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,[]))).
% 1.63/1.89 tff(7174,plain,
% 1.63/1.89 (~b(z, s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7173, 7163, 504, 5653])).
% 1.63/1.89 tff(7175,plain,
% 1.63/1.89 (r(z, s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[36, 21, 7174, 32])).
% 1.63/1.89 tff(7176,plain,
% 1.63/1.89 (b(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[5661, 331, 379, 412, 3505, 1391, 258])).
% 1.63/1.89 tff(7177,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[379, 2826])).
% 1.63/1.89 tff(7178,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[676, 7177])).
% 1.63/1.89 tff(7179,plain,((~(s(s(s(elem!1))) = elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7180,plain,
% 1.63/1.89 (~(s(s(s(elem!1))) = elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7179, 676, 379])).
% 1.63/1.89 tff(7181,plain,
% 1.63/1.89 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3895, 7180])).
% 1.63/1.89 tff(7182,plain,
% 1.63/1.89 (~(s(elem!1) = s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[210, 7181])).
% 1.63/1.89 tff(7183,plain,
% 1.63/1.89 (~(elem!1 = s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3952, 3506, 3505, 412, 2467, 944, 379, 331, 446, 1326, 7182])).
% 1.63/1.89 tff(7184,plain,
% 1.63/1.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[78, 7183])).
% 1.63/1.89 tff(7185,plain,
% 1.63/1.89 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[681, 7184, 676])).
% 1.63/1.89 tff(7186,plain,
% 1.63/1.89 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4334, 7185, 3499])).
% 1.63/1.89 tff(7187,plain,
% 1.63/1.89 (r(s(s(s(z))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1816, 7186, 3506])).
% 1.63/1.89 tff(7188,plain,
% 1.63/1.89 (~r(s(s(s(z))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[5155, 7187, 412, 3505])).
% 1.63/1.89 tff(7189,plain,
% 1.63/1.89 (b(s(s(s(z))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1155, 7188])).
% 1.63/1.89 tff(7190,plain,
% 1.63/1.89 (s(s(s(z))) = elem!1),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3766, 7189, 7187, 379, 1326, 412, 331, 3505])).
% 1.63/1.89 tff(7191,plain,
% 1.63/1.89 (s(elem!1) = s(s(s(s(z))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2605, 7190])).
% 1.63/1.89 tff(7192,plain,
% 1.63/1.89 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7191])).
% 1.63/1.89 tff(7193,plain,
% 1.63/1.89 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7192])).
% 1.63/1.89 tff(7194,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7193])).
% 1.63/1.89 tff(7195,plain,
% 1.63/1.89 (~b(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7118, 7186, 3499, 1326, 412, 377, 331, 894, 3506])).
% 1.63/1.89 tff(7196,plain,
% 1.63/1.89 (b(z, s(s(s(s(s(z)))))) <=> b(z, elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[3042])).
% 1.63/1.89 tff(7197,plain,
% 1.63/1.89 (b(z, elem!1) <=> b(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7196])).
% 1.63/1.89 tff(7198,plain,
% 1.63/1.89 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[1326, 7197])).
% 1.63/1.89 tff(7199,assumption,(~b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.89 tff(7200,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7199, 7198])).
% 1.63/1.89 tff(7201,plain,((~(s(s(s(s(s(z))))) = elem!1)) | b(z, s(s(s(s(s(z)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7202,plain,
% 1.63/1.89 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7201, 7195, 1326])).
% 1.63/1.89 tff(7203,plain,
% 1.63/1.89 (s(s(s(s(z)))) = s(elem!1)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7191])).
% 1.63/1.89 tff(7204,plain,
% 1.63/1.89 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7203])).
% 1.63/1.89 tff(7205,plain,
% 1.63/1.89 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7204])).
% 1.63/1.89 tff(7206,plain,
% 1.63/1.89 (r(elem!1, s(s(s(s(z)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[379, 7205])).
% 1.63/1.89 tff(7207,plain,
% 1.63/1.89 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7203])).
% 1.63/1.89 tff(7208,plain,
% 1.63/1.89 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7207])).
% 1.63/1.89 tff(7209,plain,
% 1.63/1.89 (r(s(elem!1), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2243, 2467, 3500])).
% 1.63/1.89 tff(7210,plain,
% 1.63/1.89 (r(s(s(s(s(z)))), elem!1)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7209, 7208])).
% 1.63/1.89 tff(7211,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7191])).
% 1.63/1.89 tff(7212,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7211])).
% 1.63/1.89 tff(7213,plain,
% 1.63/1.89 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[3499, 7212])).
% 1.63/1.89 tff(7214,plain,
% 1.63/1.89 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4045, 7213, 4038])).
% 1.63/1.89 tff(7215,plain,
% 1.63/1.89 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4859, 121, 7214])).
% 1.63/1.89 tff(7216,plain,
% 1.63/1.89 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7215, 7210, 7206])).
% 1.63/1.89 tff(7217,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[840, 7216, 7202])).
% 1.63/1.89 tff(7218,plain,
% 1.63/1.89 (b(s(s(elem!1)), elem!1)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7217, 7194])).
% 1.63/1.89 tff(7219,plain,
% 1.63/1.89 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7192])).
% 1.63/1.89 tff(7220,plain,
% 1.63/1.89 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7219])).
% 1.63/1.89 tff(7221,plain,
% 1.63/1.89 (r(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1658, 7195])).
% 1.63/1.89 tff(7222,plain,
% 1.63/1.89 (r(z, s(s(elem!1)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7221, 7220])).
% 1.63/1.89 tff(7223,plain,
% 1.63/1.89 (~(s(s(elem!1)) = s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[620, 7182])).
% 1.63/1.89 tff(7224,plain,
% 1.63/1.89 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7192, 7191])).
% 1.63/1.89 tff(7225,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7224])).
% 1.63/1.89 tff(7226,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7225])).
% 1.63/1.89 tff(7227,plain,
% 1.63/1.89 (~b(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7213, 7226])).
% 1.63/1.89 tff(7228,plain,
% 1.63/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[701, 7227, 7223])).
% 1.63/1.89 tff(7229,plain,
% 1.63/1.89 (~b(s(s(elem!1)), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4898, 7228, 1326, 7209, 331, 412, 7222])).
% 1.63/1.89 tff(7230,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7229, 7218])).
% 1.63/1.89 tff(7231,plain,(b(s(s(s(z))), s(elem!1)) | (~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (z = elem!1) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(elem!1)) | (elem!1 = s(elem!1)) | b(z, s(z)) | r(s(s(s(elem!1))), s(elem!1)) | b(s(elem!1), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7232,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7231, 5653, 379, 3506, 412, 3499, 377, 894, 331, 2467, 944, 7176])).
% 1.63/1.89 tff(7233,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7234,plain,
% 1.63/1.89 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7235,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7234])).
% 1.63/1.89 tff(7236,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.63/1.89 inference(transitivity,[status(thm)],[7235, 7233])).
% 1.63/1.89 tff(7237,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(7238,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7237, 7236])).
% 1.63/1.89 tff(7239,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7238, 121, 7232, 7175, 412, 7165])).
% 1.63/1.89 tff(7240,plain,((z = elem!1) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (elem!1 = s(elem!1)) | b(z, s(z)) | b(s(elem!1), elem!1) | (s(s(s(z))) = s(s(elem!1))) | r(z, elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7241,plain,
% 1.63/1.89 (z = elem!1),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7240, 3506, 504, 379, 412, 3499, 377, 894, 2467, 944, 1391, 258])).
% 1.63/1.89 tff(7242,plain,
% 1.63/1.89 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7241])).
% 1.63/1.89 tff(7243,plain,
% 1.63/1.89 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7242])).
% 1.63/1.89 tff(7244,plain,
% 1.63/1.89 (s(z) = s(elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7241])).
% 1.63/1.89 tff(7245,plain,
% 1.63/1.89 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7244])).
% 1.63/1.89 tff(7246,plain,
% 1.63/1.89 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7245])).
% 1.63/1.89 tff(7247,plain,
% 1.63/1.89 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.63/1.89 inference(transitivity,[status(thm)],[7246, 7243])).
% 1.63/1.89 tff(7248,plain,
% 1.63/1.89 (r(s(z), z)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7209, 7247])).
% 1.63/1.89 tff(7249,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7244])).
% 1.63/1.89 tff(7250,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7249])).
% 1.63/1.89 tff(7251,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7250])).
% 1.63/1.89 tff(7252,plain,
% 1.63/1.89 (~b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[3499, 7251])).
% 1.63/1.89 tff(7253,plain,
% 1.63/1.89 (r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1682, 7252])).
% 1.63/1.89 tff(7254,plain,
% 1.63/1.89 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1669, 7253, 3505, 7248])).
% 1.63/1.89 tff(7255,plain,
% 1.63/1.89 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1658, 7254])).
% 1.63/1.89 tff(7256,plain,
% 1.63/1.89 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7241])).
% 1.63/1.89 tff(7257,plain,
% 1.63/1.89 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7256])).
% 1.63/1.89 tff(7258,plain,
% 1.63/1.89 (s(s(z)) = s(s(elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7244])).
% 1.63/1.89 tff(7259,plain,
% 1.63/1.89 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7258])).
% 1.63/1.89 tff(7260,plain,
% 1.63/1.89 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7259])).
% 1.63/1.89 tff(7261,plain,
% 1.63/1.89 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7260])).
% 1.63/1.89 tff(7262,plain,
% 1.63/1.89 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.63/1.89 inference(transitivity,[status(thm)],[7261, 7257])).
% 1.63/1.89 tff(7263,plain,
% 1.63/1.89 (b(s(s(s(z))), z)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[504, 7262])).
% 1.63/1.89 tff(7264,plain,
% 1.63/1.89 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7259])).
% 1.63/1.89 tff(7265,plain,
% 1.63/1.89 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7264])).
% 1.63/1.89 tff(7266,plain,
% 1.63/1.89 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7265])).
% 1.63/1.89 tff(7267,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7266])).
% 1.63/1.89 tff(7268,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7267])).
% 1.63/1.89 tff(7269,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7268])).
% 1.63/1.89 tff(7270,plain,
% 1.63/1.89 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[3499, 7269])).
% 1.63/1.89 tff(7271,plain,
% 1.63/1.89 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[814, 7241])).
% 1.63/1.89 tff(7272,plain,
% 1.63/1.89 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[818, 21, 7271, 7270])).
% 1.63/1.89 tff(7273,plain,
% 1.63/1.89 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7259])).
% 1.63/1.89 tff(7274,plain,
% 1.63/1.89 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7273])).
% 1.63/1.89 tff(7275,plain,
% 1.63/1.89 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[3506, 7274])).
% 1.63/1.89 tff(7276,plain,
% 1.63/1.89 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.63/1.89 inference(monotonicity,[status(thm)],[72])).
% 1.63/1.89 tff(7277,plain,
% 1.63/1.89 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.89 inference(symmetry,[status(thm)],[7276])).
% 1.63/1.89 tff(7278,plain,
% 1.63/1.89 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7277])).
% 1.63/1.89 tff(7279,plain,
% 1.63/1.89 (~b(s(s(s(elem!1))), elem!1)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[2467, 7278])).
% 1.63/1.89 tff(7280,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[504, 7279])).
% 1.63/1.89 tff(7281,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,[]))).
% 1.63/1.89 tff(7282,plain,
% 1.63/1.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7281, 2467, 504])).
% 1.63/1.89 tff(7283,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[679, 21, 7282, 7275])).
% 1.63/1.89 tff(7284,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7285,plain,
% 1.63/1.89 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7286,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[7285])).
% 1.63/1.89 tff(7287,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[7286, 7284])).
% 1.63/1.89 tff(7288,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(7289,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7288, 7287])).
% 1.63/1.89 tff(7290,plain,
% 1.63/1.89 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7289, 121, 7209, 7283, 7272])).
% 1.63/1.89 tff(7291,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[779, 705])).
% 1.63/1.89 tff(7292,plain,
% 1.63/1.89 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(symmetry,[status(thm)],[7291])).
% 1.63/1.89 tff(7293,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[1477, 7292])).
% 1.63/1.89 tff(7294,assumption,(~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.63/1.89 tff(7295,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7294, 7293])).
% 1.63/1.89 tff(7296,plain,(r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7297,plain,
% 1.63/1.89 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7296, 7290, 7241])).
% 1.63/1.89 tff(7298,plain,
% 1.63/1.89 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1494, 7297])).
% 1.63/1.89 tff(7299,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7300,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(7301,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[7300, 7299])).
% 1.63/1.89 tff(7302,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7301, 121, 7209, 7283, 7272])).
% 1.63/1.89 tff(7303,plain,
% 1.63/1.89 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6039, 7302, 7241])).
% 1.63/1.89 tff(7304,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1733, 7303])).
% 1.63/1.89 tff(7305,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4072, 7304, 7298, 7263, 7255])).
% 1.63/1.89 tff(7306,plain,(b(s(s(s(z))), s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | b(z, s(z)) | b(s(elem!1), elem!1) | (s(s(s(z))) = s(s(elem!1))) | r(z, elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(7307,plain,
% 1.63/1.89 (b(s(s(s(z))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7306, 7162, 7065, 3502, 3501, 377, 894, 3499, 3504, 1391, 243])).
% 1.63/1.89 tff(7308,plain,
% 1.63/1.89 (~(s(s(s(z))) = elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6165, 7307, 317])).
% 1.63/1.89 tff(7309,plain,
% 1.63/1.89 (r(s(elem!1), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2243, 7162, 3500])).
% 1.63/1.89 tff(7310,plain,
% 1.63/1.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7281, 7162, 7065])).
% 1.63/1.89 tff(7311,plain,
% 1.63/1.89 (~b(s(s(s(elem!1))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7080, 271, 1326, 261, 504])).
% 1.63/1.89 tff(7312,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1904, 21, 30, 7311])).
% 1.63/1.89 tff(7313,plain,
% 1.63/1.89 (~b(z, s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7173, 261, 504, 1326])).
% 1.63/1.89 tff(7314,plain,
% 1.63/1.89 (r(z, s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[36, 21, 7313, 32])).
% 1.63/1.89 tff(7315,plain,
% 1.63/1.89 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7238, 121, 7314, 412, 7312])).
% 1.63/1.89 tff(7316,plain,
% 1.63/1.89 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[681, 82, 7315])).
% 1.63/1.89 tff(7317,plain,
% 1.63/1.89 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6215, 121, 7314, 412, 7312])).
% 1.63/1.89 tff(7318,plain,
% 1.63/1.89 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2293, 21, 7317])).
% 1.63/1.89 tff(7319,plain,
% 1.63/1.89 (b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[7318, 2280])).
% 1.63/1.89 tff(7320,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(7321,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(7322,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))))),
% 1.63/1.90 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 1.63/1.90 tff(7323,plain,
% 1.63/1.90 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[7322, 271, 1422, 7319, 7316])).
% 1.63/1.90 tff(7324,plain,
% 1.63/1.90 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[2069, 21, 7323, 2065])).
% 1.63/1.90 tff(7325,plain,
% 1.63/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.63/1.90 inference(rewrite,[status(thm)],[])).
% 1.63/1.90 tff(7326,plain,
% 1.63/1.90 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.63/1.90 inference(rewrite,[status(thm)],[])).
% 1.63/1.90 tff(7327,plain,
% 1.63/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.63/1.90 inference(monotonicity,[status(thm)],[7326])).
% 1.63/1.90 tff(7328,plain,
% 1.63/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.63/1.90 inference(transitivity,[status(thm)],[7327, 7325])).
% 1.63/1.90 tff(7329,plain,
% 1.63/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.63/1.90 inference(quant_inst,[status(thm)],[])).
% 1.63/1.90 tff(7330,plain,
% 1.63/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.63/1.90 inference(modus_ponens,[status(thm)],[7329, 7328])).
% 1.63/1.90 tff(7331,plain,
% 1.63/1.90 (~r(s(s(s(z))), z)),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[7330, 121, 7314, 7312, 7324])).
% 1.63/1.90 tff(7332,plain,
% 1.63/1.90 (b(s(s(s(z))), z)),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[1155, 7331])).
% 1.63/1.90 tff(7333,plain,
% 1.63/1.90 (~b(s(s(s(z))), elem!1)),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[3764, 271, 1326, 261, 7332])).
% 1.63/1.90 tff(7334,plain,
% 1.63/1.90 (r(s(s(s(z))), elem!1)),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[255, 7333, 907])).
% 1.63/1.90 tff(7335,plain,
% 1.63/1.90 (~(s(s(s(z))) = s(elem!1))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[4334, 7316, 3499])).
% 1.63/1.90 tff(7336,plain,
% 1.63/1.90 (~(s(elem!1) = s(s(s(z))))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[2035, 7335])).
% 1.63/1.90 tff(7337,plain,
% 1.63/1.90 (~r(s(elem!1), s(s(s(z))))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[6290, 121, 379, 622, 7334])).
% 1.63/1.90 tff(7338,plain,
% 1.63/1.90 (b(s(elem!1), s(s(s(z))))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[2044, 7337, 7336])).
% 1.63/1.90 tff(7339,plain,
% 1.63/1.90 (b(s(elem!1), s(z))),
% 1.63/1.90 inference(unit_resolution,[status(thm)],[429, 3793, 422])).
% 1.63/1.90 tff(7340,plain,
% 1.63/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7341,plain,
% 1.73/1.90 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7342,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7341])).
% 1.73/1.90 tff(7343,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[7342, 7340])).
% 1.73/1.90 tff(7344,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(7345,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7344, 7343])).
% 1.73/1.90 tff(7346,plain,
% 1.73/1.90 (~r(s(z), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7345, 121, 379, 357, 145])).
% 1.73/1.90 tff(7347,plain,
% 1.73/1.90 (b(s(z), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[105, 7346])).
% 1.73/1.90 tff(7348,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7349,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(7350,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7349, 7348])).
% 1.73/1.90 tff(7351,plain,
% 1.73/1.90 (~r(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7350, 121, 379, 357, 145])).
% 1.73/1.90 tff(7352,plain,
% 1.73/1.90 (b(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2325, 7351])).
% 1.73/1.90 tff(7353,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3622, 7352, 7347, 7339, 3870])).
% 1.73/1.90 tff(7354,plain,((~r(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(7355,plain,
% 1.73/1.90 (~r(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7354, 7338, 379, 7334, 422, 909, 412])).
% 1.73/1.90 tff(7356,plain,
% 1.73/1.90 (b(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[236, 7355, 231])).
% 1.73/1.90 tff(7357,plain,
% 1.73/1.90 (~b(s(z), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3964, 7356, 1326, 261])).
% 1.73/1.90 tff(7358,plain,
% 1.73/1.90 (r(s(z), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[25, 7357])).
% 1.73/1.90 tff(7359,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7360,plain,
% 1.73/1.90 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7361,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7360])).
% 1.73/1.90 tff(7362,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[7361, 7359])).
% 1.73/1.90 tff(7363,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(7364,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7363, 7362])).
% 1.73/1.90 tff(7365,plain,
% 1.73/1.90 (~r(z, s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7364, 121, 7314, 7312, 7324])).
% 1.73/1.90 tff(7366,plain,
% 1.73/1.90 (b(z, s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1214, 7365])).
% 1.73/1.90 tff(7367,plain,
% 1.73/1.90 (~b(z, s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6298, 271, 1422, 7366, 7338])).
% 1.73/1.90 tff(7368,plain,
% 1.73/1.90 (r(z, s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1439, 7367])).
% 1.73/1.90 tff(7369,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7370,plain,
% 1.73/1.90 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7371,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7370])).
% 1.73/1.90 tff(7372,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.90 inference(transitivity,[status(thm)],[7371, 7369])).
% 1.73/1.90 tff(7373,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(7374,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7373, 7372])).
% 1.73/1.90 tff(7375,plain,
% 1.73/1.90 (~r(s(z), s(s(s(elem!1))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7374, 121, 7368, 7358, 7312])).
% 1.73/1.90 tff(7376,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7377,plain,
% 1.73/1.90 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7378,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7377])).
% 1.73/1.90 tff(7379,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.90 inference(transitivity,[status(thm)],[7378, 7376])).
% 1.73/1.90 tff(7380,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(7381,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7380, 7379])).
% 1.73/1.90 tff(7382,plain,
% 1.73/1.90 (~b(s(z), s(s(s(elem!1))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7381, 271, 7356, 261, 504])).
% 1.73/1.90 tff(7383,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[760, 7382, 7375])).
% 1.73/1.90 tff(7384,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(7385,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7384, 5654, 351, 504, 82, 231, 379, 1422, 909, 412, 5653, 622, 907, 2064, 3499])).
% 1.73/1.90 tff(7386,plain,((z = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(7387,plain,
% 1.73/1.90 (z = elem!1),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7386, 7310, 7065, 231, 3502, 7307, 3505, 3501, 7309, 7308, 3499, 1391])).
% 1.73/1.90 tff(7388,plain,
% 1.73/1.90 (s(z) = s(elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.90 tff(7389,plain,
% 1.73/1.90 (s(s(z)) = s(s(elem!1))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7388])).
% 1.73/1.90 tff(7390,plain,
% 1.73/1.90 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7389])).
% 1.73/1.90 tff(7391,plain,
% 1.73/1.90 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7390])).
% 1.73/1.90 tff(7392,plain,
% 1.73/1.90 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7391])).
% 1.73/1.90 tff(7393,plain,
% 1.73/1.90 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7392])).
% 1.73/1.90 tff(7394,plain,
% 1.73/1.90 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7391])).
% 1.73/1.90 tff(7395,plain,
% 1.73/1.90 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7394, 7393])).
% 1.73/1.90 tff(7396,plain,
% 1.73/1.90 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7395])).
% 1.73/1.90 tff(7397,plain,
% 1.73/1.90 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7394, 7393])).
% 1.73/1.90 tff(7398,plain,
% 1.73/1.90 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7397])).
% 1.73/1.90 tff(7399,plain,
% 1.73/1.90 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7392, 7389])).
% 1.73/1.90 tff(7400,plain,
% 1.73/1.90 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7399])).
% 1.73/1.90 tff(7401,plain,
% 1.73/1.90 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[877, 7400])).
% 1.73/1.90 tff(7402,plain,
% 1.73/1.90 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7401, 1706])).
% 1.73/1.90 tff(7403,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7392, 7390])).
% 1.73/1.90 tff(7404,plain,
% 1.73/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7403])).
% 1.73/1.90 tff(7405,plain,
% 1.73/1.90 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7404])).
% 1.73/1.90 tff(7406,plain,
% 1.73/1.90 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7393])).
% 1.73/1.90 tff(7407,plain,
% 1.73/1.90 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7406])).
% 1.73/1.90 tff(7408,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.90 tff(7409,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[7408, 7407])).
% 1.73/1.90 tff(7410,plain,
% 1.73/1.90 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.90 tff(7411,plain,
% 1.73/1.90 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.73/1.90 inference(symmetry,[status(thm)],[7410])).
% 1.73/1.90 tff(7412,plain,
% 1.73/1.90 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7388])).
% 1.73/1.90 tff(7413,plain,
% 1.73/1.90 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.73/1.90 inference(symmetry,[status(thm)],[7412])).
% 1.73/1.90 tff(7414,plain,
% 1.73/1.90 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.73/1.90 inference(transitivity,[status(thm)],[7413, 7411])).
% 1.73/1.90 tff(7415,plain,
% 1.73/1.90 (r(s(z), z)),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7309, 7414])).
% 1.73/1.90 tff(7416,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7388])).
% 1.73/1.90 tff(7417,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7416])).
% 1.73/1.90 tff(7418,plain,
% 1.73/1.90 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7417])).
% 1.73/1.90 tff(7419,plain,
% 1.73/1.90 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[3499, 7418])).
% 1.73/1.90 tff(7420,plain,
% 1.73/1.90 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1682, 7419])).
% 1.73/1.90 tff(7421,plain,
% 1.73/1.90 (~r(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1669, 7420, 3505, 7415])).
% 1.73/1.90 tff(7422,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1658, 7421])).
% 1.73/1.90 tff(7423,plain,
% 1.73/1.90 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[7422, 7409])).
% 1.73/1.90 tff(7424,plain,
% 1.73/1.90 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.90 tff(7425,plain,
% 1.73/1.90 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7424])).
% 1.73/1.90 tff(7426,plain,
% 1.73/1.90 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[711, 7425])).
% 1.73/1.90 tff(7427,plain,
% 1.73/1.90 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7393])).
% 1.73/1.90 tff(7428,plain,
% 1.73/1.90 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7427])).
% 1.73/1.90 tff(7429,plain,
% 1.73/1.90 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7393])).
% 1.73/1.90 tff(7430,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/1.90 inference(symmetry,[status(thm)],[7429])).
% 1.73/1.90 tff(7431,plain,
% 1.73/1.90 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7430])).
% 1.73/1.90 tff(7432,plain,
% 1.73/1.90 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[3499, 7431])).
% 1.73/1.90 tff(7433,plain,
% 1.73/1.90 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[814, 7387])).
% 1.73/1.90 tff(7434,plain,
% 1.73/1.90 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[818, 21, 7433, 7432])).
% 1.73/1.90 tff(7435,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7436,plain,
% 1.73/1.90 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(7437,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[7436])).
% 1.73/1.90 tff(7438,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/1.91 inference(transitivity,[status(thm)],[7437, 7435])).
% 1.73/1.91 tff(7439,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(7440,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7439, 7438])).
% 1.73/1.91 tff(7441,plain,
% 1.73/1.91 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7440, 121, 3502, 7309, 7434])).
% 1.73/1.91 tff(7442,plain,
% 1.73/1.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7441, 7428])).
% 1.73/1.91 tff(7443,plain,
% 1.73/1.91 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[840, 7442, 7426])).
% 1.73/1.91 tff(7444,plain,
% 1.73/1.91 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[835, 7443, 7387])).
% 1.73/1.91 tff(7445,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7446,plain,
% 1.73/1.91 (((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7447,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7446])).
% 1.73/1.91 tff(7448,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[7447, 7445])).
% 1.73/1.91 tff(7449,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(7450,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7449, 7448])).
% 1.73/1.91 tff(7451,plain,
% 1.73/1.91 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7450, 271, 7065, 7444, 7423])).
% 1.73/1.91 tff(7452,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7451, 7405])).
% 1.73/1.91 tff(7453,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1733, 7452])).
% 1.73/1.91 tff(7454,plain,
% 1.73/1.91 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6039, 7453, 7387])).
% 1.73/1.91 tff(7455,plain,
% 1.73/1.91 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.73/1.91 inference(symmetry,[status(thm)],[7390])).
% 1.73/1.91 tff(7456,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7455, 7393])).
% 1.73/1.91 tff(7457,plain,
% 1.73/1.91 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7456])).
% 1.73/1.91 tff(7458,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7459,plain,
% 1.73/1.91 (((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7460,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7459])).
% 1.73/1.91 tff(7461,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.91 inference(transitivity,[status(thm)],[7460, 7458])).
% 1.73/1.91 tff(7462,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(7463,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7462, 7461])).
% 1.73/1.91 tff(7464,plain,
% 1.73/1.91 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7463, 271, 7065, 7444, 7423])).
% 1.73/1.91 tff(7465,plain,
% 1.73/1.91 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7464, 7457])).
% 1.73/1.91 tff(7466,plain,
% 1.73/1.91 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1494, 7465])).
% 1.73/1.91 tff(7467,plain,
% 1.73/1.91 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7296, 7466, 7387])).
% 1.73/1.91 tff(7468,plain,
% 1.73/1.91 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[614, 7310])).
% 1.73/1.91 tff(7469,plain,
% 1.73/1.91 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7388])).
% 1.73/1.91 tff(7470,plain,
% 1.73/1.91 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.73/1.91 inference(symmetry,[status(thm)],[7469])).
% 1.73/1.91 tff(7471,plain,
% 1.73/1.91 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7470])).
% 1.73/1.91 tff(7472,assumption,(r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.73/1.91 tff(7473,assumption,(r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.73/1.91 tff(7474,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7475,plain,
% 1.73/1.91 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7476,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7475])).
% 1.73/1.91 tff(7477,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[7476, 7474])).
% 1.73/1.91 tff(7478,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(7479,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7478, 7477])).
% 1.73/1.91 tff(7480,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7479, 121, 798, 7473, 6026, 7472])).
% 1.73/1.91 tff(7481,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(7482,plain,
% 1.73/1.91 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7481, 7467, 7454, 7434])).
% 1.73/1.91 tff(7483,plain,
% 1.73/1.91 (~r(s(z), s(s(s(elem!1))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7482, 7471])).
% 1.73/1.91 tff(7484,plain,
% 1.73/1.91 (b(s(z), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[760, 7483])).
% 1.73/1.91 tff(7485,plain,
% 1.73/1.91 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.91 tff(7486,plain,
% 1.73/1.91 (r(elem!1, s(z))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[3505, 7485])).
% 1.73/1.91 tff(7487,plain,
% 1.73/1.91 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7390])).
% 1.73/1.91 tff(7488,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7307, 7487])).
% 1.73/1.91 tff(7489,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[82, 5502])).
% 1.73/1.91 tff(7490,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(7491,plain,
% 1.73/1.91 (~(elem!1 = s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7490, 7310])).
% 1.73/1.91 tff(7492,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[779])).
% 1.73/1.91 tff(7493,plain,
% 1.73/1.91 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.91 inference(symmetry,[status(thm)],[5910])).
% 1.73/1.91 tff(7494,plain,
% 1.73/1.91 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7493])).
% 1.73/1.91 tff(7495,plain,
% 1.73/1.91 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7450, 271, 504, 785, 6004])).
% 1.73/1.91 tff(7496,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7495, 7494])).
% 1.73/1.91 tff(7497,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1733, 7496])).
% 1.73/1.91 tff(7498,plain,
% 1.73/1.91 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6039, 7497, 107])).
% 1.73/1.91 tff(7499,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[779, 705])).
% 1.73/1.91 tff(7500,plain,
% 1.73/1.91 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7499])).
% 1.73/1.91 tff(7501,plain,
% 1.73/1.91 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7463, 271, 504, 785, 6004])).
% 1.73/1.91 tff(7502,plain,
% 1.73/1.91 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7501, 7500])).
% 1.73/1.91 tff(7503,plain,
% 1.73/1.91 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1494, 7502])).
% 1.73/1.91 tff(7504,plain,
% 1.73/1.91 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7296, 7503, 107])).
% 1.73/1.91 tff(7505,plain,
% 1.73/1.91 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[704])).
% 1.73/1.91 tff(7506,plain,
% 1.73/1.91 (b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(symmetry,[status(thm)],[7505])).
% 1.73/1.91 tff(7507,plain,
% 1.73/1.91 ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7506])).
% 1.73/1.91 tff(7508,plain,
% 1.73/1.91 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[107])).
% 1.73/1.91 tff(7509,plain,
% 1.73/1.91 (b(elem!1, s(s(elem!1)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[1894, 7508])).
% 1.73/1.91 tff(7510,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6018, 271, 588, 785, 6003, 6004])).
% 1.73/1.91 tff(7511,plain,((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(7512,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7511, 7509, 785, 6004])).
% 1.73/1.91 tff(7513,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7512, 7507])).
% 1.73/1.91 tff(7514,plain,
% 1.73/1.91 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1719, 7513, 107])).
% 1.73/1.91 tff(7515,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7516,plain,
% 1.73/1.91 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7517,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7516])).
% 1.73/1.91 tff(7518,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[7517, 7515])).
% 1.73/1.91 tff(7519,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(7520,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7519, 7518])).
% 1.73/1.91 tff(7521,plain,
% 1.73/1.91 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7520, 121, 7514, 7504, 7498])).
% 1.73/1.91 tff(7522,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[586, 7521, 563])).
% 1.73/1.91 tff(7523,plain,
% 1.73/1.91 (b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7522, 7492])).
% 1.73/1.91 tff(7524,plain,
% 1.73/1.91 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.73/1.91 inference(monotonicity,[status(thm)],[107])).
% 1.73/1.91 tff(7525,plain,
% 1.73/1.91 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.73/1.91 inference(symmetry,[status(thm)],[7524])).
% 1.73/1.91 tff(7526,plain,
% 1.73/1.91 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.73/1.91 inference(monotonicity,[status(thm)],[135])).
% 1.73/1.91 tff(7527,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.73/1.91 inference(symmetry,[status(thm)],[7526])).
% 1.73/1.91 tff(7528,plain,
% 1.73/1.91 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.73/1.91 inference(transitivity,[status(thm)],[7527, 7525])).
% 1.73/1.91 tff(7529,plain,
% 1.73/1.91 (b(s(s(s(z))), z)),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[504, 7528])).
% 1.73/1.91 tff(7530,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7531,plain,
% 1.73/1.91 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(7532,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[7531])).
% 1.73/1.91 tff(7533,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[7532, 7530])).
% 1.73/1.91 tff(7534,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(7535,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[7534, 7533])).
% 1.73/1.91 tff(7536,plain,
% 1.73/1.91 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7535, 121, 7514, 7504, 7498])).
% 1.73/1.91 tff(7537,plain,
% 1.73/1.91 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[556, 7536, 1])).
% 1.73/1.91 tff(7538,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[989, 7537, 504, 750])).
% 1.73/1.91 tff(7539,plain,
% 1.73/1.91 (r(s(s(elem!1)), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2143, 7538])).
% 1.73/1.91 tff(7540,plain,
% 1.73/1.91 (~r(s(s(elem!1)), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2422, 7539, 909, 110])).
% 1.73/1.91 tff(7541,plain,
% 1.73/1.91 (b(s(s(elem!1)), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2430, 7540])).
% 1.73/1.91 tff(7542,plain,
% 1.73/1.91 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2454, 7541, 7529, 1894])).
% 1.73/1.91 tff(7543,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7542, 7523])).
% 1.73/1.91 tff(7544,plain,((~b(z, s(s(elem!1)))) | (~(z = elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(7545,plain,
% 1.73/1.91 (~b(z, s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7544, 7387, 3505, 7415, 7065, 7484, 7468, 7444, 7423])).
% 1.73/1.91 tff(7546,plain,
% 1.73/1.91 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.73/1.91 inference(symmetry,[status(thm)],[7508])).
% 1.73/1.91 tff(7547,plain,
% 1.73/1.91 (b(z, s(s(elem!1)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[588, 7546])).
% 1.73/1.91 tff(7548,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.73/1.91 tff(7549,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7548, 7547])).
% 1.73/1.91 tff(7550,plain,((~(z = elem!1)) | b(z, s(s(elem!1))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(7551,plain,
% 1.73/1.91 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[7550, 7545, 7387])).
% 1.73/1.91 tff(7552,plain,
% 1.73/1.91 (r(elem!1, s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[599, 7551, 7491])).
% 1.73/1.91 tff(7553,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[5852, 7552, 7488, 7486, 7484])).
% 1.73/1.91 tff(7554,plain,
% 1.73/1.91 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[556, 7553, 7468])).
% 1.73/1.91 tff(7555,plain,
% 1.73/1.91 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7556,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7555])).
% 1.73/1.92 tff(7557,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7556, 7530])).
% 1.73/1.92 tff(7558,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7559,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7558, 7557])).
% 1.73/1.92 tff(7560,plain,
% 1.73/1.92 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7559, 121, 7554, 7467, 7454])).
% 1.73/1.92 tff(7561,plain,
% 1.73/1.92 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1716, 21, 7560])).
% 1.73/1.92 tff(7562,plain,
% 1.73/1.92 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7561, 7402])).
% 1.73/1.92 tff(7563,plain,
% 1.73/1.92 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5833, 7310])).
% 1.73/1.92 tff(7564,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.73/1.92 tff(7565,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7566,plain,
% 1.73/1.92 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7567,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7566])).
% 1.73/1.92 tff(7568,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7567, 7565])).
% 1.73/1.92 tff(7569,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7570,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7569, 7568])).
% 1.73/1.92 tff(7571,plain,
% 1.73/1.92 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7570, 271, 785, 6003])).
% 1.73/1.92 tff(7572,plain,
% 1.73/1.92 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7571, 7564])).
% 1.73/1.92 tff(7573,plain,
% 1.73/1.92 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 7572])).
% 1.73/1.92 tff(7574,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7575,plain,
% 1.73/1.92 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7576,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7575])).
% 1.73/1.92 tff(7577,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7576, 7574])).
% 1.73/1.92 tff(7578,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7579,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7578, 7577])).
% 1.73/1.92 tff(7580,plain,
% 1.73/1.92 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7579, 121, 623, 624, 7573])).
% 1.73/1.92 tff(7581,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7582,plain,
% 1.73/1.92 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7583,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7582])).
% 1.73/1.92 tff(7584,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7583, 7581])).
% 1.73/1.92 tff(7585,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7586,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7585, 7584])).
% 1.73/1.92 tff(7587,plain,
% 1.73/1.92 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7586, 271, 785, 6004])).
% 1.73/1.92 tff(7588,plain,
% 1.73/1.92 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7587, 7564])).
% 1.73/1.92 tff(7589,plain,
% 1.73/1.92 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5877, 21, 7588])).
% 1.73/1.92 tff(7590,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7589, 7580, 5874])).
% 1.73/1.92 tff(7591,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(7592,plain,
% 1.73/1.92 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7591, 7554, 7552, 7387, 7563, 7444, 7423, 7562])).
% 1.73/1.92 tff(7593,plain,
% 1.73/1.92 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7592, 7398])).
% 1.73/1.92 tff(7594,plain,
% 1.73/1.92 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1776, 7593, 1772])).
% 1.73/1.92 tff(7595,plain,
% 1.73/1.92 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7594, 7396])).
% 1.73/1.92 tff(7596,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7597,plain,
% 1.73/1.92 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7598,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(s(elem!1)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7597])).
% 1.73/1.92 tff(7599,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7598, 7596])).
% 1.73/1.92 tff(7600,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7601,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7600, 7599])).
% 1.73/1.92 tff(7602,plain,
% 1.73/1.92 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7601, 121, 7467, 7454])).
% 1.73/1.92 tff(7603,plain,
% 1.73/1.92 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7602, 7595])).
% 1.73/1.92 tff(7604,plain,
% 1.73/1.92 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1576, 7468])).
% 1.73/1.92 tff(7605,plain,
% 1.73/1.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1594, 21, 7604, 7603])).
% 1.73/1.92 tff(7606,plain,
% 1.73/1.92 ((s(elem!1) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.73/1.92 inference(commutativity,[status(thm)],[])).
% 1.73/1.92 tff(7607,plain,
% 1.73/1.92 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(symmetry,[status(thm)],[7606])).
% 1.73/1.92 tff(7608,plain,
% 1.73/1.92 ((~(s(s(s(s(s(elem!1))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7607])).
% 1.73/1.92 tff(7609,plain,
% 1.73/1.92 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7433, 7608])).
% 1.73/1.92 tff(7610,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7611,plain,
% 1.73/1.92 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7612,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7611])).
% 1.73/1.92 tff(7613,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7612, 7610])).
% 1.73/1.92 tff(7614,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7615,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7614, 7613])).
% 1.73/1.92 tff(7616,plain,
% 1.73/1.92 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7615, 121, 7554, 7467, 7454])).
% 1.73/1.92 tff(7617,plain,
% 1.73/1.92 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[881, 21, 7401, 7616])).
% 1.73/1.92 tff(7618,plain,
% 1.73/1.92 (~(s(elem!1) = s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[210, 7468])).
% 1.73/1.92 tff(7619,plain,
% 1.73/1.92 (r(z, s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2106, 7545])).
% 1.73/1.92 tff(7620,plain,
% 1.73/1.92 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.92 tff(7621,plain,
% 1.73/1.92 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.73/1.92 inference(symmetry,[status(thm)],[7620])).
% 1.73/1.92 tff(7622,plain,
% 1.73/1.92 (r(z, s(elem!1))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[3502, 7621])).
% 1.73/1.92 tff(7623,plain,
% 1.73/1.92 (~r(s(elem!1), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6878, 7554, 7622, 7619])).
% 1.73/1.92 tff(7624,plain,
% 1.73/1.92 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[526, 7623, 7618])).
% 1.73/1.92 tff(7625,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7626,plain,
% 1.73/1.92 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7627,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[7626])).
% 1.73/1.92 tff(7628,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[7627, 7625])).
% 1.73/1.92 tff(7629,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7630,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7629, 7628])).
% 1.73/1.92 tff(7631,plain,
% 1.73/1.92 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7630, 271, 7624, 7617, 7562])).
% 1.73/1.92 tff(7632,plain,
% 1.73/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7633,plain,
% 1.73/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(7634,plain,
% 1.73/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7633, 7632])).
% 1.73/1.92 tff(7635,plain,
% 1.73/1.92 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7634, 21, 7631])).
% 1.73/1.92 tff(7636,plain,
% 1.73/1.92 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7635, 7609])).
% 1.73/1.92 tff(7637,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(7638,plain,
% 1.73/1.92 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7639,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7638])).
% 1.73/1.93 tff(7640,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[7639, 7637])).
% 1.73/1.93 tff(7641,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7642,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7641, 7640])).
% 1.73/1.93 tff(7643,plain,
% 1.73/1.93 ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7642, 121, 7454, 7636])).
% 1.73/1.93 tff(7644,plain,
% 1.73/1.93 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7643, 7595])).
% 1.73/1.93 tff(7645,plain,
% 1.73/1.93 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7387])).
% 1.73/1.93 tff(7646,plain,
% 1.73/1.93 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7645])).
% 1.73/1.93 tff(7647,plain,
% 1.73/1.93 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[30, 7646])).
% 1.73/1.93 tff(7648,plain,
% 1.73/1.93 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2837, 7647])).
% 1.73/1.93 tff(7649,plain,
% 1.73/1.93 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3112, 21, 7648, 7644])).
% 1.73/1.93 tff(7650,plain,
% 1.73/1.93 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[84, 7310])).
% 1.73/1.93 tff(7651,plain,
% 1.73/1.93 (b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2293, 21, 7482, 7650])).
% 1.73/1.93 tff(7652,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7653,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7654,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7653, 7652])).
% 1.73/1.93 tff(7655,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7654, 271, 7651, 7488, 7649, 7605])).
% 1.73/1.93 tff(7656,plain,(r(z, elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(z) = elem!1) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1)) | b(z, s(z)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(7657,plain,
% 1.73/1.93 (r(z, elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7656, 317, 231, 3499, 377, 894, 3498])).
% 1.73/1.93 tff(7658,plain,
% 1.73/1.93 (~r(s(elem!1), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3683, 7657, 3502, 3501])).
% 1.73/1.93 tff(7659,plain,
% 1.73/1.93 (b(s(elem!1), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2243, 7658, 3500])).
% 1.73/1.93 tff(7660,plain,
% 1.73/1.93 (~(z = elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7069, 7659, 3498])).
% 1.73/1.93 tff(7661,plain,
% 1.73/1.93 (~(s(z) = s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[343, 7660])).
% 1.73/1.93 tff(7662,plain,
% 1.73/1.93 (b(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5645, 7657, 3502, 3499, 3500, 3501, 3505])).
% 1.73/1.93 tff(7663,plain,
% 1.73/1.93 (~r(s(z), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6159, 7660, 3500, 7662, 3501, 3502, 3505])).
% 1.73/1.93 tff(7664,plain,
% 1.73/1.93 (b(s(z), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[444, 7663, 7661])).
% 1.73/1.93 tff(7665,plain,
% 1.73/1.93 (~r(elem!1, z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1417, 3502, 3505, 3501])).
% 1.73/1.93 tff(7666,plain,
% 1.73/1.93 (~(elem!1 = z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[333, 7660])).
% 1.73/1.93 tff(7667,plain,
% 1.73/1.93 (b(elem!1, z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[284, 7666, 7665])).
% 1.73/1.93 tff(7668,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3722, 271, 7659, 7662, 7667, 7664])).
% 1.73/1.93 tff(7669,plain,(b(elem!1, s(elem!1)) | b(s(elem!1), z) | b(s(s(s(s(s(z))))), s(elem!1)) | (s(z) = elem!1) | (elem!1 = s(elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(7670,plain,
% 1.73/1.93 (b(elem!1, s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7669, 231, 3499, 3498, 377, 894])).
% 1.73/1.93 tff(7671,plain,
% 1.73/1.93 (~(z = elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1543, 7670, 894])).
% 1.73/1.93 tff(7672,plain,
% 1.73/1.93 (~(s(z) = s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[343, 7671])).
% 1.73/1.93 tff(7673,plain,
% 1.73/1.93 (r(s(elem!1), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2243, 2467, 2564])).
% 1.73/1.93 tff(7674,plain,
% 1.73/1.93 (~b(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5323, 1326, 307, 412, 909, 348])).
% 1.73/1.93 tff(7675,plain,
% 1.73/1.93 (r(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[236, 7674, 231])).
% 1.73/1.93 tff(7676,plain,
% 1.73/1.93 (~r(s(elem!1), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1254, 7675, 909, 412])).
% 1.73/1.93 tff(7677,plain,
% 1.73/1.93 (b(s(elem!1), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[429, 7676, 2282])).
% 1.73/1.93 tff(7678,plain,
% 1.73/1.93 (~b(z, s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4122, 7677, 307, 1326])).
% 1.73/1.93 tff(7679,plain,
% 1.73/1.93 (r(z, s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1439, 7678])).
% 1.73/1.93 tff(7680,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7681,plain,
% 1.73/1.93 (((~b(elem!1, 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(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7682,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7681])).
% 1.73/1.93 tff(7683,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[7682, 7680])).
% 1.73/1.93 tff(7684,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7685,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7684, 7683])).
% 1.73/1.93 tff(7686,plain,
% 1.73/1.93 (~b(z, s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7685, 271, 307, 1326, 504])).
% 1.73/1.93 tff(7687,plain,
% 1.73/1.93 (r(z, s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[36, 21, 7686, 32])).
% 1.73/1.93 tff(7688,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7689,plain,
% 1.73/1.93 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7690,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7689])).
% 1.73/1.93 tff(7691,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[7690, 7688])).
% 1.73/1.93 tff(7692,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7693,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7692, 7691])).
% 1.73/1.93 tff(7694,plain,
% 1.73/1.93 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7693, 121])).
% 1.73/1.93 tff(7695,plain,
% 1.73/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7694, 7687, 622, 7679])).
% 1.73/1.93 tff(7696,plain,
% 1.73/1.93 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[681, 7695, 82])).
% 1.73/1.93 tff(7697,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7698,plain,
% 1.73/1.93 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7699,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7698])).
% 1.73/1.93 tff(7700,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[7699, 7697])).
% 1.73/1.93 tff(7701,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7702,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7701, 7700])).
% 1.73/1.93 tff(7703,plain,
% 1.73/1.93 (~b(s(s(s(elem!1))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7702, 271, 307, 1326, 504])).
% 1.73/1.93 tff(7704,plain,
% 1.73/1.93 (r(s(s(s(elem!1))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1904, 21, 30, 7703])).
% 1.73/1.93 tff(7705,plain,
% 1.73/1.93 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6215, 121, 7687, 412, 7704])).
% 1.73/1.93 tff(7706,plain,
% 1.73/1.93 (b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2293, 21, 7705, 2280])).
% 1.73/1.93 tff(7707,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7708,plain,
% 1.73/1.93 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7709,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7708])).
% 1.73/1.93 tff(7710,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[7709, 7707])).
% 1.73/1.93 tff(7711,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7712,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7711, 7710])).
% 1.73/1.93 tff(7713,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7712, 271, 307, 7706, 7696, 504])).
% 1.73/1.93 tff(7714,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (s(z) = elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(7715,plain,
% 1.73/1.93 (~b(z, elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7714, 7282, 504, 412, 307, 7673, 909, 231, 344])).
% 1.73/1.93 tff(7716,plain,
% 1.73/1.93 (r(z, elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[355, 7715, 331])).
% 1.73/1.93 tff(7717,plain,
% 1.73/1.93 (~r(elem!1, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5343, 7716, 7673, 412])).
% 1.73/1.93 tff(7718,plain,
% 1.73/1.93 (b(elem!1, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[299, 7717, 243])).
% 1.73/1.93 tff(7719,plain,
% 1.73/1.93 (~r(elem!1, z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5358, 7716, 7673, 412])).
% 1.73/1.93 tff(7720,plain,
% 1.73/1.93 (b(elem!1, z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[284, 7719, 358])).
% 1.73/1.93 tff(7721,plain,
% 1.73/1.93 (b(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1305, 7715, 307, 331, 412, 909, 231])).
% 1.73/1.93 tff(7722,plain,
% 1.73/1.93 (~(elem!1 = s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7490, 7282])).
% 1.73/1.93 tff(7723,plain,
% 1.73/1.93 (b(s(z), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5347, 7721, 307, 2564, 7716, 412, 909, 344])).
% 1.73/1.93 tff(7724,plain,
% 1.73/1.93 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4497, 7723, 307, 7721])).
% 1.73/1.93 tff(7725,plain,
% 1.73/1.93 (~r(z, s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5454, 7724, 412, 7722, 7718, 7721])).
% 1.73/1.93 tff(7726,plain,
% 1.73/1.93 (b(z, s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2106, 7725])).
% 1.73/1.93 tff(7727,plain,
% 1.73/1.93 (~b(s(elem!1), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[456, 7723, 307, 7718])).
% 1.73/1.93 tff(7728,plain,
% 1.73/1.93 (r(s(elem!1), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[429, 7727, 351])).
% 1.73/1.93 tff(7729,plain,
% 1.73/1.93 (~r(s(z), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[420, 7728, 412, 7716])).
% 1.73/1.93 tff(7730,plain,
% 1.73/1.93 (b(s(z), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[25, 7729])).
% 1.73/1.93 tff(7731,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5420, 7730, 7726, 7720, 7718])).
% 1.73/1.93 tff(7732,plain,(b(s(elem!1), elem!1) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~r(z, s(z))) | (z = elem!1) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(7733,plain,
% 1.73/1.93 (b(s(elem!1), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7732, 307, 412, 3500, 3505, 6509, 231, 504])).
% 1.73/1.93 tff(7734,plain,
% 1.73/1.93 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3177, 271, 307, 7733, 504])).
% 1.73/1.93 tff(7735,plain,
% 1.73/1.93 (~b(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5323, 1326, 307, 412, 3505, 6510])).
% 1.73/1.93 tff(7736,plain,
% 1.73/1.93 (r(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[236, 7735, 231])).
% 1.73/1.93 tff(7737,plain,
% 1.73/1.93 (~r(s(elem!1), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1254, 7736, 3505, 412])).
% 1.73/1.93 tff(7738,plain,
% 1.73/1.93 (b(s(elem!1), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[429, 7737, 6511])).
% 1.73/1.93 tff(7739,plain,
% 1.73/1.93 (~b(z, s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4122, 7738, 307, 1326])).
% 1.73/1.93 tff(7740,plain,
% 1.73/1.93 (r(z, s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1439, 7739])).
% 1.73/1.93 tff(7741,plain,
% 1.73/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7087, 121, 7740, 412, 7704])).
% 1.73/1.93 tff(7742,plain,
% 1.73/1.93 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[681, 7741, 7734])).
% 1.73/1.93 tff(7743,plain,
% 1.73/1.93 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7742])).
% 1.73/1.93 tff(7744,plain,
% 1.73/1.93 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[7743])).
% 1.73/1.93 tff(7745,plain,
% 1.73/1.93 (elem!1 = s(s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[78, 7742])).
% 1.73/1.93 tff(7746,plain,
% 1.73/1.93 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3917, 7745, 6510])).
% 1.73/1.93 tff(7747,plain,
% 1.73/1.93 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2035, 7746])).
% 1.73/1.93 tff(7748,plain,
% 1.73/1.93 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7742])).
% 1.73/1.93 tff(7749,plain,
% 1.73/1.93 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[7748])).
% 1.73/1.93 tff(7750,plain,
% 1.73/1.93 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6358, 7745, 7746])).
% 1.73/1.93 tff(7751,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4138, 7750, 3499])).
% 1.73/1.93 tff(7752,plain,
% 1.73/1.93 (~r(z, s(s(s(s(s(z))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7111, 121, 7740, 412, 7751])).
% 1.73/1.93 tff(7753,plain,
% 1.73/1.93 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1658, 7752])).
% 1.73/1.93 tff(7754,plain,
% 1.73/1.93 (b(s(s(s(z))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7118, 7753, 3499, 6509, 412, 377, 7746, 894, 1326])).
% 1.73/1.93 tff(7755,plain,
% 1.73/1.93 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7754, 7749])).
% 1.73/1.93 tff(7756,plain,
% 1.73/1.93 (b(s(z), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6618, 7754, 412, 3499, 307, 3500, 7735, 894])).
% 1.73/1.93 tff(7757,plain,
% 1.73/1.93 (~b(elem!1, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[456, 7756, 307, 7738])).
% 1.73/1.93 tff(7758,plain,
% 1.73/1.93 (r(elem!1, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[299, 7757, 243])).
% 1.73/1.93 tff(7759,plain,
% 1.73/1.93 (~(s(s(s(z))) = elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3906, 7745])).
% 1.73/1.93 tff(7760,plain,
% 1.73/1.93 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7745])).
% 1.73/1.93 tff(7761,plain,
% 1.73/1.93 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.73/1.93 inference(symmetry,[status(thm)],[7760])).
% 1.73/1.93 tff(7762,plain,
% 1.73/1.93 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7761])).
% 1.73/1.93 tff(7763,plain,
% 1.73/1.93 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7742])).
% 1.73/1.93 tff(7764,plain,
% 1.73/1.93 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2479, 7745, 307])).
% 1.73/1.93 tff(7765,plain,
% 1.73/1.93 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7764, 7763])).
% 1.73/1.93 tff(7766,plain,
% 1.73/1.93 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3787, 7745, 7733])).
% 1.73/1.93 tff(7767,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7768,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7769,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7768, 7767])).
% 1.73/1.93 tff(7770,plain,
% 1.73/1.93 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7769, 271, 7766, 7754, 7765])).
% 1.73/1.93 tff(7771,plain,
% 1.73/1.93 (~b(s(s(s(z))), elem!1)),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7770, 7762])).
% 1.73/1.93 tff(7772,plain,
% 1.73/1.93 (r(s(s(s(z))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[255, 7771, 7759])).
% 1.73/1.93 tff(7773,plain,
% 1.73/1.93 (~r(s(z), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4112, 7772, 7758, 7736])).
% 1.73/1.93 tff(7774,plain,
% 1.73/1.93 (b(s(z), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[105, 7773])).
% 1.73/1.93 tff(7775,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7776,plain,
% 1.73/1.93 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(7777,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[7776])).
% 1.73/1.93 tff(7778,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[7777, 7775])).
% 1.73/1.93 tff(7779,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(7780,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[7779, 7778])).
% 1.73/1.94 tff(7781,plain,
% 1.73/1.94 ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7780, 271])).
% 1.73/1.94 tff(7782,plain,
% 1.73/1.94 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7781, 7774, 7738, 7755])).
% 1.73/1.94 tff(7783,plain,
% 1.73/1.94 (r(s(elem!1), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2044, 7782, 7747])).
% 1.73/1.94 tff(7784,plain,
% 1.73/1.94 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7783, 7744])).
% 1.73/1.94 tff(7785,plain,
% 1.73/1.94 (r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2462, 21, 7770, 3504])).
% 1.73/1.94 tff(7786,plain,
% 1.73/1.94 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7742])).
% 1.73/1.94 tff(7787,plain,
% 1.73/1.94 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7786])).
% 1.73/1.94 tff(7788,plain,
% 1.73/1.94 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7751, 7787])).
% 1.73/1.94 tff(7789,plain,
% 1.73/1.94 (b(z, s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6558, 7774, 7738, 7740, 7747, 7771, 3505, 7736, 1326])).
% 1.73/1.94 tff(7790,plain,
% 1.73/1.94 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6049, 7789, 7754, 7753])).
% 1.73/1.94 tff(7791,plain,
% 1.73/1.94 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1733, 7790])).
% 1.73/1.94 tff(7792,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.73/1.94 tff(7793,assumption,(r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.94 tff(7794,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.73/1.94 tff(7795,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(7796,plain,
% 1.73/1.94 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), 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(elem!1)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(7797,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7796])).
% 1.73/1.94 tff(7798,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7797, 7795])).
% 1.73/1.94 tff(7799,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), 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(elem!1))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(7800,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7799, 7798])).
% 1.73/1.94 tff(7801,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7800, 121, 1736, 7794, 7793, 7792])).
% 1.73/1.94 tff(7802,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(7803,plain,
% 1.73/1.94 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7802, 7791, 7788, 7785])).
% 1.73/1.94 tff(7804,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7803, 7784])).
% 1.73/1.94 tff(7805,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(elem!1)) | b(z, s(z)) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(7806,plain,
% 1.73/1.94 (~b(z, elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7805, 7670, 3501, 3499, 894, 377, 7065, 231])).
% 1.73/1.94 tff(7807,plain,
% 1.73/1.94 (r(z, elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[355, 7806, 7671])).
% 1.73/1.94 tff(7808,plain,
% 1.73/1.94 (b(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1305, 7806, 7670, 7671, 3501, 3505, 231])).
% 1.73/1.94 tff(7809,plain,
% 1.73/1.94 (b(s(elem!1), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7732, 7670, 3501, 3500, 3505, 7671, 231, 7065])).
% 1.73/1.94 tff(7810,plain,
% 1.73/1.94 (~b(s(z), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3435, 7808, 7670, 7809])).
% 1.73/1.94 tff(7811,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5347, 7810, 7808, 7670, 3500, 7807, 3501, 3505, 7672])).
% 1.73/1.94 tff(7812,plain,((s(z) = elem!1) | b(s(s(s(s(s(z))))), s(elem!1)) | b(z, s(z)) | (elem!1 = s(elem!1)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(7813,plain,
% 1.73/1.94 (s(z) = elem!1),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7812, 377, 894, 3499, 3498])).
% 1.73/1.94 tff(7814,plain,
% 1.73/1.94 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.94 tff(7815,plain,
% 1.73/1.94 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7814])).
% 1.73/1.94 tff(7816,plain,
% 1.73/1.94 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3049, 7813])).
% 1.73/1.94 tff(7817,plain,
% 1.73/1.94 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5001, 7816])).
% 1.73/1.94 tff(7818,plain,
% 1.73/1.94 (s(s(z)) = s(elem!1)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.94 tff(7819,plain,
% 1.73/1.94 (s(s(s(z))) = s(s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7818])).
% 1.73/1.94 tff(7820,plain,
% 1.73/1.94 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7819])).
% 1.73/1.94 tff(7821,plain,
% 1.73/1.94 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7820])).
% 1.73/1.94 tff(7822,plain,
% 1.73/1.94 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7821])).
% 1.73/1.94 tff(7823,plain,
% 1.73/1.94 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7822])).
% 1.73/1.94 tff(7824,plain,
% 1.73/1.94 ((~r(elem!1, s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7823])).
% 1.73/1.94 tff(7825,plain,
% 1.73/1.94 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7821])).
% 1.73/1.94 tff(7826,plain,
% 1.73/1.94 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7825])).
% 1.73/1.94 tff(7827,plain,
% 1.73/1.94 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[3499, 7826])).
% 1.73/1.94 tff(7828,plain,
% 1.73/1.94 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7822])).
% 1.73/1.94 tff(7829,plain,
% 1.73/1.94 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7828])).
% 1.73/1.94 tff(7830,plain,
% 1.73/1.94 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7829])).
% 1.73/1.94 tff(7831,plain,
% 1.73/1.94 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7818])).
% 1.73/1.94 tff(7832,plain,
% 1.73/1.94 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7831])).
% 1.73/1.94 tff(7833,plain,
% 1.73/1.94 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[877, 7832])).
% 1.73/1.94 tff(7834,plain,
% 1.73/1.94 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7833, 7830])).
% 1.73/1.94 tff(7835,plain,
% 1.73/1.94 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3112, 21, 7834, 7827])).
% 1.73/1.94 tff(7836,plain,
% 1.73/1.94 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.94 tff(7837,plain,
% 1.73/1.94 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7836])).
% 1.73/1.94 tff(7838,plain,
% 1.73/1.94 (~(elem!1 = s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[2137, 7837])).
% 1.73/1.94 tff(7839,plain,
% 1.73/1.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[78, 7838])).
% 1.73/1.94 tff(7840,plain,
% 1.73/1.94 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[84, 7839])).
% 1.73/1.94 tff(7841,plain,
% 1.73/1.94 (r(z, elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1402, 7813, 894])).
% 1.73/1.94 tff(7842,plain,
% 1.73/1.94 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.94 tff(7843,plain,
% 1.73/1.94 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.73/1.94 inference(symmetry,[status(thm)],[7842])).
% 1.73/1.94 tff(7844,plain,
% 1.73/1.94 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7843])).
% 1.73/1.94 tff(7845,plain,
% 1.73/1.94 (~b(s(z), elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[192, 7844])).
% 1.73/1.94 tff(7846,plain,
% 1.73/1.94 (~r(elem!1, s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5645, 7845, 7841, 3499, 3500, 3501, 3505])).
% 1.73/1.94 tff(7847,plain,
% 1.73/1.94 (b(elem!1, s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[392, 7846, 377])).
% 1.73/1.94 tff(7848,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4951])).
% 1.73/1.94 tff(7849,plain,
% 1.73/1.94 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7848])).
% 1.73/1.94 tff(7850,plain,
% 1.73/1.94 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1036])).
% 1.73/1.94 tff(7851,plain,
% 1.73/1.94 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7850, 3535])).
% 1.73/1.94 tff(7852,plain,
% 1.73/1.94 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7851])).
% 1.73/1.94 tff(7853,plain,
% 1.73/1.94 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[1136, 7852])).
% 1.73/1.94 tff(7854,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(7855,plain,
% 1.73/1.94 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(7856,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7855])).
% 1.73/1.94 tff(7857,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7856, 7854])).
% 1.73/1.94 tff(7858,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(7859,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 1.73/1.94 tff(7860,plain,
% 1.73/1.94 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7859, 121, 622, 4966, 6898])).
% 1.73/1.94 tff(7861,plain,
% 1.73/1.94 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7860, 4983])).
% 1.73/1.94 tff(7862,plain,
% 1.73/1.94 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1494, 7861])).
% 1.73/1.94 tff(7863,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[1519, 4981])).
% 1.73/1.94 tff(7864,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1711, 7863])).
% 1.73/1.94 tff(7865,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(7866,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7865, 7862, 223])).
% 1.73/1.94 tff(7867,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7866, 4980])).
% 1.73/1.94 tff(7868,plain,
% 1.73/1.94 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[223])).
% 1.73/1.94 tff(7869,plain,
% 1.73/1.94 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7868])).
% 1.73/1.94 tff(7870,plain,
% 1.73/1.94 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1037])).
% 1.73/1.94 tff(7871,plain,
% 1.73/1.94 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7870])).
% 1.73/1.94 tff(7872,plain,
% 1.73/1.94 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[223])).
% 1.73/1.94 tff(7873,plain,
% 1.73/1.94 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7872, 7871, 7869])).
% 1.73/1.94 tff(7874,plain,
% 1.73/1.94 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[223])).
% 1.73/1.94 tff(7875,plain,
% 1.73/1.94 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7874])).
% 1.73/1.94 tff(7876,plain,
% 1.73/1.94 (r(s(elem!1), s(z))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[622, 7875])).
% 1.73/1.94 tff(7877,plain,
% 1.73/1.94 (~r(s(z), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4423, 7876, 412, 909])).
% 1.73/1.94 tff(7878,plain,
% 1.73/1.94 (b(s(z), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2167, 7877])).
% 1.73/1.94 tff(7879,plain,
% 1.73/1.94 (b(s(z), s(s(s(z))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7878, 7873])).
% 1.73/1.94 tff(7880,plain,
% 1.73/1.94 (r(elem!1, z) <=> r(s(z), z)),
% 1.73/1.94 inference(symmetry,[status(thm)],[1407])).
% 1.73/1.94 tff(7881,plain,
% 1.73/1.94 ((~r(elem!1, z)) <=> (~r(s(z), z))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7880])).
% 1.73/1.94 tff(7882,plain,
% 1.73/1.94 (~r(elem!1, z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5358, 622, 378, 412])).
% 1.73/1.94 tff(7883,plain,
% 1.73/1.94 (~r(s(z), z)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 1.73/1.94 tff(7884,plain,
% 1.73/1.94 (b(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[25, 7883])).
% 1.73/1.94 tff(7885,plain,
% 1.73/1.94 (~r(s(s(s(z))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5155, 1500, 412, 909])).
% 1.73/1.94 tff(7886,plain,
% 1.73/1.94 (b(s(s(s(z))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1155, 7885])).
% 1.73/1.94 tff(7887,plain,
% 1.73/1.94 (~b(z, s(s(s(s(s(z))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4302, 7886, 7884, 7879])).
% 1.73/1.94 tff(7888,plain,
% 1.73/1.94 (r(z, s(s(s(s(s(z))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1658, 7887])).
% 1.73/1.94 tff(7889,plain,
% 1.73/1.94 (b(elem!1, s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7878, 7872])).
% 1.73/1.94 tff(7890,plain,
% 1.73/1.94 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3049, 223])).
% 1.73/1.94 tff(7891,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(7892,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(7893,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7892, 7891])).
% 1.73/1.94 tff(7894,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7893, 121, 622, 4966, 6898])).
% 1.73/1.94 tff(7895,plain,
% 1.73/1.94 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[3057, 4951])).
% 1.73/1.94 tff(7896,plain,
% 1.73/1.94 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7895, 1487])).
% 1.73/1.94 tff(7897,plain,
% 1.73/1.94 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7896])).
% 1.73/1.94 tff(7898,plain,
% 1.73/1.94 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7897])).
% 1.73/1.94 tff(7899,plain,
% 1.73/1.94 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[1489, 7898])).
% 1.73/1.94 tff(7900,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5954, 21, 7899, 7894])).
% 1.73/1.94 tff(7901,plain,
% 1.73/1.94 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5065, 7900, 378, 7890, 223, 7889, 7888])).
% 1.73/1.94 tff(7902,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7901, 7867])).
% 1.73/1.94 tff(7903,plain,((~r(s(s(s(z))), s(elem!1))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(7904,plain,
% 1.73/1.94 (~r(s(s(s(z))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7903, 622, 378, 223, 6898, 412, 909])).
% 1.73/1.94 tff(7905,plain,
% 1.73/1.94 (b(s(s(s(z))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1816, 7904, 7853])).
% 1.73/1.94 tff(7906,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7905, 7849])).
% 1.73/1.94 tff(7907,plain,
% 1.73/1.94 ((s(z) = z) <=> (elem!1 = z)),
% 1.73/1.94 inference(transitivity,[status(thm)],[1389, 361])).
% 1.73/1.94 tff(7908,plain,
% 1.73/1.94 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7907])).
% 1.73/1.94 tff(7909,plain,
% 1.73/1.94 (~(elem!1 = z)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11, 7908])).
% 1.73/1.94 tff(7910,plain,
% 1.73/1.94 (b(elem!1, z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[284, 7882, 7909])).
% 1.73/1.94 tff(7911,plain,
% 1.73/1.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3895, 5087])).
% 1.73/1.94 tff(7912,plain,
% 1.73/1.94 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4951])).
% 1.73/1.94 tff(7913,plain,
% 1.73/1.94 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(z))) = s(elem!1))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7912, 3535])).
% 1.73/1.94 tff(7914,plain,
% 1.73/1.94 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7913])).
% 1.73/1.94 tff(7915,plain,
% 1.73/1.94 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7914])).
% 1.73/1.94 tff(7916,plain,
% 1.73/1.94 (~(s(elem!1) = s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7853, 7915])).
% 1.73/1.94 tff(7917,plain,
% 1.73/1.94 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[223])).
% 1.73/1.94 tff(7918,plain,
% 1.73/1.94 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7917])).
% 1.73/1.94 tff(7919,plain,
% 1.73/1.94 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1036])).
% 1.73/1.94 tff(7920,plain,
% 1.73/1.94 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7919])).
% 1.73/1.94 tff(7921,plain,
% 1.73/1.94 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7920, 7918])).
% 1.73/1.94 tff(7922,plain,
% 1.73/1.94 (b(s(z), s(s(z)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[307, 7921])).
% 1.73/1.94 tff(7923,plain,
% 1.73/1.94 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[1404])).
% 1.73/1.94 tff(7924,plain,
% 1.73/1.94 (b(s(s(s(z))), s(s(z)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7905, 7923])).
% 1.73/1.94 tff(7925,plain,
% 1.73/1.94 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6772, 7924, 1222, 7879, 7922])).
% 1.73/1.94 tff(7926,plain,
% 1.73/1.94 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2369, 7925, 1222])).
% 1.73/1.94 tff(7927,plain,
% 1.73/1.94 (r(s(elem!1), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[526, 7926, 7916])).
% 1.73/1.94 tff(7928,plain,
% 1.73/1.94 (~r(z, s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6916, 7927, 7889, 223, 7911, 7906, 378, 412, 307, 7909, 2564, 6898])).
% 1.73/1.94 tff(7929,plain,
% 1.73/1.94 (b(z, s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2106, 7928])).
% 1.73/1.94 tff(7930,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6924, 271, 7929, 7889, 7910, 7906])).
% 1.73/1.94 tff(7931,plain,((~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(7932,plain,
% 1.73/1.94 (~r(s(elem!1), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7931, 7813, 7841, 3501, 7847, 3500, 7835, 3505])).
% 1.73/1.94 tff(7933,plain,
% 1.73/1.94 (b(s(elem!1), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2243, 7932, 3500])).
% 1.73/1.94 tff(7934,plain,
% 1.73/1.94 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2930, 271, 7847, 7933, 7065])).
% 1.73/1.94 tff(7935,plain,
% 1.73/1.94 (r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2293, 21, 7934, 7840])).
% 1.73/1.94 tff(7936,plain,
% 1.73/1.94 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3177, 271, 7847, 7933, 7065])).
% 1.73/1.94 tff(7937,plain,
% 1.73/1.94 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[681, 7936, 7839])).
% 1.73/1.94 tff(7938,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(7939,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(7940,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[7939, 7938])).
% 1.73/1.94 tff(7941,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7940, 121, 7937, 7935, 7835])).
% 1.73/1.94 tff(7942,plain,
% 1.73/1.94 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7820])).
% 1.73/1.94 tff(7943,plain,
% 1.73/1.94 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7822, 7942])).
% 1.73/1.94 tff(7944,plain,
% 1.73/1.94 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7943, 4032])).
% 1.73/1.94 tff(7945,plain,
% 1.73/1.94 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7944])).
% 1.73/1.94 tff(7946,plain,
% 1.73/1.94 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7945])).
% 1.73/1.94 tff(7947,plain,
% 1.73/1.94 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[1772, 7946])).
% 1.73/1.94 tff(7948,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1594, 21, 7947, 7941])).
% 1.73/1.94 tff(7949,plain,
% 1.73/1.94 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.94 tff(7950,plain,
% 1.73/1.94 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.73/1.94 inference(transitivity,[status(thm)],[7949, 653])).
% 1.73/1.94 tff(7951,plain,
% 1.73/1.94 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7950])).
% 1.73/1.94 tff(7952,plain,
% 1.73/1.94 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[61, 7951])).
% 1.73/1.94 tff(7953,plain,
% 1.73/1.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3895, 7952])).
% 1.73/1.94 tff(7954,plain,
% 1.73/1.94 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.73/1.94 inference(transitivity,[status(thm)],[7836, 2212])).
% 1.73/1.94 tff(7955,plain,
% 1.73/1.94 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7954])).
% 1.73/1.94 tff(7956,plain,
% 1.73/1.94 (~(s(s(elem!1)) = elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[2137, 7955])).
% 1.73/1.94 tff(7957,plain,
% 1.73/1.94 (elem!1 = s(z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1221, 7813])).
% 1.73/1.94 tff(7958,plain,
% 1.73/1.94 (~b(z, elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1397, 7957, 894])).
% 1.73/1.94 tff(7959,plain,
% 1.73/1.94 ((s(z) = z) <=> (elem!1 = z)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.94 tff(7960,plain,
% 1.73/1.94 ((s(z) = z) <=> (z = elem!1)),
% 1.73/1.94 inference(transitivity,[status(thm)],[7959, 360])).
% 1.73/1.94 tff(7961,plain,
% 1.73/1.94 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7960])).
% 1.73/1.94 tff(7962,plain,
% 1.73/1.94 (~(z = elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11, 7961])).
% 1.73/1.94 tff(7963,plain,
% 1.73/1.94 (s(s(elem!1)) = s(s(s(z)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7819])).
% 1.73/1.94 tff(7964,plain,
% 1.73/1.94 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7963])).
% 1.73/1.94 tff(7965,plain,
% 1.73/1.94 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(z))) = s(elem!1))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7964, 3535])).
% 1.73/1.94 tff(7966,plain,
% 1.73/1.94 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[7965])).
% 1.73/1.94 tff(7967,plain,
% 1.73/1.94 ((s(s(s(z))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.73/1.94 inference(transitivity,[status(thm)],[7966, 4446])).
% 1.73/1.94 tff(7968,plain,
% 1.73/1.94 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[7967])).
% 1.73/1.94 tff(7969,plain,
% 1.73/1.95 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7818])).
% 1.73/1.95 tff(7970,plain,
% 1.73/1.95 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.73/1.95 inference(transitivity,[status(thm)],[7969, 3535])).
% 1.73/1.95 tff(7971,plain,
% 1.73/1.95 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7970])).
% 1.73/1.95 tff(7972,plain,
% 1.73/1.95 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[1136, 7971])).
% 1.73/1.95 tff(7973,plain,
% 1.73/1.95 (~(s(s(elem!1)) = s(elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[7972, 7968])).
% 1.73/1.95 tff(7974,plain,
% 1.73/1.95 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7822, 7963])).
% 1.73/1.95 tff(7975,plain,
% 1.73/1.95 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[7974, 1487])).
% 1.73/1.95 tff(7976,plain,
% 1.73/1.95 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.73/1.95 inference(symmetry,[status(thm)],[7975])).
% 1.73/1.95 tff(7977,plain,
% 1.73/1.95 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7976])).
% 1.73/1.95 tff(7978,plain,
% 1.73/1.95 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[1489, 7977])).
% 1.73/1.95 tff(7979,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.95 tff(7980,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4969, 121, 412, 683, 6898])).
% 1.73/1.95 tff(7981,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 7980])).
% 1.73/1.95 tff(7982,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(7983,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(7984,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[7983, 7982])).
% 1.73/1.95 tff(7985,plain,
% 1.73/1.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7984, 121, 684, 412, 683])).
% 1.73/1.95 tff(7986,plain,
% 1.73/1.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[586, 7985, 563])).
% 1.73/1.95 tff(7987,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(7988,plain,
% 1.73/1.95 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(7989,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7988])).
% 1.73/1.95 tff(7990,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[7989, 7987])).
% 1.73/1.95 tff(7991,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(7992,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[7991, 7990])).
% 1.73/1.95 tff(7993,plain,
% 1.73/1.95 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7992, 121, 684, 412, 683])).
% 1.73/1.95 tff(7994,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[556, 7993, 1])).
% 1.73/1.95 tff(7995,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(7996,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(7997,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[7996, 7995])).
% 1.73/1.95 tff(7998,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7997, 271, 7994, 7986, 7981, 7979])).
% 1.73/1.95 tff(7999,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(8000,plain,
% 1.73/1.95 (~r(s(s(elem!1)), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7999, 7948, 7978, 7953, 3501, 7835, 7937])).
% 1.73/1.95 tff(8001,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[701, 8000, 7973])).
% 1.73/1.95 tff(8002,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8003,plain,
% 1.73/1.95 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8004,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[8003])).
% 1.73/1.95 tff(8005,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[8004, 8002])).
% 1.73/1.95 tff(8006,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(8007,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8006, 8005])).
% 1.73/1.95 tff(8008,plain,
% 1.73/1.95 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[8007, 271, 7847, 7933, 8001])).
% 1.73/1.95 tff(8009,plain,
% 1.73/1.95 (r(elem!1, s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[599, 8008, 7838])).
% 1.73/1.95 tff(8010,plain,
% 1.73/1.95 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3310, 8009, 7962, 7958, 7956, 7846, 7839])).
% 1.73/1.95 tff(8011,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[556, 8010, 7953])).
% 1.73/1.95 tff(8012,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8013,plain,
% 1.73/1.95 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8014,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[8013])).
% 1.73/1.95 tff(8015,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[8014, 8012])).
% 1.73/1.95 tff(8016,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(8017,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8016, 8015])).
% 1.73/1.95 tff(8018,plain,
% 1.73/1.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[8017, 271, 8011, 7065, 7948])).
% 1.73/1.95 tff(8019,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[5954, 21, 7978, 8018])).
% 1.73/1.95 tff(8020,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7963, 7822])).
% 1.73/1.95 tff(8021,plain,
% 1.73/1.95 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[8020])).
% 1.73/1.95 tff(8022,plain,
% 1.73/1.95 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7819])).
% 1.73/1.95 tff(8023,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[8022])).
% 1.73/1.95 tff(8024,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7822])).
% 1.73/1.95 tff(8025,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[8024, 8023])).
% 1.73/1.95 tff(8026,plain,
% 1.73/1.95 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[8025])).
% 1.73/1.95 tff(8027,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8028,plain,
% 1.73/1.95 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8029,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[8028])).
% 1.73/1.95 tff(8030,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[8029, 8027])).
% 1.73/1.95 tff(8031,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(8032,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8031, 8030])).
% 1.73/1.95 tff(8033,plain,
% 1.73/1.95 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[8032, 271, 8011, 7065, 7948])).
% 1.73/1.95 tff(8034,plain,
% 1.73/1.95 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8033, 8026])).
% 1.73/1.95 tff(8035,plain,
% 1.73/1.95 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1494, 8034])).
% 1.73/1.95 tff(8036,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8035, 8021])).
% 1.73/1.95 tff(8037,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8038,plain,
% 1.73/1.95 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8039,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[8038])).
% 1.73/1.95 tff(8040,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[8039, 8037])).
% 1.73/1.95 tff(8041,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(8042,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8041, 8040])).
% 1.73/1.95 tff(8043,plain,
% 1.73/1.95 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[8042, 121, 8009, 8036, 8019])).
% 1.73/1.95 tff(8044,plain,
% 1.73/1.95 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8043, 7824])).
% 1.73/1.95 tff(8045,plain,
% 1.73/1.95 (b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1847, 8044, 7817])).
% 1.73/1.95 tff(8046,plain,
% 1.73/1.95 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8045, 7815])).
% 1.73/1.95 tff(8047,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8048,plain,
% 1.73/1.95 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(8049,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[8048])).
% 1.73/1.95 tff(8050,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[8049, 8047])).
% 1.73/1.95 tff(8051,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(8052,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[8051, 8050])).
% 1.73/1.95 tff(8053,plain,
% 1.73/1.95 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[8052, 121, 7937, 7935, 7835])).
% 1.73/1.95 tff(8054,plain,
% 1.73/1.95 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6896, 8053, 7813])).
% 1.73/1.95 tff(8055,plain,
% 1.73/1.95 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1776, 8054, 1772])).
% 1.73/1.95 tff(8056,plain,
% 1.73/1.95 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/1.95 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.95 tff(8057,plain,
% 1.73/1.95 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.73/1.96 inference(symmetry,[status(thm)],[8056])).
% 1.73/1.96 tff(8058,plain,
% 1.73/1.96 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[7820])).
% 1.73/1.96 tff(8059,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/1.96 inference(symmetry,[status(thm)],[8058])).
% 1.73/1.96 tff(8060,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8059, 8057])).
% 1.73/1.96 tff(8061,plain,
% 1.73/1.96 (b(s(s(s(s(z)))), s(z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[7065, 8060])).
% 1.73/1.96 tff(8062,plain,
% 1.73/1.96 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[7813])).
% 1.73/1.96 tff(8063,plain,
% 1.73/1.96 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.96 inference(symmetry,[status(thm)],[8062])).
% 1.73/1.96 tff(8064,plain,
% 1.73/1.96 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[7822])).
% 1.73/1.96 tff(8065,plain,
% 1.73/1.96 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8064, 8063])).
% 1.73/1.96 tff(8066,plain,
% 1.73/1.96 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8065])).
% 1.73/1.96 tff(8067,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8068,plain,
% 1.73/1.96 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8069,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8068])).
% 1.73/1.96 tff(8070,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8069, 8067])).
% 1.73/1.96 tff(8071,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(8072,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8071, 8070])).
% 1.73/1.96 tff(8073,plain,
% 1.73/1.96 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8072, 121, 8009, 8036, 8019])).
% 1.73/1.96 tff(8074,plain,
% 1.73/1.96 (~r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8073, 8066])).
% 1.73/1.96 tff(8075,plain,
% 1.73/1.96 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1682, 8074])).
% 1.73/1.96 tff(8076,plain,
% 1.73/1.96 (~b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1785, 8075, 8061, 8055])).
% 1.73/1.96 tff(8077,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8076, 8046])).
% 1.73/1.96 tff(8078,plain,((elem!1 = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | b(z, s(z)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8079,plain,
% 1.73/1.96 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8078, 3454, 219, 894])).
% 1.73/1.96 tff(8080,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8079, 3497])).
% 1.73/1.96 tff(8081,plain,
% 1.73/1.96 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3049, 3492])).
% 1.73/1.96 tff(8082,plain,
% 1.73/1.96 (r(s(s(s(z))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[255, 2346, 2316])).
% 1.73/1.96 tff(8083,plain,
% 1.73/1.96 (r(s(s(elem!1)), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6824, 3492, 8082])).
% 1.73/1.96 tff(8084,plain,
% 1.73/1.96 (~r(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2422, 8083, 110, 905])).
% 1.73/1.96 tff(8085,plain,
% 1.73/1.96 (b(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2430, 8084])).
% 1.73/1.96 tff(8086,plain,
% 1.73/1.96 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6679, 3491, 71])).
% 1.73/1.96 tff(8087,plain,
% 1.73/1.96 (r(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[599, 8086, 68])).
% 1.73/1.96 tff(8088,plain,
% 1.73/1.96 (~r(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5075, 8087, 378, 8083])).
% 1.73/1.96 tff(8089,plain,
% 1.73/1.96 (b(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2106, 8088])).
% 1.73/1.96 tff(8090,plain,
% 1.73/1.96 (r(s(z), z) <=> r(elem!1, z)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[3492])).
% 1.73/1.96 tff(8091,plain,
% 1.73/1.96 (r(elem!1, z)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[110, 8090])).
% 1.73/1.96 tff(8092,plain,
% 1.73/1.96 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3091, 8091, 8082, 378, 3492, 8087, 8089, 8085])).
% 1.73/1.96 tff(8093,plain,
% 1.73/1.96 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[840, 8092, 8081])).
% 1.73/1.96 tff(8094,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[831, 5041])).
% 1.73/1.96 tff(8095,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5869, 8094])).
% 1.73/1.96 tff(8096,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(elem!1)))), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8097,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8096, 8093, 3492])).
% 1.73/1.96 tff(8098,plain,
% 1.73/1.96 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[3492])).
% 1.73/1.96 tff(8099,plain,
% 1.73/1.96 (~r(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[420, 3455, 110, 378])).
% 1.73/1.96 tff(8100,plain,
% 1.73/1.96 (b(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[429, 8099, 2282])).
% 1.73/1.96 tff(8101,plain,
% 1.73/1.96 (b(s(elem!1), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8100, 8098])).
% 1.73/1.96 tff(8102,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3107, 271, 2345, 8101, 8097, 8080])).
% 1.73/1.96 tff(8103,plain,(b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (s(z) = s(elem!1)) | b(z, s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8104,plain,
% 1.73/1.96 (b(s(s(s(z))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8103, 573, 110, 68, 71, 344, 894, 1, 199, 2344, 2343, 2326, 750, 503, 232, 356])).
% 1.73/1.96 tff(8105,plain,
% 1.73/1.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[223])).
% 1.73/1.96 tff(8106,plain,
% 1.73/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.73/1.96 inference(symmetry,[status(thm)],[8105])).
% 1.73/1.96 tff(8107,plain,
% 1.73/1.96 (b(s(s(s(z))), s(z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[257, 8106])).
% 1.73/1.96 tff(8108,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2319, 8107])).
% 1.73/1.96 tff(8109,plain,((~(s(z) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8110,plain,
% 1.73/1.96 (~(s(z) = elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8109, 8104, 2319])).
% 1.73/1.96 tff(8111,plain,
% 1.73/1.96 (b(s(z), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[236, 8110, 232])).
% 1.73/1.96 tff(8112,plain,
% 1.73/1.96 (~(elem!1 = s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[242, 8110])).
% 1.73/1.96 tff(8113,plain,
% 1.73/1.96 (~r(s(elem!1), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3490, 8112, 106, 905, 356, 344, 351, 2345])).
% 1.73/1.96 tff(8114,plain,
% 1.73/1.96 (b(s(elem!1), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[409, 8113])).
% 1.73/1.96 tff(8115,plain,
% 1.73/1.96 (~(s(s(z)) = s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[960, 8110])).
% 1.73/1.96 tff(8116,plain,
% 1.73/1.96 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[953, 8115])).
% 1.73/1.96 tff(8117,plain,
% 1.73/1.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2464, 8116, 2343, 2326, 905, 110, 750, 503])).
% 1.73/1.96 tff(8118,plain,
% 1.73/1.96 (b(s(elem!1), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3432, 8117, 110, 1, 106, 199, 8114, 2344])).
% 1.73/1.96 tff(8119,plain,
% 1.73/1.96 (~b(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3247, 271, 2345, 8118, 8111])).
% 1.73/1.96 tff(8120,plain,
% 1.73/1.96 (r(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[429, 8119, 351])).
% 1.73/1.96 tff(8121,plain,
% 1.73/1.96 (~r(z, s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2186, 8120, 106, 905])).
% 1.73/1.96 tff(8122,plain,
% 1.73/1.96 (b(z, s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1439, 8121])).
% 1.73/1.96 tff(8123,plain,
% 1.73/1.96 (~r(elem!1, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4202, 356, 110, 905])).
% 1.73/1.96 tff(8124,plain,
% 1.73/1.96 (b(elem!1, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[299, 8112, 8123])).
% 1.73/1.96 tff(8125,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8126,plain,
% 1.73/1.96 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8127,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8126])).
% 1.73/1.96 tff(8128,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8127, 8125])).
% 1.73/1.96 tff(8129,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(8130,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8129, 8128])).
% 1.73/1.96 tff(8131,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8130, 271, 260, 448, 504, 503])).
% 1.73/1.96 tff(8132,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8133,plain,
% 1.73/1.96 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8132, 8111, 503, 8124])).
% 1.73/1.96 tff(8134,plain,
% 1.73/1.96 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3288, 8114, 2345, 8104])).
% 1.73/1.96 tff(8135,plain,
% 1.73/1.96 (~b(s(z), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3435, 8118, 2345, 8111])).
% 1.73/1.96 tff(8136,plain,
% 1.73/1.96 (r(s(z), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[444, 8135, 344])).
% 1.73/1.96 tff(8137,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8138,plain,
% 1.73/1.96 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8139,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8138])).
% 1.73/1.96 tff(8140,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8139, 8137])).
% 1.73/1.96 tff(8141,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(8142,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8141, 8140])).
% 1.73/1.96 tff(8143,plain,
% 1.73/1.96 (~r(s(s(s(z))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8142, 121, 8136, 8120, 2326])).
% 1.73/1.96 tff(8144,plain,
% 1.73/1.96 (s(s(s(z))) = s(elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1816, 8143, 8134])).
% 1.73/1.96 tff(8145,plain,
% 1.73/1.96 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2596, 8144])).
% 1.73/1.96 tff(8146,plain,
% 1.73/1.96 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[486, 8145, 8133])).
% 1.73/1.96 tff(8147,plain,
% 1.73/1.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[556, 8117, 1])).
% 1.73/1.96 tff(8148,plain,
% 1.73/1.96 (~r(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3310, 8147, 199, 198, 331, 2344, 79])).
% 1.73/1.96 tff(8149,plain,
% 1.73/1.96 (b(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[599, 8148, 68])).
% 1.73/1.96 tff(8150,plain,
% 1.73/1.96 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3324, 8149, 2345, 8114])).
% 1.73/1.96 tff(8151,plain,
% 1.73/1.96 (r(s(s(elem!1)), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[701, 8150, 3313])).
% 1.73/1.96 tff(8152,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8153,plain,
% 1.73/1.96 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8154,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8153])).
% 1.73/1.96 tff(8155,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8154, 8152])).
% 1.73/1.96 tff(8156,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(8157,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8156, 8155])).
% 1.73/1.96 tff(8158,plain,
% 1.73/1.96 (~r(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8157, 121, 8147, 111, 573])).
% 1.73/1.96 tff(8159,plain,
% 1.73/1.96 (b(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2430, 8158])).
% 1.73/1.96 tff(8160,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8161,plain,
% 1.73/1.96 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8162,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8161])).
% 1.73/1.96 tff(8163,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8162, 8160])).
% 1.73/1.96 tff(8164,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(8165,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8164, 8163])).
% 1.73/1.96 tff(8166,plain,
% 1.73/1.96 (~r(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8165, 121, 8147, 111, 573])).
% 1.73/1.96 tff(8167,plain,
% 1.73/1.96 (b(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2106, 8166])).
% 1.73/1.96 tff(8168,plain,
% 1.73/1.96 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(8169,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8168])).
% 1.73/1.96 tff(8170,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[8169, 2798])).
% 1.73/1.96 tff(8171,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(8172,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8171, 8170])).
% 1.73/1.96 tff(8173,plain,
% 1.73/1.96 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8172, 271, 8114, 8167, 8159])).
% 1.73/1.96 tff(8174,plain,
% 1.73/1.96 (r(s(elem!1), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[526, 8173, 211])).
% 1.73/1.96 tff(8175,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3201, 8174, 8147, 8151])).
% 1.73/1.96 tff(8176,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[681, 8175, 79])).
% 1.73/1.96 tff(8177,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3351, 8176, 8146, 2345, 8114, 358, 8122])).
% 1.73/1.96 tff(8178,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | b(z, elem!1) | (z = elem!1) | r(elem!1, s(elem!1)) | (~r(s(z), z)) | (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))) | r(s(z), elem!1) | b(s(s(s(z))), s(z)) | b(s(z), s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8179,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8178, 2344, 68, 199, 331, 111, 110, 1, 750, 503, 232, 2319, 71, 894])).
% 1.73/1.96 tff(8180,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[586, 8179, 563])).
% 1.73/1.96 tff(8181,plain,
% 1.73/1.96 (b(s(z), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[236, 231, 232])).
% 1.73/1.96 tff(8182,plain,
% 1.73/1.96 (~r(s(elem!1), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3490, 243, 108, 909, 378, 348, 2282, 2345])).
% 1.73/1.96 tff(8183,plain,
% 1.73/1.96 (b(s(elem!1), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[409, 8182])).
% 1.73/1.96 tff(8184,plain,
% 1.73/1.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2464, 3504, 1935, 2327, 909, 110, 750, 503])).
% 1.73/1.96 tff(8185,plain,
% 1.73/1.96 (b(s(elem!1), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3432, 8184, 110, 1, 108, 199, 8183, 2344])).
% 1.73/1.96 tff(8186,plain,
% 1.73/1.96 (~b(s(z), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3435, 8185, 2345, 8181])).
% 1.73/1.96 tff(8187,plain,
% 1.73/1.96 (r(s(z), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[444, 8186, 348])).
% 1.73/1.96 tff(8188,plain,
% 1.73/1.96 (~r(s(elem!1), s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3445, 8187, 108, 2356])).
% 1.73/1.96 tff(8189,plain,
% 1.73/1.96 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2354, 271, 8183, 2348, 1935])).
% 1.73/1.96 tff(8190,plain,
% 1.73/1.96 (s(elem!1) = s(s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2044, 8189, 8188])).
% 1.73/1.96 tff(8191,plain,
% 1.73/1.96 (s(s(s(z))) = s(elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2035, 8190])).
% 1.73/1.96 tff(8192,plain,
% 1.73/1.96 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8191])).
% 1.73/1.96 tff(8193,plain,
% 1.73/1.96 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.73/1.96 inference(symmetry,[status(thm)],[8192])).
% 1.73/1.96 tff(8194,plain,
% 1.73/1.96 (b(s(s(s(z))), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[8185, 8193])).
% 1.73/1.96 tff(8195,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2346, 8194])).
% 1.73/1.96 tff(8196,plain,((s(z) = elem!1) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(8197,plain,
% 1.73/1.96 (s(z) = elem!1),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[8196, 2346, 2343, 106, 344, 110, 1, 199, 2344, 2327, 909, 750, 503, 356, 232])).
% 1.73/1.96 tff(8198,plain,
% 1.73/1.96 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3049, 8197])).
% 1.73/1.96 tff(8199,plain,
% 1.73/1.96 (r(s(s(elem!1)), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6824, 8197, 8082])).
% 1.73/1.96 tff(8200,plain,
% 1.73/1.96 (~r(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2422, 8199, 110, 909])).
% 1.73/1.96 tff(8201,plain,
% 1.73/1.96 (b(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2430, 8200])).
% 1.73/1.96 tff(8202,plain,
% 1.73/1.96 (elem!1 = s(z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1221, 8197])).
% 1.73/1.96 tff(8203,plain,
% 1.73/1.96 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6679, 8202, 71])).
% 1.73/1.96 tff(8204,plain,
% 1.73/1.96 (r(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[599, 8203, 68])).
% 1.73/1.96 tff(8205,plain,
% 1.73/1.96 (~r(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5075, 8204, 356, 8199])).
% 1.73/1.96 tff(8206,plain,
% 1.73/1.96 (b(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2106, 8205])).
% 1.73/1.96 tff(8207,plain,
% 1.73/1.96 (r(s(z), z) <=> r(elem!1, z)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[8197])).
% 1.73/1.96 tff(8208,plain,
% 1.73/1.96 (r(elem!1, z)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[110, 8207])).
% 1.73/1.96 tff(8209,plain,
% 1.73/1.96 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3091, 8208, 8082, 356, 8197, 8204, 8206, 8201])).
% 1.73/1.97 tff(8210,plain,
% 1.73/1.97 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[840, 8209, 8198])).
% 1.73/1.97 tff(8211,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8096, 8210, 8197])).
% 1.73/1.97 tff(8212,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8197])).
% 1.73/1.97 tff(8213,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[503, 8212])).
% 1.73/1.97 tff(8214,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8215,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(8216,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8215, 8214])).
% 1.73/1.97 tff(8217,plain,
% 1.73/1.97 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8216, 271, 2345, 8213, 8211])).
% 1.73/1.97 tff(8218,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.97 tff(8219,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.97 tff(8220,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1594, 21, 1591, 8219, 8218])).
% 1.73/1.97 tff(8221,plain,(r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8222,plain,
% 1.73/1.97 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8221, 8217, 1577])).
% 1.73/1.97 tff(8223,plain,
% 1.73/1.97 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3310, 8204, 199, 198, 331, 2344, 79])).
% 1.73/1.97 tff(8224,plain,
% 1.73/1.97 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[556, 8223, 1])).
% 1.73/1.97 tff(8225,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1900, 271, 8224, 589, 8206])).
% 1.73/1.97 tff(8226,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.73/1.97 tff(8227,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.73/1.97 tff(8228,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1904, 21, 30, 8227, 8226])).
% 1.73/1.97 tff(8229,plain,(r(s(s(s(elem!1))), z) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8230,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8229, 8225])).
% 1.73/1.97 tff(8231,plain,
% 1.73/1.97 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[750, 6792])).
% 1.73/1.97 tff(8232,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[657, 8231])).
% 1.73/1.97 tff(8233,plain,((~b(s(z), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8234,plain,
% 1.73/1.97 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8233, 8197, 750])).
% 1.73/1.97 tff(8235,plain,
% 1.73/1.97 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[747, 8213, 2345, 8234])).
% 1.73/1.97 tff(8236,plain,
% 1.73/1.97 (r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2293, 21, 8235, 85])).
% 1.73/1.97 tff(8237,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8238,plain,
% 1.73/1.97 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8239,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8238])).
% 1.73/1.97 tff(8240,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[8239, 8237])).
% 1.73/1.97 tff(8241,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(8242,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8241, 8240])).
% 1.73/1.97 tff(8243,plain,
% 1.73/1.97 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8242, 121, 8236, 8230, 8222])).
% 1.73/1.97 tff(8244,plain,
% 1.73/1.97 (s(s(z)) = s(elem!1)),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8197])).
% 1.73/1.97 tff(8245,plain,
% 1.73/1.97 (s(s(s(z))) = s(s(elem!1))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8244])).
% 1.73/1.97 tff(8246,plain,
% 1.73/1.97 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8245])).
% 1.73/1.97 tff(8247,plain,
% 1.73/1.97 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8246])).
% 1.73/1.97 tff(8248,plain,
% 1.73/1.97 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[8247])).
% 1.73/1.97 tff(8249,plain,
% 1.73/1.97 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8248])).
% 1.73/1.97 tff(8250,plain,
% 1.73/1.97 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.97 inference(symmetry,[status(thm)],[8249])).
% 1.73/1.97 tff(8251,plain,
% 1.73/1.97 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8250])).
% 1.73/1.97 tff(8252,plain,
% 1.73/1.97 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8244])).
% 1.73/1.97 tff(8253,plain,
% 1.73/1.97 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8252])).
% 1.73/1.97 tff(8254,plain,
% 1.73/1.97 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[877, 8253])).
% 1.73/1.97 tff(8255,plain,
% 1.73/1.97 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8254, 8251])).
% 1.73/1.97 tff(8256,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3112, 21, 8255, 8243])).
% 1.73/1.97 tff(8257,plain,
% 1.73/1.97 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8197])).
% 1.73/1.97 tff(8258,plain,
% 1.73/1.97 (r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[106, 8257])).
% 1.73/1.97 tff(8259,plain,
% 1.73/1.97 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8244])).
% 1.73/1.97 tff(8260,plain,
% 1.73/1.97 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.73/1.97 inference(transitivity,[status(thm)],[8259, 3535])).
% 1.73/1.97 tff(8261,plain,
% 1.73/1.97 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8260])).
% 1.73/1.97 tff(8262,plain,
% 1.73/1.97 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[1136, 8261])).
% 1.73/1.97 tff(8263,plain,
% 1.73/1.97 (~r(z, s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2335, 2327, 106, 909])).
% 1.73/1.97 tff(8264,plain,
% 1.73/1.97 (b(z, s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1214, 8263])).
% 1.73/1.97 tff(8265,plain,
% 1.73/1.97 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8266,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8265])).
% 1.73/1.97 tff(8267,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[8266, 6210])).
% 1.73/1.97 tff(8268,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(8269,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8268, 8267])).
% 1.73/1.97 tff(8270,plain,
% 1.73/1.97 (~r(s(elem!1), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8269, 121, 111, 8236, 8230])).
% 1.73/1.97 tff(8271,plain,
% 1.73/1.97 (b(s(elem!1), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[409, 8270])).
% 1.73/1.97 tff(8272,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8273,plain,
% 1.73/1.97 (((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8274,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8273])).
% 1.73/1.97 tff(8275,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[8274, 8272])).
% 1.73/1.97 tff(8276,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(8277,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8276, 8275])).
% 1.73/1.97 tff(8278,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8277, 271, 394, 1422, 1307, 1935])).
% 1.73/1.97 tff(8279,plain,((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8280,plain,
% 1.73/1.97 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8279, 8271, 2343, 8264])).
% 1.73/1.97 tff(8281,plain,
% 1.73/1.97 (r(s(s(s(z))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1816, 8280, 8262])).
% 1.73/1.97 tff(8282,plain,
% 1.73/1.97 (~r(s(elem!1), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5181, 8281, 8258, 8082])).
% 1.73/1.97 tff(8283,plain,
% 1.73/1.97 (b(s(elem!1), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2243, 8282, 2207])).
% 1.73/1.97 tff(8284,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3107, 271, 2345, 8283, 8211, 8256])).
% 1.73/1.97 tff(8285,plain,(b(s(s(s(z))), elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | (z = elem!1) | r(elem!1, s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(z, s(z))) | b(s(z), s(s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8286,plain,
% 1.73/1.97 (b(s(s(s(z))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8285, 8180, 111, 503, 110, 1, 199, 331, 2344, 68, 905, 71, 750, 2326, 232])).
% 1.73/1.97 tff(8287,plain,
% 1.73/1.97 (~(s(z) = elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8109, 8286, 2319])).
% 1.73/1.97 tff(8288,plain,
% 1.73/1.97 (~(elem!1 = s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[242, 8287])).
% 1.73/1.97 tff(8289,plain,
% 1.73/1.97 (~r(s(elem!1), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3490, 8288, 106, 905, 356, 344, 351, 2345])).
% 1.73/1.97 tff(8290,plain,
% 1.73/1.97 (b(s(elem!1), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[409, 8289])).
% 1.73/1.97 tff(8291,plain,
% 1.73/1.97 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8279, 8290, 2343, 2337])).
% 1.73/1.97 tff(8292,plain,
% 1.73/1.97 (b(s(z), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[236, 8287, 232])).
% 1.73/1.97 tff(8293,plain,
% 1.73/1.97 (~(s(s(z)) = s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[960, 8287])).
% 1.73/1.97 tff(8294,plain,
% 1.73/1.97 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[953, 8293])).
% 1.73/1.97 tff(8295,plain,
% 1.73/1.97 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2464, 8294, 2343, 2326, 905, 110, 750, 503])).
% 1.73/1.97 tff(8296,plain,
% 1.73/1.97 (b(s(elem!1), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3432, 8295, 110, 1, 106, 199, 8290, 2344])).
% 1.73/1.97 tff(8297,plain,
% 1.73/1.97 (~b(s(elem!1), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3247, 271, 2345, 8296, 8292])).
% 1.73/1.97 tff(8298,plain,
% 1.73/1.97 (r(s(elem!1), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[429, 8297, 351])).
% 1.73/1.97 tff(8299,plain,
% 1.73/1.97 (~b(s(z), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3435, 8296, 2345, 8292])).
% 1.73/1.97 tff(8300,plain,
% 1.73/1.97 (r(s(z), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[444, 8299, 344])).
% 1.73/1.97 tff(8301,plain,
% 1.73/1.97 (~r(s(s(s(z))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8142, 121, 8300, 8298, 2326])).
% 1.73/1.97 tff(8302,plain,
% 1.73/1.97 (s(s(s(z))) = s(elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1816, 8301, 8291])).
% 1.73/1.97 tff(8303,plain,
% 1.73/1.97 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8302])).
% 1.73/1.97 tff(8304,plain,
% 1.73/1.97 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.97 inference(symmetry,[status(thm)],[8303])).
% 1.73/1.97 tff(8305,plain,
% 1.73/1.97 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[556, 8295, 1])).
% 1.73/1.97 tff(8306,plain,
% 1.73/1.97 (~r(elem!1, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3310, 8305, 199, 198, 331, 2344, 79])).
% 1.73/1.97 tff(8307,plain,
% 1.73/1.97 (b(elem!1, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[599, 8306, 68])).
% 1.73/1.97 tff(8308,plain,
% 1.73/1.97 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3324, 8307, 2345, 8290])).
% 1.73/1.97 tff(8309,plain,
% 1.73/1.97 (r(s(s(elem!1)), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[701, 8308, 3313])).
% 1.73/1.97 tff(8310,plain,
% 1.73/1.97 (~r(z, s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2186, 8298, 106, 905])).
% 1.73/1.97 tff(8311,plain,
% 1.73/1.97 (b(z, s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1439, 8310])).
% 1.73/1.97 tff(8312,plain,
% 1.73/1.97 (b(elem!1, s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[299, 8288, 8123])).
% 1.73/1.97 tff(8313,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8132, 8292, 503, 8312])).
% 1.73/1.97 tff(8314,plain,
% 1.73/1.97 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2596, 8302])).
% 1.73/1.97 tff(8315,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[486, 8314, 8313])).
% 1.73/1.97 tff(8316,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3351, 8315, 2345, 8290, 358, 8311])).
% 1.73/1.97 tff(8317,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[681, 8316, 79])).
% 1.73/1.97 tff(8318,plain,
% 1.73/1.97 (~r(s(elem!1), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3201, 8317, 8305, 8309])).
% 1.73/1.97 tff(8319,plain,
% 1.73/1.97 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[526, 8318, 211])).
% 1.73/1.97 tff(8320,plain,
% 1.73/1.97 (b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8319, 8304])).
% 1.73/1.97 tff(8321,plain,
% 1.73/1.97 (~r(z, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3425, 8315, 111, 8305])).
% 1.73/1.97 tff(8322,plain,
% 1.73/1.97 (b(z, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2106, 8321])).
% 1.73/1.97 tff(8323,plain,
% 1.73/1.97 (~b(elem!1, z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1315, 8290, 2337, 2345])).
% 1.73/1.97 tff(8324,plain,
% 1.73/1.97 (r(elem!1, z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[284, 8323, 358])).
% 1.73/1.97 tff(8325,plain,
% 1.73/1.97 (~r(s(s(elem!1)), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6958, 8315, 8324, 1, 563, 356])).
% 1.73/1.97 tff(8326,plain,
% 1.73/1.97 (b(s(s(elem!1)), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[862, 8325, 198])).
% 1.73/1.97 tff(8327,plain,
% 1.73/1.97 (~b(s(s(elem!1)), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5441, 8326, 8312, 8292])).
% 1.73/1.97 tff(8328,plain,
% 1.73/1.97 (r(s(s(elem!1)), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2143, 8327])).
% 1.73/1.97 tff(8329,plain,
% 1.73/1.97 (~r(s(s(elem!1)), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2422, 8328, 110, 905])).
% 1.73/1.97 tff(8330,plain,
% 1.73/1.97 (b(s(s(elem!1)), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2430, 8329])).
% 1.73/1.97 tff(8331,plain,
% 1.73/1.97 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2454, 8330, 2343, 8322])).
% 1.73/1.97 tff(8332,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8331, 8320])).
% 1.73/1.97 tff(8333,plain,(r(elem!1, s(elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | b(z, elem!1) | (z = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | b(s(s(s(z))), s(z)) | b(s(z), s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8334,plain,
% 1.73/1.97 (r(elem!1, s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8333, 750, 1, 111, 68, 199, 331, 110, 503, 232, 2319, 71, 894])).
% 1.73/1.97 tff(8335,plain,
% 1.73/1.97 (~r(elem!1, s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4202, 378, 110, 909])).
% 1.73/1.97 tff(8336,plain,
% 1.73/1.97 (~(elem!1 = s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[218, 216])).
% 1.73/1.97 tff(8337,plain,
% 1.73/1.97 (~(s(elem!1) = elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2206, 8336])).
% 1.73/1.97 tff(8338,plain,
% 1.73/1.97 (~b(elem!1, s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3490, 412, 108, 909, 378, 348, 2282, 258])).
% 1.73/1.97 tff(8339,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3700, 8338, 412, 2564, 199, 293, 258, 909, 379])).
% 1.73/1.97 tff(8340,plain,((~r(s(elem!1), z)) | (s(elem!1) = elem!1) | b(z, elem!1) | r(elem!1, s(z)) | (elem!1 = s(z)) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(8341,plain,
% 1.73/1.97 (~r(s(elem!1), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8340, 243, 199, 293, 2564, 909, 379, 108, 378, 348])).
% 1.73/1.97 tff(8342,plain,
% 1.73/1.97 (b(s(elem!1), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[409, 8341])).
% 1.73/1.97 tff(8343,plain,
% 1.73/1.97 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2354, 271, 8342, 1307, 1935])).
% 1.73/1.97 tff(8344,plain,
% 1.73/1.97 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8279, 8342, 1935, 1307])).
% 1.73/1.97 tff(8345,plain,
% 1.73/1.97 (b(elem!1, s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[299, 243, 293])).
% 1.73/1.97 tff(8346,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8132, 8181, 503, 8345])).
% 1.73/1.97 tff(8347,plain,
% 1.73/1.97 (~r(s(elem!1), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6290, 121, 379, 622, 145])).
% 1.73/1.97 tff(8348,plain,
% 1.73/1.97 (s(elem!1) = s(s(s(z)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2044, 8347, 2039])).
% 1.73/1.97 tff(8349,plain,
% 1.73/1.97 (s(s(s(z))) = s(elem!1)),
% 1.73/1.97 inference(symmetry,[status(thm)],[8348])).
% 1.73/1.97 tff(8350,plain,
% 1.73/1.97 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(elem!1))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8349])).
% 1.73/1.97 tff(8351,plain,
% 1.73/1.97 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[8350])).
% 1.73/1.97 tff(8352,plain,
% 1.73/1.97 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8348])).
% 1.73/1.97 tff(8353,plain,
% 1.73/1.97 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.73/1.97 inference(symmetry,[status(thm)],[8352])).
% 1.73/1.97 tff(8354,plain,
% 1.73/1.97 (s(s(z)) = elem!1),
% 1.73/1.97 inference(transitivity,[status(thm)],[92, 8353, 70])).
% 1.73/1.97 tff(8355,plain,
% 1.73/1.97 (r(s(s(z)), s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8354, 8348])).
% 1.73/1.97 tff(8356,plain,
% 1.73/1.97 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(elem!1))),
% 1.73/1.97 inference(symmetry,[status(thm)],[8355])).
% 1.73/1.97 tff(8357,plain,
% 1.73/1.97 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8348])).
% 1.73/1.97 tff(8358,plain,
% 1.73/1.97 (r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[379, 8357])).
% 1.73/1.97 tff(8359,plain,
% 1.73/1.97 (r(s(s(z)), s(elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8358, 8356])).
% 1.73/1.97 tff(8360,plain,
% 1.73/1.97 (r(s(s(z)), s(s(s(z))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8359, 8351])).
% 1.73/1.97 tff(8361,plain,
% 1.73/1.97 (elem!1 = s(s(z))),
% 1.73/1.97 inference(transitivity,[status(thm)],[75, 8352, 91])).
% 1.73/1.97 tff(8362,plain,
% 1.73/1.97 (r(z, elem!1) <=> r(z, s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8361])).
% 1.73/1.97 tff(8363,plain,
% 1.73/1.97 (r(z, s(s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[378, 8362])).
% 1.73/1.97 tff(8364,plain,
% 1.73/1.97 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8348])).
% 1.73/1.97 tff(8365,plain,
% 1.73/1.97 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8364])).
% 1.73/1.97 tff(8366,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8365])).
% 1.73/1.97 tff(8367,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8361])).
% 1.73/1.97 tff(8368,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8369,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(8370,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8369, 8368])).
% 1.73/1.97 tff(8371,plain,
% 1.73/1.97 (~r(s(s(s(z))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[8370, 121, 379, 622, 145])).
% 1.73/1.97 tff(8372,plain,
% 1.73/1.97 (s(s(s(z))) = s(elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1816, 8371, 3506])).
% 1.73/1.97 tff(8373,plain,
% 1.73/1.97 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2596, 8372])).
% 1.73/1.97 tff(8374,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[486, 8373, 479])).
% 1.73/1.97 tff(8375,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8374, 8367])).
% 1.73/1.97 tff(8376,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[8375, 8366])).
% 1.73/1.97 tff(8377,plain,
% 1.73/1.97 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8365])).
% 1.73/1.97 tff(8378,plain,
% 1.73/1.97 (r(z, s(s(s(s(s(z))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[111, 8377])).
% 1.73/1.97 tff(8379,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8380,plain,
% 1.73/1.97 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(8381,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[8380])).
% 1.73/1.97 tff(8382,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[8381, 8379])).
% 1.73/1.97 tff(8383,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(8384,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8383, 8382])).
% 1.73/1.98 tff(8385,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8384, 121, 8378, 8376, 8363, 8360])).
% 1.73/1.98 tff(8386,plain,((~r(s(elem!1), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(z))), s(elem!1)) | b(s(elem!1), s(s(s(z)))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8387,plain,
% 1.73/1.98 (~r(s(elem!1), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8386, 8346, 378, 379, 111, 8344, 8343, 2356])).
% 1.73/1.98 tff(8388,plain,
% 1.73/1.98 (b(s(elem!1), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2243, 8387, 2564])).
% 1.73/1.98 tff(8389,plain,
% 1.73/1.98 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.73/1.98 inference(monotonicity,[status(thm)],[2031])).
% 1.73/1.98 tff(8390,plain,
% 1.73/1.98 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.73/1.98 inference(symmetry,[status(thm)],[8389])).
% 1.73/1.98 tff(8391,plain,
% 1.73/1.98 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8390])).
% 1.73/1.98 tff(8392,plain,
% 1.73/1.98 (~b(s(elem!1), elem!1)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[2346, 8391])).
% 1.73/1.98 tff(8393,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2618, 8392])).
% 1.73/1.98 tff(8394,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(s(elem!1), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8395,plain,
% 1.73/1.98 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8394, 8388, 2346])).
% 1.73/1.98 tff(8396,plain,
% 1.73/1.98 (r(s(elem!1), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2044, 8395, 8343])).
% 1.73/1.98 tff(8397,plain,
% 1.73/1.98 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[3535])).
% 1.73/1.98 tff(8398,plain,
% 1.73/1.98 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8395, 8397])).
% 1.73/1.98 tff(8399,plain,
% 1.73/1.98 (r(s(s(s(z))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1816, 8398, 8344])).
% 1.73/1.98 tff(8400,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8401,plain,
% 1.73/1.98 (((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8402,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8401])).
% 1.73/1.98 tff(8403,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[8402, 8400])).
% 1.73/1.98 tff(8404,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(8405,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8404, 8403])).
% 1.73/1.98 tff(8406,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8405, 121, 379, 2356, 8399, 8396])).
% 1.73/1.98 tff(8407,plain,((s(z) = elem!1) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), elem!1) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(z, elem!1) | r(elem!1, s(z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8408,plain,
% 1.73/1.98 (s(z) = elem!1),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8407, 2346, 379, 8337, 378, 111, 1307, 2343, 199, 8335, 909, 106, 348, 503, 232])).
% 1.73/1.98 tff(8409,plain,
% 1.73/1.98 (r(s(s(elem!1)), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6824, 8408, 8082])).
% 1.73/1.98 tff(8410,plain,
% 1.73/1.98 (~r(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2422, 8409, 110, 909])).
% 1.73/1.98 tff(8411,plain,
% 1.73/1.98 (b(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2430, 8410])).
% 1.73/1.98 tff(8412,plain,
% 1.73/1.98 (elem!1 = s(z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1221, 8408])).
% 1.73/1.98 tff(8413,plain,
% 1.73/1.98 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6679, 8412, 71])).
% 1.73/1.98 tff(8414,plain,
% 1.73/1.98 (r(elem!1, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[599, 8413, 68])).
% 1.73/1.98 tff(8415,plain,
% 1.73/1.98 (~r(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5075, 8414, 378, 8409])).
% 1.73/1.98 tff(8416,plain,
% 1.73/1.98 (b(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2106, 8415])).
% 1.73/1.98 tff(8417,plain,
% 1.73/1.98 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8408])).
% 1.73/1.98 tff(8418,plain,
% 1.73/1.98 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.73/1.98 inference(symmetry,[status(thm)],[8417])).
% 1.73/1.98 tff(8419,plain,
% 1.73/1.98 (r(s(z), s(s(elem!1)))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8414, 8418])).
% 1.73/1.98 tff(8420,plain,
% 1.73/1.98 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8408])).
% 1.73/1.98 tff(8421,plain,
% 1.73/1.98 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.73/1.98 inference(symmetry,[status(thm)],[8420])).
% 1.73/1.98 tff(8422,plain,
% 1.73/1.98 (r(s(z), s(elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[379, 8421])).
% 1.73/1.98 tff(8423,plain,
% 1.73/1.98 (~(s(s(elem!1)) = s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[620, 216])).
% 1.73/1.98 tff(8424,plain,
% 1.73/1.98 (r(s(z), z) <=> r(elem!1, z)),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8408])).
% 1.73/1.98 tff(8425,plain,
% 1.73/1.98 (r(elem!1, z)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[110, 8424])).
% 1.73/1.98 tff(8426,plain,
% 1.73/1.98 (~r(s(elem!1), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1417, 8425, 909, 379])).
% 1.73/1.98 tff(8427,plain,
% 1.73/1.98 (b(s(elem!1), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[409, 8426])).
% 1.73/1.98 tff(8428,plain,
% 1.73/1.98 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2528, 8427, 8411, 8416])).
% 1.73/1.98 tff(8429,plain,
% 1.73/1.98 (r(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[701, 8428, 8423])).
% 1.73/1.98 tff(8430,plain,
% 1.73/1.98 (~r(s(elem!1), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3275, 8429, 8422, 8419])).
% 1.73/1.98 tff(8431,plain,
% 1.73/1.98 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[526, 8430, 216])).
% 1.73/1.98 tff(8432,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8172, 271, 8427, 8431, 8416, 8411])).
% 1.73/1.98 tff(8433,plain,(b(s(s(s(z))), elem!1) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | b(z, elem!1) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8434,plain,
% 1.73/1.98 (b(s(s(s(z))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8433, 8334, 905, 211, 110, 356, 68, 71, 111, 2337, 199, 344, 503, 232])).
% 1.73/1.98 tff(8435,plain,
% 1.73/1.98 (~(s(z) = elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8109, 8434, 2319])).
% 1.73/1.98 tff(8436,plain,
% 1.73/1.98 (~(elem!1 = s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[242, 8435])).
% 1.73/1.98 tff(8437,plain,
% 1.73/1.98 (~r(s(elem!1), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8340, 8436, 199, 8123, 2207, 905, 8334, 106, 356, 344])).
% 1.73/1.98 tff(8438,plain,
% 1.73/1.98 (b(s(elem!1), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[409, 8437])).
% 1.73/1.98 tff(8439,plain,
% 1.73/1.98 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2354, 271, 8438, 2337, 2343])).
% 1.73/1.98 tff(8440,plain,
% 1.73/1.98 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8279, 8438, 2343, 2337])).
% 1.73/1.98 tff(8441,plain,
% 1.73/1.98 (b(s(z), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[236, 8435, 232])).
% 1.73/1.98 tff(8442,plain,
% 1.73/1.98 (b(elem!1, s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[299, 8436, 8123])).
% 1.73/1.98 tff(8443,plain,
% 1.73/1.98 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8132, 8441, 503, 8442])).
% 1.73/1.98 tff(8444,plain,
% 1.73/1.98 (~(s(s(z)) = s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[960, 8435])).
% 1.73/1.98 tff(8445,plain,
% 1.73/1.98 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[953, 8444])).
% 1.73/1.98 tff(8446,plain,
% 1.73/1.98 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2464, 8445, 2343, 2326, 905, 110, 750, 503])).
% 1.73/1.98 tff(8447,plain,
% 1.73/1.98 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[556, 8446, 1])).
% 1.73/1.98 tff(8448,plain,
% 1.73/1.98 (r(s(elem!1), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2243, 2467, 8337])).
% 1.73/1.98 tff(8449,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8450,plain,
% 1.73/1.98 (((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8451,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8450])).
% 1.73/1.98 tff(8452,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.73/1.98 inference(transitivity,[status(thm)],[8451, 8449])).
% 1.73/1.98 tff(8453,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(8454,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8453, 8452])).
% 1.73/1.98 tff(8455,plain,
% 1.73/1.98 (~r(z, s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8454, 121, 379, 8448, 378])).
% 1.73/1.98 tff(8456,plain,
% 1.73/1.98 (b(z, s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1439, 8455])).
% 1.73/1.98 tff(8457,plain,
% 1.73/1.98 (~r(s(s(s(z))), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[129, 108, 110, 111])).
% 1.73/1.98 tff(8458,plain,
% 1.73/1.98 (b(s(s(s(z))), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1155, 8457])).
% 1.73/1.98 tff(8459,plain,
% 1.73/1.98 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2354, 271, 394, 2348, 8458])).
% 1.73/1.98 tff(8460,plain,
% 1.73/1.98 (b(s(elem!1), elem!1)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[257, 8390])).
% 1.73/1.98 tff(8461,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2467, 8460])).
% 1.73/1.98 tff(8462,plain,((~(s(elem!1) = s(s(s(z))))) | b(s(elem!1), elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8463,plain,
% 1.73/1.98 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8462, 2467, 257])).
% 1.73/1.98 tff(8464,plain,
% 1.73/1.98 (r(s(elem!1), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2044, 8463, 8459])).
% 1.73/1.98 tff(8465,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8466,plain,
% 1.73/1.98 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8467,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8466])).
% 1.73/1.98 tff(8468,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[8467, 8465])).
% 1.73/1.98 tff(8469,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(8470,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8469, 8468])).
% 1.73/1.98 tff(8471,plain,
% 1.73/1.98 (~r(s(elem!1), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8470, 121, 2327, 108, 8464])).
% 1.73/1.98 tff(8472,plain,
% 1.73/1.98 (b(s(elem!1), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[429, 8471, 422])).
% 1.73/1.98 tff(8473,plain,
% 1.73/1.98 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6253, 271, 260, 447, 503])).
% 1.73/1.98 tff(8474,plain,
% 1.73/1.98 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[681, 8473, 82])).
% 1.73/1.98 tff(8475,plain,
% 1.73/1.98 (~r(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[692, 8474, 622, 623])).
% 1.73/1.98 tff(8476,plain,
% 1.73/1.98 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[701, 8475, 8423])).
% 1.73/1.98 tff(8477,plain,
% 1.73/1.98 (~b(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2528, 8476, 394, 1894])).
% 1.73/1.98 tff(8478,plain,
% 1.73/1.98 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6273, 271, 260, 447, 503])).
% 1.73/1.98 tff(8479,plain,
% 1.73/1.98 (~r(s(elem!1), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3190, 8478, 82, 623, 8473])).
% 1.73/1.98 tff(8480,plain,
% 1.73/1.98 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[526, 8479, 216])).
% 1.73/1.98 tff(8481,plain,
% 1.73/1.98 (~b(s(s(elem!1)), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2152, 8480, 1421, 1894])).
% 1.73/1.98 tff(8482,plain,
% 1.73/1.98 (r(s(s(elem!1)), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2143, 8481])).
% 1.73/1.98 tff(8483,plain,
% 1.73/1.98 (~r(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2422, 8482, 110, 909])).
% 1.73/1.98 tff(8484,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2430, 8483, 8477])).
% 1.73/1.98 tff(8485,plain,((~b(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8486,plain,
% 1.73/1.98 (~b(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8485, 8472, 909, 394, 110, 8456, 8448, 623, 216, 82, 260, 503])).
% 1.73/1.98 tff(8487,plain,
% 1.73/1.98 (r(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2106, 8486])).
% 1.73/1.98 tff(8488,plain,
% 1.73/1.98 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3425, 8487, 111, 623])).
% 1.73/1.98 tff(8489,plain,
% 1.73/1.98 (s(s(s(elem!1))) = elem!1),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[486, 8488, 479])).
% 1.73/1.98 tff(8490,plain,
% 1.73/1.98 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7179, 8489, 379])).
% 1.73/1.98 tff(8491,plain,
% 1.73/1.98 (~r(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[692, 8490, 8448, 623])).
% 1.73/1.98 tff(8492,plain,
% 1.73/1.98 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[701, 8491, 8423])).
% 1.73/1.98 tff(8493,plain,
% 1.73/1.98 (r(s(s(elem!1)), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2511, 8489, 623])).
% 1.73/1.98 tff(8494,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8495,plain,
% 1.73/1.98 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8496,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8495])).
% 1.73/1.98 tff(8497,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.73/1.98 inference(transitivity,[status(thm)],[8496, 8494])).
% 1.73/1.98 tff(8498,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(8499,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8498, 8497])).
% 1.73/1.98 tff(8500,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8499, 121, 379, 378, 1624, 2417])).
% 1.73/1.98 tff(8501,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8502,plain,
% 1.73/1.98 (~r(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8501, 8493, 378, 379])).
% 1.73/1.98 tff(8503,plain,
% 1.73/1.98 (b(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2430, 8502])).
% 1.73/1.98 tff(8504,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2853, 8503, 8492, 8456, 394])).
% 1.73/1.98 tff(8505,plain,(b(s(elem!1), elem!1) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(8506,plain,
% 1.73/1.98 (b(s(elem!1), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8505, 8438, 356, 8334, 8447, 8443, 111, 905, 110, 211, 79, 8441, 503, 351, 2326, 106, 8434])).
% 1.73/1.98 tff(8507,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8508,plain,
% 1.73/1.98 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(8509,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[8508])).
% 1.73/1.98 tff(8510,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[8509, 8507])).
% 1.73/1.98 tff(8511,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(8512,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[8511, 8510])).
% 1.73/1.98 tff(8513,plain,
% 1.73/1.98 (~r(s(z), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[8512, 121, 2326, 108, 2046])).
% 1.73/1.98 tff(8514,plain,
% 1.73/1.98 (b(s(z), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[444, 8513, 348])).
% 1.73/1.99 tff(8515,plain,
% 1.73/1.99 (~r(s(elem!1), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8470, 121, 2326, 108, 2046])).
% 1.73/1.99 tff(8516,plain,
% 1.73/1.99 (b(s(elem!1), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[429, 8515, 2282])).
% 1.73/1.99 tff(8517,plain,
% 1.73/1.99 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6195, 8516, 2319])).
% 1.73/1.99 tff(8518,plain,
% 1.73/1.99 (r(s(s(s(z))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1816, 8517, 3506])).
% 1.73/1.99 tff(8519,plain,
% 1.73/1.99 (~r(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2054, 8518, 379, 2046])).
% 1.73/1.99 tff(8520,plain,
% 1.73/1.99 (b(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1192, 8519, 1102])).
% 1.73/1.99 tff(8521,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(8522,plain,
% 1.73/1.99 (((~b(elem!1, s(s(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), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(8523,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z)))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8522])).
% 1.73/1.99 tff(8524,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[8523, 8521])).
% 1.73/1.99 tff(8525,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(8526,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8525, 8524])).
% 1.73/1.99 tff(8527,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8526, 271, 2618, 260, 8520, 8514])).
% 1.73/1.99 tff(8528,plain,((~r(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | b(s(s(s(z))), s(z)) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8529,plain,
% 1.73/1.99 (~r(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8528, 8506, 8441, 2338, 8334, 8440, 2319, 344, 106])).
% 1.73/1.99 tff(8530,plain,
% 1.73/1.99 (s(elem!1) = s(s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2044, 8529, 8439])).
% 1.73/1.99 tff(8531,plain,
% 1.73/1.99 (s(s(s(z))) = s(elem!1)),
% 1.73/1.99 inference(symmetry,[status(thm)],[8530])).
% 1.73/1.99 tff(8532,plain,
% 1.73/1.99 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(elem!1))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8531])).
% 1.73/1.99 tff(8533,plain,
% 1.73/1.99 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/1.99 inference(symmetry,[status(thm)],[8532])).
% 1.73/1.99 tff(8534,plain,
% 1.73/1.99 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8530])).
% 1.73/1.99 tff(8535,plain,
% 1.73/1.99 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.73/1.99 inference(symmetry,[status(thm)],[8534])).
% 1.73/1.99 tff(8536,plain,
% 1.73/1.99 (s(s(z)) = elem!1),
% 1.73/1.99 inference(transitivity,[status(thm)],[92, 8535, 70])).
% 1.73/1.99 tff(8537,plain,
% 1.73/1.99 (r(s(s(z)), s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8536, 8530])).
% 1.73/1.99 tff(8538,plain,
% 1.73/1.99 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(elem!1))),
% 1.73/1.99 inference(symmetry,[status(thm)],[8537])).
% 1.73/1.99 tff(8539,plain,
% 1.73/1.99 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8530])).
% 1.73/1.99 tff(8540,plain,
% 1.73/1.99 (r(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8334, 8539])).
% 1.73/1.99 tff(8541,plain,
% 1.73/1.99 (r(s(s(z)), s(elem!1))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8540, 8538])).
% 1.73/1.99 tff(8542,plain,
% 1.73/1.99 (r(s(s(z)), s(s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8541, 8533])).
% 1.73/1.99 tff(8543,plain,
% 1.73/1.99 (elem!1 = s(s(z))),
% 1.73/1.99 inference(transitivity,[status(thm)],[75, 8534, 91])).
% 1.73/1.99 tff(8544,plain,
% 1.73/1.99 (r(z, elem!1) <=> r(z, s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8543])).
% 1.73/1.99 tff(8545,plain,
% 1.73/1.99 (r(z, s(s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[356, 8544])).
% 1.73/1.99 tff(8546,plain,
% 1.73/1.99 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8530])).
% 1.73/1.99 tff(8547,plain,
% 1.73/1.99 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8546])).
% 1.73/1.99 tff(8548,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8547])).
% 1.73/1.99 tff(8549,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8543])).
% 1.73/1.99 tff(8550,plain,
% 1.73/1.99 (s(s(s(z))) = s(elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2035, 8530])).
% 1.73/1.99 tff(8551,plain,
% 1.73/1.99 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2596, 8550])).
% 1.73/1.99 tff(8552,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[486, 8551, 8443])).
% 1.73/1.99 tff(8553,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8552, 8549])).
% 1.73/1.99 tff(8554,plain,
% 1.73/1.99 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8553, 8548])).
% 1.73/1.99 tff(8555,plain,
% 1.73/1.99 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8547])).
% 1.73/1.99 tff(8556,plain,
% 1.73/1.99 (r(z, s(s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[111, 8555])).
% 1.73/1.99 tff(8557,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8384, 121, 8556, 8554, 8545, 8542])).
% 1.73/1.99 tff(8558,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(z)) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | r(s(z), elem!1) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (z = elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8559,plain,
% 1.73/1.99 (~b(s(z), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8558, 2319, 37, 110, 503, 1, 199, 232, 68, 71, 2339, 894])).
% 1.73/1.99 tff(8560,plain,
% 1.73/1.99 (r(s(z), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[760, 8559])).
% 1.73/1.99 tff(8561,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[581, 8560, 37, 110])).
% 1.73/1.99 tff(8562,plain,
% 1.73/1.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[586, 8561, 563])).
% 1.73/1.99 tff(8563,plain,
% 1.73/1.99 (r(s(elem!1), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2243, 2467, 2207])).
% 1.73/1.99 tff(8564,plain,
% 1.73/1.99 (~r(elem!1, s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6817, 412, 378, 622])).
% 1.73/1.99 tff(8565,plain,
% 1.73/1.99 (elem!1 = s(z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3490, 412, 108, 909, 378, 348, 2282, 307])).
% 1.73/1.99 tff(8566,plain,
% 1.73/1.99 (s(z) = elem!1),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[242, 8565])).
% 1.73/1.99 tff(8567,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1045, 8566, 8564, 572])).
% 1.73/1.99 tff(8568,plain,((~r(s(elem!1), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8569,plain,
% 1.73/1.99 (~r(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8568, 8563, 378, 572, 108, 909, 348, 2345])).
% 1.73/1.99 tff(8570,plain,
% 1.73/1.99 (b(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[409, 8569])).
% 1.73/1.99 tff(8571,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3432, 8570, 110, 1, 108, 199, 2344, 2467])).
% 1.73/1.99 tff(8572,plain,
% 1.73/1.99 (~b(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1921, 8571, 110, 572, 589])).
% 1.73/1.99 tff(8573,plain,
% 1.73/1.99 (r(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2106, 8572])).
% 1.73/1.99 tff(8574,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(8575,plain,
% 1.73/1.99 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(8576,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8575])).
% 1.73/1.99 tff(8577,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[8576, 8574])).
% 1.73/1.99 tff(8578,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(8579,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8578, 8577])).
% 1.73/1.99 tff(8580,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8579, 121, 2088, 572, 2117, 909])).
% 1.73/1.99 tff(8581,plain,((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8582,plain,
% 1.73/1.99 (~r(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8581, 8573, 909, 572])).
% 1.73/1.99 tff(8583,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2143, 8582])).
% 1.73/1.99 tff(8584,plain,
% 1.73/1.99 (~r(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2335, 2326, 108, 909])).
% 1.73/1.99 tff(8585,plain,
% 1.73/1.99 (b(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1214, 8584])).
% 1.73/1.99 tff(8586,plain,
% 1.73/1.99 (~b(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1315, 8570, 8585, 2345])).
% 1.73/1.99 tff(8587,plain,
% 1.73/1.99 (r(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[284, 8586, 259])).
% 1.73/1.99 tff(8588,plain,
% 1.73/1.99 (~b(s(s(elem!1)), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5441, 8345, 981, 8181])).
% 1.73/1.99 tff(8589,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 1.73/1.99 inference(monotonicity,[status(thm)],[2505])).
% 1.73/1.99 tff(8590,plain,
% 1.73/1.99 (b(s(s(elem!1)), elem!1)),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[543, 8589])).
% 1.73/1.99 tff(8591,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[859, 8590])).
% 1.73/1.99 tff(8592,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(elem!1)), elem!1) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8593,plain,
% 1.73/1.99 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8592, 8588, 543])).
% 1.73/1.99 tff(8594,plain,
% 1.73/1.99 (r(s(s(elem!1)), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[862, 8588, 851])).
% 1.73/1.99 tff(8595,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6958, 8594, 1409, 1, 563, 378])).
% 1.73/1.99 tff(8596,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[486, 8595, 8593, 8346])).
% 1.73/1.99 tff(8597,plain,((s(z) = elem!1) | (~r(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8598,plain,
% 1.73/1.99 (s(z) = elem!1),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8597, 8587, 1, 378, 8571, 851, 8583, 503, 8335, 232])).
% 1.73/1.99 tff(8599,plain,
% 1.73/1.99 (~b(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8109, 8598, 2319])).
% 1.73/1.99 tff(8600,plain,
% 1.73/1.99 (~r(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6824, 8598, 8582])).
% 1.73/1.99 tff(8601,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[255, 8600, 8599, 251])).
% 1.73/1.99 tff(8602,plain,(b(s(elem!1), elem!1) | b(s(s(s(z))), s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = z) | (~r(s(z), s(s(s(z))))) | b(z, elem!1) | r(elem!1, s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8603,plain,
% 1.73/1.99 (b(s(elem!1), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8602, 2344, 1, 356, 198, 503, 232, 909, 572, 110, 589, 358, 106, 199, 2319, 344])).
% 1.73/1.99 tff(8604,plain,
% 1.73/1.99 (~r(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2335, 2326, 106, 909])).
% 1.73/1.99 tff(8605,plain,
% 1.73/1.99 (b(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1214, 8604])).
% 1.73/1.99 tff(8606,plain,
% 1.73/1.99 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8394, 2346, 2618])).
% 1.73/1.99 tff(8607,plain,
% 1.73/1.99 (~b(s(z), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3435, 8181, 307, 2618])).
% 1.73/1.99 tff(8608,plain,
% 1.73/1.99 (r(s(z), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[444, 8607, 348])).
% 1.73/1.99 tff(8609,plain,
% 1.73/1.99 (~r(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3445, 8608, 108, 145])).
% 1.73/1.99 tff(8610,plain,
% 1.73/1.99 (b(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2044, 8609, 2037])).
% 1.73/1.99 tff(8611,plain,
% 1.73/1.99 (~r(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3490, 243, 108, 909, 378, 348, 2282, 307])).
% 1.73/1.99 tff(8612,plain,
% 1.73/1.99 (b(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[409, 8611])).
% 1.73/1.99 tff(8613,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2354, 271, 8612, 1307, 8610, 1935])).
% 1.73/1.99 tff(8614,plain,((s(z) = elem!1) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8615,plain,
% 1.73/1.99 (s(z) = elem!1),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8614, 8606, 1935, 1307, 106, 8082, 344, 2345, 2618, 909, 356, 232])).
% 1.73/1.99 tff(8616,plain,
% 1.73/1.99 (elem!1 = s(z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1221, 8615])).
% 1.73/1.99 tff(8617,plain,
% 1.73/1.99 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6679, 8616, 71])).
% 1.73/1.99 tff(8618,plain,
% 1.73/1.99 (r(elem!1, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[599, 8617, 68])).
% 1.73/1.99 tff(8619,plain,
% 1.73/1.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3310, 8618, 199, 198, 331, 2344, 79])).
% 1.73/1.99 tff(8620,plain,
% 1.73/1.99 (r(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6824, 8615, 8082])).
% 1.73/1.99 tff(8621,plain,
% 1.73/1.99 (~r(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8581, 8620, 909, 572])).
% 1.73/1.99 tff(8622,plain,
% 1.73/1.99 (b(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2106, 8621])).
% 1.73/1.99 tff(8623,plain,
% 1.73/1.99 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1921, 8622, 110, 572, 589])).
% 1.73/1.99 tff(8624,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[556, 8623, 8619, 1])).
% 1.73/1.99 tff(8625,plain,(b(s(s(s(z))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(z, elem!1) | (z = elem!1) | r(elem!1, s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(z, s(z))) | b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8626,plain,
% 1.73/1.99 (b(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8625, 2344, 110, 572, 589, 199, 331, 1, 68, 909, 71, 1935, 8605, 8603, 232])).
% 1.73/1.99 tff(8627,plain,
% 1.73/1.99 (~(s(z) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8109, 8626, 2319])).
% 1.73/1.99 tff(8628,plain,
% 1.73/1.99 (b(s(z), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[236, 8627, 232])).
% 1.73/1.99 tff(8629,plain,
% 1.73/1.99 (~r(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4202, 356, 110, 909])).
% 1.73/1.99 tff(8630,plain,
% 1.73/1.99 (~(elem!1 = s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[242, 8627])).
% 1.73/1.99 tff(8631,plain,
% 1.73/1.99 (b(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[299, 8630, 8629])).
% 1.73/1.99 tff(8632,plain,
% 1.73/1.99 (~r(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3490, 8630, 106, 909, 356, 344, 351, 2345])).
% 1.73/1.99 tff(8633,plain,
% 1.73/1.99 (b(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[409, 8632])).
% 1.73/1.99 tff(8634,plain,
% 1.73/1.99 (~b(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1315, 8633, 8605, 2345])).
% 1.73/1.99 tff(8635,plain,
% 1.73/1.99 (r(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[284, 8634, 358])).
% 1.73/1.99 tff(8636,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8132, 8628, 503, 8631])).
% 1.73/1.99 tff(8637,plain,
% 1.73/1.99 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8279, 8633, 1935, 8605])).
% 1.73/1.99 tff(8638,plain,
% 1.73/1.99 (~b(s(elem!1), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3247, 271, 2345, 8603, 8628])).
% 1.73/1.99 tff(8639,plain,
% 1.73/1.99 (r(s(elem!1), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[429, 8638, 351])).
% 1.73/1.99 tff(8640,plain,
% 1.73/1.99 (~b(s(z), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3435, 8628, 2345, 8603])).
% 1.73/1.99 tff(8641,plain,
% 1.73/1.99 (r(s(z), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[444, 8640, 344])).
% 1.73/1.99 tff(8642,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8142, 121, 8641, 8639, 2326])).
% 1.73/1.99 tff(8643,plain,
% 1.73/1.99 (s(s(s(z))) = s(elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1816, 8642, 8637])).
% 1.73/1.99 tff(8644,plain,
% 1.73/1.99 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2596, 8643])).
% 1.73/1.99 tff(8645,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[486, 8644, 8636])).
% 1.73/1.99 tff(8646,plain,
% 1.73/1.99 (~r(s(s(elem!1)), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6958, 8645, 8635, 1, 563, 356])).
% 1.73/1.99 tff(8647,plain,
% 1.73/1.99 (b(s(s(elem!1)), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[862, 8646, 198])).
% 1.73/1.99 tff(8648,plain,
% 1.73/1.99 (~b(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5441, 8647, 8631, 8628])).
% 1.73/1.99 tff(8649,plain,
% 1.73/1.99 (r(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2143, 8648])).
% 1.73/1.99 tff(8650,plain,
% 1.73/1.99 (~r(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8581, 8649, 909, 572])).
% 1.73/1.99 tff(8651,plain,
% 1.73/1.99 (b(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2106, 8650])).
% 1.73/1.99 tff(8652,plain,
% 1.73/1.99 (~r(z, s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2186, 8639, 106, 909])).
% 1.73/1.99 tff(8653,plain,
% 1.73/1.99 (b(z, s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1439, 8652])).
% 1.73/1.99 tff(8654,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3351, 8645, 2345, 8633, 358, 8653])).
% 1.73/1.99 tff(8655,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[681, 8654, 79])).
% 1.73/1.99 tff(8656,plain,
% 1.73/1.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2125, 8649, 572, 8655])).
% 1.73/1.99 tff(8657,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[556, 8656, 1])).
% 1.73/1.99 tff(8658,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1921, 8657, 8651, 110, 572, 589])).
% 1.73/1.99 tff(8659,plain,(r(elem!1, s(elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | b(s(s(s(z))), s(z)) | b(z, elem!1) | (z = elem!1) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8660,plain,
% 1.73/1.99 (r(elem!1, s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8659, 8560, 110, 8562, 1, 905, 2318, 503, 232, 2319, 199, 2339, 68, 71])).
% 1.73/1.99 tff(8661,plain,
% 1.73/1.99 (~r(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4202, 2341, 110, 905])).
% 1.73/1.99 tff(8662,plain,
% 1.73/1.99 (b(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8433, 8660, 905, 211, 110, 2341, 68, 71, 37, 2337, 199, 2340, 503, 232])).
% 1.73/1.99 tff(8663,plain,
% 1.73/1.99 (~(s(z) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8109, 8662, 2319])).
% 1.73/1.99 tff(8664,plain,
% 1.73/1.99 (~(elem!1 = s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[242, 8663])).
% 1.73/1.99 tff(8665,plain,
% 1.73/1.99 (~r(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8340, 8664, 199, 8661, 2207, 905, 8660, 106, 2341, 2340])).
% 1.73/1.99 tff(8666,plain,
% 1.73/1.99 (b(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[409, 8665])).
% 1.73/1.99 tff(8667,plain,
% 1.73/1.99 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2354, 271, 8666, 2337, 2318])).
% 1.73/1.99 tff(8668,plain,
% 1.73/1.99 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8279, 8666, 2318, 2337])).
% 1.73/1.99 tff(8669,plain,
% 1.73/1.99 (b(s(z), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[236, 8663, 232])).
% 1.73/1.99 tff(8670,plain,
% 1.73/1.99 (~(elem!1 = z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[333, 2339])).
% 1.73/1.99 tff(8671,plain,
% 1.73/1.99 (~(s(elem!1) = s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[350, 2340])).
% 1.73/1.99 tff(8672,plain,
% 1.73/1.99 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2354, 271, 394, 8585, 8458])).
% 1.73/1.99 tff(8673,plain,
% 1.73/1.99 (r(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2044, 8463, 8672])).
% 1.73/1.99 tff(8674,plain,
% 1.73/1.99 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8279, 394, 8458, 8585])).
% 1.73/1.99 tff(8675,plain,
% 1.73/1.99 (~r(s(elem!1), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8470, 121, 2326, 108, 8673])).
% 1.73/1.99 tff(8676,plain,
% 1.73/1.99 (b(s(elem!1), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[429, 8675, 422])).
% 1.73/1.99 tff(8677,plain,
% 1.73/1.99 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6195, 8676, 2319])).
% 1.73/1.99 tff(8678,plain,
% 1.73/1.99 (r(s(s(s(z))), s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1816, 8677, 8674])).
% 1.73/1.99 tff(8679,plain,
% 1.73/1.99 (~r(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2054, 8678, 379, 8673])).
% 1.73/1.99 tff(8680,plain,
% 1.73/1.99 (b(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1192, 8679, 2357])).
% 1.73/1.99 tff(8681,plain,
% 1.73/1.99 (~(s(z) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8109, 257, 2319])).
% 1.73/1.99 tff(8682,plain,
% 1.73/1.99 (b(s(z), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[236, 8681, 232])).
% 1.73/1.99 tff(8683,plain,
% 1.73/1.99 (~(elem!1 = s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[242, 8681])).
% 1.73/1.99 tff(8684,plain,
% 1.73/1.99 (b(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[299, 8683, 8335])).
% 1.73/1.99 tff(8685,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8132, 8682, 503, 8684])).
% 1.73/1.99 tff(8686,plain,
% 1.73/1.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8505, 2467, 378, 379, 394, 8685, 111, 909, 110, 211, 82, 8682, 503, 422, 2326, 108, 257])).
% 1.73/1.99 tff(8687,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[556, 8686, 1])).
% 1.73/1.99 tff(8688,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[581, 572, 111, 110])).
% 1.73/1.99 tff(8689,plain,
% 1.73/1.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[586, 8688, 563])).
% 1.73/1.99 tff(8690,plain,
% 1.73/1.99 (~b(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1921, 8687, 110, 572, 8689])).
% 1.73/1.99 tff(8691,plain,
% 1.73/1.99 (r(z, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2106, 8690])).
% 1.73/1.99 tff(8692,plain,
% 1.73/1.99 (~r(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8581, 8691, 909, 572])).
% 1.73/1.99 tff(8693,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2143, 8692])).
% 1.73/1.99 tff(8694,plain,
% 1.73/1.99 (~r(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8597, 8693, 1, 378, 8681, 851, 8687, 503, 8335, 232])).
% 1.73/1.99 tff(8695,plain,
% 1.73/1.99 (b(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[284, 8694, 259])).
% 1.73/1.99 tff(8696,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5208, 271, 8695, 8680, 8585, 8458])).
% 1.73/1.99 tff(8697,plain,(b(s(elem!1), elem!1) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(z)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(z))))) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8698,plain,
% 1.73/1.99 (b(s(elem!1), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8697, 8660, 2319, 8671, 106, 8670, 1, 2341, 198, 503, 232, 905, 8560, 110, 8666, 37, 79, 8662])).
% 1.73/1.99 tff(8699,plain,
% 1.73/1.99 (~r(s(elem!1), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8528, 8698, 8660, 2338, 8669, 8668, 2319, 2340, 106])).
% 1.73/1.99 tff(8700,plain,
% 1.73/1.99 (s(elem!1) = s(s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2044, 8699, 8667])).
% 1.73/1.99 tff(8701,plain,
% 1.73/1.99 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8700])).
% 1.73/1.99 tff(8702,plain,
% 1.73/1.99 (elem!1 = s(s(z))),
% 1.73/1.99 inference(transitivity,[status(thm)],[75, 8701, 91])).
% 1.73/1.99 tff(8703,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8702])).
% 1.73/1.99 tff(8704,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(symmetry,[status(thm)],[8703])).
% 1.73/1.99 tff(8705,plain,
% 1.73/1.99 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8704])).
% 1.73/1.99 tff(8706,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1471, 8560, 37, 110])).
% 1.73/1.99 tff(8707,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8706, 8705])).
% 1.73/1.99 tff(8708,plain,
% 1.73/1.99 (b(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[299, 8664, 8661])).
% 1.73/1.99 tff(8709,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8132, 8669, 503, 8708])).
% 1.73/1.99 tff(8710,plain,
% 1.73/1.99 (s(s(s(z))) = s(elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2035, 8700])).
% 1.73/1.99 tff(8711,plain,
% 1.73/1.99 (~(s(s(s(elem!1))) = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2596, 8710])).
% 1.73/1.99 tff(8712,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[486, 8711, 8709])).
% 1.73/1.99 tff(8713,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8712, 8707])).
% 1.73/1.99 tff(8714,plain,(b(s(s(s(z))), s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | (~r(s(z), z)) | b(z, elem!1) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | b(z, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8715,plain,
% 1.73/1.99 (b(s(s(s(z))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8714, 894, 67, 232, 26, 199, 68, 71, 1, 33])).
% 1.73/1.99 tff(8716,plain,
% 1.73/1.99 (z = elem!1),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[355, 1391, 199])).
% 1.73/1.99 tff(8717,plain,
% 1.73/1.99 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.73/1.99 inference(monotonicity,[status(thm)],[8716])).
% 1.73/1.99 tff(8718,plain,
% 1.73/1.99 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.73/1.99 inference(symmetry,[status(thm)],[8717])).
% 1.73/1.99 tff(8719,plain,
% 1.73/1.99 (b(s(z), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[236, 5772, 232])).
% 1.73/1.99 tff(8720,plain,
% 1.73/1.99 (b(s(z), z)),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8719, 8718])).
% 1.73/1.99 tff(8721,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2, 8720])).
% 1.73/1.99 tff(8722,plain,(r(z, elem!1) | b(s(z), z) | r(s(z), elem!1) | b(z, s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(8723,plain,
% 1.73/1.99 (r(z, elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8722, 894, 232, 2, 199])).
% 1.73/1.99 tff(8724,plain,
% 1.73/1.99 (b(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[299, 243, 8335])).
% 1.73/1.99 tff(8725,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8132, 8724, 503, 8181])).
% 1.73/1.99 tff(8726,plain,
% 1.73/1.99 (~(z = elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[490, 8725, 2342])).
% 1.73/1.99 tff(8727,plain,
% 1.73/1.99 (~(s(z) = s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[343, 8726])).
% 1.73/1.99 tff(8728,plain,
% 1.73/1.99 (~(elem!1 = z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[333, 8726])).
% 1.73/1.99 tff(8729,plain,
% 1.73/1.99 (~b(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[305, 8728, 222, 8181, 111, 110, 243])).
% 1.73/1.99 tff(8730,plain,
% 1.73/1.99 (r(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[255, 8729, 2316])).
% 1.73/1.99 tff(8731,plain,
% 1.73/1.99 (~r(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3375, 8730, 106, 110])).
% 1.73/1.99 tff(8732,plain,
% 1.73/1.99 (b(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1214, 8731])).
% 1.73/1.99 tff(8733,plain,
% 1.73/1.99 (~r(elem!1, s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[8433, 8732, 909, 211, 110, 378, 68, 71, 111, 8729, 199, 8727, 503, 232])).
% 1.73/1.99 tff(8734,plain,
% 1.73/1.99 (b(elem!1, s(elem!1))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[392, 8733, 219])).
% 1.73/1.99 tff(8735,plain,
% 1.73/1.99 (~(s(elem!1) = s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[350, 8727])).
% 1.73/1.99 tff(8736,plain,
% 1.73/1.99 (~r(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3490, 8734, 106, 909, 378, 8727, 8735, 243])).
% 1.73/1.99 tff(8737,plain,
% 1.73/1.99 (b(s(elem!1), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[409, 8736])).
% 1.73/1.99 tff(8738,plain,
% 1.73/1.99 (~b(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1315, 8737, 8732, 8734])).
% 1.73/1.99 tff(8739,plain,
% 1.73/1.99 (r(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[284, 8738, 8728])).
% 1.73/1.99 tff(8740,plain,
% 1.73/1.99 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2063, 8727])).
% 1.73/1.99 tff(8741,plain,
% 1.73/1.99 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[8740, 6199])).
% 1.73/1.99 tff(8742,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(8743,plain,
% 1.73/1.99 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(8744,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8743])).
% 1.73/2.00 tff(8745,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[8744, 8742])).
% 1.73/2.00 tff(8746,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(8747,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8746, 8745])).
% 1.73/2.00 tff(8748,plain,
% 1.73/2.00 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8747, 271, 8181, 222, 503])).
% 1.73/2.00 tff(8749,plain,
% 1.73/2.00 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6237, 21, 8748])).
% 1.73/2.00 tff(8750,plain,
% 1.73/2.00 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8749, 8741])).
% 1.73/2.00 tff(8751,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8752,plain,
% 1.73/2.00 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8753,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8752])).
% 1.73/2.00 tff(8754,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[8753, 8751])).
% 1.73/2.00 tff(8755,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(8756,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8755, 8754])).
% 1.73/2.00 tff(8757,plain,
% 1.73/2.00 (~r(s(z), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8756, 121, 8730, 106, 8750])).
% 1.73/2.00 tff(8758,plain,
% 1.73/2.00 (b(s(z), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[760, 8757])).
% 1.73/2.00 tff(8759,plain,
% 1.73/2.00 (~r(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3490, 2345, 108, 909, 378, 348, 2282, 243])).
% 1.73/2.00 tff(8760,plain,
% 1.73/2.00 (b(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[409, 8759])).
% 1.73/2.00 tff(8761,plain,
% 1.73/2.00 (~r(z, s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3387, 8563, 378, 1409])).
% 1.73/2.00 tff(8762,plain,
% 1.73/2.00 (b(z, s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1439, 8761])).
% 1.73/2.00 tff(8763,plain,
% 1.73/2.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3432, 2467, 110, 1, 108, 199, 2344, 8760])).
% 1.73/2.00 tff(8764,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8597, 8763, 1, 378, 231, 851, 1409, 503, 8335, 232])).
% 1.73/2.00 tff(8765,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2143, 8764])).
% 1.73/2.00 tff(8766,plain,
% 1.73/2.00 (~r(s(s(elem!1)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2422, 8765, 110, 909])).
% 1.73/2.00 tff(8767,plain,
% 1.73/2.00 (b(s(s(elem!1)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2430, 8766])).
% 1.73/2.00 tff(8768,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2853, 8767, 8762, 8760])).
% 1.73/2.00 tff(8769,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[701, 8768, 3313])).
% 1.73/2.00 tff(8770,plain,
% 1.73/2.00 (~b(s(z), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2437, 271, 8763, 750, 503])).
% 1.73/2.00 tff(8771,plain,
% 1.73/2.00 (r(s(z), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2167, 8770])).
% 1.73/2.00 tff(8772,plain,
% 1.73/2.00 (~r(z, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2445, 121, 8771, 8765, 909])).
% 1.73/2.00 tff(8773,plain,
% 1.73/2.00 (b(z, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2106, 8772])).
% 1.73/2.00 tff(8774,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8775,plain,
% 1.73/2.00 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8776,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8775])).
% 1.73/2.00 tff(8777,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[8776, 8774])).
% 1.73/2.00 tff(8778,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(8779,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8778, 8777])).
% 1.73/2.00 tff(8780,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8779, 271, 543, 517, 1894, 1421])).
% 1.73/2.00 tff(8781,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8782,plain,
% 1.73/2.00 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8781, 8773, 8763, 8762])).
% 1.73/2.00 tff(8783,plain,
% 1.73/2.00 (r(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[526, 8782, 211])).
% 1.73/2.00 tff(8784,plain,
% 1.73/2.00 (~r(s(z), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3275, 8783, 8771, 8769])).
% 1.73/2.00 tff(8785,plain,
% 1.73/2.00 (b(s(z), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[444, 8784, 348])).
% 1.73/2.00 tff(8786,plain,
% 1.73/2.00 (~b(s(elem!1), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[456, 8785, 2345, 8724])).
% 1.73/2.00 tff(8787,plain,
% 1.73/2.00 (r(s(elem!1), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[429, 8786, 2282])).
% 1.73/2.00 tff(8788,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8789,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(8790,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8789, 8788])).
% 1.73/2.00 tff(8791,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8790, 121, 8771, 8783, 8765, 8787])).
% 1.73/2.00 tff(8792,plain,(b(s(elem!1), elem!1) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(z) = elem!1) | (s(s(elem!1)) = elem!1) | (~r(elem!1, z)) | r(s(z), elem!1) | (~r(s(z), s(s(s(z))))) | b(z, elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8793,plain,
% 1.73/2.00 (b(s(elem!1), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8792, 8727, 909, 8758, 503, 110, 1, 378, 231, 198, 8739, 232, 106, 199, 8733])).
% 1.73/2.00 tff(8794,plain,
% 1.73/2.00 (~(s(elem!1) = s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8394, 8793, 8729])).
% 1.73/2.00 tff(8795,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8614, 8794, 8793, 2343, 8730, 106, 231, 8727, 8732, 8734, 909, 378, 232])).
% 1.73/2.00 tff(8796,plain,((s(z) = elem!1) | (~r(z, s(z))) | (~r(z, elem!1)) | r(s(z), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8797,plain,
% 1.73/2.00 (s(z) = elem!1),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8796, 905, 8723, 232, 67, 26, 1, 199, 8715, 68, 71, 37])).
% 1.73/2.00 tff(8798,plain,
% 1.73/2.00 (s(s(z)) = s(elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8797])).
% 1.73/2.00 tff(8799,plain,
% 1.73/2.00 (s(s(s(z))) = s(s(elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8798])).
% 1.73/2.00 tff(8800,plain,
% 1.73/2.00 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8799])).
% 1.73/2.00 tff(8801,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8799, 8800])).
% 1.73/2.00 tff(8802,plain,
% 1.73/2.00 (elem!1 = s(z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1221, 8797])).
% 1.73/2.00 tff(8803,plain,
% 1.73/2.00 (~r(s(s(s(s(z)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1238, 8797, 38])).
% 1.73/2.00 tff(8804,plain,
% 1.73/2.00 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8797])).
% 1.73/2.00 tff(8805,plain,
% 1.73/2.00 (b(s(s(s(z))), elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8715, 8804])).
% 1.73/2.00 tff(8806,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1924, 8805, 1, 894, 8715, 199, 33, 67, 2, 68, 2338, 8803, 106])).
% 1.73/2.00 tff(8807,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[1226])).
% 1.73/2.00 tff(8808,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/2.00 inference(symmetry,[status(thm)],[8807])).
% 1.73/2.00 tff(8809,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5499, 8808])).
% 1.73/2.00 tff(8810,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.73/2.00 tff(8811,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8810, 8809])).
% 1.73/2.00 tff(8812,plain,(r(s(s(s(z))), s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8813,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8812, 8806, 8802])).
% 1.73/2.00 tff(8814,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8813, 8801])).
% 1.73/2.00 tff(8815,plain,
% 1.73/2.00 ((s(z) = z) <=> (elem!1 = z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8797])).
% 1.73/2.00 tff(8816,plain,
% 1.73/2.00 ((s(z) = z) <=> (z = elem!1)),
% 1.73/2.00 inference(transitivity,[status(thm)],[8815, 360])).
% 1.73/2.00 tff(8817,plain,
% 1.73/2.00 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8816])).
% 1.73/2.00 tff(8818,plain,
% 1.73/2.00 (~(z = elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11, 8817])).
% 1.73/2.00 tff(8819,plain,
% 1.73/2.00 (~b(elem!1, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6679, 8802, 71])).
% 1.73/2.00 tff(8820,plain,
% 1.73/2.00 (r(elem!1, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[599, 8819, 68])).
% 1.73/2.00 tff(8821,plain,
% 1.73/2.00 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8799])).
% 1.73/2.00 tff(8822,plain,
% 1.73/2.00 (b(s(s(elem!1)), elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8805, 8821])).
% 1.73/2.00 tff(8823,plain,
% 1.73/2.00 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8797])).
% 1.73/2.00 tff(8824,plain,
% 1.73/2.00 (b(s(s(s(elem!1))), elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[67, 8823])).
% 1.73/2.00 tff(8825,plain,
% 1.73/2.00 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3310, 2344, 199, 851, 624, 331, 82])).
% 1.73/2.00 tff(8826,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[551, 2345, 504, 542])).
% 1.73/2.00 tff(8827,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[556, 8826, 8825, 1])).
% 1.73/2.00 tff(8828,plain,(r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | b(z, elem!1) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (z = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8829,plain,
% 1.73/2.00 (r(elem!1, s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8828, 8824, 1, 8822, 199, 198, 8820, 8818, 79])).
% 1.73/2.00 tff(8830,plain,
% 1.73/2.00 (r(s(z), z) <=> r(elem!1, z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8797])).
% 1.73/2.00 tff(8831,plain,
% 1.73/2.00 (r(elem!1, z)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[26, 8830])).
% 1.73/2.00 tff(8832,plain,
% 1.73/2.00 (~r(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1417, 8829, 905, 8831])).
% 1.73/2.00 tff(8833,plain,
% 1.73/2.00 (b(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[409, 8832])).
% 1.73/2.00 tff(8834,plain,
% 1.73/2.00 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[1037])).
% 1.73/2.00 tff(8835,plain,
% 1.73/2.00 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.73/2.00 inference(symmetry,[status(thm)],[8834])).
% 1.73/2.00 tff(8836,plain,
% 1.73/2.00 (~r(z, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2502, 623, 378, 624])).
% 1.73/2.00 tff(8837,plain,
% 1.73/2.00 (b(z, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2106, 8836])).
% 1.73/2.00 tff(8838,plain,
% 1.73/2.00 (b(z, s(s(s(z))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8837, 8835])).
% 1.73/2.00 tff(8839,plain,
% 1.73/2.00 (~r(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2199, 623, 624, 379])).
% 1.73/2.00 tff(8840,plain,
% 1.73/2.00 (b(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[526, 8839, 216])).
% 1.73/2.00 tff(8841,plain,
% 1.73/2.00 (b(s(elem!1), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2369, 8840, 1222])).
% 1.73/2.00 tff(8842,plain,
% 1.73/2.00 (~b(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2029, 8841, 222, 394])).
% 1.73/2.00 tff(8843,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8842, 8838])).
% 1.73/2.00 tff(8844,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8845,plain,
% 1.73/2.00 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8844, 8797, 8715, 8833, 211, 8820, 8829, 8723])).
% 1.73/2.00 tff(8846,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8845, 8814])).
% 1.73/2.00 tff(8847,plain,(b(z, s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | b(z, s(s(s(elem!1)))) | b(s(z), z) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | r(s(s(s(elem!1))), s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8848,plain,
% 1.73/2.00 (b(z, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8847, 199, 1, 33, 2, 68, 71, 38, 232])).
% 1.73/2.00 tff(8849,plain,
% 1.73/2.00 (~(s(z) = elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[229, 8848, 199])).
% 1.73/2.00 tff(8850,plain,
% 1.73/2.00 (b(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[236, 8849, 232])).
% 1.73/2.00 tff(8851,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8132, 325, 1529, 503, 260])).
% 1.73/2.00 tff(8852,plain,((~(z = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8853,plain,
% 1.73/2.00 (~(z = elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8852, 8850, 67, 8848, 2264])).
% 1.73/2.00 tff(8854,plain,
% 1.73/2.00 (~(s(z) = s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[343, 8853])).
% 1.73/2.00 tff(8855,plain,
% 1.73/2.00 (~(s(elem!1) = s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[350, 8854])).
% 1.73/2.00 tff(8856,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8857,plain,
% 1.73/2.00 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8858,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[8857])).
% 1.73/2.00 tff(8859,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[8858, 8856])).
% 1.73/2.00 tff(8860,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(8861,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[8860, 8859])).
% 1.73/2.00 tff(8862,plain,
% 1.73/2.00 (~b(s(s(s(elem!1))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8861, 271, 8850, 8848, 67])).
% 1.73/2.00 tff(8863,plain,
% 1.73/2.00 (r(s(s(s(elem!1))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8229, 8862])).
% 1.73/2.00 tff(8864,plain,
% 1.73/2.00 (r(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[355, 8853, 199])).
% 1.73/2.00 tff(8865,plain,
% 1.73/2.00 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6858, 121, 378, 412, 6842])).
% 1.73/2.00 tff(8866,plain,
% 1.73/2.00 (b(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2293, 21, 8865, 6201])).
% 1.73/2.00 tff(8867,plain,
% 1.73/2.00 (~r(s(elem!1), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[420, 412, 110, 378])).
% 1.73/2.00 tff(8868,plain,
% 1.73/2.00 (b(s(elem!1), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[429, 8867, 422])).
% 1.73/2.00 tff(8869,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6273, 271, 260, 8868, 8866, 503])).
% 1.73/2.00 tff(8870,plain,((~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8871,plain,
% 1.73/2.00 (~r(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8870, 8850, 67, 85, 8864, 8863, 8855, 26])).
% 1.73/2.00 tff(8872,plain,
% 1.73/2.00 (b(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[409, 8871])).
% 1.73/2.00 tff(8873,plain,
% 1.73/2.00 (~(elem!1 = z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[333, 8853])).
% 1.73/2.00 tff(8874,plain,
% 1.73/2.00 (~(elem!1 = s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[242, 8849])).
% 1.73/2.00 tff(8875,plain,
% 1.73/2.00 (~r(s(z), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[436, 412, 110, 378])).
% 1.73/2.00 tff(8876,plain,
% 1.73/2.00 (b(s(z), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[444, 8875, 348])).
% 1.73/2.00 tff(8877,plain,
% 1.73/2.00 (~b(s(elem!1), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3435, 8876, 260, 307])).
% 1.73/2.00 tff(8878,plain,
% 1.73/2.00 (r(s(elem!1), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2243, 8877, 2564])).
% 1.73/2.00 tff(8879,plain,
% 1.73/2.00 (b(s(elem!1), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[429, 8867, 2282])).
% 1.73/2.00 tff(8880,plain,
% 1.73/2.00 (~b(elem!1, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[456, 8876, 8879, 307])).
% 1.73/2.00 tff(8881,plain,
% 1.73/2.00 (r(elem!1, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[299, 8880, 258])).
% 1.73/2.00 tff(8882,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5343, 8881, 8878, 378, 412])).
% 1.73/2.00 tff(8883,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (s(elem!1) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(8884,plain,
% 1.73/2.00 (~r(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8883, 307, 258, 2564, 378, 260, 348, 110])).
% 1.73/2.00 tff(8885,plain,
% 1.73/2.00 (b(s(elem!1), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[409, 8884])).
% 1.73/2.00 tff(8886,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8887,plain,
% 1.73/2.00 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(8888,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8887])).
% 1.73/2.01 tff(8889,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8888, 8886])).
% 1.73/2.01 tff(8890,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8891,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8890, 8889])).
% 1.73/2.01 tff(8892,plain,
% 1.73/2.01 (~b(s(elem!1), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8891, 271, 8885, 220, 1935])).
% 1.73/2.01 tff(8893,plain,
% 1.73/2.01 (~b(elem!1, z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[402, 8885, 220, 307])).
% 1.73/2.01 tff(8894,plain,
% 1.73/2.01 (r(elem!1, z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[284, 8893, 259])).
% 1.73/2.01 tff(8895,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8896,plain,
% 1.73/2.01 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8897,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8896])).
% 1.73/2.01 tff(8898,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8897, 8895])).
% 1.73/2.01 tff(8899,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8900,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8899, 8898])).
% 1.73/2.01 tff(8901,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8900, 121, 378, 110, 1409, 3456])).
% 1.73/2.01 tff(8902,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(8903,plain,
% 1.73/2.01 (~r(elem!1, s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8902, 8894, 110, 378])).
% 1.73/2.01 tff(8904,plain,
% 1.73/2.01 (b(elem!1, s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[299, 8903, 258])).
% 1.73/2.01 tff(8905,plain,
% 1.73/2.01 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8132, 8904, 503, 260])).
% 1.73/2.01 tff(8906,plain,
% 1.73/2.01 (~b(s(s(s(elem!1))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8861, 271, 260, 220, 503])).
% 1.73/2.01 tff(8907,plain,
% 1.73/2.01 (r(s(s(s(elem!1))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8229, 8906])).
% 1.73/2.01 tff(8908,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8909,plain,
% 1.73/2.01 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8910,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8909])).
% 1.73/2.01 tff(8911,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8910, 8908])).
% 1.73/2.01 tff(8912,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8913,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8912, 8911])).
% 1.73/2.01 tff(8914,plain,
% 1.73/2.01 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8913, 121, 378, 8894, 8907])).
% 1.73/2.01 tff(8915,plain,
% 1.73/2.01 (s(s(s(elem!1))) = elem!1),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[486, 8914, 8905])).
% 1.73/2.01 tff(8916,plain,
% 1.73/2.01 (~(s(s(s(z))) = s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2596, 8915])).
% 1.73/2.01 tff(8917,plain,
% 1.73/2.01 (~(s(elem!1) = s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2035, 8916])).
% 1.73/2.01 tff(8918,plain,
% 1.73/2.01 (r(s(elem!1), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2044, 8917, 8892])).
% 1.73/2.01 tff(8919,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8920,plain,
% 1.73/2.01 (((~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(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8921,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8920])).
% 1.73/2.01 tff(8922,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8921, 8919])).
% 1.73/2.01 tff(8923,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8924,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8923, 8922])).
% 1.73/2.01 tff(8925,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8924, 271, 394, 260, 220, 447])).
% 1.73/2.01 tff(8926,plain,((~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(8927,plain,
% 1.73/2.01 (~b(s(elem!1), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8926, 8885, 220, 260])).
% 1.73/2.01 tff(8928,plain,
% 1.73/2.01 (r(s(elem!1), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[429, 8927, 2282])).
% 1.73/2.01 tff(8929,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8930,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8931,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8930, 8929])).
% 1.73/2.01 tff(8932,plain,
% 1.73/2.01 (~b(s(s(s(z))), s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8931, 271, 8885, 220, 1935])).
% 1.73/2.01 tff(8933,plain,
% 1.73/2.01 (r(s(s(s(z))), s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1816, 8916, 8932])).
% 1.73/2.01 tff(8934,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8935,plain,
% 1.73/2.01 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8936,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8935])).
% 1.73/2.01 tff(8937,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8936, 8934])).
% 1.73/2.01 tff(8938,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8939,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8938, 8937])).
% 1.73/2.01 tff(8940,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8939, 121, 8933, 8928, 108, 8918])).
% 1.73/2.01 tff(8941,plain,((~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(s(z), z)) | (elem!1 = z) | (s(elem!1) = elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(8942,plain,
% 1.73/2.01 (~b(elem!1, s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8941, 8864, 106, 8848, 2265, 67, 8850, 8874, 26, 8873, 2207, 8854])).
% 1.73/2.01 tff(8943,plain,
% 1.73/2.01 (r(elem!1, s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[392, 8942, 219])).
% 1.73/2.01 tff(8944,plain,
% 1.73/2.01 (~b(s(elem!1), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8926, 8872, 8848, 8850])).
% 1.73/2.01 tff(8945,plain,
% 1.73/2.01 (r(s(elem!1), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[429, 8944, 8855])).
% 1.73/2.01 tff(8946,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8947,plain,
% 1.73/2.01 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8948,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8947])).
% 1.73/2.01 tff(8949,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8948, 8946])).
% 1.73/2.01 tff(8950,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8951,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8950, 8949])).
% 1.73/2.01 tff(8952,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8951, 121, 379, 110, 3456, 411])).
% 1.73/2.01 tff(8953,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(8954,plain,
% 1.73/2.01 (~r(elem!1, s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8953, 8945, 26, 8943])).
% 1.73/2.01 tff(8955,plain,
% 1.73/2.01 (b(elem!1, s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[299, 8954, 8874])).
% 1.73/2.01 tff(8956,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8957,plain,
% 1.73/2.01 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8958,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8957])).
% 1.73/2.01 tff(8959,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8958, 8956])).
% 1.73/2.01 tff(8960,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8961,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8960, 8959])).
% 1.73/2.01 tff(8962,plain,
% 1.73/2.01 ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8961, 271])).
% 1.73/2.01 tff(8963,plain,
% 1.73/2.01 (~b(elem!1, z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8962, 8955, 8848, 8850])).
% 1.73/2.01 tff(8964,plain,
% 1.73/2.01 (r(elem!1, z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[284, 8963, 8873])).
% 1.73/2.01 tff(8965,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8966,plain,
% 1.73/2.01 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(8967,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[8966])).
% 1.73/2.01 tff(8968,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[8967, 8965])).
% 1.73/2.01 tff(8969,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(8970,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[8969, 8968])).
% 1.73/2.01 tff(8971,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8970, 121, 379, 378, 139, 6842])).
% 1.73/2.01 tff(8972,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(8973,plain,
% 1.73/2.01 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8972, 8943, 8863, 8864])).
% 1.73/2.01 tff(8974,plain,
% 1.73/2.01 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[8132, 8955, 67, 8850])).
% 1.73/2.01 tff(8975,plain,
% 1.73/2.01 (s(s(s(elem!1))) = elem!1),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[486, 8974, 8973])).
% 1.73/2.01 tff(8976,plain,
% 1.73/2.01 (~(s(s(s(z))) = s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2596, 8975])).
% 1.73/2.01 tff(8977,plain,
% 1.73/2.01 (~(s(elem!1) = s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2035, 8976])).
% 1.73/2.01 tff(8978,plain,
% 1.73/2.01 (~b(s(elem!1), s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8891, 271, 8872, 8848, 2265])).
% 1.73/2.02 tff(8979,plain,
% 1.73/2.02 (r(s(elem!1), s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2044, 8978, 8977])).
% 1.73/2.02 tff(8980,plain,
% 1.73/2.02 (~b(s(s(s(z))), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8931, 271, 8872, 8848, 2265])).
% 1.73/2.02 tff(8981,plain,
% 1.73/2.02 (r(s(s(s(z))), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1816, 8980, 8976])).
% 1.73/2.02 tff(8982,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(8983,plain,
% 1.73/2.02 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(8984,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[8983])).
% 1.73/2.02 tff(8985,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[8984, 8982])).
% 1.73/2.02 tff(8986,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(8987,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[8986, 8985])).
% 1.73/2.02 tff(8988,plain,
% 1.73/2.02 (~r(s(s(s(z))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8987, 121, 8943, 8981, 8945])).
% 1.73/2.02 tff(8989,plain,
% 1.73/2.02 (~b(s(s(s(z))), s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[892, 8988, 1, 37, 26, 106, 67, 68, 199, 8848])).
% 1.73/2.02 tff(8990,plain,
% 1.73/2.02 (~b(s(elem!1), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8528, 8989, 8850, 2338, 8943, 8980, 8979, 8854, 106])).
% 1.73/2.02 tff(8991,plain,
% 1.73/2.02 (r(s(elem!1), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2243, 8990, 2207])).
% 1.73/2.02 tff(8992,plain,
% 1.73/2.02 (~r(z, s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[3387, 8991, 8864, 8964])).
% 1.73/2.02 tff(8993,plain,
% 1.73/2.02 (b(z, s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1439, 8992])).
% 1.73/2.02 tff(8994,plain,
% 1.73/2.02 (~r(s(z), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[6221, 121, 37, 26, 8863])).
% 1.73/2.02 tff(8995,plain,
% 1.73/2.02 (b(s(z), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[760, 8994])).
% 1.73/2.02 tff(8996,plain,
% 1.73/2.02 (b(s(z), elem!1)),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[750, 2557])).
% 1.73/2.02 tff(8997,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(8998,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(8999,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[8998, 8997])).
% 1.73/2.02 tff(9000,plain,
% 1.73/2.02 (~r(s(s(s(z))), s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8999, 121, 622, 431, 1500])).
% 1.73/2.02 tff(9001,plain,
% 1.73/2.02 (b(s(s(s(z))), s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2323, 21, 97, 9000])).
% 1.73/2.02 tff(9002,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9003,plain,
% 1.73/2.02 (((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9004,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[9003])).
% 1.73/2.02 tff(9005,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[9004, 9002])).
% 1.73/2.02 tff(9006,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(9007,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[9006, 9005])).
% 1.73/2.02 tff(9008,plain,
% 1.73/2.02 (~r(elem!1, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9007, 121, 379, 622, 431])).
% 1.73/2.02 tff(9009,plain,
% 1.73/2.02 (b(elem!1, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[297, 21, 9008, 258])).
% 1.73/2.02 tff(9010,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9011,plain,
% 1.73/2.02 (((~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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9012,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[9011])).
% 1.73/2.02 tff(9013,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.02 inference(transitivity,[status(thm)],[9012, 9010])).
% 1.73/2.02 tff(9014,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(9015,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[9014, 9013])).
% 1.73/2.02 tff(9016,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9015, 271, 260, 9009, 9001, 257])).
% 1.73/2.02 tff(9017,plain,((~r(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(9018,plain,
% 1.73/2.02 (~b(s(s(s(z))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9017, 8996, 431, 258, 622, 3750, 379])).
% 1.73/2.02 tff(9019,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[255, 9018, 3839, 2612])).
% 1.73/2.02 tff(9020,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), s(elem!1))) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(9021,plain,
% 1.73/2.02 (~r(s(z), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9020, 8991, 8943, 8874, 8975, 8980, 8995])).
% 1.73/2.02 tff(9022,plain,
% 1.73/2.02 (b(s(z), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[444, 9021, 8854])).
% 1.73/2.02 tff(9023,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9024,plain,
% 1.73/2.02 (((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9025,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[9024])).
% 1.73/2.02 tff(9026,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[9025, 9023])).
% 1.73/2.02 tff(9027,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(9028,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[9027, 9026])).
% 1.73/2.02 tff(9029,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9028, 271, 394, 220, 446, 1421])).
% 1.73/2.02 tff(9030,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(9031,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9030, 9022, 8993, 8848, 8872])).
% 1.73/2.02 tff(9032,plain,(b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | r(s(z), elem!1) | b(z, s(s(s(elem!1)))) | b(s(z), z) | b(s(z), s(s(s(z)))) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(9033,plain,
% 1.73/2.02 (b(z, elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9032, 232, 68, 1, 33, 2, 71, 38])).
% 1.73/2.02 tff(9034,plain,
% 1.73/2.02 (b(s(z), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1276, 223, 307])).
% 1.73/2.02 tff(9035,plain,
% 1.73/2.02 (b(z, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1402, 223, 1391])).
% 1.73/2.02 tff(9036,plain,
% 1.73/2.02 (~b(s(s(s(elem!1))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7702, 271, 307, 1326, 1385])).
% 1.73/2.02 tff(9037,plain,
% 1.73/2.02 (r(s(s(s(elem!1))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8229, 9036])).
% 1.73/2.02 tff(9038,plain,
% 1.73/2.02 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 1.73/2.02 inference(monotonicity,[status(thm)],[1038])).
% 1.73/2.02 tff(9039,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.73/2.02 inference(symmetry,[status(thm)],[9038])).
% 1.73/2.02 tff(9040,plain,
% 1.73/2.02 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(z)))), z))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[9039])).
% 1.73/2.02 tff(9041,plain,
% 1.73/2.02 (~b(s(s(s(s(z)))), z)),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[9036, 9040])).
% 1.73/2.02 tff(9042,plain,
% 1.73/2.02 (r(s(s(s(s(z)))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1095, 9041])).
% 1.73/2.02 tff(9043,plain,
% 1.73/2.02 (~r(s(z), s(s(s(s(z)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1034, 9042, 110, 111])).
% 1.73/2.02 tff(9044,plain,
% 1.73/2.02 (~r(s(z), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1053, 9043, 223])).
% 1.73/2.02 tff(9045,plain,
% 1.73/2.02 (b(s(z), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[760, 9044])).
% 1.73/2.02 tff(9046,plain,
% 1.73/2.02 (b(elem!1, s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8233, 9045, 223])).
% 1.73/2.02 tff(9047,plain,
% 1.73/2.02 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[747, 9046, 307, 1385])).
% 1.73/2.02 tff(9048,plain,
% 1.73/2.02 (r(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2293, 21, 9047, 6201])).
% 1.73/2.02 tff(9049,plain,
% 1.73/2.02 (~r(s(elem!1), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[8269, 121, 111, 9048, 9037])).
% 1.73/2.02 tff(9050,plain,
% 1.73/2.02 (b(s(elem!1), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[409, 9049])).
% 1.73/2.02 tff(9051,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9052,plain,
% 1.73/2.02 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9053,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[9052])).
% 1.73/2.02 tff(9054,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.02 inference(transitivity,[status(thm)],[9053, 9051])).
% 1.73/2.02 tff(9055,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(9056,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[9055, 9054])).
% 1.73/2.02 tff(9057,plain,
% 1.73/2.02 (~r(z, s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9056, 121, 111, 9048, 9037])).
% 1.73/2.02 tff(9058,plain,
% 1.73/2.02 (b(z, s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1439, 9057])).
% 1.73/2.02 tff(9059,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9030, 9058, 9050, 9035, 9034])).
% 1.73/2.02 tff(9060,plain,((~(s(z) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(9061,plain,
% 1.73/2.02 (~(s(z) = elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9060, 307, 6201, 37, 110, 1326, 503, 1391])).
% 1.73/2.02 tff(9062,plain,
% 1.73/2.02 (~(elem!1 = s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[242, 9061])).
% 1.73/2.02 tff(9063,plain,
% 1.73/2.02 (~r(s(s(s(z))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[129, 108, 110, 37])).
% 1.73/2.02 tff(9064,plain,
% 1.73/2.02 (b(s(s(s(z))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1155, 9063])).
% 1.73/2.02 tff(9065,plain,
% 1.73/2.02 (~b(s(s(s(z))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1940, 307, 9064, 1326])).
% 1.73/2.02 tff(9066,plain,
% 1.73/2.02 (r(s(s(s(z))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[255, 9065, 251])).
% 1.73/2.02 tff(9067,plain,
% 1.73/2.02 (~r(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[3375, 9066, 108, 110])).
% 1.73/2.02 tff(9068,plain,
% 1.73/2.02 (~(z = elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1202, 9067, 2357, 33])).
% 1.73/2.02 tff(9069,plain,
% 1.73/2.02 (~(s(z) = s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[343, 9068])).
% 1.73/2.02 tff(9070,plain,
% 1.73/2.02 (~(s(elem!1) = s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[350, 9069])).
% 1.73/2.02 tff(9071,plain,
% 1.73/2.02 (b(s(z), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[236, 9061, 232])).
% 1.73/2.02 tff(9072,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9073,plain,
% 1.73/2.02 (((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(9074,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[9073])).
% 1.73/2.02 tff(9075,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[9074, 9072])).
% 1.73/2.02 tff(9076,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(9077,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[9076, 9075])).
% 1.73/2.02 tff(9078,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9077, 271, 307, 1326, 260, 220])).
% 1.73/2.02 tff(9079,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(9080,plain,
% 1.73/2.02 (~b(z, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[9079, 9071, 1326, 307])).
% 1.73/2.02 tff(9081,plain,
% 1.73/2.02 (r(z, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[904, 9080])).
% 1.73/2.02 tff(9082,plain,
% 1.73/2.02 (~r(s(elem!1), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5323, 9081, 1326, 307, 9071, 9069])).
% 1.73/2.02 tff(9083,plain,
% 1.73/2.02 (b(s(elem!1), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[409, 9082])).
% 1.73/2.02 tff(9084,plain,
% 1.73/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9085,plain,
% 1.85/2.03 (((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9086,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9085])).
% 1.85/2.03 tff(9087,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[9086, 9084])).
% 1.85/2.03 tff(9088,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(9089,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9088, 9087])).
% 1.85/2.03 tff(9090,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9089, 271, 307, 1326, 394, 1421])).
% 1.85/2.03 tff(9091,plain,((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9092,plain,
% 1.85/2.03 (~b(z, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9091, 307, 1326, 9083])).
% 1.85/2.03 tff(9093,plain,
% 1.85/2.03 (r(z, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1439, 9092])).
% 1.85/2.03 tff(9094,plain,
% 1.85/2.03 (~r(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2186, 9093, 108, 9081])).
% 1.85/2.03 tff(9095,plain,
% 1.85/2.03 (b(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[429, 9094, 9070])).
% 1.85/2.03 tff(9096,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9097,plain,
% 1.85/2.03 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9098,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9097])).
% 1.85/2.03 tff(9099,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.03 inference(transitivity,[status(thm)],[9098, 9096])).
% 1.85/2.03 tff(9100,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(9101,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9100, 9099])).
% 1.85/2.03 tff(9102,plain,
% 1.85/2.03 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9101, 271, 1326, 9083, 9064])).
% 1.85/2.03 tff(9103,plain,
% 1.85/2.03 (~b(s(elem!1), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4613, 9071, 1326, 307, 9069])).
% 1.85/2.03 tff(9104,plain,
% 1.85/2.03 (r(s(elem!1), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2243, 9103, 2564])).
% 1.85/2.03 tff(9105,plain,
% 1.85/2.03 (~(s(s(s(z))) = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3377, 9093, 110, 108, 9104])).
% 1.85/2.03 tff(9106,plain,
% 1.85/2.03 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2035, 9105])).
% 1.85/2.03 tff(9107,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2044, 9106, 9102])).
% 1.85/2.03 tff(9108,plain,
% 1.85/2.03 (~r(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3445, 9107, 108, 9066])).
% 1.85/2.03 tff(9109,plain,
% 1.85/2.03 (b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[444, 9108, 9069])).
% 1.85/2.03 tff(9110,plain,
% 1.85/2.03 (~b(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[456, 9109, 307, 9095])).
% 1.85/2.03 tff(9111,plain,
% 1.85/2.03 (r(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[299, 9110, 9062])).
% 1.85/2.03 tff(9112,plain,
% 1.85/2.03 (~(elem!1 = z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[333, 9068])).
% 1.85/2.03 tff(9113,plain,
% 1.85/2.03 (b(z, s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1214, 9067])).
% 1.85/2.03 tff(9114,plain,
% 1.85/2.03 (~b(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1315, 9083, 9113, 307])).
% 1.85/2.03 tff(9115,plain,
% 1.85/2.03 (r(elem!1, z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[284, 9114, 9112])).
% 1.85/2.03 tff(9116,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9117,plain,
% 1.85/2.03 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9118,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9117])).
% 1.85/2.03 tff(9119,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[9118, 9116])).
% 1.85/2.03 tff(9120,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(9121,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9120, 9119])).
% 1.85/2.03 tff(9122,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9121, 121, 110, 9081, 9115, 9111])).
% 1.85/2.03 tff(9123,plain,((~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | r(s(z), elem!1) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | r(z, elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9124,plain,
% 1.85/2.03 (~b(elem!1, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9123, 1391, 106, 1326, 2207, 232, 85, 503, 26, 33])).
% 1.85/2.03 tff(9125,plain,
% 1.85/2.03 (~r(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2278, 121, 111, 110, 3501])).
% 1.85/2.03 tff(9126,plain,
% 1.85/2.03 (~r(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2271, 121, 111, 110, 3501])).
% 1.85/2.03 tff(9127,plain,
% 1.85/2.03 (s(z) = s(elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2310, 3501, 111, 82, 503, 9126, 9125])).
% 1.85/2.03 tff(9128,plain,
% 1.85/2.03 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9127])).
% 1.85/2.03 tff(9129,plain,
% 1.85/2.03 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.85/2.03 inference(symmetry,[status(thm)],[9128])).
% 1.85/2.03 tff(9130,plain,
% 1.85/2.03 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), elem!1))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9129])).
% 1.85/2.03 tff(9131,plain,
% 1.85/2.03 (z = elem!1),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[343, 9127])).
% 1.85/2.03 tff(9132,plain,
% 1.85/2.03 (~b(s(elem!1), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7069, 9131, 3498])).
% 1.85/2.03 tff(9133,plain,
% 1.85/2.03 (~b(s(z), elem!1)),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9132, 9130])).
% 1.85/2.03 tff(9134,plain,
% 1.85/2.03 (~b(z, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[327, 9131, 317])).
% 1.85/2.03 tff(9135,plain,
% 1.85/2.03 (~(s(z) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1402, 9134, 1391])).
% 1.85/2.03 tff(9136,plain,
% 1.85/2.03 (b(s(z), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[236, 9135, 232])).
% 1.85/2.03 tff(9137,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9136, 9133])).
% 1.85/2.03 tff(9138,plain,(b(s(elem!1), z) | r(s(z), elem!1) | r(z, elem!1) | b(elem!1, s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9139,plain,
% 1.85/2.03 (b(s(elem!1), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9138, 1391, 232, 9124, 37, 79, 503, 26])).
% 1.85/2.03 tff(9140,plain,
% 1.85/2.03 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.85/2.03 inference(monotonicity,[status(thm)],[338])).
% 1.85/2.03 tff(9141,plain,
% 1.85/2.03 (b(s(elem!1), z) <=> b(s(z), z)),
% 1.85/2.03 inference(symmetry,[status(thm)],[9140])).
% 1.85/2.03 tff(9142,plain,
% 1.85/2.03 (b(s(z), z)),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[394, 9141])).
% 1.85/2.03 tff(9143,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2, 9142])).
% 1.85/2.03 tff(9144,plain,((~(s(z) = s(elem!1))) | b(s(z), z) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9145,plain,
% 1.85/2.03 (~(s(z) = s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9144, 9139, 2])).
% 1.85/2.03 tff(9146,plain,
% 1.85/2.03 (r(elem!1, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[392, 9124, 219])).
% 1.85/2.03 tff(9147,plain,
% 1.85/2.03 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1956, 394, 2343, 1326])).
% 1.85/2.03 tff(9148,plain,
% 1.85/2.03 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9101, 271, 1326, 394, 2343])).
% 1.85/2.03 tff(9149,plain,
% 1.85/2.03 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2063, 348])).
% 1.85/2.03 tff(9150,plain,
% 1.85/2.03 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1956, 394, 8458, 1326])).
% 1.85/2.03 tff(9151,plain,
% 1.85/2.03 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9101, 271, 1326, 394, 8458])).
% 1.85/2.03 tff(9152,plain,
% 1.85/2.03 (~b(z, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[8926, 447, 394, 260])).
% 1.85/2.03 tff(9153,plain,
% 1.85/2.03 (r(z, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[904, 9152])).
% 1.85/2.03 tff(9154,plain,
% 1.85/2.03 (r(s(s(s(z))), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1816, 2033, 3506])).
% 1.85/2.03 tff(9155,plain,
% 1.85/2.03 (~r(z, s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1508, 9154, 108, 909])).
% 1.85/2.03 tff(9156,plain,
% 1.85/2.03 (b(z, s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1214, 9155])).
% 1.85/2.03 tff(9157,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2044, 6284, 2039])).
% 1.85/2.03 tff(9158,plain,
% 1.85/2.03 (~r(elem!1, s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2054, 9154, 379, 9157])).
% 1.85/2.03 tff(9159,plain,
% 1.85/2.03 (b(elem!1, s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1192, 9158, 1101])).
% 1.85/2.03 tff(9160,plain,
% 1.85/2.03 (~b(s(s(s(z))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2020, 9159, 1326, 9156])).
% 1.85/2.03 tff(9161,plain,
% 1.85/2.03 (r(s(s(s(z))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[255, 9160, 907])).
% 1.85/2.03 tff(9162,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3838, 121, 379, 622, 9161, 9154])).
% 1.85/2.03 tff(9163,plain,((s(s(s(z))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | b(s(elem!1), s(s(s(z)))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9164,plain,
% 1.85/2.03 (s(s(s(z))) = s(elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9163, 9153, 622, 907, 1326, 108, 379, 9151, 9150])).
% 1.85/2.03 tff(9165,plain,
% 1.85/2.03 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9164])).
% 1.85/2.03 tff(9166,plain,
% 1.85/2.03 (s(s(z)) = elem!1),
% 1.85/2.03 inference(transitivity,[status(thm)],[92, 9165, 70])).
% 1.85/2.03 tff(9167,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9166])).
% 1.85/2.03 tff(9168,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.85/2.03 inference(symmetry,[status(thm)],[9167])).
% 1.85/2.03 tff(9169,plain,
% 1.85/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2596, 9164])).
% 1.85/2.03 tff(9170,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[486, 9169, 479])).
% 1.85/2.03 tff(9171,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), s(s(z)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9170, 9168])).
% 1.85/2.03 tff(9172,plain,
% 1.85/2.03 (~r(s(z), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1471, 9171, 111, 110])).
% 1.85/2.03 tff(9173,plain,
% 1.85/2.03 (b(s(s(s(z))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6195, 9164, 447])).
% 1.85/2.03 tff(9174,plain,
% 1.85/2.03 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9164])).
% 1.85/2.03 tff(9175,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.03 inference(symmetry,[status(thm)],[9174])).
% 1.85/2.03 tff(9176,plain,
% 1.85/2.03 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9175])).
% 1.85/2.03 tff(9177,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9178,plain,
% 1.85/2.03 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9179,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9178])).
% 1.85/2.03 tff(9180,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.85/2.03 inference(transitivity,[status(thm)],[9179, 9177])).
% 1.85/2.03 tff(9181,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(9182,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9181, 9180])).
% 1.85/2.03 tff(9183,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9182, 121, 379, 622, 139, 798])).
% 1.85/2.03 tff(9184,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9185,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9184, 9170, 379, 622])).
% 1.85/2.03 tff(9186,plain,
% 1.85/2.03 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9185, 9176])).
% 1.85/2.03 tff(9187,plain,
% 1.85/2.03 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2071, 9186, 2065])).
% 1.85/2.03 tff(9188,plain,
% 1.85/2.03 (~b(s(z), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2081, 9187, 9173, 503])).
% 1.85/2.03 tff(9189,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[760, 9188, 9172])).
% 1.85/2.03 tff(9190,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | b(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9191,plain,
% 1.85/2.03 (~b(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9190, 479, 111, 110, 2065, 379, 622, 503, 907, 1326, 108, 394, 260])).
% 1.85/2.03 tff(9192,plain,
% 1.85/2.03 (r(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[429, 9191, 422])).
% 1.85/2.03 tff(9193,plain,
% 1.85/2.03 (~r(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[8953, 9192, 110, 379])).
% 1.85/2.03 tff(9194,plain,
% 1.85/2.03 (b(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[299, 9193, 258])).
% 1.85/2.03 tff(9195,plain,
% 1.85/2.03 (~b(z, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4817, 9194, 1326, 260])).
% 1.85/2.03 tff(9196,plain,
% 1.85/2.03 (r(z, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[904, 9195])).
% 1.85/2.03 tff(9197,plain,
% 1.85/2.03 (s(s(s(z))) = s(elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9163, 9196, 622, 907, 1326, 108, 379, 9151, 9150])).
% 1.85/2.03 tff(9198,plain,
% 1.85/2.03 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9197])).
% 1.85/2.03 tff(9199,plain,
% 1.85/2.03 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.85/2.03 inference(symmetry,[status(thm)],[9198])).
% 1.85/2.03 tff(9200,plain,
% 1.85/2.03 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9197])).
% 1.85/2.03 tff(9201,plain,
% 1.85/2.03 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.85/2.03 inference(symmetry,[status(thm)],[9200])).
% 1.85/2.03 tff(9202,plain,
% 1.85/2.03 (r(s(s(s(z))), s(z))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9192, 9201])).
% 1.85/2.03 tff(9203,plain,
% 1.85/2.03 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9197])).
% 1.85/2.03 tff(9204,plain,
% 1.85/2.03 (s(s(z)) = elem!1),
% 1.85/2.03 inference(transitivity,[status(thm)],[92, 9203, 70])).
% 1.85/2.03 tff(9205,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9204])).
% 1.85/2.03 tff(9206,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.85/2.03 inference(symmetry,[status(thm)],[9205])).
% 1.85/2.03 tff(9207,plain,
% 1.85/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2596, 9197])).
% 1.85/2.03 tff(9208,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[486, 9207, 479])).
% 1.85/2.03 tff(9209,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), s(s(z)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9208, 9206])).
% 1.85/2.03 tff(9210,plain,
% 1.85/2.03 (~r(s(z), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1471, 9209, 111, 110])).
% 1.85/2.03 tff(9211,plain,
% 1.85/2.03 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[760, 9210])).
% 1.85/2.03 tff(9212,plain,
% 1.85/2.03 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2464, 9211, 8458, 944, 9196, 110, 9202, 503])).
% 1.85/2.03 tff(9213,plain,
% 1.85/2.03 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[556, 9212, 1])).
% 1.85/2.03 tff(9214,plain,
% 1.85/2.03 (~r(z, s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3425, 9213, 111, 9208])).
% 1.85/2.03 tff(9215,plain,
% 1.85/2.03 (b(z, s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2106, 9214])).
% 1.85/2.03 tff(9216,plain,
% 1.85/2.03 (~b(elem!1, s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2238, 9215, 1326, 379, 622, 68])).
% 1.85/2.03 tff(9217,plain,
% 1.85/2.03 (r(elem!1, s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[599, 9216, 68])).
% 1.85/2.03 tff(9218,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[635, 9217, 622, 9213])).
% 1.85/2.03 tff(9219,plain,
% 1.85/2.03 (b(s(elem!1), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[526, 9218, 211])).
% 1.85/2.03 tff(9220,plain,
% 1.85/2.03 (b(s(s(s(z))), s(s(elem!1)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9219, 9199])).
% 1.85/2.03 tff(9221,plain,
% 1.85/2.03 (~r(z, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2186, 9196, 108, 9192])).
% 1.85/2.03 tff(9222,plain,
% 1.85/2.03 (b(z, s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1439, 9221])).
% 1.85/2.03 tff(9223,plain,
% 1.85/2.03 (~b(s(s(elem!1)), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2152, 9219, 9222, 9215])).
% 1.85/2.03 tff(9224,plain,
% 1.85/2.03 (r(s(s(elem!1)), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2143, 9223])).
% 1.85/2.03 tff(9225,plain,
% 1.85/2.03 (~r(s(s(elem!1)), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2422, 9224, 110, 9196])).
% 1.85/2.03 tff(9226,plain,
% 1.85/2.03 (b(s(s(elem!1)), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2430, 9225])).
% 1.85/2.03 tff(9227,plain,
% 1.85/2.03 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2454, 9226, 8458, 9215])).
% 1.85/2.03 tff(9228,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9227, 9220])).
% 1.85/2.03 tff(9229,plain,(b(s(s(s(elem!1))), elem!1) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9230,plain,
% 1.85/2.03 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9229, 622, 110, 68, 1326, 379, 111, 1, 3504, 503, 106, 2316, 8181, 243, 2282, 9149, 394])).
% 1.85/2.03 tff(9231,plain,
% 1.85/2.03 (~b(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[8132, 9230, 503, 8181])).
% 1.85/2.03 tff(9232,plain,
% 1.85/2.03 (r(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[299, 243, 294])).
% 1.85/2.03 tff(9233,plain,
% 1.85/2.03 (~b(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[8926, 8181, 394, 220])).
% 1.85/2.03 tff(9234,plain,
% 1.85/2.03 (r(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[429, 9233, 2282])).
% 1.85/2.03 tff(9235,plain,
% 1.85/2.03 (~r(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[8953, 9234, 379, 9232])).
% 1.85/2.03 tff(9236,plain,
% 1.85/2.03 (b(s(z), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[25, 9235])).
% 1.85/2.03 tff(9237,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9238,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(9239,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9238, 9237])).
% 1.85/2.03 tff(9240,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9239, 271, 394, 1281, 220, 446])).
% 1.85/2.03 tff(9241,plain,((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(9242,plain,
% 1.85/2.03 (~b(s(z), s(elem!1))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9241, 9236, 220, 394])).
% 1.85/2.03 tff(9243,plain,
% 1.85/2.03 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[4396])).
% 1.85/2.03 tff(9244,plain,
% 1.85/2.03 (~(s(elem!1) = s(z))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[348, 9243])).
% 1.85/2.03 tff(9245,plain,
% 1.85/2.03 (~r(s(elem!1), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3709, 3456, 379, 431])).
% 1.85/2.03 tff(9246,plain,
% 1.85/2.03 (b(s(elem!1), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[408, 21, 405, 9245])).
% 1.85/2.03 tff(9247,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9248,plain,
% 1.85/2.03 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(9249,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[9248])).
% 1.85/2.03 tff(9250,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 1.85/2.03 inference(transitivity,[status(thm)],[9249, 9247])).
% 1.85/2.03 tff(9251,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(9252,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), z))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[9251, 9250])).
% 1.85/2.03 tff(9253,plain,
% 1.85/2.03 (~b(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9252, 271, 1326, 9246, 1281])).
% 1.85/2.03 tff(9254,plain,
% 1.85/2.03 ((s(elem!1) = s(z)) | r(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[427, 21, 9253])).
% 1.85/2.03 tff(9255,plain,
% 1.85/2.03 (r(s(elem!1), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[9254, 9244])).
% 1.85/2.03 tff(9256,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9257,plain,
% 1.85/2.04 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9258,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9257])).
% 1.85/2.04 tff(9259,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[9258, 9256])).
% 1.85/2.04 tff(9260,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(9261,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9260, 9259])).
% 1.85/2.04 tff(9262,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9261, 121, 379, 3456, 431, 9255])).
% 1.85/2.04 tff(9263,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9264,plain,
% 1.85/2.04 (~r(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9263, 9232, 431, 1326, 348, 1281])).
% 1.85/2.04 tff(9265,plain,
% 1.85/2.04 (b(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[392, 9264, 377])).
% 1.85/2.04 tff(9266,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4084, 271, 9265, 1326, 8181, 1281])).
% 1.85/2.04 tff(9267,plain,((s(z) = elem!1) | (~b(z, elem!1)) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (~r(s(z), s(elem!1))) | (s(z) = s(elem!1)) | b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9268,plain,
% 1.85/2.04 (~r(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9267, 9236, 1326, 377, 231, 348, 294, 232])).
% 1.85/2.04 tff(9269,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[444, 9268, 9242, 348])).
% 1.85/2.04 tff(9270,plain,((s(z) = elem!1) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | b(elem!1, s(z)) | r(s(z), elem!1) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9271,plain,
% 1.85/2.04 (~b(z, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9270, 9231, 232, 219, 1326, 394, 231, 379, 348])).
% 1.85/2.04 tff(9272,plain,
% 1.85/2.04 (r(z, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[904, 9271])).
% 1.85/2.04 tff(9273,plain,
% 1.85/2.04 (s(s(s(z))) = s(elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9163, 9272, 622, 2316, 1326, 106, 379, 9148, 9147])).
% 1.85/2.04 tff(9274,plain,
% 1.85/2.04 (b(s(z), s(s(s(z))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[446, 4925])).
% 1.85/2.04 tff(9275,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[71, 9274])).
% 1.85/2.04 tff(9276,plain,((~(s(s(s(z))) = s(elem!1))) | b(s(z), s(s(s(z)))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9277,plain,
% 1.85/2.04 (~b(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9276, 9273, 71])).
% 1.85/2.04 tff(9278,plain,
% 1.85/2.04 (r(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[444, 9277, 348])).
% 1.85/2.04 tff(9279,plain,
% 1.85/2.04 (r(elem!1, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[299, 9231, 243])).
% 1.85/2.04 tff(9280,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9007, 121, 379, 622, 9279, 9278])).
% 1.85/2.04 tff(9281,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z)))) | (~b(z, elem!1)) | r(s(z), elem!1) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9282,plain,
% 1.85/2.04 (~r(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9281, 348, 379, 71, 1326, 232, 394, 231, 503, 110, 68, 111, 1])).
% 1.85/2.04 tff(9283,plain,
% 1.85/2.04 (b(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2243, 9282, 2207])).
% 1.85/2.04 tff(9284,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9285,plain,
% 1.85/2.04 (((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9286,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9285])).
% 1.85/2.04 tff(9287,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[9286, 9284])).
% 1.85/2.04 tff(9288,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(9289,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9288, 9287])).
% 1.85/2.04 tff(9290,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9289, 271, 2618, 1326, 394, 1195])).
% 1.85/2.04 tff(9291,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9292,plain,
% 1.85/2.04 (~b(elem!1, s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9291, 9283, 1326, 394])).
% 1.85/2.04 tff(9293,plain,
% 1.85/2.04 (r(elem!1, s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1192, 9292, 2338])).
% 1.85/2.04 tff(9294,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2054, 9157, 9154, 379, 1184])).
% 1.85/2.04 tff(9295,plain,((s(s(s(z))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | b(s(elem!1), s(s(s(z)))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9296,plain,
% 1.85/2.04 (s(s(s(z))) = s(elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9295, 9293, 379, 9148, 9147])).
% 1.85/2.04 tff(9297,plain,
% 1.85/2.04 (~(z = elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[500, 348])).
% 1.85/2.04 tff(9298,plain,
% 1.85/2.04 (~(elem!1 = z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[333, 9297])).
% 1.85/2.04 tff(9299,plain,
% 1.85/2.04 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9296])).
% 1.85/2.04 tff(9300,plain,
% 1.85/2.04 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.85/2.04 inference(symmetry,[status(thm)],[9299])).
% 1.85/2.04 tff(9301,plain,
% 1.85/2.04 (b(s(s(s(z))), elem!1)),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9283, 9300])).
% 1.85/2.04 tff(9302,plain,
% 1.85/2.04 (~b(s(s(s(z))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[305, 9301, 8181, 9298, 111, 110, 243])).
% 1.85/2.04 tff(9303,plain,
% 1.85/2.04 (~b(s(elem!1), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6195, 9302, 9296])).
% 1.85/2.04 tff(9304,plain,
% 1.85/2.04 (~b(elem!1, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4827, 9301, 1326, 8181])).
% 1.85/2.04 tff(9305,plain,
% 1.85/2.04 (r(elem!1, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[299, 9304, 243])).
% 1.85/2.04 tff(9306,plain,
% 1.85/2.04 (~r(s(elem!1), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[8953, 9305, 110, 379])).
% 1.85/2.04 tff(9307,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[429, 9306, 9303, 2282])).
% 1.85/2.04 tff(9308,plain,((s(z) = s(elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | b(s(z), s(s(s(z)))) | r(s(z), elem!1) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9309,plain,
% 1.85/2.04 (s(z) = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9308, 9145, 9146, 37, 1326, 9139, 71, 232, 26, 503, 68, 1])).
% 1.85/2.04 tff(9310,plain,
% 1.85/2.04 (elem!1 = s(z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1221, 9309])).
% 1.85/2.04 tff(9311,plain,
% 1.85/2.04 (~b(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3576, 9310, 9124])).
% 1.85/2.04 tff(9312,plain,
% 1.85/2.04 (r(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[444, 9311, 9145])).
% 1.85/2.04 tff(9313,plain,
% 1.85/2.04 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9101, 271, 1326, 9139, 2265])).
% 1.85/2.04 tff(9314,plain,
% 1.85/2.04 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2369, 9310, 9313])).
% 1.85/2.04 tff(9315,plain,
% 1.85/2.04 (r(s(elem!1), s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[526, 9314, 211])).
% 1.85/2.04 tff(9316,plain,
% 1.85/2.04 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9309])).
% 1.85/2.04 tff(9317,plain,
% 1.85/2.04 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9316])).
% 1.85/2.04 tff(9318,plain,
% 1.85/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6679, 9310, 71])).
% 1.85/2.04 tff(9319,plain,
% 1.85/2.04 (r(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[599, 9318, 68])).
% 1.85/2.04 tff(9320,plain,
% 1.85/2.04 (r(s(z), s(s(elem!1)))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9319, 9317])).
% 1.85/2.04 tff(9321,plain,
% 1.85/2.04 (s(s(z)) = s(elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9309])).
% 1.85/2.04 tff(9322,plain,
% 1.85/2.04 (s(s(s(z))) = s(s(elem!1))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9321])).
% 1.85/2.04 tff(9323,plain,
% 1.85/2.04 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9322])).
% 1.85/2.04 tff(9324,plain,
% 1.85/2.04 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9323])).
% 1.85/2.04 tff(9325,plain,
% 1.85/2.04 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9324])).
% 1.85/2.04 tff(9326,plain,
% 1.85/2.04 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9325])).
% 1.85/2.04 tff(9327,plain,
% 1.85/2.04 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1956, 9139, 2265, 1326])).
% 1.85/2.04 tff(9328,plain,
% 1.85/2.04 (~b(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9327, 9326])).
% 1.85/2.04 tff(9329,plain,
% 1.85/2.04 (r(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[699, 21, 9328, 3313])).
% 1.85/2.04 tff(9330,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3275, 9329, 9320, 9315, 9312])).
% 1.85/2.04 tff(9331,plain,(r(z, elem!1) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (~b(z, elem!1)) | r(s(z), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9332,plain,
% 1.85/2.04 (r(z, elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9331, 9033, 71, 68, 232, 67, 1, 2, 33])).
% 1.85/2.04 tff(9333,plain,
% 1.85/2.04 (~r(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[436, 3501, 110, 378])).
% 1.85/2.04 tff(9334,plain,
% 1.85/2.04 (~r(s(elem!1), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[420, 3501, 110, 378])).
% 1.85/2.04 tff(9335,plain,
% 1.85/2.04 (s(z) = s(elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2310, 9334, 111, 82, 503, 3501, 9333])).
% 1.85/2.04 tff(9336,plain,
% 1.85/2.04 (z = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[343, 9335])).
% 1.85/2.04 tff(9337,plain,
% 1.85/2.04 (~b(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7069, 9336, 3498])).
% 1.85/2.04 tff(9338,plain,
% 1.85/2.04 (r(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2243, 9337, 3500])).
% 1.85/2.04 tff(9339,plain,
% 1.85/2.04 (~r(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3683, 9338, 378, 3501])).
% 1.85/2.04 tff(9340,plain,
% 1.85/2.04 (~r(s(s(s(elem!1))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[143, 9336, 141])).
% 1.85/2.04 tff(9341,plain,
% 1.85/2.04 (~r(s(s(s(z))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[149, 9340, 9336])).
% 1.85/2.04 tff(9342,plain,
% 1.85/2.04 (b(s(s(s(z))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[255, 9341, 907])).
% 1.85/2.04 tff(9343,plain,
% 1.85/2.04 (~b(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1940, 9342, 4010, 1326])).
% 1.85/2.04 tff(9344,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[392, 9343, 9339, 377])).
% 1.85/2.04 tff(9345,plain,(b(s(elem!1), z) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), z) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9346,plain,
% 1.85/2.04 (b(s(elem!1), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9345, 9033, 219, 9332, 2316, 2264, 37, 79, 67, 26])).
% 1.85/2.04 tff(9347,plain,
% 1.85/2.04 (~(s(z) = s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9144, 9346, 2])).
% 1.85/2.04 tff(9348,plain,
% 1.85/2.04 (~(z = elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[500, 9347])).
% 1.85/2.04 tff(9349,plain,
% 1.85/2.04 (~(elem!1 = z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[333, 9348])).
% 1.85/2.04 tff(9350,plain,
% 1.85/2.04 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1956, 1935, 394, 1326])).
% 1.85/2.04 tff(9351,plain,
% 1.85/2.04 (s(s(s(z))) = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[255, 5188, 221])).
% 1.85/2.04 tff(9352,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4909, 9351, 9350, 307])).
% 1.85/2.04 tff(9353,plain,((~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | r(s(s(s(z))), elem!1) | (~b(s(elem!1), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9354,plain,
% 1.85/2.04 (r(s(s(s(z))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9353, 307, 1935, 1326, 394])).
% 1.85/2.04 tff(9355,plain,
% 1.85/2.04 (~r(z, s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3375, 9354, 108, 110])).
% 1.85/2.04 tff(9356,plain,
% 1.85/2.04 (b(z, s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1214, 9355])).
% 1.85/2.04 tff(9357,plain,
% 1.85/2.04 (~b(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4598, 307, 1326, 394])).
% 1.85/2.04 tff(9358,plain,
% 1.85/2.04 (r(s(elem!1), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2243, 9357, 2564])).
% 1.85/2.04 tff(9359,plain,
% 1.85/2.04 (~b(z, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9091, 307, 1326, 394])).
% 1.85/2.04 tff(9360,plain,
% 1.85/2.04 (r(z, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1439, 9359])).
% 1.85/2.04 tff(9361,plain,
% 1.85/2.04 (~r(elem!1, z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3387, 9360, 378, 9358])).
% 1.85/2.04 tff(9362,plain,
% 1.85/2.04 (b(elem!1, z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[284, 9361, 259])).
% 1.85/2.04 tff(9363,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1315, 9362, 9356, 394, 307])).
% 1.85/2.04 tff(9364,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (elem!1 = z) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9365,plain,
% 1.85/2.04 (~b(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9364, 9346, 9349, 9332, 2207, 106, 26, 9033, 2265])).
% 1.85/2.04 tff(9366,plain,
% 1.85/2.04 (r(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[392, 9365, 219])).
% 1.85/2.04 tff(9367,plain,
% 1.85/2.04 (s(z) = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9308, 9366, 9347, 37, 9033, 9346, 71, 232, 26, 67, 68, 1])).
% 1.85/2.04 tff(9368,plain,
% 1.85/2.04 (elem!1 = s(z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1221, 9367])).
% 1.85/2.04 tff(9369,plain,
% 1.85/2.04 (~b(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3576, 9368, 9365])).
% 1.85/2.04 tff(9370,plain,
% 1.85/2.04 (r(s(z), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[444, 9369, 9347])).
% 1.85/2.04 tff(9371,plain,
% 1.85/2.04 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9101, 271, 9033, 9346, 2265])).
% 1.85/2.04 tff(9372,plain,
% 1.85/2.04 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2369, 9368, 9371])).
% 1.85/2.04 tff(9373,plain,
% 1.85/2.04 (r(s(elem!1), s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[526, 9372, 211])).
% 1.85/2.04 tff(9374,plain,
% 1.85/2.04 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9367])).
% 1.85/2.04 tff(9375,plain,
% 1.85/2.04 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9374])).
% 1.85/2.04 tff(9376,plain,
% 1.85/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6679, 9368, 71])).
% 1.85/2.04 tff(9377,plain,
% 1.85/2.04 (r(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[599, 9376, 68])).
% 1.85/2.04 tff(9378,plain,
% 1.85/2.04 (r(s(z), s(s(elem!1)))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9377, 9375])).
% 1.85/2.04 tff(9379,plain,
% 1.85/2.04 (s(s(z)) = s(elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9367])).
% 1.85/2.04 tff(9380,plain,
% 1.85/2.04 (s(s(s(z))) = s(s(elem!1))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9379])).
% 1.85/2.04 tff(9381,plain,
% 1.85/2.04 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9380])).
% 1.85/2.04 tff(9382,plain,
% 1.85/2.04 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9381])).
% 1.85/2.04 tff(9383,plain,
% 1.85/2.04 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9382])).
% 1.85/2.04 tff(9384,plain,
% 1.85/2.04 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9383])).
% 1.85/2.04 tff(9385,plain,
% 1.85/2.04 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1956, 9346, 2265, 9033])).
% 1.85/2.04 tff(9386,plain,
% 1.85/2.04 (~b(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9385, 9384])).
% 1.85/2.04 tff(9387,plain,
% 1.85/2.04 (r(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[699, 21, 9386, 3313])).
% 1.85/2.04 tff(9388,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3275, 9387, 9378, 9373, 9370])).
% 1.85/2.04 tff(9389,plain,(r(s(z), elem!1) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), z) | b(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9390,plain,
% 1.85/2.04 (r(s(z), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9389, 71, 68, 1, 2, 33, 38])).
% 1.85/2.04 tff(9391,plain,
% 1.85/2.04 (b(elem!1, z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[375, 199, 9390, 2315, 26])).
% 1.85/2.04 tff(9392,plain,
% 1.85/2.04 (r(z, elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[355, 199, 2262])).
% 1.85/2.04 tff(9393,plain,
% 1.85/2.04 (~r(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[387, 9392, 26, 9390])).
% 1.85/2.04 tff(9394,plain,
% 1.85/2.04 (b(elem!1, s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[392, 9393, 219])).
% 1.85/2.04 tff(9395,plain,
% 1.85/2.04 (~b(z, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3404, 9394, 9391, 2314])).
% 1.85/2.04 tff(9396,plain,
% 1.85/2.04 (r(z, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2106, 9395])).
% 1.85/2.04 tff(9397,plain,
% 1.85/2.04 (~b(z, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[466, 199, 26, 9390, 219, 2262])).
% 1.85/2.04 tff(9398,plain,
% 1.85/2.04 (r(z, s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[904, 9397])).
% 1.85/2.04 tff(9399,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9400,plain,
% 1.85/2.04 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9401,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9400])).
% 1.85/2.04 tff(9402,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.85/2.04 inference(transitivity,[status(thm)],[9401, 9399])).
% 1.85/2.04 tff(9403,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(9404,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9403, 9402])).
% 1.85/2.04 tff(9405,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9404, 121, 378, 357, 624, 909])).
% 1.85/2.04 tff(9406,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9407,plain,
% 1.85/2.04 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9406, 9398, 9390, 9392])).
% 1.85/2.04 tff(9408,plain,
% 1.85/2.04 (b(elem!1, s(s(elem!1)))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[599, 9407, 68])).
% 1.85/2.04 tff(9409,plain,
% 1.85/2.04 (~b(z, s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1315, 9394, 2314, 9391])).
% 1.85/2.04 tff(9410,plain,
% 1.85/2.04 (r(z, s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1214, 9409])).
% 1.85/2.04 tff(9411,plain,
% 1.85/2.04 (~r(s(s(s(z))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3375, 9410, 106, 26])).
% 1.85/2.04 tff(9412,plain,
% 1.85/2.04 (~r(s(s(s(z))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1508, 9410, 106, 9398])).
% 1.85/2.04 tff(9413,plain,
% 1.85/2.04 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1485, 9410, 26, 106])).
% 1.85/2.04 tff(9414,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9415,plain,
% 1.85/2.04 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(9416,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9415])).
% 1.85/2.04 tff(9417,plain,
% 1.85/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[9416, 9414])).
% 1.85/2.04 tff(9418,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(9419,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9418, 9417])).
% 1.85/2.04 tff(9420,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9419, 121, 110, 2327, 1140, 108])).
% 1.85/2.04 tff(9421,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(9422,plain,
% 1.85/2.04 (~r(s(s(s(z))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[9421, 9410, 26, 106])).
% 1.85/2.04 tff(9423,plain,
% 1.85/2.04 (b(s(s(s(z))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2325, 9422])).
% 1.85/2.04 tff(9424,plain,
% 1.85/2.04 (s(s(s(z))) = elem!1),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2259, 894, 106, 1, 222, 906, 68, 33, 2, 38, 221])).
% 1.85/2.04 tff(9425,plain,
% 1.85/2.04 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.04 tff(9426,plain,
% 1.85/2.04 (b(elem!1, s(z))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[222, 9425])).
% 1.85/2.04 tff(9427,plain,
% 1.85/2.04 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.04 tff(9428,plain,
% 1.85/2.04 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.85/2.04 inference(transitivity,[status(thm)],[9427, 653])).
% 1.85/2.04 tff(9429,plain,
% 1.85/2.04 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9428])).
% 1.85/2.04 tff(9430,plain,
% 1.85/2.04 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9429])).
% 1.85/2.04 tff(9431,plain,
% 1.85/2.04 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2611, 9424])).
% 1.85/2.04 tff(9432,plain,
% 1.85/2.04 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[9431, 9430])).
% 1.85/2.04 tff(9433,plain,
% 1.85/2.04 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2071, 9432, 906])).
% 1.85/2.04 tff(9434,plain,
% 1.85/2.04 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.04 tff(9435,plain,
% 1.85/2.04 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9434])).
% 1.85/2.04 tff(9436,plain,
% 1.85/2.04 (~b(s(z), elem!1)),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[71, 9435])).
% 1.85/2.04 tff(9437,plain,
% 1.85/2.04 (~b(s(z), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2081, 9433, 222, 67])).
% 1.85/2.04 tff(9438,plain,
% 1.85/2.04 (r(s(z), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[760, 9437])).
% 1.85/2.04 tff(9439,plain,
% 1.85/2.04 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[2606])).
% 1.85/2.04 tff(9440,plain,
% 1.85/2.04 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9439, 2606])).
% 1.85/2.04 tff(9441,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[9440])).
% 1.85/2.04 tff(9442,plain,
% 1.85/2.04 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[9439])).
% 1.85/2.04 tff(9443,plain,
% 1.85/2.04 (r(s(z), elem!1)),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[108, 245])).
% 1.85/2.04 tff(9444,plain,
% 1.85/2.04 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[244])).
% 1.85/2.05 tff(9445,plain,
% 1.85/2.05 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.85/2.05 inference(transitivity,[status(thm)],[9444, 360])).
% 1.85/2.05 tff(9446,plain,
% 1.85/2.05 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9445])).
% 1.85/2.05 tff(9447,plain,
% 1.85/2.05 (~(z = elem!1)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[166, 9446])).
% 1.85/2.05 tff(9448,plain,
% 1.85/2.05 (r(z, elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[355, 199, 9447])).
% 1.85/2.05 tff(9449,plain,
% 1.85/2.05 (~r(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[387, 9448, 110, 9443])).
% 1.85/2.05 tff(9450,plain,
% 1.85/2.05 (b(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[392, 9449, 377])).
% 1.85/2.05 tff(9451,plain,
% 1.85/2.05 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.85/2.05 inference(transitivity,[status(thm)],[9445, 361])).
% 1.85/2.05 tff(9452,plain,
% 1.85/2.05 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9451])).
% 1.85/2.05 tff(9453,plain,
% 1.85/2.05 (~(elem!1 = z)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[166, 9452])).
% 1.85/2.05 tff(9454,plain,
% 1.85/2.05 (b(elem!1, z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[375, 199, 9453, 9443, 110])).
% 1.85/2.05 tff(9455,plain,
% 1.85/2.05 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[244])).
% 1.85/2.05 tff(9456,plain,
% 1.85/2.05 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 1.85/2.05 inference(transitivity,[status(thm)],[9455, 238])).
% 1.85/2.05 tff(9457,plain,
% 1.85/2.05 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9456])).
% 1.85/2.05 tff(9458,plain,
% 1.85/2.05 (~(s(z) = elem!1)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[97, 9457])).
% 1.85/2.05 tff(9459,plain,
% 1.85/2.05 (~r(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1305, 9450, 909, 199, 9458, 9447, 1242])).
% 1.85/2.05 tff(9460,plain,
% 1.85/2.05 (b(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[409, 9459])).
% 1.85/2.05 tff(9461,plain,
% 1.85/2.05 (~b(z, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3404, 9460, 9454, 9450])).
% 1.85/2.05 tff(9462,plain,
% 1.85/2.05 (r(z, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2106, 9461])).
% 1.85/2.05 tff(9463,plain,
% 1.85/2.05 (r(z, s(s(s(s(s(z))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9462, 9442])).
% 1.85/2.05 tff(9464,plain,
% 1.85/2.05 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[244])).
% 1.85/2.05 tff(9465,plain,
% 1.85/2.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[9464])).
% 1.85/2.05 tff(9466,plain,
% 1.85/2.05 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[2606])).
% 1.85/2.05 tff(9467,plain,
% 1.85/2.05 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9466, 9465])).
% 1.85/2.05 tff(9468,plain,
% 1.85/2.05 (b(s(s(s(z))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4909, 9450, 244])).
% 1.85/2.05 tff(9469,plain,
% 1.85/2.05 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2114, 9460, 9468, 2073])).
% 1.85/2.05 tff(9470,plain,
% 1.85/2.05 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[681, 9469, 79])).
% 1.85/2.05 tff(9471,plain,
% 1.85/2.05 (~b(z, s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4210, 199, 244])).
% 1.85/2.05 tff(9472,plain,
% 1.85/2.05 (r(z, s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1214, 9471])).
% 1.85/2.05 tff(9473,plain,
% 1.85/2.05 (~r(s(s(s(z))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1148, 9472, 108, 909])).
% 1.85/2.05 tff(9474,plain,
% 1.85/2.05 (~b(z, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1427, 9468, 9473, 9460])).
% 1.85/2.05 tff(9475,plain,
% 1.85/2.05 (r(z, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1439, 9474])).
% 1.85/2.05 tff(9476,plain,
% 1.85/2.05 (~r(s(elem!1), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7694, 9475, 111, 9470])).
% 1.85/2.05 tff(9477,plain,
% 1.85/2.05 (b(s(elem!1), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2243, 9476, 3500])).
% 1.85/2.05 tff(9478,plain,
% 1.85/2.05 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9477, 9467])).
% 1.85/2.05 tff(9479,plain,
% 1.85/2.05 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[2606])).
% 1.85/2.05 tff(9480,plain,
% 1.85/2.05 (b(s(s(s(s(z)))), z)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9460, 9479])).
% 1.85/2.05 tff(9481,plain,
% 1.85/2.05 (~b(z, s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1177, 9480, 108, 110, 9472, 909])).
% 1.85/2.05 tff(9482,plain,
% 1.85/2.05 (r(z, s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1121, 9481])).
% 1.85/2.05 tff(9483,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9484,plain,
% 1.85/2.05 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9485,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9484])).
% 1.85/2.05 tff(9486,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9485, 9483])).
% 1.85/2.05 tff(9487,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(9488,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9487, 9486])).
% 1.85/2.05 tff(9489,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9488, 121, 572, 909, 911, 1518])).
% 1.85/2.05 tff(9490,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9491,plain,
% 1.85/2.05 (~r(s(s(s(s(z)))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9490, 9482, 909, 572])).
% 1.85/2.05 tff(9492,plain,
% 1.85/2.05 (b(s(s(s(s(z)))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[932, 9491])).
% 1.85/2.05 tff(9493,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9494,plain,
% 1.85/2.05 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9495,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9494])).
% 1.85/2.05 tff(9496,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9495, 9493])).
% 1.85/2.05 tff(9497,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(9498,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9497, 9496])).
% 1.85/2.05 tff(9499,plain,
% 1.85/2.05 ((~b(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(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9498, 271])).
% 1.85/2.05 tff(9500,plain,
% 1.85/2.05 (~b(s(z), s(s(s(s(s(z))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9499, 9492, 222, 9478])).
% 1.85/2.05 tff(9501,plain,
% 1.85/2.05 (r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1756, 9500])).
% 1.85/2.05 tff(9502,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.05 tff(9503,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9504,plain,
% 1.85/2.05 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9505,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9504])).
% 1.85/2.05 tff(9506,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9505, 9503])).
% 1.85/2.05 tff(9507,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(9508,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9507, 9506])).
% 1.85/2.05 tff(9509,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9508, 121, 909, 1661, 9502, 1735])).
% 1.85/2.05 tff(9510,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9511,plain,
% 1.85/2.05 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9510, 9501, 909, 9463])).
% 1.85/2.05 tff(9512,plain,
% 1.85/2.05 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4045, 4038])).
% 1.85/2.05 tff(9513,plain,
% 1.85/2.05 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9512, 9511])).
% 1.85/2.05 tff(9514,plain,
% 1.85/2.05 (b(s(s(elem!1)), s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9513, 9441])).
% 1.85/2.05 tff(9515,plain,
% 1.85/2.05 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9406, 9448, 9443, 909])).
% 1.85/2.05 tff(9516,plain,
% 1.85/2.05 (b(elem!1, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[599, 9515, 68])).
% 1.85/2.05 tff(9517,plain,
% 1.85/2.05 (~b(s(s(elem!1)), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3324, 9460, 9450, 9516])).
% 1.85/2.05 tff(9518,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9517, 9514])).
% 1.85/2.05 tff(9519,plain,(b(z, elem!1) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~(s(s(s(z))) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(z), elem!1) | (elem!1 = s(s(elem!1))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9520,plain,
% 1.85/2.05 (b(z, elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9519, 905, 222, 9438, 106, 26, 9424, 37, 9433, 9436, 68, 219])).
% 1.85/2.05 tff(9521,plain,
% 1.85/2.05 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[581, 9438, 37, 26])).
% 1.85/2.05 tff(9522,plain,
% 1.85/2.05 (b(s(s(s(z))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4909, 307, 244])).
% 1.85/2.05 tff(9523,plain,
% 1.85/2.05 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.85/2.05 inference(commutativity,[status(thm)],[])).
% 1.85/2.05 tff(9524,plain,
% 1.85/2.05 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[2606])).
% 1.85/2.05 tff(9525,plain,
% 1.85/2.05 ((s(z) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9524, 9523])).
% 1.85/2.05 tff(9526,plain,
% 1.85/2.05 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.85/2.05 inference(symmetry,[status(thm)],[9525])).
% 1.85/2.05 tff(9527,plain,
% 1.85/2.05 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9526])).
% 1.85/2.05 tff(9528,plain,
% 1.85/2.05 (~(s(z) = s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[927, 9527])).
% 1.85/2.05 tff(9529,plain,
% 1.85/2.05 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9526, 4396])).
% 1.85/2.05 tff(9530,plain,
% 1.85/2.05 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9529])).
% 1.85/2.05 tff(9531,plain,
% 1.85/2.05 (~(s(elem!1) = s(z))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[927, 9530])).
% 1.85/2.05 tff(9532,plain,
% 1.85/2.05 (~r(s(z), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1300, 412, 110, 909])).
% 1.85/2.05 tff(9533,plain,
% 1.85/2.05 (b(s(z), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[444, 9532, 348])).
% 1.85/2.05 tff(9534,plain,
% 1.85/2.05 (~r(s(elem!1), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1254, 412, 357, 909])).
% 1.85/2.05 tff(9535,plain,
% 1.85/2.05 (b(s(elem!1), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[429, 9534, 422])).
% 1.85/2.05 tff(9536,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[456, 9535, 9533, 448, 307])).
% 1.85/2.05 tff(9537,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(z)) | (s(z) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9538,plain,
% 1.85/2.05 (~r(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9537, 307, 448, 9531, 9528, 9443, 909, 110])).
% 1.85/2.05 tff(9539,plain,
% 1.85/2.05 (b(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[409, 9538])).
% 1.85/2.05 tff(9540,plain,
% 1.85/2.05 (~b(s(s(s(z))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1956, 9539, 1326, 9522])).
% 1.85/2.05 tff(9541,plain,
% 1.85/2.05 (r(s(s(s(z))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1155, 9540])).
% 1.85/2.05 tff(9542,plain,
% 1.85/2.05 (~r(z, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2096, 9541, 108, 110])).
% 1.85/2.05 tff(9543,plain,
% 1.85/2.05 (b(z, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2106, 9542])).
% 1.85/2.05 tff(9544,plain,
% 1.85/2.05 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2114, 9539, 9522, 2073])).
% 1.85/2.05 tff(9545,plain,
% 1.85/2.05 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[681, 9544, 82])).
% 1.85/2.05 tff(9546,plain,
% 1.85/2.05 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[586, 4438, 563])).
% 1.85/2.05 tff(9547,plain,
% 1.85/2.05 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1921, 9543, 110, 572, 9546])).
% 1.85/2.05 tff(9548,plain,
% 1.85/2.05 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[556, 9547, 1])).
% 1.85/2.05 tff(9549,plain,
% 1.85/2.05 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2189, 9548, 909, 9545, 108, 9531, 572, 9543])).
% 1.85/2.05 tff(9550,plain,
% 1.85/2.05 (~b(s(elem!1), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4598, 9539, 1326, 307])).
% 1.85/2.05 tff(9551,plain,
% 1.85/2.05 (r(s(elem!1), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2243, 9550, 2207])).
% 1.85/2.05 tff(9552,plain,
% 1.85/2.05 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2611, 244])).
% 1.85/2.05 tff(9553,plain,
% 1.85/2.05 (r(elem!1, s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4488, 9547, 9552, 9550, 9544, 4438])).
% 1.85/2.05 tff(9554,plain,
% 1.85/2.05 (~r(s(elem!1), s(s(elem!1)))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[635, 9553, 9551, 9548])).
% 1.85/2.05 tff(9555,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[526, 9554, 9549, 211])).
% 1.85/2.05 tff(9556,plain,((~b(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9557,plain,
% 1.85/2.05 (~b(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9556, 905, 106, 9438, 9521, 1, 26, 79, 9520, 9433, 9426, 9424])).
% 1.85/2.05 tff(9558,plain,
% 1.85/2.05 (r(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[392, 9557, 219])).
% 1.85/2.05 tff(9559,plain,
% 1.85/2.05 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.05 tff(9560,plain,
% 1.85/2.05 (r(s(z), elem!1)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[106, 9559])).
% 1.85/2.05 tff(9561,plain,
% 1.85/2.05 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.05 tff(9562,plain,
% 1.85/2.05 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(elem!1), elem!1))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9561])).
% 1.85/2.05 tff(9563,plain,
% 1.85/2.05 (b(z, s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6548, 9520, 9424])).
% 1.85/2.05 tff(9564,plain,
% 1.85/2.05 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.05 tff(9565,plain,
% 1.85/2.05 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 1.85/2.05 inference(transitivity,[status(thm)],[9564, 238])).
% 1.85/2.05 tff(9566,plain,
% 1.85/2.05 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9565, 1218])).
% 1.85/2.05 tff(9567,plain,
% 1.85/2.05 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9566])).
% 1.85/2.05 tff(9568,plain,
% 1.85/2.05 (~(elem!1 = s(z))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[97, 9567])).
% 1.85/2.05 tff(9569,plain,
% 1.85/2.05 (~r(z, elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3673, 9558, 9560, 905])).
% 1.85/2.05 tff(9570,plain,
% 1.85/2.05 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9424])).
% 1.85/2.05 tff(9571,plain,
% 1.85/2.05 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.85/2.05 inference(transitivity,[status(thm)],[9570, 360])).
% 1.85/2.05 tff(9572,plain,
% 1.85/2.05 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9571])).
% 1.85/2.05 tff(9573,plain,
% 1.85/2.05 (~(z = elem!1)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[166, 9572])).
% 1.85/2.05 tff(9574,plain,
% 1.85/2.05 (s(elem!1) = s(s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2605, 9424])).
% 1.85/2.05 tff(9575,plain,
% 1.85/2.05 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[244])).
% 1.85/2.05 tff(9576,plain,
% 1.85/2.05 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[9575])).
% 1.85/2.05 tff(9577,plain,
% 1.85/2.05 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9576])).
% 1.85/2.05 tff(9578,plain,
% 1.85/2.05 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[657, 9577])).
% 1.85/2.05 tff(9579,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2073, 9578])).
% 1.85/2.05 tff(9580,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9581,plain,
% 1.85/2.05 (b(elem!1, s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9580, 9433, 9424])).
% 1.85/2.05 tff(9582,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9583,plain,
% 1.85/2.05 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(9584,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9583])).
% 1.85/2.05 tff(9585,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9584, 9582])).
% 1.85/2.05 tff(9586,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(9587,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9586, 9585])).
% 1.85/2.05 tff(9588,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9587, 271, 448, 503, 1067, 738])).
% 1.85/2.05 tff(9589,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9590,plain,
% 1.85/2.05 (~b(s(z), s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9589, 9426, 67, 9581])).
% 1.85/2.05 tff(9591,plain,
% 1.85/2.05 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[4024])).
% 1.85/2.05 tff(9592,plain,
% 1.85/2.05 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.85/2.05 inference(symmetry,[status(thm)],[9591])).
% 1.85/2.05 tff(9593,plain,
% 1.85/2.05 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9592])).
% 1.85/2.05 tff(9594,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.05 tff(9595,plain,
% 1.85/2.05 (~b(s(z), s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9594, 9593])).
% 1.85/2.05 tff(9596,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[446, 9595])).
% 1.85/2.05 tff(9597,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(9598,plain,
% 1.85/2.05 (~b(s(z), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[9597, 9590, 9574])).
% 1.85/2.05 tff(9599,plain,
% 1.85/2.05 (~r(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[5661, 9598, 9573, 9569, 9558, 905, 9568])).
% 1.85/2.05 tff(9600,plain,
% 1.85/2.05 (b(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[409, 9599])).
% 1.85/2.05 tff(9601,plain,
% 1.85/2.05 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2029, 9600, 9563, 222])).
% 1.85/2.05 tff(9602,plain,
% 1.85/2.05 (~b(s(elem!1), elem!1)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[9601, 9562])).
% 1.85/2.05 tff(9603,plain,
% 1.85/2.05 (r(s(elem!1), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2243, 9602, 2207])).
% 1.85/2.05 tff(9604,plain,
% 1.85/2.05 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9574])).
% 1.85/2.05 tff(9605,plain,
% 1.85/2.05 ((s(z) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 1.85/2.05 inference(transitivity,[status(thm)],[9604, 9523])).
% 1.85/2.05 tff(9606,plain,
% 1.85/2.05 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.85/2.05 inference(symmetry,[status(thm)],[9605])).
% 1.85/2.05 tff(9607,plain,
% 1.85/2.05 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[9606])).
% 1.85/2.05 tff(9608,plain,
% 1.85/2.05 (~(s(z) = s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[927, 9607])).
% 1.85/2.05 tff(9609,plain,
% 1.85/2.05 (r(s(z), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[444, 9598, 9608])).
% 1.85/2.05 tff(9610,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9611,plain,
% 1.85/2.06 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9612,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9611])).
% 1.85/2.06 tff(9613,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[9612, 9610])).
% 1.85/2.06 tff(9614,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(9615,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9614, 9613])).
% 1.85/2.06 tff(9616,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9615, 121, 622, 684, 572, 431])).
% 1.85/2.06 tff(9617,plain,((~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9618,plain,
% 1.85/2.06 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9617, 9603, 9438, 9609])).
% 1.85/2.06 tff(9619,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[681, 9618, 79])).
% 1.85/2.06 tff(9620,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9621,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(9622,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9621, 9620])).
% 1.85/2.06 tff(9623,plain,
% 1.85/2.06 (~r(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9622, 121, 379, 622, 357])).
% 1.85/2.06 tff(9624,plain,
% 1.85/2.06 (b(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[444, 9623, 348])).
% 1.85/2.06 tff(9625,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9626,plain,
% 1.85/2.06 (((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9627,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9626])).
% 1.85/2.06 tff(9628,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[9627, 9625])).
% 1.85/2.06 tff(9629,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(9630,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9629, 9628])).
% 1.85/2.06 tff(9631,plain,
% 1.85/2.06 (~r(s(elem!1), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9630, 121, 379, 622, 357])).
% 1.85/2.06 tff(9632,plain,
% 1.85/2.06 (b(s(elem!1), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[427, 21, 9631, 2282])).
% 1.85/2.06 tff(9633,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3976, 271, 9632, 9624, 638])).
% 1.85/2.06 tff(9634,plain,
% 1.85/2.06 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[66, 21, 9633])).
% 1.85/2.06 tff(9635,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9634, 2861])).
% 1.85/2.06 tff(9636,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3796, 121, 379, 357, 139, 9635])).
% 1.85/2.06 tff(9637,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9638,plain,
% 1.85/2.06 (~r(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9637, 9619, 9560, 9558, 9608, 9603])).
% 1.85/2.06 tff(9639,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[486, 9638, 9431])).
% 1.85/2.06 tff(9640,plain,
% 1.85/2.06 (~b(s(z), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[513, 9639, 67, 9426])).
% 1.85/2.06 tff(9641,plain,
% 1.85/2.06 (r(s(z), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2167, 9640])).
% 1.85/2.06 tff(9642,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2910, 121, 622, 357, 624, 431])).
% 1.85/2.06 tff(9643,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9644,plain,
% 1.85/2.06 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9643, 9603, 9560, 9609])).
% 1.85/2.06 tff(9645,plain,
% 1.85/2.06 (b(elem!1, s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[599, 9644, 68])).
% 1.85/2.06 tff(9646,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[586, 9521, 563])).
% 1.85/2.06 tff(9647,plain,
% 1.85/2.06 (~b(s(s(elem!1)), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[594, 9639, 9646, 9645])).
% 1.85/2.06 tff(9648,plain,
% 1.85/2.06 (r(s(s(elem!1)), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[862, 9647, 198])).
% 1.85/2.06 tff(9649,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1633, 9648, 9641, 9560, 9558])).
% 1.85/2.06 tff(9650,plain,(b(z, s(z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), s(s(s(z)))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9651,plain,
% 1.85/2.06 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9650, 9423, 68, 1, 9397, 71, 33, 2, 38, 9411])).
% 1.85/2.06 tff(9652,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.06 inference(symmetry,[status(thm)],[4651])).
% 1.85/2.06 tff(9653,plain,
% 1.85/2.06 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[1997])).
% 1.85/2.06 tff(9654,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[5499, 9653])).
% 1.85/2.06 tff(9655,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9654, 9652])).
% 1.85/2.06 tff(9656,plain,
% 1.85/2.06 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[4652])).
% 1.85/2.06 tff(9657,assumption,(~r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.85/2.06 tff(9658,plain,
% 1.85/2.06 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9657, 9656])).
% 1.85/2.06 tff(9659,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9658, 9655])).
% 1.85/2.06 tff(9660,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9661,plain,
% 1.85/2.06 (~(s(s(s(z))) = s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9660, 9651, 9413])).
% 1.85/2.06 tff(9662,plain,
% 1.85/2.06 (b(s(s(s(z))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1816, 9661, 9412])).
% 1.85/2.06 tff(9663,plain,
% 1.85/2.06 (~b(s(s(s(z))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3288, 9662, 2314, 9394])).
% 1.85/2.06 tff(9664,plain,
% 1.85/2.06 (s(s(s(z))) = elem!1),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[255, 9663, 9411])).
% 1.85/2.06 tff(9665,plain,
% 1.85/2.06 (s(elem!1) = s(s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2605, 9664])).
% 1.85/2.06 tff(9666,plain,
% 1.85/2.06 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9665])).
% 1.85/2.06 tff(9667,plain,
% 1.85/2.06 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9666])).
% 1.85/2.06 tff(9668,plain,
% 1.85/2.06 (r(z, s(s(s(s(s(z))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9396, 9667])).
% 1.85/2.06 tff(9669,plain,
% 1.85/2.06 (~b(z, s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1427, 9662, 2314, 2264])).
% 1.85/2.06 tff(9670,plain,
% 1.85/2.06 (r(z, s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1439, 9669])).
% 1.85/2.06 tff(9671,plain,
% 1.85/2.06 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9665])).
% 1.85/2.06 tff(9672,plain,
% 1.85/2.06 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.06 inference(symmetry,[status(thm)],[9671])).
% 1.85/2.06 tff(9673,plain,
% 1.85/2.06 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9666, 9665])).
% 1.85/2.06 tff(9674,plain,
% 1.85/2.06 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.06 inference(transitivity,[status(thm)],[9673, 9672])).
% 1.85/2.06 tff(9675,plain,
% 1.85/2.06 (~b(s(s(elem!1)), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3324, 9408, 9394, 2314])).
% 1.85/2.06 tff(9676,plain,
% 1.85/2.06 (r(s(s(elem!1)), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[701, 9675, 3313])).
% 1.85/2.06 tff(9677,plain,
% 1.85/2.06 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9676, 9674])).
% 1.85/2.06 tff(9678,plain,
% 1.85/2.06 (~r(s(elem!1), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6368, 9677, 9670, 9668])).
% 1.85/2.06 tff(9679,plain,
% 1.85/2.06 (b(s(elem!1), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[526, 9678, 211])).
% 1.85/2.06 tff(9680,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9681,plain,
% 1.85/2.06 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9682,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9681])).
% 1.85/2.06 tff(9683,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[9682, 9680])).
% 1.85/2.06 tff(9684,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(9685,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9684, 9683])).
% 1.85/2.06 tff(9686,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9685, 271, 307, 543, 517, 588])).
% 1.85/2.06 tff(9687,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9688,plain,
% 1.85/2.06 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9687, 9679, 9394, 9408])).
% 1.85/2.06 tff(9689,plain,
% 1.85/2.06 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[556, 9688, 1])).
% 1.85/2.06 tff(9690,plain,
% 1.85/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2611, 9664])).
% 1.85/2.06 tff(9691,plain,
% 1.85/2.06 (~r(elem!1, s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4202, 9398, 26, 9392])).
% 1.85/2.06 tff(9692,plain,
% 1.85/2.06 (~(elem!1 = s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6679, 9408, 71])).
% 1.85/2.06 tff(9693,plain,
% 1.85/2.06 (b(elem!1, s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[299, 9692, 9691])).
% 1.85/2.06 tff(9694,plain,
% 1.85/2.06 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9676, 9673])).
% 1.85/2.06 tff(9695,plain,
% 1.85/2.06 (~r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9510, 9694, 9398, 9668])).
% 1.85/2.06 tff(9696,plain,
% 1.85/2.06 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[4024])).
% 1.85/2.06 tff(9697,plain,
% 1.85/2.06 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9696])).
% 1.85/2.06 tff(9698,plain,
% 1.85/2.06 (r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[1625, 9697])).
% 1.85/2.06 tff(9699,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1750, 9698])).
% 1.85/2.06 tff(9700,plain,((~r(s(z), s(s(elem!1)))) | r(s(z), s(s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9701,plain,
% 1.85/2.06 (~r(s(z), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9700, 9695, 9665])).
% 1.85/2.06 tff(9702,plain,
% 1.85/2.06 (b(s(z), s(s(elem!1)))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2167, 9701])).
% 1.85/2.06 tff(9703,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[513, 9702, 67, 9693])).
% 1.85/2.06 tff(9704,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[486, 9703, 9690])).
% 1.85/2.06 tff(9705,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3425, 9704, 9689, 37, 9396])).
% 1.85/2.06 tff(9706,plain,(b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(9707,plain,
% 1.85/2.06 (b(z, elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9706, 71, 68, 1, 33, 2, 38])).
% 1.85/2.06 tff(9708,plain,
% 1.85/2.06 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9101, 271, 9707, 2314, 2265])).
% 1.85/2.06 tff(9709,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2044, 6284, 9708])).
% 1.85/2.06 tff(9710,plain,
% 1.85/2.06 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1956, 9707, 2265, 2314])).
% 1.85/2.06 tff(9711,plain,
% 1.85/2.06 (r(s(s(s(z))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1816, 2033, 9710])).
% 1.85/2.06 tff(9712,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9713,plain,
% 1.85/2.06 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9714,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9713])).
% 1.85/2.06 tff(9715,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[9714, 9712])).
% 1.85/2.06 tff(9716,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(9717,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9716, 9715])).
% 1.85/2.06 tff(9718,plain,
% 1.85/2.06 (~r(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9717, 121, 9711, 106, 9709])).
% 1.85/2.06 tff(9719,plain,
% 1.85/2.06 (b(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[444, 9718, 2263])).
% 1.85/2.06 tff(9720,plain,
% 1.85/2.06 (~(s(elem!1) = s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[350, 2263])).
% 1.85/2.06 tff(9721,plain,
% 1.85/2.06 (~r(s(elem!1), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[8939, 121, 9711, 106, 9709])).
% 1.85/2.06 tff(9722,plain,
% 1.85/2.06 (b(s(elem!1), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[429, 9721, 9720])).
% 1.85/2.06 tff(9723,plain,
% 1.85/2.06 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2289, 271, 9722, 9719, 67])).
% 1.85/2.06 tff(9724,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2293, 21, 9723, 85])).
% 1.85/2.06 tff(9725,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2300, 271, 9722, 9719, 67])).
% 1.85/2.06 tff(9726,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[681, 9725, 79])).
% 1.85/2.06 tff(9727,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9728,plain,
% 1.85/2.06 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9729,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[9728])).
% 1.85/2.06 tff(9730,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[9729, 9727])).
% 1.85/2.06 tff(9731,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(9732,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[9731, 9730])).
% 1.85/2.06 tff(9733,plain,
% 1.85/2.06 (~r(z, s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9732, 121, 9726, 37, 9724])).
% 1.85/2.06 tff(9734,plain,
% 1.85/2.06 (b(z, s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1439, 9733])).
% 1.85/2.06 tff(9735,plain,
% 1.85/2.06 (~(s(s(s(z))) = s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3377, 9358, 110, 108, 9360])).
% 1.85/2.06 tff(9736,plain,
% 1.85/2.06 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2035, 9735])).
% 1.85/2.06 tff(9737,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2044, 9736, 9151])).
% 1.85/2.06 tff(9738,plain,
% 1.85/2.06 (r(s(s(s(z))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9353, 307, 8458, 1326, 394])).
% 1.85/2.06 tff(9739,plain,
% 1.85/2.06 (~r(elem!1, s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4112, 9738, 108, 357])).
% 1.85/2.06 tff(9740,plain,
% 1.85/2.06 (~r(z, elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9364, 307, 259, 394, 2564, 108, 110, 1326, 8458])).
% 1.85/2.06 tff(9741,plain,
% 1.85/2.06 (~(s(z) = elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[9060, 9740, 6201, 111, 110, 1326, 503, 307])).
% 1.85/2.06 tff(9742,plain,
% 1.85/2.06 (~(elem!1 = s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[242, 9741])).
% 1.85/2.06 tff(9743,plain,
% 1.85/2.06 (b(elem!1, s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[299, 9742, 9739])).
% 1.85/2.06 tff(9744,plain,
% 1.85/2.06 (~r(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3445, 9737, 108, 9738])).
% 1.85/2.06 tff(9745,plain,
% 1.85/2.06 (b(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[444, 9744, 348])).
% 1.85/2.06 tff(9746,plain,
% 1.85/2.06 (~b(s(elem!1), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[456, 9745, 307, 9743])).
% 1.85/2.06 tff(9747,plain,
% 1.85/2.06 (r(s(elem!1), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[429, 9746, 2282])).
% 1.85/2.06 tff(9748,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9749,plain,
% 1.85/2.06 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(9750,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9749])).
% 1.85/2.07 tff(9751,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9750, 9748])).
% 1.85/2.07 tff(9752,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9753,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9752, 9751])).
% 1.85/2.07 tff(9754,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9753, 121, 9738, 9747, 108, 9737])).
% 1.85/2.07 tff(9755,plain,((~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~b(s(elem!1), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(9756,plain,
% 1.85/2.07 (~b(elem!1, s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9755, 106, 2263, 26, 2207, 85, 37, 9707, 67, 9390, 2314, 2315])).
% 1.85/2.07 tff(9757,plain,
% 1.85/2.07 (r(elem!1, s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[392, 9756, 219])).
% 1.85/2.07 tff(9758,plain,
% 1.85/2.07 (~r(s(s(s(z))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[8405, 121, 9757, 9711, 9709])).
% 1.85/2.07 tff(9759,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9760,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9761,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9760, 9759])).
% 1.85/2.07 tff(9762,plain,
% 1.85/2.07 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9761, 121, 9726, 9711, 9724])).
% 1.85/2.07 tff(9763,plain,
% 1.85/2.07 (~b(z, s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9030, 9734, 2314, 9719])).
% 1.85/2.07 tff(9764,plain,
% 1.85/2.07 (~b(s(s(s(z))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9650, 9763, 68, 1, 9762, 71, 33, 2, 38, 9758])).
% 1.85/2.07 tff(9765,plain,
% 1.85/2.07 (r(s(s(s(z))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2325, 9764])).
% 1.85/2.07 tff(9766,plain,
% 1.85/2.07 (r(z, s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[904, 9763])).
% 1.85/2.07 tff(9767,plain,
% 1.85/2.07 (~(elem!1 = s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[3576, 9719, 9756])).
% 1.85/2.07 tff(9768,plain,
% 1.85/2.07 (~(s(z) = elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1221, 9767])).
% 1.85/2.07 tff(9769,plain,
% 1.85/2.07 (~(s(s(z)) = s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[960, 9768])).
% 1.85/2.07 tff(9770,plain,
% 1.85/2.07 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[953, 9769])).
% 1.85/2.07 tff(9771,plain,
% 1.85/2.07 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2063, 2263])).
% 1.85/2.07 tff(9772,plain,
% 1.85/2.07 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2071, 9762, 9771])).
% 1.85/2.07 tff(9773,plain,
% 1.85/2.07 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9771, 6199])).
% 1.85/2.07 tff(9774,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9775,plain,
% 1.85/2.07 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9776,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9775])).
% 1.85/2.07 tff(9777,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9776, 9774])).
% 1.85/2.07 tff(9778,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9779,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9778, 9777])).
% 1.85/2.07 tff(9780,plain,
% 1.85/2.07 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9779, 121, 9726, 9711, 9724])).
% 1.85/2.07 tff(9781,plain,
% 1.85/2.07 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6237, 21, 9780])).
% 1.85/2.07 tff(9782,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9781, 9773])).
% 1.85/2.07 tff(9783,plain,
% 1.85/2.07 (~r(z, s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1508, 9766, 106, 9711])).
% 1.85/2.07 tff(9784,plain,
% 1.85/2.07 (b(z, s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1214, 9783])).
% 1.85/2.07 tff(9785,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9786,plain,
% 1.85/2.07 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9787,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9786])).
% 1.85/2.07 tff(9788,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9787, 9785])).
% 1.85/2.07 tff(9789,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9790,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9789, 9788])).
% 1.85/2.07 tff(9791,plain,
% 1.85/2.07 (~b(s(s(s(elem!1))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9790, 271, 9784, 9782, 9772])).
% 1.85/2.07 tff(9792,plain,
% 1.85/2.07 (r(s(s(s(elem!1))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[8229, 9791])).
% 1.85/2.07 tff(9793,plain,
% 1.85/2.07 (~r(s(z), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6221, 121, 37, 26, 9792])).
% 1.85/2.07 tff(9794,plain,
% 1.85/2.07 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[760, 9793])).
% 1.85/2.07 tff(9795,plain,
% 1.85/2.07 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2464, 9794, 2265, 9770, 9766, 26, 9765, 67])).
% 1.85/2.07 tff(9796,plain,
% 1.85/2.07 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[556, 9795, 1])).
% 1.85/2.07 tff(9797,plain,
% 1.85/2.07 (~r(s(s(elem!1)), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[3132, 9796, 9726, 9724])).
% 1.85/2.07 tff(9798,plain,
% 1.85/2.07 (b(s(s(elem!1)), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[701, 9797, 3313])).
% 1.85/2.07 tff(9799,plain,
% 1.85/2.07 (~b(s(s(elem!1)), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2853, 9798, 2314, 9734])).
% 1.85/2.07 tff(9800,plain,
% 1.85/2.07 (r(s(s(elem!1)), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2430, 9799])).
% 1.85/2.07 tff(9801,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9802,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9803,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9802, 9801])).
% 1.85/2.07 tff(9804,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9803, 121, 9796, 9726, 37, 9800])).
% 1.85/2.07 tff(9805,plain,((s(s(s(z))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(9806,plain,
% 1.85/2.07 (s(s(s(z))) = s(elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9805, 71, 68, 1, 33, 2, 38])).
% 1.85/2.07 tff(9807,plain,
% 1.85/2.07 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9806])).
% 1.85/2.07 tff(9808,plain,
% 1.85/2.07 (s(s(z)) = elem!1),
% 1.85/2.07 inference(transitivity,[status(thm)],[92, 9807, 70])).
% 1.85/2.07 tff(9809,plain,
% 1.85/2.07 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9808])).
% 1.85/2.07 tff(9810,plain,
% 1.85/2.07 ((~r(s(s(z)), z)) <=> (~r(elem!1, z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9809])).
% 1.85/2.07 tff(9811,plain,
% 1.85/2.07 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9808])).
% 1.85/2.07 tff(9812,plain,
% 1.85/2.07 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9811])).
% 1.85/2.07 tff(9813,plain,
% 1.85/2.07 (r(s(z), s(s(z)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9390, 9812])).
% 1.85/2.07 tff(9814,plain,
% 1.85/2.07 (~r(s(s(z)), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[535, 9813, 37, 26])).
% 1.85/2.07 tff(9815,plain,
% 1.85/2.07 (~r(elem!1, z)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9814, 9810])).
% 1.85/2.07 tff(9816,plain,
% 1.85/2.07 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9806])).
% 1.85/2.07 tff(9817,plain,
% 1.85/2.07 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(z))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9816])).
% 1.85/2.07 tff(9818,plain,
% 1.85/2.07 ((elem!1 = s(elem!1)) <=> (s(s(s(z))) = elem!1)),
% 1.85/2.07 inference(transitivity,[status(thm)],[9817, 160])).
% 1.85/2.07 tff(9819,plain,
% 1.85/2.07 ((~(elem!1 = s(elem!1))) <=> (~(s(s(s(z))) = elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9818])).
% 1.85/2.07 tff(9820,plain,
% 1.85/2.07 (~(s(s(s(z))) = elem!1)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[219, 9819])).
% 1.85/2.07 tff(9821,plain,
% 1.85/2.07 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9806])).
% 1.85/2.07 tff(9822,plain,
% 1.85/2.07 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9821])).
% 1.85/2.07 tff(9823,plain,
% 1.85/2.07 (r(elem!1, s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9757, 9822])).
% 1.85/2.07 tff(9824,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9825,plain,
% 1.85/2.07 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9826,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9825])).
% 1.85/2.07 tff(9827,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9826, 9824])).
% 1.85/2.07 tff(9828,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9829,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9828, 9827])).
% 1.85/2.07 tff(9830,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9829, 121, 357, 1184, 145, 108])).
% 1.85/2.07 tff(9831,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(9832,plain,
% 1.85/2.07 (~r(s(s(s(z))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9831, 9823, 106, 9390])).
% 1.85/2.07 tff(9833,plain,
% 1.85/2.07 (b(s(s(s(z))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[255, 9832, 9820])).
% 1.85/2.07 tff(9834,plain,
% 1.85/2.07 (~b(elem!1, z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1947, 9833, 2265, 9707])).
% 1.85/2.07 tff(9835,plain,
% 1.85/2.07 (r(elem!1, z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[284, 9834, 2315])).
% 1.85/2.07 tff(9836,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9835, 9815])).
% 1.85/2.07 tff(9837,plain,(b(s(z), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(9838,plain,
% 1.85/2.07 (b(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9837, 68, 1, 33, 2, 38])).
% 1.85/2.07 tff(9839,plain,
% 1.85/2.07 (s(z) = s(elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2312, 3501, 79, 503, 111, 26])).
% 1.85/2.07 tff(9840,plain,
% 1.85/2.07 (z = elem!1),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[343, 9839])).
% 1.85/2.07 tff(9841,plain,
% 1.85/2.07 (s(z) = s(elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9840])).
% 1.85/2.07 tff(9842,plain,
% 1.85/2.07 (s(s(z)) = s(s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9841])).
% 1.85/2.07 tff(9843,plain,
% 1.85/2.07 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9842])).
% 1.85/2.07 tff(9844,plain,
% 1.85/2.07 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9843])).
% 1.85/2.07 tff(9845,plain,
% 1.85/2.07 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9844])).
% 1.85/2.07 tff(9846,plain,
% 1.85/2.07 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9840])).
% 1.85/2.07 tff(9847,plain,
% 1.85/2.07 (r(elem!1, s(s(s(elem!1))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[111, 9846])).
% 1.85/2.07 tff(9848,plain,
% 1.85/2.07 (r(elem!1, s(s(s(z))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9847, 9845])).
% 1.85/2.07 tff(9849,plain,
% 1.85/2.07 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.85/2.07 inference(commutativity,[status(thm)],[])).
% 1.85/2.07 tff(9850,plain,
% 1.85/2.07 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9842])).
% 1.85/2.07 tff(9851,plain,
% 1.85/2.07 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9850, 9849])).
% 1.85/2.07 tff(9852,plain,
% 1.85/2.07 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9851])).
% 1.85/2.07 tff(9853,plain,
% 1.85/2.07 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1136, 9852])).
% 1.85/2.07 tff(9854,plain,
% 1.85/2.07 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9841])).
% 1.85/2.07 tff(9855,plain,
% 1.85/2.07 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9854])).
% 1.85/2.07 tff(9856,plain,
% 1.85/2.07 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9843])).
% 1.85/2.07 tff(9857,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9856])).
% 1.85/2.07 tff(9858,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9857, 9855])).
% 1.85/2.07 tff(9859,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9841])).
% 1.85/2.07 tff(9860,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[503, 9859])).
% 1.85/2.07 tff(9861,plain,
% 1.85/2.07 (b(s(s(s(z))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9860, 9858])).
% 1.85/2.07 tff(9862,plain,
% 1.85/2.07 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9840])).
% 1.85/2.07 tff(9863,plain,
% 1.85/2.07 (r(s(z), elem!1)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[26, 9862])).
% 1.85/2.07 tff(9864,plain,
% 1.85/2.07 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9840])).
% 1.85/2.07 tff(9865,plain,
% 1.85/2.07 ((~b(s(z), z)) <=> (~b(s(z), elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9864])).
% 1.85/2.07 tff(9866,plain,
% 1.85/2.07 (~b(s(z), elem!1)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[2, 9865])).
% 1.85/2.07 tff(9867,plain,
% 1.85/2.07 (elem!1 = z),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[364, 9840])).
% 1.85/2.07 tff(9868,plain,
% 1.85/2.07 (s(elem!1) = s(z)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[329])).
% 1.85/2.07 tff(9869,plain,
% 1.85/2.07 (s(s(elem!1)) = s(s(z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9868])).
% 1.85/2.07 tff(9870,plain,
% 1.85/2.07 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9869])).
% 1.85/2.07 tff(9871,plain,
% 1.85/2.07 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9870])).
% 1.85/2.07 tff(9872,plain,
% 1.85/2.07 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9871])).
% 1.85/2.07 tff(9873,plain,
% 1.85/2.07 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[3871, 9872])).
% 1.85/2.07 tff(9874,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.85/2.07 tff(9875,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9874, 9873])).
% 1.85/2.07 tff(9876,plain,((~(elem!1 = z)) | b(s(z), s(s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(9877,plain,
% 1.85/2.07 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9876, 9867, 3871])).
% 1.85/2.07 tff(9878,plain,
% 1.85/2.07 (z = elem!1),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[343, 338])).
% 1.85/2.07 tff(9879,plain,
% 1.85/2.07 (s(z) = s(elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9878])).
% 1.85/2.07 tff(9880,plain,
% 1.85/2.07 (s(s(z)) = s(s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9879])).
% 1.85/2.07 tff(9881,plain,
% 1.85/2.07 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9880])).
% 1.85/2.07 tff(9882,plain,
% 1.85/2.07 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9881])).
% 1.85/2.07 tff(9883,plain,
% 1.85/2.07 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9882])).
% 1.85/2.07 tff(9884,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9883])).
% 1.85/2.07 tff(9885,plain,
% 1.85/2.07 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[9881])).
% 1.85/2.07 tff(9886,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9885, 9884])).
% 1.85/2.07 tff(9887,plain,
% 1.85/2.07 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9886])).
% 1.85/2.07 tff(9888,plain,
% 1.85/2.07 (~b(z, s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[327, 317, 9878])).
% 1.85/2.07 tff(9889,plain,
% 1.85/2.07 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[8078, 9888, 219, 3498])).
% 1.85/2.07 tff(9890,plain,
% 1.85/2.07 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[705])).
% 1.85/2.07 tff(9891,plain,
% 1.85/2.07 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9890])).
% 1.85/2.07 tff(9892,assumption,(~b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.85/2.07 tff(9893,plain,
% 1.85/2.07 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9892, 9891])).
% 1.85/2.07 tff(9894,assumption,(b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.85/2.07 tff(9895,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9894, 9893])).
% 1.85/2.07 tff(9896,plain,(b(s(s(s(s(s(elem!1))))), s(elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(9897,plain,
% 1.85/2.07 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9896, 9889, 9878])).
% 1.85/2.07 tff(9898,plain,
% 1.85/2.07 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[754, 750, 9878])).
% 1.85/2.07 tff(9899,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9900,plain,
% 1.85/2.07 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(9901,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9900])).
% 1.85/2.07 tff(9902,plain,
% 1.85/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9901, 9899])).
% 1.85/2.07 tff(9903,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(9904,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9903, 9902])).
% 1.85/2.07 tff(9905,plain,
% 1.85/2.07 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[9904, 271, 9898, 638, 9897])).
% 1.85/2.07 tff(9906,plain,
% 1.85/2.07 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[9905, 9887])).
% 1.85/2.07 tff(9907,plain,
% 1.85/2.07 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1494, 9906])).
% 1.85/2.07 tff(9908,plain,
% 1.85/2.07 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7296, 9907, 9878])).
% 1.85/2.07 tff(9909,plain,
% 1.85/2.07 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[9878])).
% 1.85/2.07 tff(9910,plain,
% 1.85/2.07 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[9909, 1837])).
% 1.85/2.07 tff(9911,plain,
% 1.85/2.07 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9910])).
% 1.85/2.08 tff(9912,plain,
% 1.85/2.08 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[711, 9911])).
% 1.85/2.08 tff(9913,plain,
% 1.85/2.08 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9884])).
% 1.85/2.08 tff(9914,plain,
% 1.85/2.08 ((~r(elem!1, s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9913])).
% 1.85/2.08 tff(9915,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9881])).
% 1.85/2.08 tff(9916,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9915])).
% 1.85/2.08 tff(9917,plain,
% 1.85/2.08 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9884])).
% 1.85/2.08 tff(9918,plain,
% 1.85/2.08 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[9917, 9916])).
% 1.85/2.08 tff(9919,plain,
% 1.85/2.08 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9918])).
% 1.85/2.08 tff(9920,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(9921,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(9922,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9921, 9920])).
% 1.85/2.08 tff(9923,plain,
% 1.85/2.08 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9922, 271, 9898, 638, 9897])).
% 1.85/2.08 tff(9924,plain,
% 1.85/2.08 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9923, 9919])).
% 1.85/2.08 tff(9925,plain,
% 1.85/2.08 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1733, 9924])).
% 1.85/2.08 tff(9926,plain,
% 1.85/2.08 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6039, 9925, 9878])).
% 1.85/2.08 tff(9927,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(9928,plain,
% 1.85/2.08 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(9929,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9928])).
% 1.85/2.08 tff(9930,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[9929, 9927])).
% 1.85/2.08 tff(9931,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(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(s(elem!1))))))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(9932,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9931, 9930])).
% 1.85/2.08 tff(9933,plain,
% 1.85/2.08 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9932, 121, 727, 9908, 9926])).
% 1.85/2.08 tff(9934,plain,
% 1.85/2.08 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9933, 9914])).
% 1.85/2.08 tff(9935,plain,
% 1.85/2.08 (b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1847, 9934, 9912])).
% 1.85/2.08 tff(9936,plain,
% 1.85/2.08 (s(s(z)) = s(s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[338])).
% 1.85/2.08 tff(9937,plain,
% 1.85/2.08 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9936])).
% 1.85/2.08 tff(9938,plain,
% 1.85/2.08 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9937])).
% 1.85/2.08 tff(9939,plain,
% 1.85/2.08 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9938])).
% 1.85/2.08 tff(9940,plain,
% 1.85/2.08 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9939])).
% 1.85/2.08 tff(9941,plain,
% 1.85/2.08 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9940])).
% 1.85/2.08 tff(9942,plain,
% 1.85/2.08 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9941])).
% 1.85/2.08 tff(9943,plain,
% 1.85/2.08 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[1849, 9942])).
% 1.85/2.08 tff(9944,assumption,(~b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.85/2.08 tff(9945,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9944, 9943])).
% 1.85/2.08 tff(9946,plain,((~b(elem!1, s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(9947,plain,
% 1.85/2.08 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9946, 9935, 338])).
% 1.85/2.08 tff(9948,plain,
% 1.85/2.08 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9909])).
% 1.85/2.08 tff(9949,plain,
% 1.85/2.08 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[711, 9948])).
% 1.85/2.08 tff(9950,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(9951,plain,
% 1.85/2.08 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(9952,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9951])).
% 1.85/2.08 tff(9953,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[9952, 9950])).
% 1.85/2.08 tff(9954,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(9955,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9954, 9953])).
% 1.85/2.08 tff(9956,plain,
% 1.85/2.08 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9955, 121, 727, 9908, 9926])).
% 1.85/2.08 tff(9957,plain,
% 1.85/2.08 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9940])).
% 1.85/2.08 tff(9958,plain,
% 1.85/2.08 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.85/2.08 inference(symmetry,[status(thm)],[9957])).
% 1.85/2.08 tff(9959,plain,
% 1.85/2.08 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[3061, 9958])).
% 1.85/2.08 tff(9960,assumption,(~r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.85/2.08 tff(9961,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9960, 9959])).
% 1.85/2.08 tff(9962,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(elem!1))))), elem!1) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(9963,plain,
% 1.85/2.08 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9962, 9956, 338])).
% 1.85/2.08 tff(9964,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[840, 9963, 9949])).
% 1.85/2.08 tff(9965,plain,
% 1.85/2.08 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[835, 9964, 9878])).
% 1.85/2.08 tff(9966,plain,
% 1.85/2.08 (r(z, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[904, 9888])).
% 1.85/2.08 tff(9967,plain,
% 1.85/2.08 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9878])).
% 1.85/2.08 tff(9968,plain,
% 1.85/2.08 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 1.85/2.08 inference(symmetry,[status(thm)],[9967])).
% 1.85/2.08 tff(9969,plain,
% 1.85/2.08 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9968])).
% 1.85/2.08 tff(9970,plain,
% 1.85/2.08 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(9971,plain,
% 1.85/2.08 (~r(elem!1, elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[9970, 177])).
% 1.85/2.08 tff(9972,plain,
% 1.85/2.08 (~r(z, elem!1)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9971, 9969])).
% 1.85/2.08 tff(9973,plain,
% 1.85/2.08 (b(s(z), s(elem!1)) <=> b(s(elem!1), s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9879])).
% 1.85/2.08 tff(9974,plain,
% 1.85/2.08 (b(s(elem!1), s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9973])).
% 1.85/2.08 tff(9975,plain,
% 1.85/2.08 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(z), s(elem!1)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9974])).
% 1.85/2.08 tff(9976,plain,
% 1.85/2.08 (~b(s(z), s(elem!1))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[5770, 9975])).
% 1.85/2.08 tff(9977,plain,
% 1.85/2.08 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9881])).
% 1.85/2.08 tff(9978,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9977])).
% 1.85/2.08 tff(9979,plain,
% 1.85/2.08 (b(s(s(s(z))), s(elem!1))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[638, 9978])).
% 1.85/2.08 tff(9980,plain,
% 1.85/2.08 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9878])).
% 1.85/2.08 tff(9981,plain,
% 1.85/2.08 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9980])).
% 1.85/2.08 tff(9982,plain,
% 1.85/2.08 (~(s(z) = elem!1)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[11, 9981])).
% 1.85/2.08 tff(9983,plain,
% 1.85/2.08 (r(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[392, 317, 219])).
% 1.85/2.08 tff(9984,plain,
% 1.85/2.08 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9878])).
% 1.85/2.08 tff(9985,plain,
% 1.85/2.08 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9984])).
% 1.85/2.08 tff(9986,plain,
% 1.85/2.08 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[9913, 9985])).
% 1.85/2.08 tff(9987,plain,
% 1.85/2.08 ((~r(elem!1, s(s(s(s(s(elem!1))))))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9986])).
% 1.85/2.08 tff(9988,plain,
% 1.85/2.08 (~r(z, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[9933, 9987])).
% 1.85/2.08 tff(9989,plain,
% 1.85/2.08 (b(z, s(s(s(s(s(z))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1658, 9988])).
% 1.85/2.08 tff(9990,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6121, 9989, 68, 3501, 9983, 9982, 9979, 9966, 9976, 2207, 317, 9972, 1242])).
% 1.85/2.08 tff(9991,plain,
% 1.85/2.08 (~b(z, s(s(elem!1)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7544, 9990, 110, 9966, 9965, 750, 1, 9947, 9878])).
% 1.85/2.08 tff(9992,plain,
% 1.85/2.08 (~b(elem!1, s(s(elem!1)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7550, 9991, 9878])).
% 1.85/2.08 tff(9993,plain,
% 1.85/2.08 (r(elem!1, s(s(elem!1)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[599, 9992, 68])).
% 1.85/2.08 tff(9994,plain,
% 1.85/2.08 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.85/2.08 inference(transitivity,[status(thm)],[9980, 1218])).
% 1.85/2.08 tff(9995,plain,
% 1.85/2.08 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9994])).
% 1.85/2.08 tff(9996,plain,
% 1.85/2.08 (~(elem!1 = s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[11, 9995])).
% 1.85/2.08 tff(9997,plain,
% 1.85/2.08 (b(s(elem!1), s(z)) <=> b(s(elem!1), s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9879])).
% 1.85/2.08 tff(9998,plain,
% 1.85/2.08 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[9997])).
% 1.85/2.08 tff(9999,plain,
% 1.85/2.08 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), s(z)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9998])).
% 1.85/2.08 tff(10000,plain,
% 1.85/2.08 (~b(s(elem!1), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[5770, 9999])).
% 1.85/2.08 tff(10001,plain,
% 1.85/2.08 (r(s(elem!1), s(z)) <=> r(s(elem!1), s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[9879])).
% 1.85/2.08 tff(10002,plain,
% 1.85/2.08 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[10001])).
% 1.85/2.08 tff(10003,plain,
% 1.85/2.08 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), s(z)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[10002])).
% 1.85/2.08 tff(10004,plain,
% 1.85/2.08 ((~![X: $i] : (~r(X, X))) | (~r(s(elem!1), s(elem!1)))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(10005,plain,
% 1.85/2.08 (~r(s(elem!1), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[10004, 177])).
% 1.85/2.08 tff(10006,plain,
% 1.85/2.08 (~r(s(elem!1), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10005, 10003])).
% 1.85/2.08 tff(10007,plain,
% 1.85/2.08 (s(elem!1) = s(z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[429, 10006, 10000])).
% 1.85/2.08 tff(10008,plain,
% 1.85/2.08 (~b(elem!1, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3660, 317, 10007])).
% 1.85/2.08 tff(10009,plain,
% 1.85/2.08 (r(elem!1, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[299, 10008, 9996])).
% 1.85/2.08 tff(10010,plain,
% 1.85/2.08 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5852, 9993, 750, 10009, 638])).
% 1.85/2.08 tff(10011,plain,
% 1.85/2.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[556, 10010, 1])).
% 1.85/2.08 tff(10012,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(10013,plain,
% 1.85/2.08 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(10014,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[10013])).
% 1.85/2.08 tff(10015,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[10014, 10012])).
% 1.85/2.08 tff(10016,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(10017,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10016, 10015])).
% 1.85/2.08 tff(10018,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[10017, 121, 10011, 9993, 727, 9908])).
% 1.85/2.08 tff(10019,plain,(b(elem!1, s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(z), z)) | b(s(z), elem!1) | (~(s(z) = s(elem!1))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(10020,plain,
% 1.85/2.08 (b(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[10019, 9847, 1, 9877, 9860, 68, 26, 9866, 9839, 3498])).
% 1.85/2.08 tff(10021,plain,
% 1.85/2.08 (b(z, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1543, 10020, 9840])).
% 1.85/2.08 tff(10022,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[133])).
% 1.85/2.08 tff(10023,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[10022])).
% 1.85/2.08 tff(10024,plain,
% 1.85/2.08 (~r(s(s(s(z))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[475, 107, 221])).
% 1.85/2.08 tff(10025,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[490, 10024, 107])).
% 1.85/2.08 tff(10026,plain,
% 1.85/2.08 (s(s(z)) = s(s(elem!1))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[1536])).
% 1.85/2.08 tff(10027,plain,
% 1.85/2.08 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[10026])).
% 1.85/2.08 tff(10028,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[10027])).
% 1.85/2.08 tff(10029,plain,
% 1.85/2.08 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[1536])).
% 1.85/2.08 tff(10030,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[3871, 10029])).
% 1.85/2.08 tff(10031,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10030, 10028])).
% 1.85/2.08 tff(10032,plain,
% 1.85/2.08 (b(s(elem!1), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2488, 107, 394])).
% 1.85/2.08 tff(10033,plain,
% 1.85/2.08 (b(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[327, 107, 220])).
% 1.85/2.08 tff(10034,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2930, 271, 10033, 10032, 10031, 10025])).
% 1.85/2.08 tff(10035,plain,((~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | r(s(s(s(z))), elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(10036,plain,
% 1.85/2.08 (~b(s(elem!1), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[10035, 107, 3871, 221, 220])).
% 1.85/2.08 tff(10037,plain,
% 1.85/2.08 (~b(s(elem!1), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7069, 10036, 107])).
% 1.85/2.08 tff(10038,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[490, 107, 10024])).
% 1.85/2.08 tff(10039,plain,
% 1.85/2.08 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7281, 10038, 10037])).
% 1.85/2.08 tff(10040,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[135])).
% 1.85/2.08 tff(10041,plain,
% 1.85/2.08 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[133])).
% 1.85/2.08 tff(10042,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[3871, 10041])).
% 1.85/2.08 tff(10043,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10042, 10040])).
% 1.85/2.08 tff(10044,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7712, 271, 307, 739, 638, 504])).
% 1.85/2.08 tff(10045,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(10046,plain,
% 1.85/2.08 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[10045, 10033, 10043, 10038])).
% 1.85/2.08 tff(10047,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[681, 10046, 10039])).
% 1.85/2.08 tff(10048,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10047, 10023])).
% 1.85/2.08 tff(10049,plain,
% 1.85/2.08 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[107])).
% 1.85/2.08 tff(10050,plain,
% 1.85/2.08 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.85/2.08 inference(symmetry,[status(thm)],[10049])).
% 1.85/2.08 tff(10051,plain,
% 1.85/2.08 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.85/2.08 inference(symmetry,[status(thm)],[1686])).
% 1.85/2.08 tff(10052,plain,
% 1.85/2.08 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.85/2.08 inference(transitivity,[status(thm)],[10051, 10050])).
% 1.85/2.08 tff(10053,plain,
% 1.85/2.08 (r(s(elem!1), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2243, 10037, 2564])).
% 1.85/2.08 tff(10054,plain,
% 1.85/2.08 (r(s(z), z)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10053, 10052])).
% 1.85/2.08 tff(10055,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[134])).
% 1.85/2.08 tff(10056,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.85/2.08 inference(symmetry,[status(thm)],[10055])).
% 1.85/2.08 tff(10057,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[749])).
% 1.85/2.08 tff(10058,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[10040, 10057])).
% 1.85/2.08 tff(10059,plain,
% 1.85/2.08 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[10042, 10058])).
% 1.85/2.08 tff(10060,plain,
% 1.85/2.08 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[107])).
% 1.85/2.08 tff(10061,plain,
% 1.85/2.08 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.85/2.08 inference(symmetry,[status(thm)],[10060])).
% 1.85/2.08 tff(10062,plain,
% 1.85/2.08 (r(z, s(s(elem!1)))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[624, 10061])).
% 1.85/2.08 tff(10063,plain,
% 1.85/2.08 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7490, 82])).
% 1.85/2.08 tff(10064,plain,
% 1.85/2.08 (~(s(s(elem!1)) = elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[197, 10063])).
% 1.85/2.08 tff(10065,plain,
% 1.85/2.08 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[890, 624, 107, 307, 82, 622, 10064])).
% 1.85/2.08 tff(10066,plain,
% 1.85/2.08 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[556, 10065, 615])).
% 1.85/2.08 tff(10067,plain,
% 1.85/2.08 (~b(s(s(elem!1)), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[989, 10066, 504, 750])).
% 1.85/2.08 tff(10068,plain,
% 1.85/2.08 (r(s(s(elem!1)), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2143, 10067])).
% 1.85/2.08 tff(10069,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(10070,plain,
% 1.85/2.08 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(10071,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[10070])).
% 1.85/2.08 tff(10072,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.08 inference(transitivity,[status(thm)],[10071, 10069])).
% 1.85/2.08 tff(10073,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(10074,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10073, 10072])).
% 1.85/2.09 tff(10075,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10074, 271, 543, 517, 739, 504])).
% 1.85/2.09 tff(10076,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10077,plain,
% 1.85/2.09 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10076, 10066, 504, 739])).
% 1.85/2.09 tff(10078,plain,
% 1.85/2.09 (r(s(elem!1), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[526, 10077, 616])).
% 1.85/2.09 tff(10079,plain,
% 1.85/2.09 (~r(z, s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5431, 10078, 412, 10068])).
% 1.85/2.09 tff(10080,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10079, 10062])).
% 1.85/2.09 tff(10081,plain,((~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10082,plain,
% 1.85/2.09 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10081, 107, 412, 10038, 10059, 10043, 10033, 10039, 10053])).
% 1.85/2.09 tff(10083,plain,
% 1.85/2.09 (~(elem!1 = s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[7490, 10039])).
% 1.85/2.09 tff(10084,plain,
% 1.85/2.09 (~(s(s(elem!1)) = elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[197, 10083])).
% 1.85/2.09 tff(10085,plain,
% 1.85/2.09 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[135])).
% 1.85/2.09 tff(10086,plain,
% 1.85/2.09 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[162])).
% 1.85/2.09 tff(10087,plain,
% 1.85/2.09 (~(elem!1 = s(s(s(z))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[166, 10086])).
% 1.85/2.09 tff(10088,plain,
% 1.85/2.09 (~b(elem!1, s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[747, 10043, 10038, 10033])).
% 1.85/2.09 tff(10089,plain,
% 1.85/2.09 (~b(elem!1, s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1198, 10088, 107])).
% 1.85/2.09 tff(10090,plain,
% 1.85/2.09 (r(elem!1, s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1192, 10089, 10087])).
% 1.85/2.09 tff(10091,plain,
% 1.85/2.09 (r(elem!1, s(s(s(elem!1))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10090, 10085])).
% 1.85/2.09 tff(10092,plain,
% 1.85/2.09 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[614, 10039])).
% 1.85/2.09 tff(10093,plain,
% 1.85/2.09 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.85/2.09 inference(symmetry,[status(thm)],[1584])).
% 1.85/2.09 tff(10094,plain,
% 1.85/2.09 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10085, 10093])).
% 1.85/2.09 tff(10095,plain,
% 1.85/2.09 (r(z, s(s(s(elem!1))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10090, 10094])).
% 1.85/2.09 tff(10096,plain,
% 1.85/2.09 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[134])).
% 1.85/2.09 tff(10097,plain,
% 1.85/2.09 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[107])).
% 1.85/2.09 tff(10098,plain,
% 1.85/2.09 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(transitivity,[status(thm)],[10097, 10096])).
% 1.85/2.09 tff(10099,plain,
% 1.85/2.09 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10098])).
% 1.85/2.09 tff(10100,plain,
% 1.85/2.09 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[133, 134])).
% 1.85/2.09 tff(10101,plain,
% 1.85/2.09 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.85/2.09 inference(symmetry,[status(thm)],[10100])).
% 1.85/2.09 tff(10102,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4712, 121, 623, 684, 727, 1624])).
% 1.85/2.09 tff(10103,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10104,plain,
% 1.85/2.09 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10103, 1624, 727, 684])).
% 1.85/2.09 tff(10105,plain,
% 1.85/2.09 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[556, 10104, 1])).
% 1.85/2.09 tff(10106,plain,
% 1.85/2.09 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10076, 10105, 504, 739])).
% 1.85/2.09 tff(10107,plain,
% 1.85/2.09 (r(s(elem!1), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[526, 10106, 211])).
% 1.85/2.09 tff(10108,plain,
% 1.85/2.09 (r(s(z), s(s(z)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10107, 10101])).
% 1.85/2.09 tff(10109,plain,
% 1.85/2.09 (~r(s(s(z)), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[535, 10108, 111, 110])).
% 1.85/2.09 tff(10110,plain,
% 1.85/2.09 (~r(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10109, 10099])).
% 1.85/2.09 tff(10111,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1624, 10110])).
% 1.85/2.09 tff(10112,plain,((~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10113,plain,
% 1.85/2.09 (~r(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10112, 107, 10095, 10054, 10038, 10043, 10092, 10091, 10047])).
% 1.85/2.09 tff(10114,plain,
% 1.85/2.09 (b(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[862, 10113, 10084])).
% 1.85/2.09 tff(10115,plain,
% 1.85/2.09 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[551, 10114, 10033, 10038])).
% 1.85/2.09 tff(10116,plain,
% 1.85/2.09 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4488, 10115, 10046, 626, 10037, 10082])).
% 1.85/2.09 tff(10117,plain,
% 1.85/2.09 (r(s(s(s(elem!1))), s(s(z)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10116, 10056])).
% 1.85/2.09 tff(10118,plain,
% 1.85/2.09 (~r(s(s(z)), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4675, 10117, 10054, 10048])).
% 1.85/2.09 tff(10119,plain,
% 1.85/2.09 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[107])).
% 1.85/2.09 tff(10120,plain,
% 1.85/2.09 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10119])).
% 1.85/2.09 tff(10121,plain,
% 1.85/2.09 (~(s(s(z)) = elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[95, 10120])).
% 1.85/2.09 tff(10122,plain,
% 1.85/2.09 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.85/2.09 inference(symmetry,[status(thm)],[10096])).
% 1.85/2.09 tff(10123,plain,
% 1.85/2.09 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(z)), elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10122])).
% 1.85/2.09 tff(10124,plain,
% 1.85/2.09 (~r(s(s(z)), elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10113, 10123])).
% 1.85/2.09 tff(10125,plain,
% 1.85/2.09 (b(s(s(z)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3613, 10124, 10121])).
% 1.85/2.09 tff(10126,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10127,plain,
% 1.85/2.09 (((~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(z)), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10128,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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(z)), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10127])).
% 1.85/2.09 tff(10129,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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(z)), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10128, 10126])).
% 1.85/2.09 tff(10130,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(10131,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10130, 10129])).
% 1.85/2.09 tff(10132,plain,
% 1.85/2.09 ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10131, 271])).
% 1.85/2.09 tff(10133,plain,
% 1.85/2.09 (~b(s(s(z)), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10132, 10125, 3871, 325])).
% 1.85/2.09 tff(10134,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4670, 10133, 10118])).
% 1.85/2.09 tff(10135,plain,((~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | r(s(s(s(z))), elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10136,plain,
% 1.85/2.09 (r(s(s(s(z))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10135, 10021, 3871, 2207, 3501, 9840])).
% 1.85/2.09 tff(10137,plain,
% 1.85/2.09 (~r(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5239, 10136, 9863, 9861, 9853, 9848])).
% 1.85/2.09 tff(10138,plain,
% 1.85/2.09 (b(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[862, 10137, 198])).
% 1.85/2.09 tff(10139,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.85/2.09 tff(10140,plain,
% 1.85/2.09 (s(s(s(s(elem!1)))) = z),
% 1.85/2.09 inference(transitivity,[status(thm)],[10139, 804])).
% 1.85/2.09 tff(10141,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[812, 10140])).
% 1.85/2.09 tff(10142,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10143,plain,
% 1.85/2.09 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10142, 9840])).
% 1.85/2.09 tff(10144,plain,
% 1.85/2.09 (~b(s(elem!1), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[7069, 9840, 3498])).
% 1.85/2.09 tff(10145,plain,
% 1.85/2.09 (r(s(elem!1), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2243, 10144, 2207])).
% 1.85/2.09 tff(10146,plain,
% 1.85/2.09 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.85/2.09 inference(symmetry,[status(thm)],[1927])).
% 1.85/2.09 tff(10147,plain,
% 1.85/2.09 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[9841])).
% 1.85/2.09 tff(10148,plain,
% 1.85/2.09 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10147, 1927])).
% 1.85/2.09 tff(10149,plain,
% 1.85/2.09 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10148, 10146])).
% 1.85/2.09 tff(10150,plain,
% 1.85/2.09 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10149])).
% 1.85/2.09 tff(10151,plain,
% 1.85/2.09 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[927, 10150])).
% 1.85/2.09 tff(10152,plain,
% 1.85/2.09 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[754, 9877, 9840])).
% 1.85/2.09 tff(10153,plain,
% 1.85/2.09 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[9840])).
% 1.85/2.09 tff(10154,plain,
% 1.85/2.09 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10153])).
% 1.85/2.09 tff(10155,plain,
% 1.85/2.09 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[30, 10154])).
% 1.85/2.09 tff(10156,plain,
% 1.85/2.09 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10045, 10020, 10152, 9860])).
% 1.85/2.09 tff(10157,plain,
% 1.85/2.09 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[486, 10156, 10155])).
% 1.85/2.09 tff(10158,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5891, 271, 739, 638, 1586])).
% 1.85/2.09 tff(10159,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8221, 10158, 1591])).
% 1.85/2.09 tff(10160,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.85/2.09 tff(10161,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10162,plain,
% 1.85/2.09 (((~b(s(elem!1), s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10163,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10162])).
% 1.85/2.09 tff(10164,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10163, 10161])).
% 1.85/2.09 tff(10165,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(10166,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10165, 10164])).
% 1.85/2.09 tff(10167,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10166, 271, 307, 739, 1586])).
% 1.85/2.09 tff(10168,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5877, 21, 10167, 10160])).
% 1.85/2.09 tff(10169,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10170,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(10171,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10170, 10169])).
% 1.85/2.09 tff(10172,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10171, 121, 139, 727, 10168, 10159])).
% 1.85/2.09 tff(10173,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(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(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10174,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10173, 10157, 9847, 10143, 1577, 10152, 9860, 10020])).
% 1.85/2.09 tff(10175,plain,
% 1.85/2.09 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1566, 10174, 9840])).
% 1.85/2.09 tff(10176,plain,
% 1.85/2.09 (r(s(s(s(s(z)))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1559, 10175, 10151])).
% 1.85/2.09 tff(10177,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[1578])).
% 1.85/2.09 tff(10178,plain,
% 1.85/2.09 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.09 inference(symmetry,[status(thm)],[10177])).
% 1.85/2.09 tff(10179,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[1551, 10178])).
% 1.85/2.09 tff(10180,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.85/2.09 tff(10181,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10180, 10179])).
% 1.85/2.09 tff(10182,plain,((~r(s(s(s(s(z)))), s(elem!1))) | r(s(s(s(s(elem!1)))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10183,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10182, 10176, 9840])).
% 1.85/2.09 tff(10184,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.85/2.09 tff(10185,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10186,plain,
% 1.85/2.09 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10187,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10186])).
% 1.85/2.09 tff(10188,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10187, 10185])).
% 1.85/2.09 tff(10189,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(10190,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10189, 10188])).
% 1.85/2.09 tff(10191,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10190, 121, 622, 727, 10184, 6898])).
% 1.85/2.09 tff(10192,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10193,plain,
% 1.85/2.09 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10192, 10183, 9847, 10145])).
% 1.85/2.09 tff(10194,assumption,(~r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.85/2.09 tff(10195,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5877, 21, 5869, 10194, 10160])).
% 1.85/2.09 tff(10196,plain,(b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10197,plain,
% 1.85/2.09 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10196, 10193, 10143])).
% 1.85/2.09 tff(10198,assumption,(~r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.85/2.09 tff(10199,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10200,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(10201,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10200, 10199])).
% 1.85/2.09 tff(10202,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10201, 271, 307, 5606, 542])).
% 1.85/2.09 tff(10203,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 10202, 10198])).
% 1.85/2.09 tff(10204,plain,(r(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10205,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10204, 10020, 5834, 10197, 10138])).
% 1.85/2.09 tff(10206,plain,
% 1.85/2.09 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[9842, 9841])).
% 1.85/2.09 tff(10207,plain,
% 1.85/2.09 ((~b(s(s(z)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10206])).
% 1.85/2.09 tff(10208,plain,
% 1.85/2.09 (b(elem!1, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[324, 10021, 9840])).
% 1.85/2.09 tff(10209,plain,
% 1.85/2.09 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[9842])).
% 1.85/2.09 tff(10210,plain,
% 1.85/2.09 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.85/2.09 inference(symmetry,[status(thm)],[10209])).
% 1.85/2.09 tff(10211,plain,
% 1.85/2.09 (b(s(s(z)), elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10138, 10210])).
% 1.85/2.09 tff(10212,plain,
% 1.85/2.09 (~b(s(s(z)), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10132, 10211, 3871, 10208])).
% 1.85/2.09 tff(10213,plain,
% 1.85/2.09 (~b(s(s(elem!1)), s(elem!1))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10212, 10207])).
% 1.85/2.09 tff(10214,plain,
% 1.85/2.09 (r(s(s(elem!1)), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[699, 21, 10213, 3313])).
% 1.85/2.09 tff(10215,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[7893, 121, 10145, 10214, 10183, 10205])).
% 1.85/2.09 tff(10216,plain,(b(s(elem!1), z) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10217,plain,
% 1.85/2.09 (b(s(elem!1), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10216, 9838, 1, 68, 67, 2, 37])).
% 1.85/2.09 tff(10218,plain,
% 1.85/2.09 (~(s(z) = s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[9144, 10217, 2])).
% 1.85/2.09 tff(10219,plain,
% 1.85/2.09 (r(z, elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[355, 199, 9297])).
% 1.85/2.09 tff(10220,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10221,plain,
% 1.85/2.09 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(10222,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[10221])).
% 1.85/2.09 tff(10223,plain,
% 1.85/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.85/2.09 inference(transitivity,[status(thm)],[10222, 10220])).
% 1.85/2.09 tff(10224,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(10225,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[10224, 10223])).
% 1.85/2.09 tff(10226,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10225, 121, 379, 378, 111, 139])).
% 1.85/2.09 tff(10227,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(10228,plain,
% 1.85/2.09 (~r(s(s(s(elem!1))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[10227, 378, 379, 111])).
% 1.85/2.09 tff(10229,plain,
% 1.85/2.09 (~r(s(z), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[387, 378, 110, 379])).
% 1.85/2.09 tff(10230,plain,
% 1.85/2.09 (b(s(z), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[236, 1257, 10229])).
% 1.85/2.09 tff(10231,plain,
% 1.85/2.09 (~r(z, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4202, 3456, 110, 378])).
% 1.85/2.09 tff(10232,plain,
% 1.85/2.09 (b(z, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[904, 10231])).
% 1.85/2.09 tff(10233,plain,
% 1.85/2.09 (~r(s(elem!1), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8953, 3456, 110, 379])).
% 1.85/2.09 tff(10234,plain,
% 1.85/2.09 (b(s(elem!1), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[429, 10233, 422])).
% 1.85/2.10 tff(10235,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8926, 10234, 10232, 394, 260])).
% 1.85/2.10 tff(10236,plain,((~r(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10237,plain,
% 1.85/2.10 (~r(elem!1, s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10236, 10230, 394, 2282, 110, 379, 378])).
% 1.85/2.10 tff(10238,plain,
% 1.85/2.10 (b(elem!1, s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[299, 10237, 258])).
% 1.85/2.10 tff(10239,plain,
% 1.85/2.10 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8132, 448, 503, 260])).
% 1.85/2.10 tff(10240,plain,
% 1.85/2.10 (s(s(s(elem!1))) = elem!1),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[486, 10239, 147])).
% 1.85/2.10 tff(10241,plain,
% 1.85/2.10 (~(s(s(s(z))) = elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2611, 10240])).
% 1.85/2.10 tff(10242,plain,
% 1.85/2.10 (b(s(s(s(z))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[255, 10241, 221])).
% 1.85/2.10 tff(10243,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10244,plain,
% 1.85/2.10 (((~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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10245,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10244])).
% 1.85/2.10 tff(10246,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10245, 10243])).
% 1.85/2.10 tff(10247,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10248,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10247, 10246])).
% 1.85/2.10 tff(10249,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10248, 271, 260, 448, 3871, 10242])).
% 1.85/2.10 tff(10250,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10251,plain,
% 1.85/2.10 (r(s(s(s(z))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10250, 10238, 3871, 10230, 10228, 503])).
% 1.85/2.10 tff(10252,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10253,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10254,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10253, 10252])).
% 1.85/2.10 tff(10255,plain,
% 1.85/2.10 (~r(s(s(s(z))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10254, 121, 379, 378, 10251])).
% 1.85/2.10 tff(10256,plain,
% 1.85/2.10 (b(s(s(s(z))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1155, 10255])).
% 1.85/2.10 tff(10257,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10258,plain,
% 1.85/2.10 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10259,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10258])).
% 1.85/2.10 tff(10260,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10259, 10257])).
% 1.85/2.10 tff(10261,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10262,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10261, 10260])).
% 1.85/2.10 tff(10263,plain,
% 1.85/2.10 (~r(z, s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10262, 121, 379, 378, 10251])).
% 1.85/2.10 tff(10264,plain,
% 1.85/2.10 (b(z, s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1214, 10263])).
% 1.85/2.10 tff(10265,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10266,plain,
% 1.85/2.10 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10267,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10266])).
% 1.85/2.10 tff(10268,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10267, 10265])).
% 1.85/2.10 tff(10269,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10270,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10269, 10268])).
% 1.85/2.10 tff(10271,plain,
% 1.85/2.10 (~b(z, s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10270, 271, 10264, 3871, 10256])).
% 1.85/2.10 tff(10272,plain,
% 1.85/2.10 (r(z, s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[904, 10271])).
% 1.85/2.10 tff(10273,plain,
% 1.85/2.10 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8279, 10264, 10256, 394])).
% 1.85/2.10 tff(10274,plain,
% 1.85/2.10 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8132, 10238, 503, 10230])).
% 1.85/2.10 tff(10275,plain,
% 1.85/2.10 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2354, 271, 394, 10264, 10256])).
% 1.85/2.10 tff(10276,plain,
% 1.85/2.10 (~r(s(elem!1), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8386, 10275, 378, 379, 111, 10274, 10251, 10273])).
% 1.85/2.10 tff(10277,plain,
% 1.85/2.10 (b(s(elem!1), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2243, 10276, 2564])).
% 1.85/2.10 tff(10278,plain,
% 1.85/2.10 (~r(elem!1, s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[4202, 909, 110, 378])).
% 1.85/2.10 tff(10279,plain,
% 1.85/2.10 (b(elem!1, s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[299, 258, 10278])).
% 1.85/2.10 tff(10280,plain,
% 1.85/2.10 (~b(s(elem!1), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3691, 271, 2618, 10230, 10279])).
% 1.85/2.10 tff(10281,plain,
% 1.85/2.10 (r(s(elem!1), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[429, 10280, 2282])).
% 1.85/2.10 tff(10282,plain,
% 1.85/2.10 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8132, 10230, 503, 10279])).
% 1.85/2.10 tff(10283,plain,
% 1.85/2.10 (s(s(s(elem!1))) = elem!1),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[486, 10282, 147])).
% 1.85/2.10 tff(10284,plain,
% 1.85/2.10 (~(s(s(s(z))) = s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2596, 10283])).
% 1.85/2.10 tff(10285,plain,
% 1.85/2.10 (~b(s(z), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3696, 271, 2618, 10230, 10279])).
% 1.85/2.10 tff(10286,plain,
% 1.85/2.10 (r(s(z), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[444, 10285, 348])).
% 1.85/2.10 tff(10287,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10288,plain,
% 1.85/2.10 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10289,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10288])).
% 1.85/2.10 tff(10290,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10289, 10287])).
% 1.85/2.10 tff(10291,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10292,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10291, 10290])).
% 1.85/2.10 tff(10293,plain,
% 1.85/2.10 (~r(z, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10292, 121, 909, 10286, 10281])).
% 1.85/2.10 tff(10294,plain,
% 1.85/2.10 (b(z, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1439, 10293])).
% 1.85/2.10 tff(10295,plain,
% 1.85/2.10 (b(s(s(s(z))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[255, 221, 2612])).
% 1.85/2.10 tff(10296,plain,
% 1.85/2.10 (b(s(s(s(z))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[255, 2612, 221])).
% 1.85/2.10 tff(10297,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.85/2.10 tff(10298,plain,
% 1.85/2.10 (b(elem!1, s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1192, 5676, 10297])).
% 1.85/2.10 tff(10299,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10300,plain,
% 1.85/2.10 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10301,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10300])).
% 1.85/2.10 tff(10302,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10301, 10299])).
% 1.85/2.10 tff(10303,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10304,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10303, 10302])).
% 1.85/2.10 tff(10305,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10304, 271, 260, 10298, 3871, 10296])).
% 1.85/2.10 tff(10306,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10307,plain,
% 1.85/2.10 (r(elem!1, s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10306, 221, 3871, 2505, 2065, 260])).
% 1.85/2.10 tff(10308,plain,
% 1.85/2.10 (~b(s(s(s(z))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[305, 10295, 259, 260, 111, 110, 258])).
% 1.85/2.10 tff(10309,plain,
% 1.85/2.10 (r(s(s(s(z))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2325, 10308])).
% 1.85/2.10 tff(10310,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10311,plain,
% 1.85/2.10 (((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10312,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10311])).
% 1.85/2.10 tff(10313,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10312, 10310])).
% 1.85/2.10 tff(10314,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10315,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10314, 10313])).
% 1.85/2.10 tff(10316,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10315, 121, 909, 431, 109, 2327])).
% 1.85/2.10 tff(10317,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10318,plain,
% 1.85/2.10 (~r(s(s(s(z))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10317, 10309, 909, 431])).
% 1.85/2.10 tff(10319,plain,
% 1.85/2.10 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1427, 10318, 394, 1421])).
% 1.85/2.10 tff(10320,plain,
% 1.85/2.10 (b(s(elem!1), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[9295, 10319, 2597, 10307, 379])).
% 1.85/2.10 tff(10321,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10322,plain,
% 1.85/2.10 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(10323,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10322])).
% 1.85/2.10 tff(10324,plain,
% 1.85/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.85/2.10 inference(transitivity,[status(thm)],[10323, 10321])).
% 1.85/2.10 tff(10325,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(10326,plain,
% 1.85/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[10325, 10324])).
% 1.85/2.10 tff(10327,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10326, 271, 2618, 448, 10320, 10295])).
% 1.85/2.10 tff(10328,plain,(r(s(s(s(z))), elem!1) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (elem!1 = z) | (~b(s(z), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(z))))) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10329,plain,
% 1.85/2.10 (r(s(s(s(z))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10328, 10279, 2618, 379, 394, 10294, 909, 10286, 9298, 10230, 111, 110, 258, 3871, 10283, 9149])).
% 1.85/2.10 tff(10330,plain,
% 1.85/2.10 (~r(s(s(s(z))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10254, 121, 379, 378, 10329])).
% 1.85/2.10 tff(10331,plain,
% 1.85/2.10 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1427, 10330, 394, 10294])).
% 1.85/2.10 tff(10332,plain,
% 1.85/2.10 (r(s(s(s(z))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1816, 10331, 10284])).
% 1.85/2.10 tff(10333,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8987, 121, 379, 10329, 10332, 10281])).
% 1.85/2.10 tff(10334,plain,((elem!1 = s(z)) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10335,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10334, 10277, 10272, 394, 378, 10228, 258, 111, 110, 3871, 348, 379, 503])).
% 1.85/2.10 tff(10336,plain,((elem!1 = s(z)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(10337,plain,
% 1.85/2.10 (elem!1 = s(z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[10336, 10219, 394, 111, 110, 3871, 348, 9983, 503, 2207])).
% 1.85/2.10 tff(10338,plain,
% 1.85/2.10 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[10337])).
% 1.85/2.10 tff(10339,plain,
% 1.85/2.10 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.85/2.10 inference(commutativity,[status(thm)],[])).
% 1.85/2.10 tff(10340,plain,
% 1.85/2.10 ((elem!1 = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10337])).
% 1.85/2.11 tff(10341,plain,
% 1.85/2.11 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.85/2.11 inference(transitivity,[status(thm)],[10340, 10339])).
% 1.85/2.11 tff(10342,plain,
% 1.85/2.11 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[10341])).
% 1.85/2.11 tff(10343,plain,
% 1.85/2.11 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.85/2.11 inference(transitivity,[status(thm)],[10342, 160])).
% 1.85/2.11 tff(10344,plain,
% 1.85/2.11 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10343])).
% 1.85/2.11 tff(10345,plain,
% 1.85/2.11 (~(s(s(s(z))) = elem!1)),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[97, 10344])).
% 1.85/2.11 tff(10346,plain,
% 1.85/2.11 (s(z) = elem!1),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[242, 10337])).
% 1.85/2.11 tff(10347,plain,
% 1.85/2.11 (~b(z, s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[229, 10346, 199])).
% 1.85/2.11 tff(10348,plain,
% 1.85/2.11 (r(z, s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[904, 10347])).
% 1.85/2.11 tff(10349,plain,
% 1.85/2.11 (~b(s(z), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[3576, 10337, 317])).
% 1.85/2.11 tff(10350,plain,
% 1.85/2.11 (~(s(s(s(z))) = s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[4929, 10349, 3871])).
% 1.85/2.11 tff(10351,plain,
% 1.85/2.11 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10337])).
% 1.85/2.11 tff(10352,plain,
% 1.85/2.11 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.85/2.11 inference(symmetry,[status(thm)],[10351])).
% 1.85/2.11 tff(10353,plain,
% 1.85/2.11 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[503, 10352])).
% 1.85/2.11 tff(10354,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[239])).
% 1.85/2.11 tff(10355,plain,
% 1.85/2.11 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[3049, 2359])).
% 1.85/2.11 tff(10356,plain,
% 1.85/2.11 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(symmetry,[status(thm)],[6675])).
% 1.85/2.11 tff(10357,plain,
% 1.85/2.11 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.85/2.11 inference(symmetry,[status(thm)],[6674])).
% 1.85/2.11 tff(10358,plain,
% 1.85/2.11 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(transitivity,[status(thm)],[10357, 10356])).
% 1.85/2.11 tff(10359,plain,
% 1.85/2.11 (b(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[3871, 10358])).
% 1.85/2.11 tff(10360,plain,
% 1.85/2.11 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[239])).
% 1.85/2.11 tff(10361,plain,
% 1.85/2.11 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.85/2.11 inference(symmetry,[status(thm)],[10360])).
% 1.85/2.11 tff(10362,plain,
% 1.85/2.11 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[1224])).
% 1.85/2.11 tff(10363,plain,
% 1.85/2.11 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.85/2.11 inference(symmetry,[status(thm)],[10362])).
% 1.85/2.11 tff(10364,plain,
% 1.85/2.11 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.85/2.11 inference(transitivity,[status(thm)],[10363, 10361])).
% 1.85/2.11 tff(10365,plain,
% 1.85/2.11 (b(s(s(s(z))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8109, 257, 2359])).
% 1.85/2.11 tff(10366,plain,
% 1.85/2.11 (b(s(s(elem!1)), elem!1)),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10365, 10364])).
% 1.85/2.11 tff(10367,plain,
% 1.85/2.11 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[594, 10366, 504, 10359])).
% 1.85/2.11 tff(10368,plain,
% 1.85/2.11 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[586, 10367, 563])).
% 1.85/2.11 tff(10369,plain,
% 1.85/2.11 (b(s(s(elem!1)), s(z))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10365, 10363])).
% 1.85/2.11 tff(10370,plain,
% 1.85/2.11 (~r(s(z), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[581, 10368, 111, 110])).
% 1.85/2.11 tff(10371,plain,
% 1.85/2.11 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[760, 10370])).
% 1.85/2.11 tff(10372,plain,
% 1.85/2.11 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[989, 10371, 504, 10369])).
% 1.85/2.11 tff(10373,plain,
% 1.85/2.11 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[556, 10372, 1])).
% 1.85/2.11 tff(10374,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.85/2.11 inference(symmetry,[status(thm)],[4952])).
% 1.85/2.11 tff(10375,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[3057, 4951])).
% 1.85/2.11 tff(10376,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10375])).
% 1.85/2.11 tff(10377,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[5949, 271, 588, 542])).
% 1.85/2.11 tff(10378,plain,
% 1.85/2.11 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10377, 5606])).
% 1.85/2.11 tff(10379,plain,
% 1.85/2.11 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10378, 10376])).
% 1.85/2.11 tff(10380,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[795, 10379, 782])).
% 1.85/2.11 tff(10381,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10380, 10374])).
% 1.85/2.11 tff(10382,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[3057, 1373])).
% 1.85/2.11 tff(10383,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[10382])).
% 1.85/2.11 tff(10384,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.11 tff(10385,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[3057, 1373])).
% 1.85/2.11 tff(10386,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10385])).
% 1.85/2.11 tff(10387,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10388,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(10389,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10388, 10387])).
% 1.85/2.11 tff(10390,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10389, 271, 588, 504])).
% 1.85/2.11 tff(10391,plain,
% 1.85/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10390, 5606])).
% 1.85/2.11 tff(10392,plain,
% 1.85/2.11 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10391, 10386])).
% 1.85/2.11 tff(10393,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[4045, 10392, 10384])).
% 1.85/2.11 tff(10394,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10393, 10383])).
% 1.85/2.11 tff(10395,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10396,plain,
% 1.85/2.11 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), 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)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10397,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), 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)))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10396])).
% 1.85/2.11 tff(10398,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), 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))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[10397, 10395])).
% 1.85/2.11 tff(10399,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(10400,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10399, 10398])).
% 1.85/2.11 tff(10401,plain,
% 1.85/2.11 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10400, 121, 623, 573])).
% 1.85/2.11 tff(10402,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10401, 10394, 10381])).
% 1.85/2.11 tff(10403,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(z)))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(10404,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10403, 778])).
% 1.85/2.11 tff(10405,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10404, 4038])).
% 1.85/2.11 tff(10406,plain,
% 1.85/2.11 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10405, 10373, 504, 2359, 10366, 10359, 10368])).
% 1.85/2.11 tff(10407,plain,
% 1.85/2.11 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8096, 10406, 2359])).
% 1.85/2.11 tff(10408,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[840, 10407, 10355])).
% 1.85/2.11 tff(10409,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10408, 10354])).
% 1.85/2.11 tff(10410,plain,
% 1.85/2.11 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[1223])).
% 1.85/2.11 tff(10411,plain,
% 1.85/2.11 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[239])).
% 1.85/2.11 tff(10412,plain,
% 1.85/2.11 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 1.85/2.11 inference(transitivity,[status(thm)],[10411, 10410])).
% 1.85/2.11 tff(10413,plain,
% 1.85/2.11 (~r(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8844, 10373, 2359, 394, 211, 10365, 379, 378])).
% 1.85/2.11 tff(10414,plain,
% 1.85/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1234, 239, 10228])).
% 1.85/2.11 tff(10415,plain,
% 1.85/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[932, 10414])).
% 1.85/2.11 tff(10416,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10417,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(10418,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10417, 10416])).
% 1.85/2.11 tff(10419,plain,
% 1.85/2.11 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10418, 271, 3871, 10365, 10415])).
% 1.85/2.11 tff(10420,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.85/2.11 tff(10421,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.85/2.11 tff(10422,plain,
% 1.85/2.11 (((~![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)))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10423,plain,
% 1.85/2.11 ((~![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)))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(10424,plain,
% 1.85/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10423, 10422])).
% 1.85/2.11 tff(10425,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10424, 21, 10421, 1138, 10420])).
% 1.85/2.11 tff(10426,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(10427,plain,
% 1.85/2.11 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10426, 10419])).
% 1.85/2.11 tff(10428,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[991, 10371, 1, 1225, 257, 10415])).
% 1.85/2.11 tff(10429,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8812, 10428, 239])).
% 1.85/2.11 tff(10430,plain,
% 1.85/2.11 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[1225])).
% 1.85/2.11 tff(10431,plain,
% 1.85/2.11 (r(z, s(s(s(s(z)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[111, 10430])).
% 1.85/2.11 tff(10432,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10433,plain,
% 1.85/2.11 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10434,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10433])).
% 1.85/2.11 tff(10435,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[10434, 10432])).
% 1.85/2.11 tff(10436,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(10437,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10436, 10435])).
% 1.85/2.11 tff(10438,plain,
% 1.85/2.11 (~r(z, s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10437, 121, 10431, 10429, 10427])).
% 1.85/2.11 tff(10439,plain,
% 1.85/2.11 (b(z, s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1214, 10438])).
% 1.85/2.11 tff(10440,plain,
% 1.85/2.11 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2029, 10439, 10365, 394])).
% 1.85/2.11 tff(10441,plain,
% 1.85/2.11 (~b(s(elem!1), s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2369, 10440, 239])).
% 1.85/2.11 tff(10442,plain,
% 1.85/2.11 (r(s(elem!1), s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[526, 10441, 211])).
% 1.85/2.11 tff(10443,plain,
% 1.85/2.11 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[1224, 1223])).
% 1.85/2.11 tff(10444,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.85/2.11 inference(symmetry,[status(thm)],[10443])).
% 1.85/2.11 tff(10445,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10446,plain,
% 1.85/2.11 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10447,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[10446])).
% 1.85/2.11 tff(10448,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[10447, 10445])).
% 1.85/2.11 tff(10449,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(10450,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10449, 10448])).
% 1.85/2.11 tff(10451,plain,
% 1.85/2.11 (~r(s(s(s(z))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10450, 121, 10431, 10429, 10427])).
% 1.85/2.11 tff(10452,plain,
% 1.85/2.11 (b(s(s(s(z))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1155, 10451])).
% 1.85/2.11 tff(10453,plain,
% 1.85/2.11 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8279, 10439, 10452, 394])).
% 1.85/2.11 tff(10454,plain,
% 1.85/2.11 (r(s(s(s(z))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1816, 10453, 2033])).
% 1.85/2.11 tff(10455,plain,
% 1.85/2.11 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[1223])).
% 1.85/2.11 tff(10456,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(z)))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[1500, 10455])).
% 1.85/2.11 tff(10457,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1358, 10456])).
% 1.85/2.11 tff(10458,plain,((~r(s(s(s(z))), s(elem!1))) | r(s(s(s(z))), s(s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(10459,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(z)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10458, 10454, 239])).
% 1.85/2.11 tff(10460,plain,
% 1.85/2.11 (r(s(s(elem!1)), s(elem!1))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[10459, 10444])).
% 1.85/2.11 tff(10461,plain,
% 1.85/2.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[3201, 10460, 10442, 10373])).
% 1.85/2.11 tff(10462,plain,
% 1.85/2.11 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[679, 21, 676])).
% 1.85/2.11 tff(10463,plain,
% 1.85/2.11 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[10462, 82])).
% 1.85/2.11 tff(10464,plain,
% 1.85/2.11 (b(elem!1, s(s(elem!1)))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[599, 10063, 4435])).
% 1.85/2.11 tff(10465,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10466,plain,
% 1.85/2.11 (((~b(elem!1, 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(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(10467,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10466])).
% 1.85/2.12 tff(10468,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10467, 10465])).
% 1.85/2.12 tff(10469,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10470,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10469, 10468])).
% 1.85/2.12 tff(10471,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10470, 271, 2618, 10464, 10463, 504])).
% 1.85/2.12 tff(10472,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | r(elem!1, s(s(elem!1))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(10473,plain,
% 1.85/2.12 (~b(s(elem!1), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10472, 10461, 82, 504, 10413])).
% 1.85/2.12 tff(10474,plain,
% 1.85/2.12 (r(s(elem!1), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2243, 10473, 2207])).
% 1.85/2.12 tff(10475,plain,
% 1.85/2.12 (r(s(s(z)), s(z))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10474, 10412])).
% 1.85/2.12 tff(10476,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10477,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10478,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10477, 10476])).
% 1.85/2.12 tff(10479,plain,
% 1.85/2.12 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10478, 121, 110, 10475, 10409])).
% 1.85/2.12 tff(10480,plain,
% 1.85/2.12 (((~![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))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10481,plain,
% 1.85/2.12 ((~![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))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10482,plain,
% 1.85/2.12 ((~![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)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10481, 10480])).
% 1.85/2.12 tff(10483,plain,
% 1.85/2.12 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10482, 21, 877, 10479])).
% 1.85/2.12 tff(10484,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10485,plain,
% 1.85/2.12 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10486,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10485])).
% 1.85/2.12 tff(10487,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10486, 10484])).
% 1.85/2.12 tff(10488,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10489,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10488, 10487])).
% 1.85/2.12 tff(10490,plain,
% 1.85/2.12 (~r(s(s(s(s(s(z))))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10489, 121, 110, 909, 10409])).
% 1.85/2.12 tff(10491,plain,
% 1.85/2.12 (b(s(s(s(s(s(z))))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6593, 21, 711, 10490])).
% 1.85/2.12 tff(10492,plain,
% 1.85/2.12 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[1223])).
% 1.85/2.12 tff(10493,plain,
% 1.85/2.12 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.85/2.12 inference(commutativity,[status(thm)],[])).
% 1.85/2.12 tff(10494,plain,
% 1.85/2.12 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[1223, 1226])).
% 1.85/2.12 tff(10495,plain,
% 1.85/2.12 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10494, 10493])).
% 1.85/2.12 tff(10496,plain,
% 1.85/2.12 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.85/2.12 inference(symmetry,[status(thm)],[10495])).
% 1.85/2.12 tff(10497,plain,
% 1.85/2.12 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10496])).
% 1.85/2.12 tff(10498,plain,
% 1.85/2.12 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[2376])).
% 1.85/2.12 tff(10499,plain,
% 1.85/2.12 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.85/2.12 inference(symmetry,[status(thm)],[10498])).
% 1.85/2.12 tff(10500,plain,
% 1.85/2.12 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10499])).
% 1.85/2.12 tff(10501,plain,
% 1.85/2.12 (~(s(s(s(elem!1))) = s(s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[82, 10500])).
% 1.85/2.12 tff(10502,plain,
% 1.85/2.12 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10501, 10497])).
% 1.85/2.12 tff(10503,plain,
% 1.85/2.12 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[2376])).
% 1.85/2.12 tff(10504,plain,
% 1.85/2.12 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10503])).
% 1.85/2.12 tff(10505,plain,
% 1.85/2.12 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[2376])).
% 1.85/2.12 tff(10506,plain,
% 1.85/2.12 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.85/2.12 inference(symmetry,[status(thm)],[10505])).
% 1.85/2.12 tff(10507,plain,
% 1.85/2.12 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2044, 10440, 6284])).
% 1.85/2.12 tff(10508,plain,
% 1.85/2.12 (r(s(s(z)), s(s(s(z))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10507, 10506])).
% 1.85/2.12 tff(10509,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10510,plain,
% 1.85/2.12 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10511,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10510])).
% 1.85/2.12 tff(10512,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10511, 10509])).
% 1.85/2.12 tff(10513,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10514,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10513, 10512])).
% 1.85/2.12 tff(10515,plain,
% 1.85/2.12 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10514, 121, 10459, 10427])).
% 1.85/2.12 tff(10516,plain,
% 1.85/2.12 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10515, 10508])).
% 1.85/2.12 tff(10517,plain,
% 1.85/2.12 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10516, 10504])).
% 1.85/2.12 tff(10518,plain,
% 1.85/2.12 (b(s(elem!1), s(s(s(s(z)))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1995, 10517, 10502])).
% 1.85/2.12 tff(10519,plain,
% 1.85/2.12 (b(s(s(z)), s(s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10518, 10492])).
% 1.85/2.12 tff(10520,plain,
% 1.85/2.12 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.85/2.12 inference(commutativity,[status(thm)],[])).
% 1.85/2.12 tff(10521,plain,
% 1.85/2.12 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.85/2.12 inference(symmetry,[status(thm)],[10520])).
% 1.85/2.12 tff(10522,plain,
% 1.85/2.12 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10521])).
% 1.85/2.12 tff(10523,plain,
% 1.85/2.12 (~(z = s(s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[95, 10522])).
% 1.85/2.12 tff(10524,plain,
% 1.85/2.12 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[1223])).
% 1.85/2.12 tff(10525,plain,
% 1.85/2.12 ((~r(z, s(elem!1))) <=> (~r(z, s(s(z))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10524])).
% 1.85/2.12 tff(10526,plain,
% 1.85/2.12 (~r(z, s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1449, 10442, 379, 378])).
% 1.85/2.12 tff(10527,plain,
% 1.85/2.12 (~r(z, s(s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10526, 10525])).
% 1.85/2.12 tff(10528,plain,
% 1.85/2.12 (((~![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))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10529,plain,
% 1.85/2.12 ((~![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))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10530,plain,
% 1.85/2.12 ((~![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)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10529, 10528])).
% 1.85/2.12 tff(10531,plain,
% 1.85/2.12 ((z = s(s(z))) | b(z, s(s(z)))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10530, 21, 10527])).
% 1.85/2.12 tff(10532,plain,
% 1.85/2.12 (b(z, s(s(z)))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10531, 10523])).
% 1.85/2.12 tff(10533,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10534,plain,
% 1.85/2.12 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10535,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10534])).
% 1.85/2.12 tff(10536,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10535, 10533])).
% 1.85/2.12 tff(10537,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10538,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10537, 10536])).
% 1.85/2.12 tff(10539,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10538, 271, 10532, 10519, 10491, 10483])).
% 1.85/2.12 tff(10540,plain,((~b(s(s(s(z))), elem!1)) | (~(elem!1 = s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(10541,plain,
% 1.85/2.12 (~b(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10540, 10337, 110, 82, 10353, 9983, 10219, 10350, 394, 10348, 1, 111, 3871])).
% 1.85/2.12 tff(10542,plain,
% 1.85/2.12 (r(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[255, 10541, 10345])).
% 1.85/2.12 tff(10543,plain,
% 1.85/2.12 (r(s(s(s(z))), s(z))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10542, 10338])).
% 1.85/2.12 tff(10544,plain,
% 1.85/2.12 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10545,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10544])).
% 1.85/2.12 tff(10546,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10545, 4823])).
% 1.85/2.12 tff(10547,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10548,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10547, 10546])).
% 1.85/2.12 tff(10549,plain,
% 1.85/2.12 (~r(s(s(s(z))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10548, 121, 110, 10348, 10543])).
% 1.85/2.12 tff(10550,plain,
% 1.85/2.12 (b(s(s(s(z))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1155, 10549])).
% 1.85/2.12 tff(10551,plain,
% 1.85/2.12 (s(elem!1) = s(s(z))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10337])).
% 1.85/2.12 tff(10552,plain,
% 1.85/2.12 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10551])).
% 1.85/2.12 tff(10553,plain,
% 1.85/2.12 (b(s(s(z)), z)),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[394, 10552])).
% 1.85/2.12 tff(10554,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10555,plain,
% 1.85/2.12 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10556,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10555])).
% 1.85/2.12 tff(10557,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10556, 10554])).
% 1.85/2.12 tff(10558,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10559,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10558, 10557])).
% 1.85/2.12 tff(10560,plain,
% 1.85/2.12 (~r(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10559, 121, 110, 10348, 10543])).
% 1.85/2.12 tff(10561,plain,
% 1.85/2.12 (b(z, s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1214, 10560])).
% 1.85/2.12 tff(10562,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10563,plain,
% 1.85/2.12 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10564,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[10563])).
% 1.85/2.12 tff(10565,plain,
% 1.85/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.85/2.12 inference(transitivity,[status(thm)],[10564, 10562])).
% 1.85/2.12 tff(10566,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10567,plain,
% 1.85/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10566, 10565])).
% 1.85/2.12 tff(10568,plain,
% 1.85/2.12 (~b(s(s(z)), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10567, 271, 10561, 10553, 10550])).
% 1.85/2.12 tff(10569,plain,
% 1.85/2.12 (((~![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)))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(10570,plain,
% 1.85/2.12 ((~![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)))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(10571,plain,
% 1.85/2.12 ((~![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))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[10570, 10569])).
% 1.85/2.12 tff(10572,plain,
% 1.85/2.12 (r(s(s(z)), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[10571, 21, 10568, 1136])).
% 1.85/2.12 tff(10573,plain,
% 1.85/2.12 (~b(s(s(s(z))), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8279, 10561, 10550, 394])).
% 1.85/2.12 tff(10574,plain,
% 1.85/2.12 (r(s(s(s(z))), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1816, 10573, 10350])).
% 1.85/2.12 tff(10575,plain,
% 1.85/2.12 (r(s(s(s(z))), s(s(z)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10458, 10574, 10337])).
% 1.95/2.13 tff(10576,plain,
% 1.95/2.13 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10551])).
% 1.95/2.13 tff(10577,plain,
% 1.95/2.13 (r(s(z), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[444, 10349, 348])).
% 1.95/2.13 tff(10578,plain,
% 1.95/2.13 (r(s(z), s(s(z)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10577, 10576])).
% 1.95/2.13 tff(10579,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10580,plain,
% 1.95/2.13 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10581,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10580])).
% 1.95/2.13 tff(10582,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10581, 10579])).
% 1.95/2.13 tff(10583,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(10584,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10583, 10582])).
% 1.95/2.13 tff(10585,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10584, 121, 10578, 10543, 10575, 10572])).
% 1.95/2.13 tff(10586,plain,(b(z, elem!1) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10587,plain,
% 1.95/2.13 (b(z, elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10586, 317, 110, 79, 1, 111, 3871, 67, 348, 394])).
% 1.95/2.13 tff(10588,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[8902, 3456, 110, 378])).
% 1.95/2.13 tff(10589,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[284, 10588, 259])).
% 1.95/2.13 tff(10590,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[402, 10589, 10232, 394, 307])).
% 1.95/2.13 tff(10591,plain,((~r(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (elem!1 = z) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10592,plain,
% 1.95/2.13 (~r(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10591, 10219, 2345, 9298, 110, 394])).
% 1.95/2.13 tff(10593,plain,
% 1.95/2.13 (b(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[299, 10592, 258])).
% 1.95/2.13 tff(10594,plain,
% 1.95/2.13 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.95/2.13 inference(monotonicity,[status(thm)],[244])).
% 1.95/2.13 tff(10595,plain,
% 1.95/2.13 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.95/2.13 inference(symmetry,[status(thm)],[10594])).
% 1.95/2.13 tff(10596,plain,
% 1.95/2.13 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10595])).
% 1.95/2.13 tff(10597,plain,
% 1.95/2.13 (~b(s(z), s(s(s(z))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1242, 10596])).
% 1.95/2.13 tff(10598,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3871, 10597])).
% 1.95/2.13 tff(10599,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(z))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10600,plain,
% 1.95/2.13 (~(s(s(s(z))) = elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10599, 1242, 3871])).
% 1.95/2.13 tff(10601,plain,
% 1.95/2.13 (b(s(s(s(z))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[255, 10600, 221])).
% 1.95/2.13 tff(10602,plain,
% 1.95/2.13 (~(elem!1 = s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1100, 10600])).
% 1.95/2.13 tff(10603,plain,
% 1.95/2.13 (r(s(z), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[236, 1242, 231])).
% 1.95/2.13 tff(10604,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1797, 10603, 110, 378])).
% 1.95/2.13 tff(10605,plain,
% 1.95/2.13 (b(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1192, 10604, 10602])).
% 1.95/2.13 tff(10606,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10607,plain,
% 1.95/2.13 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10608,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10607])).
% 1.95/2.13 tff(10609,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10608, 10606])).
% 1.95/2.13 tff(10610,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(10611,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10610, 10609])).
% 1.95/2.13 tff(10612,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10611, 271, 448, 10605, 3871, 10601])).
% 1.95/2.13 tff(10613,plain,(b(s(z), elem!1) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, elem!1)) | r(s(s(s(z))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10614,plain,
% 1.95/2.13 (b(s(z), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10613, 221, 3871, 110, 378, 448, 231])).
% 1.95/2.13 tff(10615,plain,
% 1.95/2.13 (r(s(s(s(elem!1))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10250, 10614, 3871, 448, 221, 503])).
% 1.95/2.13 tff(10616,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10617,plain,
% 1.95/2.13 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10618,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10617])).
% 1.95/2.13 tff(10619,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10618, 10616])).
% 1.95/2.13 tff(10620,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(10621,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10620, 10619])).
% 1.95/2.13 tff(10622,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10621, 121, 378, 111, 139, 727])).
% 1.95/2.13 tff(10623,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10624,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(elem!1))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10623, 10615, 111, 378])).
% 1.95/2.13 tff(10625,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10626,plain,
% 1.95/2.13 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10627,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10626])).
% 1.95/2.13 tff(10628,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10627, 10625])).
% 1.95/2.13 tff(10629,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(10630,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10629, 10628])).
% 1.95/2.13 tff(10631,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10630, 121, 111, 572, 110, 139])).
% 1.95/2.13 tff(10632,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10633,plain,
% 1.95/2.13 (~r(s(z), s(s(s(elem!1))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10632, 10615, 110, 111])).
% 1.95/2.13 tff(10634,plain,
% 1.95/2.13 (b(s(z), s(s(s(elem!1))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[760, 10633])).
% 1.95/2.13 tff(10635,plain,
% 1.95/2.13 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[244])).
% 1.95/2.13 tff(10636,plain,
% 1.95/2.13 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.13 inference(symmetry,[status(thm)],[10635])).
% 1.95/2.13 tff(10637,plain,
% 1.95/2.13 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10636])).
% 1.95/2.13 tff(10638,plain,
% 1.95/2.13 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1043, 10637])).
% 1.95/2.13 tff(10639,plain,
% 1.95/2.13 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[244])).
% 1.95/2.13 tff(10640,plain,
% 1.95/2.13 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(symmetry,[status(thm)],[10639])).
% 1.95/2.13 tff(10641,plain,
% 1.95/2.13 (b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[448, 10640])).
% 1.95/2.13 tff(10642,plain,
% 1.95/2.13 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2081, 10641, 750, 503])).
% 1.95/2.13 tff(10643,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2071, 10642, 10638, 2065])).
% 1.95/2.13 tff(10644,plain,((~(s(s(s(z))) = elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | r(elem!1, s(s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10645,plain,
% 1.95/2.13 (~(s(s(s(z))) = elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10644, 10634, 2065, 503, 10624, 448])).
% 1.95/2.13 tff(10646,plain,
% 1.95/2.13 (b(s(s(s(z))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[255, 10645, 221])).
% 1.95/2.13 tff(10647,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10648,plain,
% 1.95/2.13 (((~b(elem!1, s(elem!1))) | (~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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10649,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10648])).
% 1.95/2.13 tff(10650,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10649, 10647])).
% 1.95/2.13 tff(10651,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(10652,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 1.95/2.13 tff(10653,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10652, 271, 307, 10614, 3871, 10646])).
% 1.95/2.13 tff(10654,plain,(r(s(s(s(z))), elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10655,plain,
% 1.95/2.13 (r(s(s(s(z))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10654, 10593, 3871, 9149, 503, 2345, 111, 10219, 110, 1257])).
% 1.95/2.13 tff(10656,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[375, 357, 358, 199, 110])).
% 1.95/2.13 tff(10657,plain,
% 1.95/2.13 (~b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1315, 10656, 394, 307])).
% 1.95/2.13 tff(10658,plain,
% 1.95/2.13 (r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1214, 10657])).
% 1.95/2.13 tff(10659,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2892, 271, 307, 394, 261, 1421])).
% 1.95/2.13 tff(10660,plain,((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10661,plain,
% 1.95/2.13 (~b(z, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10660, 10656, 394, 307])).
% 1.95/2.13 tff(10662,plain,
% 1.95/2.13 (r(z, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1439, 10661])).
% 1.95/2.13 tff(10663,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1797, 357, 110, 1243])).
% 1.95/2.13 tff(10664,plain,
% 1.95/2.13 (b(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1192, 10663, 1102])).
% 1.95/2.13 tff(10665,plain,
% 1.95/2.13 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1811, 10664, 307, 394])).
% 1.95/2.13 tff(10666,plain,
% 1.95/2.13 (~b(z, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[466, 357, 110, 331, 377, 199])).
% 1.95/2.13 tff(10667,plain,
% 1.95/2.13 (r(z, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[904, 10666])).
% 1.95/2.13 tff(10668,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10669,plain,
% 1.95/2.13 (((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10670,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10669])).
% 1.95/2.13 tff(10671,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10670, 10668])).
% 1.95/2.13 tff(10672,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(10673,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[10672, 10671])).
% 1.95/2.13 tff(10674,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10673, 121, 357, 1441, 909, 411])).
% 1.95/2.13 tff(10675,plain,((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(10676,plain,
% 1.95/2.13 (~r(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10675, 10662, 10667, 357])).
% 1.95/2.13 tff(10677,plain,
% 1.95/2.13 (b(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[429, 10676, 422])).
% 1.95/2.13 tff(10678,plain,
% 1.95/2.13 (~b(s(z), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[456, 10677, 307, 448])).
% 1.95/2.13 tff(10679,plain,
% 1.95/2.13 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4929, 10678, 3871])).
% 1.95/2.13 tff(10680,plain,
% 1.95/2.13 (r(s(s(s(z))), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1816, 10679, 10665])).
% 1.95/2.13 tff(10681,plain,
% 1.95/2.13 (~r(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6541, 10658, 357, 10667])).
% 1.95/2.13 tff(10682,plain,
% 1.95/2.13 (b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2325, 10681])).
% 1.95/2.13 tff(10683,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10684,plain,
% 1.95/2.13 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(10685,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[10684])).
% 1.95/2.13 tff(10686,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[10685, 10683])).
% 1.95/2.13 tff(10687,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10688,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10687, 10686])).
% 1.95/2.14 tff(10689,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10688, 271, 307, 1195, 3870, 222])).
% 1.95/2.14 tff(10690,plain,((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(10691,plain,
% 1.95/2.14 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10690, 10682, 307, 10664])).
% 1.95/2.14 tff(10692,plain,
% 1.95/2.14 (~(s(elem!1) = s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2035, 10679])).
% 1.95/2.14 tff(10693,plain,
% 1.95/2.14 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2044, 10692, 10691])).
% 1.95/2.14 tff(10694,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10695,plain,
% 1.95/2.14 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10696,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[10695])).
% 1.95/2.14 tff(10697,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[10696, 10694])).
% 1.95/2.14 tff(10698,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10699,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10698, 10697])).
% 1.95/2.14 tff(10700,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10699, 121, 1441, 1500, 1140, 2046])).
% 1.95/2.14 tff(10701,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(10702,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10701, 10693, 10680, 10662, 10658])).
% 1.95/2.14 tff(10703,plain,((~r(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (elem!1 = s(s(s(z)))) | (~r(s(z), z)) | b(z, elem!1) | (z = elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(10704,plain,
% 1.95/2.14 (~r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10703, 1102, 2345, 448, 2282, 394, 3871, 110, 199, 9297, 219])).
% 1.95/2.14 tff(10705,plain,
% 1.95/2.14 (~b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[402, 220, 394, 307])).
% 1.95/2.14 tff(10706,plain,
% 1.95/2.14 (r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[284, 10705, 259])).
% 1.95/2.14 tff(10707,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10708,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10709,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10708, 10707])).
% 1.95/2.14 tff(10710,plain,
% 1.95/2.14 (~r(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10709, 121, 378, 10706, 145])).
% 1.95/2.14 tff(10711,plain,
% 1.95/2.14 (b(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1155, 10710])).
% 1.95/2.14 tff(10712,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10713,plain,
% 1.95/2.14 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10714,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[10713])).
% 1.95/2.14 tff(10715,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[10714, 10712])).
% 1.95/2.14 tff(10716,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10717,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10716, 10715])).
% 1.95/2.14 tff(10718,plain,
% 1.95/2.14 (~r(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10717, 121, 378, 10706, 145])).
% 1.95/2.14 tff(10719,plain,
% 1.95/2.14 (b(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1214, 10718])).
% 1.95/2.14 tff(10720,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10270, 271, 220, 10719, 3871, 10711])).
% 1.95/2.14 tff(10721,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = z) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(10722,plain,
% 1.95/2.14 (~b(z, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10721, 10219, 3871, 145, 9298, 394, 2345])).
% 1.95/2.14 tff(10723,plain,
% 1.95/2.14 (r(z, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[904, 10722])).
% 1.95/2.14 tff(10724,plain,
% 1.95/2.14 (b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[236, 10704, 231])).
% 1.95/2.14 tff(10725,plain,
% 1.95/2.14 (~b(s(s(s(elem!1))), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[8132, 10724, 503, 448])).
% 1.95/2.14 tff(10726,plain,
% 1.95/2.14 (s(s(s(elem!1))) = elem!1),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[486, 10725, 147])).
% 1.95/2.14 tff(10727,plain,
% 1.95/2.14 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2830, 2505, 2344])).
% 1.95/2.14 tff(10728,plain,
% 1.95/2.14 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.14 inference(symmetry,[status(thm)],[5190])).
% 1.95/2.14 tff(10729,plain,
% 1.95/2.14 (b(s(z), s(s(s(elem!1))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[237, 2558])).
% 1.95/2.14 tff(10730,plain,
% 1.95/2.14 (b(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[681, 10727, 79])).
% 1.95/2.14 tff(10731,plain,
% 1.95/2.14 (~r(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10548, 121, 110, 909, 2327])).
% 1.95/2.14 tff(10732,plain,
% 1.95/2.14 (b(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1155, 10731])).
% 1.95/2.14 tff(10733,plain,
% 1.95/2.14 (~r(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10559, 121, 110, 909, 2327])).
% 1.95/2.14 tff(10734,plain,
% 1.95/2.14 (b(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1214, 10733])).
% 1.95/2.14 tff(10735,plain,
% 1.95/2.14 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2354, 271, 394, 10734, 10732])).
% 1.95/2.14 tff(10736,plain,
% 1.95/2.14 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2044, 10735, 2037])).
% 1.95/2.14 tff(10737,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2464, 10732, 909, 944, 750, 110, 2327, 503])).
% 1.95/2.14 tff(10738,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[556, 10737, 1])).
% 1.95/2.14 tff(10739,plain,
% 1.95/2.14 (~r(elem!1, s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3310, 10738, 2344, 198, 199, 331, 79])).
% 1.95/2.14 tff(10740,plain,
% 1.95/2.14 (b(elem!1, s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[599, 10739, 68])).
% 1.95/2.14 tff(10741,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3324, 10740, 2345, 394])).
% 1.95/2.14 tff(10742,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[701, 10741, 3313])).
% 1.95/2.14 tff(10743,plain,
% 1.95/2.14 (~r(z, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3387, 622, 378, 1409])).
% 1.95/2.14 tff(10744,plain,
% 1.95/2.14 (~b(z, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3359, 622, 259, 307, 623, 394, 683, 638])).
% 1.95/2.14 tff(10745,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1439, 10744, 10743])).
% 1.95/2.14 tff(10746,plain,((~r(s(elem!1), elem!1)) | (elem!1 = z) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(10747,plain,
% 1.95/2.14 (~r(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10746, 10738, 2345, 358, 394, 10742, 638, 1243, 1409])).
% 1.95/2.14 tff(10748,plain,
% 1.95/2.14 (b(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2243, 10747, 2207])).
% 1.95/2.14 tff(10749,plain,
% 1.95/2.14 (~b(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3247, 271, 2345, 10748, 260])).
% 1.95/2.14 tff(10750,plain,
% 1.95/2.14 (r(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[429, 10749, 422])).
% 1.95/2.14 tff(10751,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10752,plain,
% 1.95/2.14 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10753,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[10752])).
% 1.95/2.14 tff(10754,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[10753, 10751])).
% 1.95/2.14 tff(10755,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10756,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10755, 10754])).
% 1.95/2.14 tff(10757,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10756, 121, 110, 10750, 2327, 10736])).
% 1.95/2.14 tff(10758,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (s(elem!1) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1)) | b(z, elem!1) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(10759,plain,
% 1.95/2.14 (~r(s(s(s(z))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10758, 1409, 2282, 237, 394, 10730, 110, 3841, 68, 2344, 199, 9297, 1, 909, 3504, 10729, 503])).
% 1.95/2.14 tff(10760,plain,
% 1.95/2.14 (b(s(s(s(z))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2325, 10759])).
% 1.95/2.14 tff(10761,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10762,plain,
% 1.95/2.14 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10763,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[10762])).
% 1.95/2.14 tff(10764,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[10763, 10761])).
% 1.95/2.14 tff(10765,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10766,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10765, 10764])).
% 1.95/2.14 tff(10767,plain,
% 1.95/2.14 (~b(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10766, 271, 237, 448, 10760])).
% 1.95/2.14 tff(10768,plain,
% 1.95/2.14 (r(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1192, 10767, 1102])).
% 1.95/2.14 tff(10769,plain,
% 1.95/2.14 (~r(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6723, 10768, 10219, 145])).
% 1.95/2.14 tff(10770,plain,
% 1.95/2.14 (b(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1214, 10769])).
% 1.95/2.14 tff(10771,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10772,plain,
% 1.95/2.14 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10773,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[10772])).
% 1.95/2.14 tff(10774,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[10773, 10771])).
% 1.95/2.14 tff(10775,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10776,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10775, 10774])).
% 1.95/2.14 tff(10777,plain,
% 1.95/2.14 (~r(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10776, 121, 10219, 10768, 145])).
% 1.95/2.14 tff(10778,plain,
% 1.95/2.14 (b(s(s(s(z))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1155, 10777])).
% 1.95/2.14 tff(10779,plain,
% 1.95/2.14 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[8279, 10778, 10770, 394])).
% 1.95/2.14 tff(10780,plain,
% 1.95/2.14 (r(s(s(s(z))), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1816, 10779, 2597])).
% 1.95/2.14 tff(10781,plain,
% 1.95/2.14 (~r(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[5181, 10780, 145, 10768])).
% 1.95/2.14 tff(10782,plain,
% 1.95/2.14 (b(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2243, 10781, 2207])).
% 1.95/2.14 tff(10783,plain,
% 1.95/2.14 (b(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10782, 10728])).
% 1.95/2.14 tff(10784,plain,
% 1.95/2.14 (~b(s(z), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3019, 10782, 2345, 448])).
% 1.95/2.14 tff(10785,plain,
% 1.95/2.14 (r(s(z), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[444, 10784, 348])).
% 1.95/2.14 tff(10786,plain,
% 1.95/2.14 (~b(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3247, 271, 2345, 10782, 237])).
% 1.95/2.14 tff(10787,plain,
% 1.95/2.14 (r(s(elem!1), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[429, 10786, 2282])).
% 1.95/2.14 tff(10788,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10789,plain,
% 1.95/2.14 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(10790,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[10789])).
% 1.95/2.14 tff(10791,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[10790, 10788])).
% 1.95/2.14 tff(10792,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(10793,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[10792, 10791])).
% 1.95/2.14 tff(10794,plain,
% 1.95/2.14 (~r(z, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10793, 121, 110, 909, 10787])).
% 1.95/2.14 tff(10795,plain,
% 1.95/2.14 (b(z, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1439, 10794])).
% 1.95/2.14 tff(10796,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[701, 5855, 3313])).
% 1.95/2.14 tff(10797,plain,
% 1.95/2.14 (~r(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7179, 2505, 676])).
% 1.95/2.14 tff(10798,plain,
% 1.95/2.14 (b(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[392, 10797, 377])).
% 1.95/2.14 tff(10799,plain,
% 1.95/2.14 (~b(z, elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9089, 271, 10798, 394, 1421])).
% 1.95/2.14 tff(10800,plain,
% 1.95/2.14 (r(z, elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[355, 10799, 331])).
% 1.95/2.14 tff(10801,plain,
% 1.95/2.14 (~b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2892, 271, 10798, 394, 1421])).
% 1.95/2.14 tff(10802,plain,
% 1.95/2.14 ((elem!1 = z) | r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[282, 21, 10801])).
% 1.95/2.14 tff(10803,plain,
% 1.95/2.14 (r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10802, 2886])).
% 1.95/2.14 tff(10804,plain,
% 1.95/2.14 (~r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[373, 10803, 10800, 110])).
% 1.95/2.14 tff(10805,plain,
% 1.95/2.14 (b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[236, 10804, 231])).
% 1.95/2.14 tff(10806,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10807,plain,
% 1.95/2.15 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10808,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10807])).
% 1.95/2.15 tff(10809,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10808, 10806])).
% 1.95/2.15 tff(10810,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10811,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10810, 10809])).
% 1.95/2.15 tff(10812,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10811, 271, 10798, 10805, 505, 8590])).
% 1.95/2.15 tff(10813,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(s(elem!1)))) | (s(z) = elem!1) | (~r(s(z), z)) | (z = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (elem!1 = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(10814,plain,
% 1.95/2.15 (~b(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10813, 543, 110, 331, 676, 2505, 394, 231, 219, 1421])).
% 1.95/2.15 tff(10815,plain,
% 1.95/2.15 (r(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2167, 10814])).
% 1.95/2.15 tff(10816,plain,
% 1.95/2.15 (~r(s(elem!1), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[3275, 10815, 431, 10796])).
% 1.95/2.15 tff(10817,plain,
% 1.95/2.15 (b(s(elem!1), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[526, 10816, 211])).
% 1.95/2.15 tff(10818,plain,
% 1.95/2.15 (~b(z, s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[8781, 10817, 543, 1421])).
% 1.95/2.15 tff(10819,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[8597, 543, 1, 231, 378, 851, 1409, 503, 293, 232])).
% 1.95/2.15 tff(10820,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2143, 10819])).
% 1.95/2.15 tff(10821,plain,
% 1.95/2.15 (~r(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2422, 10820, 110, 909])).
% 1.95/2.15 tff(10822,plain,
% 1.95/2.15 (b(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2430, 10821])).
% 1.95/2.15 tff(10823,plain,
% 1.95/2.15 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1459, 638, 517, 543])).
% 1.95/2.15 tff(10824,plain,
% 1.95/2.15 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[586, 10823, 6943])).
% 1.95/2.15 tff(10825,plain,
% 1.95/2.15 (~b(z, s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[5267, 638, 2449, 543])).
% 1.95/2.15 tff(10826,plain,
% 1.95/2.15 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[36, 21, 10825])).
% 1.95/2.15 tff(10827,plain,
% 1.95/2.15 (r(z, s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10826, 3139])).
% 1.95/2.15 tff(10828,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10829,plain,
% 1.95/2.15 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10830,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10829])).
% 1.95/2.15 tff(10831,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10830, 10828])).
% 1.95/2.15 tff(10832,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10833,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10832, 10831])).
% 1.95/2.15 tff(10834,plain,
% 1.95/2.15 (~r(z, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10833, 121, 111, 573, 572])).
% 1.95/2.15 tff(10835,plain,
% 1.95/2.15 ((z = s(z)) | b(z, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[902, 21, 10834])).
% 1.95/2.15 tff(10836,plain,
% 1.95/2.15 (b(z, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10835, 4810])).
% 1.95/2.15 tff(10837,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10838,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10839,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10838, 10837])).
% 1.95/2.15 tff(10840,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10839, 271, 2538, 10836, 2449])).
% 1.95/2.15 tff(10841,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 10840])).
% 1.95/2.15 tff(10842,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10843,plain,
% 1.95/2.15 (((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10844,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10843])).
% 1.95/2.15 tff(10845,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10844, 10842])).
% 1.95/2.15 tff(10846,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10847,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10846, 10845])).
% 1.95/2.15 tff(10848,plain,
% 1.95/2.15 (~b(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10847, 271, 2538, 10836, 2449])).
% 1.95/2.15 tff(10849,plain,
% 1.95/2.15 (r(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2167, 10848])).
% 1.95/2.15 tff(10850,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10851,plain,
% 1.95/2.15 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10852,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10851])).
% 1.95/2.15 tff(10853,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10852, 10850])).
% 1.95/2.15 tff(10854,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10855,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10854, 10853])).
% 1.95/2.15 tff(10856,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10855, 121, 10849, 573, 572, 10841])).
% 1.95/2.15 tff(10857,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(10858,plain,
% 1.95/2.15 (~r(s(z), s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10857, 10827, 2449, 10824])).
% 1.95/2.15 tff(10859,plain,
% 1.95/2.15 (b(s(z), s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[760, 10858])).
% 1.95/2.15 tff(10860,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[5840, 271, 543, 10859, 638])).
% 1.95/2.15 tff(10861,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2143, 10860])).
% 1.95/2.15 tff(10862,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10863,plain,
% 1.95/2.15 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10864,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10863])).
% 1.95/2.15 tff(10865,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10864, 10862])).
% 1.95/2.15 tff(10866,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10867,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10866, 10865])).
% 1.95/2.15 tff(10868,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10867, 121, 10827, 10824, 2088, 10861])).
% 1.95/2.15 tff(10869,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(10870,plain,
% 1.95/2.15 (~r(z, s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10869, 10822, 638, 10817, 563, 543])).
% 1.95/2.15 tff(10871,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2106, 10870, 10818])).
% 1.95/2.15 tff(10872,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | r(elem!1, s(z)) | r(s(z), elem!1) | (~b(s(elem!1), s(s(s(elem!1))))) | (z = elem!1) | r(s(s(s(elem!1))), s(elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(10873,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10872, 10795, 10730, 110, 909, 10785, 1, 231, 10219, 198, 1409, 503, 10592, 232, 10783, 9297, 10727, 2505, 394])).
% 1.95/2.15 tff(10874,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[556, 10873, 1])).
% 1.95/2.15 tff(10875,plain,
% 1.95/2.15 (r(s(s(elem!1)), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2511, 10874, 2505])).
% 1.95/2.15 tff(10876,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10877,plain,
% 1.95/2.15 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10878,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10877])).
% 1.95/2.15 tff(10879,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10878, 10876])).
% 1.95/2.15 tff(10880,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10881,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10880, 10879])).
% 1.95/2.15 tff(10882,plain,
% 1.95/2.15 (~r(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10881, 121, 10219, 10768, 10875])).
% 1.95/2.15 tff(10883,plain,
% 1.95/2.15 (b(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2430, 10882])).
% 1.95/2.15 tff(10884,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10885,plain,
% 1.95/2.15 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(10886,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[10885])).
% 1.95/2.15 tff(10887,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[10886, 10884])).
% 1.95/2.15 tff(10888,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(10889,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[10888, 10887])).
% 1.95/2.15 tff(10890,plain,
% 1.95/2.15 (~r(z, s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10889, 121, 10219, 10768, 10875])).
% 1.95/2.15 tff(10891,plain,
% 1.95/2.15 (b(z, s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2106, 10890])).
% 1.95/2.15 tff(10892,plain,
% 1.95/2.15 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2454, 10891, 10778, 10883])).
% 1.95/2.15 tff(10893,plain,
% 1.95/2.15 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[5224, 121, 10768, 145, 10875])).
% 1.95/2.15 tff(10894,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2462, 21, 10893, 10892, 3504])).
% 1.95/2.15 tff(10895,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | r(s(z), elem!1) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(10896,plain,
% 1.95/2.15 (~r(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10895, 10726, 145, 1, 110, 10723, 231, 503, 10704, 394, 348, 448, 1102, 68, 2344, 199])).
% 1.95/2.15 tff(10897,plain,
% 1.95/2.15 (b(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[284, 10896, 9298])).
% 1.95/2.15 tff(10898,plain,
% 1.95/2.15 (~b(z, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1315, 10897, 394, 2345])).
% 1.95/2.15 tff(10899,plain,
% 1.95/2.15 (r(z, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1214, 10898])).
% 1.95/2.15 tff(10900,plain,
% 1.95/2.15 (~r(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6723, 10899, 10219, 145])).
% 1.95/2.15 tff(10901,plain,
% 1.95/2.15 (b(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1192, 10900, 1102])).
% 1.95/2.15 tff(10902,plain,
% 1.95/2.15 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2596, 10726])).
% 1.95/2.15 tff(10903,plain,
% 1.95/2.15 (~(s(elem!1) = s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2035, 10902])).
% 1.95/2.15 tff(10904,plain,
% 1.95/2.15 (~b(z, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10660, 10897, 394, 2345])).
% 1.95/2.15 tff(10905,plain,
% 1.95/2.15 (r(z, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1439, 10904])).
% 1.95/2.15 tff(10906,plain,
% 1.95/2.15 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1811, 10901, 2345, 394])).
% 1.95/2.15 tff(10907,plain,
% 1.95/2.15 (r(s(s(s(z))), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1816, 10906, 10902])).
% 1.95/2.15 tff(10908,plain,
% 1.95/2.15 (~r(s(elem!1), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10701, 10907, 10899, 10905])).
% 1.95/2.15 tff(10909,plain,
% 1.95/2.15 (b(s(elem!1), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2044, 10908, 10903])).
% 1.95/2.15 tff(10910,plain,
% 1.95/2.15 (~b(s(s(s(z))), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10690, 10909, 2345, 10901])).
% 1.95/2.15 tff(10911,plain,
% 1.95/2.15 (r(s(s(s(z))), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2325, 10910])).
% 1.95/2.15 tff(10912,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10559, 121, 110, 10723, 10911, 10899])).
% 1.95/2.15 tff(10913,plain,((elem!1 = s(s(s(z)))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1)) | b(z, elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(10914,plain,
% 1.95/2.16 (elem!1 = s(s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10913, 147, 394, 145, 1, 231, 503, 348, 448, 68, 2344, 199, 110, 3871])).
% 1.95/2.16 tff(10915,plain,
% 1.95/2.16 (s(s(s(z))) = elem!1),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1100, 10914])).
% 1.95/2.16 tff(10916,plain,
% 1.95/2.16 (b(s(z), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10599, 10915, 3871])).
% 1.95/2.16 tff(10917,plain,
% 1.95/2.16 (~(s(s(s(elem!1))) = elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2611, 10915])).
% 1.95/2.16 tff(10918,plain,
% 1.95/2.16 (b(s(s(s(elem!1))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[486, 10917, 147])).
% 1.95/2.16 tff(10919,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[8132, 10918, 10916, 503, 448])).
% 1.95/2.16 tff(10920,plain,(r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1) | (s(z) = s(elem!1)) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1)) | b(z, elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(10921,plain,
% 1.95/2.16 (r(s(s(s(elem!1))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10920, 10593, 503, 3871, 394, 10655, 1, 1257, 348, 68, 2344, 199, 110])).
% 1.95/2.16 tff(10922,plain,
% 1.95/2.16 (~r(elem!1, s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10623, 10921, 111, 10219])).
% 1.95/2.16 tff(10923,plain,
% 1.95/2.16 (~r(s(z), s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10632, 10921, 110, 111])).
% 1.95/2.16 tff(10924,plain,
% 1.95/2.16 (b(s(z), s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[760, 10923])).
% 1.95/2.16 tff(10925,plain,
% 1.95/2.16 (~(s(s(s(z))) = elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10644, 10924, 9149, 503, 10922, 10593])).
% 1.95/2.16 tff(10926,plain,
% 1.95/2.16 (~(elem!1 = s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1100, 10925])).
% 1.95/2.16 tff(10927,plain,
% 1.95/2.16 (~r(s(z), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10703, 10926, 2345, 10593, 2282, 394, 3871, 110, 199, 9297, 219])).
% 1.95/2.16 tff(10928,plain,
% 1.95/2.16 (b(s(z), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[236, 10927, 1257])).
% 1.95/2.16 tff(10929,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10930,plain,
% 1.95/2.16 (((~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(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10931,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10930])).
% 1.95/2.16 tff(10932,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[10931, 10929])).
% 1.95/2.16 tff(10933,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(10934,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10933, 10932])).
% 1.95/2.16 tff(10935,plain,
% 1.95/2.16 (~b(elem!1, s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10934, 271, 10928, 10593, 503])).
% 1.95/2.16 tff(10936,plain,
% 1.95/2.16 (elem!1 = s(s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[660, 21, 10922, 10935])).
% 1.95/2.16 tff(10937,plain,
% 1.95/2.16 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10936])).
% 1.95/2.16 tff(10938,plain,
% 1.95/2.16 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.95/2.16 inference(symmetry,[status(thm)],[10937])).
% 1.95/2.16 tff(10939,plain,
% 1.95/2.16 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10938])).
% 1.95/2.16 tff(10940,plain,
% 1.95/2.16 (~r(s(s(s(elem!1))), elem!1)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[179, 10939])).
% 1.95/2.16 tff(10941,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10921, 10940])).
% 1.95/2.16 tff(10942,plain,(b(z, elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(10943,plain,
% 1.95/2.16 (b(z, elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10942, 258, 394, 3871, 110, 111, 1, 348, 68, 2344, 503])).
% 1.95/2.16 tff(10944,plain,
% 1.95/2.16 (~b(z, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9091, 10943, 2345, 394])).
% 1.95/2.16 tff(10945,plain,
% 1.95/2.16 (r(z, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1439, 10944])).
% 1.95/2.16 tff(10946,plain,
% 1.95/2.16 (~b(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4598, 10943, 2345, 394])).
% 1.95/2.16 tff(10947,plain,
% 1.95/2.16 (r(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2243, 10946, 2207])).
% 1.95/2.16 tff(10948,plain,
% 1.95/2.16 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7694, 10947, 111, 10945])).
% 1.95/2.16 tff(10949,plain,
% 1.95/2.16 (b(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[681, 10948, 79])).
% 1.95/2.16 tff(10950,plain,
% 1.95/2.16 (~b(s(s(s(elem!1))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2401, 271, 2345, 394, 10949])).
% 1.95/2.16 tff(10951,plain,
% 1.95/2.16 (~r(s(elem!1), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2312, 348, 79, 503, 111, 110])).
% 1.95/2.16 tff(10952,plain,
% 1.95/2.16 (~r(s(z), s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10632, 139, 110, 111])).
% 1.95/2.16 tff(10953,plain,
% 1.95/2.16 (b(s(z), s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[760, 10952])).
% 1.95/2.16 tff(10954,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10955,plain,
% 1.95/2.16 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10956,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10955])).
% 1.95/2.16 tff(10957,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[10956, 10954])).
% 1.95/2.16 tff(10958,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(10959,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10958, 10957])).
% 1.95/2.16 tff(10960,plain,
% 1.95/2.16 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10959, 121, 622, 139, 3456])).
% 1.95/2.16 tff(10961,plain,
% 1.95/2.16 (b(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2293, 21, 10960, 6201])).
% 1.95/2.16 tff(10962,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10963,plain,
% 1.95/2.16 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10964,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10963])).
% 1.95/2.16 tff(10965,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[10964, 10962])).
% 1.95/2.16 tff(10966,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(10967,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10966, 10965])).
% 1.95/2.16 tff(10968,plain,
% 1.95/2.16 (~b(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10967, 271, 750, 10961, 638])).
% 1.95/2.16 tff(10969,plain,
% 1.95/2.16 (r(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[429, 10968, 422])).
% 1.95/2.16 tff(10970,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10971,plain,
% 1.95/2.16 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10972,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10971])).
% 1.95/2.16 tff(10973,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[10972, 10970])).
% 1.95/2.16 tff(10974,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(10975,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10974, 10973])).
% 1.95/2.16 tff(10976,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10975, 121, 622, 110, 3456, 10969])).
% 1.95/2.16 tff(10977,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(10978,plain,
% 1.95/2.16 (~r(elem!1, s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10977, 10953, 110, 422, 622, 638, 6201, 139])).
% 1.95/2.16 tff(10979,plain,
% 1.95/2.16 (b(elem!1, s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[299, 10978, 258])).
% 1.95/2.16 tff(10980,plain,
% 1.95/2.16 (r(elem!1, s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10644, 244, 2065, 503, 750, 448])).
% 1.95/2.16 tff(10981,plain,
% 1.95/2.16 (b(z, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6548, 244, 1326])).
% 1.95/2.16 tff(10982,plain,
% 1.95/2.16 (~b(elem!1, z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1315, 10981, 394, 307])).
% 1.95/2.16 tff(10983,plain,
% 1.95/2.16 (r(elem!1, z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[284, 10982, 259])).
% 1.95/2.16 tff(10984,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10985,plain,
% 1.95/2.16 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10986,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10985])).
% 1.95/2.16 tff(10987,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[10986, 10984])).
% 1.95/2.16 tff(10988,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(10989,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10988, 10987])).
% 1.95/2.16 tff(10990,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10989, 121, 111, 10983, 139, 10980])).
% 1.95/2.16 tff(10991,plain,((~(s(s(s(z))) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(10992,plain,
% 1.95/2.16 (~(s(s(s(z))) = elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10991, 139, 111, 259, 394, 307, 1326, 2065, 503, 10953, 10979])).
% 1.95/2.16 tff(10993,plain,
% 1.95/2.16 (~(elem!1 = s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1100, 10992])).
% 1.95/2.16 tff(10994,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.95/2.16 tff(10995,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10996,plain,
% 1.95/2.16 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(10997,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[10996])).
% 1.95/2.16 tff(10998,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[10997, 10995])).
% 1.95/2.16 tff(10999,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(11000,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10999, 10998])).
% 1.95/2.16 tff(11001,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11000, 271, 1326, 448, 220, 3871])).
% 1.95/2.16 tff(11002,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(11003,plain,
% 1.95/2.16 (~b(z, s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11002, 448, 3871, 1326])).
% 1.95/2.16 tff(11004,plain,
% 1.95/2.16 (r(z, s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[904, 11003])).
% 1.95/2.16 tff(11005,plain,
% 1.95/2.16 (~b(s(z), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4827, 5469, 1326, 448])).
% 1.95/2.16 tff(11006,plain,
% 1.95/2.16 (~b(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9353, 221, 307, 1326, 394])).
% 1.95/2.16 tff(11007,plain,
% 1.95/2.16 (r(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1155, 11006])).
% 1.95/2.16 tff(11008,plain,
% 1.95/2.16 ((~r(s(elem!1), z)) <=> (~r(s(s(s(z))), z))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[4003])).
% 1.95/2.16 tff(11009,plain,
% 1.95/2.16 (~r(s(s(s(z))), z)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[10994, 11008])).
% 1.95/2.16 tff(11010,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[109, 11009])).
% 1.95/2.16 tff(11011,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(s(s(s(z))), z)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(11012,plain,
% 1.95/2.16 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11011, 11007, 10994])).
% 1.95/2.16 tff(11013,plain,
% 1.95/2.16 (~b(z, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9091, 1326, 307, 394])).
% 1.95/2.16 tff(11014,plain,
% 1.95/2.16 (r(z, s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1439, 11013])).
% 1.95/2.16 tff(11015,plain,
% 1.95/2.16 (~r(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10675, 10603, 11014, 909])).
% 1.95/2.16 tff(11016,plain,
% 1.95/2.16 (b(s(elem!1), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[429, 11015, 422])).
% 1.95/2.16 tff(11017,plain,
% 1.95/2.16 (~b(z, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1978, 10601, 307, 1326])).
% 1.95/2.16 tff(11018,plain,
% 1.95/2.16 (r(z, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1214, 11017])).
% 1.95/2.16 tff(11019,plain,
% 1.95/2.16 (~r(s(s(s(z))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6541, 11018, 10603, 909])).
% 1.95/2.16 tff(11020,plain,
% 1.95/2.16 (b(s(s(s(z))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2325, 11019])).
% 1.95/2.16 tff(11021,plain,
% 1.95/2.16 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[3288, 10601, 394, 307])).
% 1.95/2.16 tff(11022,plain,
% 1.95/2.16 (r(s(s(s(z))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1816, 11021, 2033])).
% 1.95/2.16 tff(11023,plain,
% 1.95/2.16 (~r(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10701, 11022, 11018, 11014])).
% 1.95/2.16 tff(11024,plain,
% 1.95/2.16 (b(s(elem!1), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2044, 11023, 6284])).
% 1.95/2.16 tff(11025,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[3622, 11024, 11020, 3871, 11016])).
% 1.95/2.16 tff(11026,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (s(s(s(z))) = s(elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | r(s(s(s(z))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(11027,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11026, 11012, 11005, 11004, 3871, 422, 394, 307, 1326, 221, 231])).
% 1.95/2.16 tff(11028,plain,(r(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (s(z) = elem!1) | r(s(elem!1), z) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(11029,plain,
% 1.95/2.16 (r(s(s(s(z))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11028, 10979, 422, 394, 307, 1326, 1257, 10994, 3871, 10992])).
% 1.95/2.16 tff(11030,plain,
% 1.95/2.16 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1956, 1935, 1326, 394])).
% 1.95/2.16 tff(11031,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(11032,plain,
% 1.95/2.16 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(11033,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[11032])).
% 1.95/2.16 tff(11034,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[11033, 11031])).
% 1.95/2.16 tff(11035,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(11036,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[11035, 11034])).
% 1.95/2.16 tff(11037,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11036, 271, 448, 1195, 3871, 1935])).
% 1.95/2.16 tff(11038,plain,((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(11039,plain,
% 1.95/2.16 (~b(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[11038, 1935, 3871, 448])).
% 1.95/2.16 tff(11040,plain,
% 1.95/2.16 (r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1192, 11039, 1102])).
% 1.95/2.16 tff(11041,plain,
% 1.95/2.16 (~r(s(s(s(z))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[5181, 11040, 622, 145])).
% 1.95/2.16 tff(11042,plain,
% 1.95/2.16 (s(s(s(z))) = s(elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1816, 11041, 11030])).
% 1.95/2.17 tff(11043,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11042])).
% 1.95/2.17 tff(11044,plain,
% 1.95/2.17 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(symmetry,[status(thm)],[11043])).
% 1.95/2.17 tff(11045,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[307, 11044])).
% 1.95/2.17 tff(11046,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11039, 11045])).
% 1.95/2.17 tff(11047,plain,((~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11048,plain,
% 1.95/2.17 (~b(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11047, 11029, 622, 307, 10993, 3871, 10979, 1326, 394])).
% 1.95/2.17 tff(11049,plain,
% 1.95/2.17 (r(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1155, 11048])).
% 1.95/2.17 tff(11050,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11051,plain,
% 1.95/2.17 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11052,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11051])).
% 1.95/2.17 tff(11053,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[11052, 11050])).
% 1.95/2.17 tff(11054,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(11055,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11054, 11053])).
% 1.95/2.17 tff(11056,plain,
% 1.95/2.17 (~r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11055, 121, 111, 110, 11049])).
% 1.95/2.17 tff(11057,plain,
% 1.95/2.17 (b(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2325, 11056])).
% 1.95/2.17 tff(11058,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2081, 11057, 10953, 503])).
% 1.95/2.17 tff(11059,plain,
% 1.95/2.17 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2071, 11058, 2065])).
% 1.95/2.17 tff(11060,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11061,plain,
% 1.95/2.17 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11062,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11061])).
% 1.95/2.17 tff(11063,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[11062, 11060])).
% 1.95/2.17 tff(11064,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(11065,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11064, 11063])).
% 1.95/2.17 tff(11066,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11065, 121, 111, 139, 11049, 11059])).
% 1.95/2.17 tff(11067,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | r(s(elem!1), z) | (elem!1 = z) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11068,plain,
% 1.95/2.17 (~r(s(s(s(elem!1))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11067, 10947, 9149, 503, 110, 111, 2345, 3871, 10943, 394, 2282, 10951, 9298, 258, 10949, 85])).
% 1.95/2.17 tff(11069,plain,
% 1.95/2.17 (s(s(s(elem!1))) = elem!1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[486, 11068, 10950])).
% 1.95/2.17 tff(11070,plain,
% 1.95/2.17 ((~r(z, elem!1)) <=> (~r(z, s(s(s(elem!1)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2535])).
% 1.95/2.17 tff(11071,plain,
% 1.95/2.17 (~r(z, s(s(s(elem!1))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[1391, 11070])).
% 1.95/2.17 tff(11072,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[111, 11071])).
% 1.95/2.17 tff(11073,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(z, s(s(s(elem!1))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11074,plain,
% 1.95/2.17 (r(z, elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11073, 11069, 111])).
% 1.95/2.17 tff(11075,plain,
% 1.95/2.17 (~r(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[3387, 11074, 10947, 10945])).
% 1.95/2.17 tff(11076,plain,
% 1.95/2.17 (b(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[284, 11075, 9298])).
% 1.95/2.17 tff(11077,plain,
% 1.95/2.17 (~b(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1315, 11076, 394, 2345])).
% 1.95/2.17 tff(11078,plain,
% 1.95/2.17 (r(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1214, 11077])).
% 1.95/2.17 tff(11079,plain,
% 1.95/2.17 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2596, 11069])).
% 1.95/2.17 tff(11080,plain,
% 1.95/2.17 (~(s(s(s(z))) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2611, 11069])).
% 1.95/2.17 tff(11081,plain,
% 1.95/2.17 (~(elem!1 = s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1100, 11080])).
% 1.95/2.17 tff(11082,plain,
% 1.95/2.17 (~(elem!1 = s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1100, 2612])).
% 1.95/2.17 tff(11083,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2505])).
% 1.95/2.17 tff(11084,plain,
% 1.95/2.17 (b(elem!1, s(z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[503, 11083])).
% 1.95/2.17 tff(11085,plain,
% 1.95/2.17 (~b(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10250, 11084, 3871, 221, 147, 503])).
% 1.95/2.17 tff(11086,plain,
% 1.95/2.17 (r(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[236, 11085, 231])).
% 1.95/2.17 tff(11087,plain,
% 1.95/2.17 (~r(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1797, 11086, 110, 378])).
% 1.95/2.17 tff(11088,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1192, 11087, 11082])).
% 1.95/2.17 tff(11089,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10611, 271, 11084, 11088, 3871, 10296])).
% 1.95/2.17 tff(11090,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, elem!1)) | (s(z) = elem!1) | r(s(s(s(z))), elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11091,plain,
% 1.95/2.17 (r(s(s(s(z))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11090, 11069, 110, 11074, 1257, 11068, 3871, 503])).
% 1.95/2.17 tff(11092,plain,
% 1.95/2.17 (~r(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6723, 11078, 11074, 11091])).
% 1.95/2.17 tff(11093,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1192, 11092, 11081])).
% 1.95/2.17 tff(11094,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1811, 11093, 2345, 394])).
% 1.95/2.17 tff(11095,plain,
% 1.95/2.17 (r(s(s(s(z))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1816, 11094, 11079])).
% 1.95/2.17 tff(11096,plain,
% 1.95/2.17 (~(s(elem!1) = s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2035, 11079])).
% 1.95/2.17 tff(11097,plain,
% 1.95/2.17 (~b(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10721, 11074, 3871, 11091, 9298, 394, 2345])).
% 1.95/2.17 tff(11098,plain,
% 1.95/2.17 (r(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[904, 11097])).
% 1.95/2.17 tff(11099,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10559, 121, 110, 909, 2327, 1140])).
% 1.95/2.17 tff(11100,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11101,plain,
% 1.95/2.17 (~r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11100, 11078, 11098, 110])).
% 1.95/2.17 tff(11102,plain,
% 1.95/2.17 (b(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2325, 11101])).
% 1.95/2.17 tff(11103,plain,
% 1.95/2.17 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10690, 11093, 2345, 11102])).
% 1.95/2.17 tff(11104,plain,
% 1.95/2.17 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2044, 11103, 11096])).
% 1.95/2.17 tff(11105,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10701, 11104, 11095, 11078, 10945])).
% 1.95/2.17 tff(11106,plain,((elem!1 = s(z)) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11107,plain,
% 1.95/2.17 (elem!1 = s(z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11106, 2344, 110, 3871, 67, 111, 1, 348, 68, 394])).
% 1.95/2.17 tff(11108,plain,
% 1.95/2.17 (s(z) = elem!1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[242, 11107])).
% 1.95/2.17 tff(11109,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[239])).
% 1.95/2.17 tff(11110,plain,
% 1.95/2.17 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(symmetry,[status(thm)],[11109])).
% 1.95/2.17 tff(11111,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[3871, 11110])).
% 1.95/2.17 tff(11112,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.95/2.17 tff(11113,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11112, 11111])).
% 1.95/2.17 tff(11114,plain,((~(elem!1 = s(z))) | b(elem!1, s(s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11115,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11114, 11107, 3871])).
% 1.95/2.17 tff(11116,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1811, 11115, 2345, 394])).
% 1.95/2.17 tff(11117,plain,
% 1.95/2.17 (~(s(s(s(z))) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[4909, 11116, 2345])).
% 1.95/2.17 tff(11118,plain,
% 1.95/2.17 (s(elem!1) = s(s(z))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11107])).
% 1.95/2.17 tff(11119,plain,
% 1.95/2.17 (s(s(elem!1)) = s(s(s(z)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11118])).
% 1.95/2.17 tff(11120,plain,
% 1.95/2.17 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11119, 11118])).
% 1.95/2.17 tff(11121,plain,
% 1.95/2.17 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.95/2.17 inference(symmetry,[status(thm)],[11120])).
% 1.95/2.17 tff(11122,plain,
% 1.95/2.17 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11121])).
% 1.95/2.17 tff(11123,plain,
% 1.95/2.17 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11118])).
% 1.95/2.17 tff(11124,plain,
% 1.95/2.17 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11123])).
% 1.95/2.17 tff(11125,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(s(z)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11116, 11124])).
% 1.95/2.17 tff(11126,plain,
% 1.95/2.17 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11125, 11122])).
% 1.95/2.17 tff(11127,plain,
% 1.95/2.17 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[701, 11126, 3313])).
% 1.95/2.17 tff(11128,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11107])).
% 1.95/2.17 tff(11129,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.95/2.17 inference(symmetry,[status(thm)],[11128])).
% 1.95/2.17 tff(11130,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), elem!1)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[67, 11129])).
% 1.95/2.17 tff(11131,plain,
% 1.95/2.17 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[551, 10366, 307, 504])).
% 1.95/2.17 tff(11132,plain,
% 1.95/2.17 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[556, 11131, 1])).
% 1.95/2.17 tff(11133,plain,
% 1.95/2.17 (b(s(z), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1276, 2359, 307])).
% 1.95/2.17 tff(11134,plain,
% 1.95/2.17 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[3879, 257, 3871, 11133])).
% 1.95/2.17 tff(11135,plain,
% 1.95/2.17 (~b(s(elem!1), s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2369, 11134, 239])).
% 1.95/2.17 tff(11136,plain,
% 1.95/2.17 (r(s(elem!1), s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[526, 11135, 211])).
% 1.95/2.17 tff(11137,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11138,plain,
% 1.95/2.17 (((~r(s(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)))) | (~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(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11139,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11138])).
% 1.95/2.17 tff(11140,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[11139, 11137])).
% 1.95/2.17 tff(11141,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(11142,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11141, 11140])).
% 1.95/2.17 tff(11143,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11142, 121, 623, 627, 573, 798])).
% 1.95/2.17 tff(11144,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11145,plain,
% 1.95/2.17 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11144, 10368, 11136, 11132])).
% 1.95/2.17 tff(11146,plain,
% 1.95/2.17 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[3201, 11132, 683, 11136])).
% 1.95/2.17 tff(11147,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[681, 82, 676])).
% 1.95/2.17 tff(11148,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.95/2.17 tff(11149,plain,
% 1.95/2.17 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2293, 21, 11148])).
% 1.95/2.17 tff(11150,plain,
% 1.95/2.17 (b(s(elem!1), s(s(s(elem!1))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11149, 2280])).
% 1.95/2.17 tff(11151,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10045, 11150, 11147, 504, 307])).
% 1.95/2.17 tff(11152,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | r(s(elem!1), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11153,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11152, 11146, 11145, 82, 307, 504])).
% 1.95/2.17 tff(11154,plain,((~b(s(s(s(z))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(11155,plain,
% 1.95/2.17 (~b(s(s(s(z))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11154, 2345, 79, 11130, 11127, 1, 11107, 3871])).
% 1.95/2.17 tff(11156,plain,
% 1.95/2.17 (r(s(s(s(z))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[255, 11155, 11117])).
% 1.95/2.17 tff(11157,plain,
% 1.95/2.17 (~r(s(s(s(s(z)))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1238, 11108, 38])).
% 1.95/2.17 tff(11158,plain,
% 1.95/2.17 (b(s(s(s(s(z)))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[932, 11157])).
% 1.95/2.17 tff(11159,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1225])).
% 1.95/2.17 tff(11160,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1224])).
% 1.95/2.17 tff(11161,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[11160, 11159])).
% 1.95/2.17 tff(11162,plain,
% 1.95/2.17 (b(elem!1, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11114, 239, 3871])).
% 1.95/2.17 tff(11163,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1811, 11162, 307, 394])).
% 1.95/2.17 tff(11164,plain,
% 1.95/2.17 (~(s(s(s(z))) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[4909, 11163, 307])).
% 1.95/2.17 tff(11165,plain,
% 1.95/2.17 (~(elem!1 = s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1100, 11164])).
% 1.95/2.17 tff(11166,plain,
% 1.95/2.17 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1516, 11165])).
% 1.95/2.17 tff(11167,plain,
% 1.95/2.17 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1223])).
% 1.95/2.17 tff(11168,plain,
% 1.95/2.17 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.95/2.17 inference(symmetry,[status(thm)],[11167])).
% 1.95/2.17 tff(11169,plain,
% 1.95/2.17 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11168])).
% 1.95/2.17 tff(11170,plain,
% 1.95/2.17 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[239])).
% 1.95/2.17 tff(11171,plain,
% 1.95/2.17 (r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[145, 11170])).
% 1.95/2.17 tff(11172,plain,
% 1.95/2.17 (~r(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10548, 121, 110, 909, 11171])).
% 1.95/2.17 tff(11173,plain,
% 1.95/2.17 (b(s(s(s(z))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1155, 11172])).
% 1.95/2.17 tff(11174,plain,
% 1.95/2.17 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.95/2.17 inference(monotonicity,[status(thm)],[1223])).
% 1.95/2.17 tff(11175,plain,
% 1.95/2.17 (b(s(s(z)), z)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[394, 11174])).
% 1.95/2.17 tff(11176,plain,
% 1.95/2.17 (~r(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[11100, 909, 11171, 110])).
% 1.95/2.17 tff(11177,plain,
% 1.95/2.17 (b(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1214, 11176])).
% 1.95/2.17 tff(11178,plain,
% 1.95/2.17 (~b(s(s(z)), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[10567, 271, 11177, 11175, 11173])).
% 1.95/2.17 tff(11179,plain,
% 1.95/2.17 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11178, 11169])).
% 1.95/2.17 tff(11180,plain,
% 1.95/2.17 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2403, 11179, 307, 503, 239, 11166, 145, 216, 394])).
% 1.95/2.17 tff(11181,plain,
% 1.95/2.17 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[586, 11180, 6943])).
% 1.95/2.17 tff(11182,plain,
% 1.95/2.17 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[11181, 11161])).
% 1.95/2.17 tff(11183,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(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))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11184,plain,
% 1.95/2.17 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(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))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(11185,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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)))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[11184])).
% 1.95/2.17 tff(11186,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(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))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[11185, 11183])).
% 1.95/2.18 tff(11187,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11188,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11187, 11186])).
% 1.95/2.18 tff(11189,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11188, 271, 3871, 937, 11173, 11182])).
% 1.95/2.18 tff(11190,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11191,plain,
% 1.95/2.18 (~r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11190, 11158, 3871, 11107, 563, 2345, 67, 11156, 211, 394, 110])).
% 1.95/2.18 tff(11192,plain,
% 1.95/2.18 (b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[904, 11191])).
% 1.95/2.18 tff(11193,plain,
% 1.95/2.18 (~r(z, elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[10721, 11192, 3871, 11156, 9298, 394, 2345])).
% 1.95/2.18 tff(11194,plain,
% 1.95/2.18 (b(z, elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[229, 11192, 11108])).
% 1.95/2.18 tff(11195,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9060, 11194, 11193, 85, 111, 110, 2345, 67, 11108])).
% 1.95/2.18 tff(11196,plain,(r(elem!1, s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z)) | (s(z) = s(elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11197,plain,
% 1.95/2.18 (r(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11196, 3871, 110, 111, 394, 1, 38, 348, 68])).
% 1.95/2.18 tff(11198,plain,
% 1.95/2.18 (~r(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2312, 348, 79, 67, 111, 110])).
% 1.95/2.18 tff(11199,plain,
% 1.95/2.18 (b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[904, 899])).
% 1.95/2.18 tff(11200,plain,
% 1.95/2.18 (~b(elem!1, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11002, 220, 3871, 1326])).
% 1.95/2.18 tff(11201,plain,
% 1.95/2.18 (r(elem!1, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[299, 258, 11200])).
% 1.95/2.18 tff(11202,plain,
% 1.95/2.18 (b(elem!1, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9270, 220, 232, 377, 1326, 394, 231, 379, 348])).
% 1.95/2.18 tff(11203,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[4817, 11202, 220, 1326, 8181])).
% 1.95/2.18 tff(11204,plain,((~b(z, s(z))) | (~b(z, elem!1)) | r(s(z), elem!1) | (elem!1 = s(elem!1)) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11205,plain,
% 1.95/2.18 (r(s(z), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11204, 1257, 1326, 377, 394, 348, 379, 220])).
% 1.95/2.18 tff(11206,plain,
% 1.95/2.18 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.95/2.18 inference(symmetry,[status(thm)],[2202])).
% 1.95/2.18 tff(11207,plain,
% 1.95/2.18 (s(elem!1) = elem!1),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[212, 11206])).
% 1.95/2.18 tff(11208,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2564, 11207])).
% 1.95/2.18 tff(11209,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11210,plain,
% 1.95/2.18 (~(elem!1 = s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11209, 2564])).
% 1.95/2.18 tff(11211,plain,
% 1.95/2.18 (b(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[409, 10994])).
% 1.95/2.18 tff(11212,plain,
% 1.95/2.18 (~r(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6525, 3456, 357, 622])).
% 1.95/2.18 tff(11213,plain,
% 1.95/2.18 (b(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[444, 11212, 348])).
% 1.95/2.18 tff(11214,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11215,plain,
% 1.95/2.18 (((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11216,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11215])).
% 1.95/2.18 tff(11217,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11216, 11214])).
% 1.95/2.18 tff(11218,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11219,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11218, 11217])).
% 1.95/2.18 tff(11220,plain,
% 1.95/2.18 (~r(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11219, 121, 622, 357, 3456])).
% 1.95/2.18 tff(11221,plain,
% 1.95/2.18 (b(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[429, 11220, 2282])).
% 1.95/2.18 tff(11222,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11223,plain,
% 1.95/2.18 (((~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(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11224,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11223])).
% 1.95/2.18 tff(11225,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11224, 11222])).
% 1.95/2.18 tff(11226,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11227,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11226, 11225])).
% 1.95/2.18 tff(11228,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11227, 271, 394, 220, 11221, 11213])).
% 1.95/2.18 tff(11229,plain,((~r(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11230,plain,
% 1.95/2.18 (~r(s(elem!1), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11229, 3456, 220, 11211, 357, 348])).
% 1.95/2.18 tff(11231,plain,
% 1.95/2.18 (b(s(elem!1), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2243, 11230, 2564])).
% 1.95/2.18 tff(11232,plain,
% 1.95/2.18 (~b(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[4598, 11231, 11211, 1326])).
% 1.95/2.18 tff(11233,plain,
% 1.95/2.18 (r(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[392, 11232, 11210])).
% 1.95/2.18 tff(11234,plain,
% 1.95/2.18 (~b(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9241, 1281, 220, 394])).
% 1.95/2.18 tff(11235,plain,
% 1.95/2.18 (~r(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9263, 1281, 3456, 1326, 348, 379])).
% 1.95/2.18 tff(11236,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[444, 11235, 11234, 348])).
% 1.95/2.18 tff(11237,plain,((~b(s(z), z)) | (s(z) = s(elem!1)) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11238,plain,
% 1.95/2.18 (~b(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11237, 3456, 348, 1326, 11233, 220, 11211])).
% 1.95/2.18 tff(11239,plain,
% 1.95/2.18 (r(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[25, 11238])).
% 1.95/2.18 tff(11240,plain,
% 1.95/2.18 (~r(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[8953, 11239, 3456, 11233])).
% 1.95/2.18 tff(11241,plain,
% 1.95/2.18 (b(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[429, 11240, 2282])).
% 1.95/2.18 tff(11242,plain,
% 1.95/2.18 (~b(s(z), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[8926, 11241, 11211, 220])).
% 1.95/2.18 tff(11243,plain,
% 1.95/2.18 (~(s(s(s(z))) = elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[10599, 11242, 3871])).
% 1.95/2.18 tff(11244,plain,
% 1.95/2.18 (~(elem!1 = s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1100, 11243])).
% 1.95/2.18 tff(11245,plain,
% 1.95/2.18 (~b(elem!1, s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9291, 11231, 1326, 11211])).
% 1.95/2.18 tff(11246,plain,
% 1.95/2.18 (r(elem!1, s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1192, 11245, 11244])).
% 1.95/2.18 tff(11247,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11248,plain,
% 1.95/2.18 (((~r(s(z), elem!1)) | (~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(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11249,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11248])).
% 1.95/2.18 tff(11250,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11249, 11247])).
% 1.95/2.18 tff(11251,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11252,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11251, 11250])).
% 1.95/2.18 tff(11253,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11252, 121, 357, 1184, 3456, 2327])).
% 1.95/2.18 tff(11254,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11255,plain,
% 1.95/2.18 (~r(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11254, 11246, 357, 3456])).
% 1.95/2.18 tff(11256,plain,
% 1.95/2.18 (b(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2325, 11255])).
% 1.95/2.18 tff(11257,plain,
% 1.95/2.18 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3622, 11256, 3871, 11241])).
% 1.95/2.18 tff(11258,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11259,plain,
% 1.95/2.18 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11260,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11259])).
% 1.95/2.18 tff(11261,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11260, 11258])).
% 1.95/2.18 tff(11262,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11263,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11262, 11261])).
% 1.95/2.18 tff(11264,plain,
% 1.95/2.18 (~b(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11263, 271, 220, 3871, 11256])).
% 1.95/2.18 tff(11265,plain,
% 1.95/2.18 (r(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1155, 11264])).
% 1.95/2.18 tff(11266,plain,
% 1.95/2.18 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11011, 11265, 10994])).
% 1.95/2.18 tff(11267,plain,
% 1.95/2.18 (~(s(elem!1) = s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2035, 11266])).
% 1.95/2.18 tff(11268,plain,
% 1.95/2.18 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2044, 11267, 11257])).
% 1.95/2.18 tff(11269,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11270,plain,
% 1.95/2.18 (((~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11271,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11270])).
% 1.95/2.18 tff(11272,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11271, 11269])).
% 1.95/2.18 tff(11273,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11274,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11273, 11272])).
% 1.95/2.18 tff(11275,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11274, 121, 11233, 11246, 11265, 11268])).
% 1.95/2.18 tff(11276,plain,((~r(elem!1, s(z))) | r(s(elem!1), z) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11277,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11276, 11205, 11201, 3500, 3871, 10994, 1326, 348, 220])).
% 1.95/2.18 tff(11278,plain,((elem!1 = s(z)) | (~b(s(z), s(s(s(z))))) | r(s(elem!1), z) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11279,plain,
% 1.95/2.18 (elem!1 = s(z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11278, 11199, 10994, 379, 348, 3871, 377, 394, 1326])).
% 1.95/2.18 tff(11280,plain,
% 1.95/2.18 (s(z) = elem!1),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[242, 11279])).
% 1.95/2.18 tff(11281,plain,
% 1.95/2.18 (r(z, s(z)) <=> r(z, elem!1)),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11280])).
% 1.95/2.18 tff(11282,plain,
% 1.95/2.18 (r(z, elem!1) <=> r(z, s(z))),
% 1.95/2.18 inference(symmetry,[status(thm)],[11281])).
% 1.95/2.18 tff(11283,plain,
% 1.95/2.18 (elem!1 = s(z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11278, 220, 10994, 1326, 348, 3871, 377, 394, 3502])).
% 1.95/2.18 tff(11284,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11285,plain,
% 1.95/2.18 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(11286,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[11285])).
% 1.95/2.18 tff(11287,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11286, 11284])).
% 1.95/2.18 tff(11288,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(11289,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11288, 11287])).
% 1.95/2.18 tff(11290,plain,
% 1.95/2.18 (~b(s(s(s(elem!1))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11289, 271, 220, 3871, 67])).
% 1.95/2.18 tff(11291,plain,
% 1.95/2.18 (r(s(s(s(elem!1))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[8229, 11290])).
% 1.95/2.18 tff(11292,plain,
% 1.95/2.18 (~r(s(z), s(s(s(elem!1))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6221, 121, 111, 110, 11291])).
% 1.95/2.18 tff(11293,plain,
% 1.95/2.18 (s(z) = elem!1),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[242, 11283])).
% 1.95/2.18 tff(11294,plain,
% 1.95/2.18 (~r(s(s(s(s(z)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1238, 11293, 38])).
% 1.95/2.18 tff(11295,plain,
% 1.95/2.18 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[1226])).
% 1.95/2.18 tff(11296,plain,
% 1.95/2.18 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.95/2.18 inference(symmetry,[status(thm)],[11295])).
% 1.95/2.18 tff(11297,assumption,(~r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.95/2.18 tff(11298,assumption,(~(s(z) = s(s(s(elem!1))))), introduced(assumption)).
% 1.95/2.18 tff(11299,plain,
% 1.95/2.18 (b(s(z), s(s(s(elem!1))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[759, 11298, 11297])).
% 1.95/2.18 tff(11300,plain,
% 1.95/2.18 (b(s(z), s(s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[11299, 11296])).
% 1.95/2.18 tff(11301,plain,
% 1.95/2.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[2073, 6661])).
% 1.95/2.18 tff(11302,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[1226])).
% 1.95/2.18 tff(11303,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[11302, 2858])).
% 1.95/2.18 tff(11304,plain,
% 1.95/2.18 (s(z) = s(s(s(elem!1)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[923, 11303])).
% 1.95/2.18 tff(11305,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11298, 11304])).
% 1.95/2.18 tff(11306,plain,((~(s(s(s(s(z)))) = s(z))) | (s(z) = s(s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(11307,plain,
% 1.95/2.18 (~(s(s(s(s(z)))) = s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11306, 11298, 239])).
% 1.95/2.18 tff(11308,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[930, 21])).
% 1.95/2.18 tff(11309,plain,
% 1.95/2.18 (b(s(s(s(s(z)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[11308, 11307, 922])).
% 1.95/2.18 tff(11310,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11311,plain,
% 1.95/2.19 (((~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11312,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11311])).
% 1.95/2.19 tff(11313,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[11312, 11310])).
% 1.95/2.19 tff(11314,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11315,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11314, 11313])).
% 1.95/2.19 tff(11316,plain,
% 1.95/2.19 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11315, 271, 3871, 11309])).
% 1.95/2.19 tff(11317,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11316, 11301, 11300])).
% 1.95/2.19 tff(11318,plain,((s(z) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | r(s(s(s(s(z)))), s(z)) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(11319,plain,
% 1.95/2.19 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | r(s(s(s(s(z)))), s(z)) | r(s(z), s(s(s(elem!1))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11318, 61])).
% 1.95/2.19 tff(11320,plain,
% 1.95/2.19 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11319, 11294, 3871, 11292, 11283])).
% 1.95/2.19 tff(11321,plain,
% 1.95/2.19 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2071, 11320, 9149])).
% 1.95/2.19 tff(11322,plain,
% 1.95/2.19 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[8812, 11321, 11283])).
% 1.95/2.19 tff(11323,plain,
% 1.95/2.19 (s(elem!1) = s(s(z))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11283])).
% 1.95/2.19 tff(11324,plain,
% 1.95/2.19 (s(s(elem!1)) = s(s(s(z)))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11323])).
% 1.95/2.19 tff(11325,plain,
% 1.95/2.19 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11324])).
% 1.95/2.19 tff(11326,plain,
% 1.95/2.19 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11325])).
% 1.95/2.19 tff(11327,plain,
% 1.95/2.19 (r(s(s(s(s(z)))), z)),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11291, 11326])).
% 1.95/2.19 tff(11328,plain,
% 1.95/2.19 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11325])).
% 1.95/2.19 tff(11329,plain,
% 1.95/2.19 (r(z, s(s(s(s(z)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[111, 11328])).
% 1.95/2.19 tff(11330,plain,
% 1.95/2.19 (~b(s(z), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3576, 11283, 317])).
% 1.95/2.19 tff(11331,plain,
% 1.95/2.19 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4929, 11330, 3871])).
% 1.95/2.19 tff(11332,plain,
% 1.95/2.19 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11283])).
% 1.95/2.19 tff(11333,plain,
% 1.95/2.19 (~(z = elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[10035, 11211, 3871, 221, 220])).
% 1.95/2.19 tff(11334,plain,
% 1.95/2.19 (b(z, elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[355, 11333, 1391])).
% 1.95/2.19 tff(11335,plain,
% 1.95/2.19 (~b(elem!1, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11002, 11334, 220, 3871])).
% 1.95/2.19 tff(11336,plain,
% 1.95/2.19 (~(s(z) = s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[343, 11333])).
% 1.95/2.19 tff(11337,plain,
% 1.95/2.19 (~(z = elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[10035, 394, 3871, 221, 220])).
% 1.95/2.19 tff(11338,plain,
% 1.95/2.19 (~(s(z) = s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[343, 11337])).
% 1.95/2.19 tff(11339,plain,
% 1.95/2.19 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2063, 11338])).
% 1.95/2.19 tff(11340,plain,
% 1.95/2.19 (b(elem!1, s(s(s(z))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[3871, 7868])).
% 1.95/2.19 tff(11341,plain,
% 1.95/2.19 (b(elem!1, s(s(elem!1)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11340, 7870])).
% 1.95/2.19 tff(11342,plain,
% 1.95/2.19 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.95/2.19 inference(monotonicity,[status(thm)],[1037])).
% 1.95/2.19 tff(11343,plain,
% 1.95/2.19 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.95/2.19 inference(symmetry,[status(thm)],[11342])).
% 1.95/2.19 tff(11344,plain,
% 1.95/2.19 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(z))), z))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11343])).
% 1.95/2.19 tff(11345,plain,
% 1.95/2.19 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[4949])).
% 1.95/2.19 tff(11346,plain,
% 1.95/2.19 (~r(s(s(elem!1)), elem!1)),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[221, 11345])).
% 1.95/2.19 tff(11347,plain,
% 1.95/2.19 (b(s(s(elem!1)), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[540, 21, 11346, 6796])).
% 1.95/2.19 tff(11348,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11349,plain,
% 1.95/2.19 (((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11350,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11349])).
% 1.95/2.19 tff(11351,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[11350, 11348])).
% 1.95/2.19 tff(11352,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11353,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11352, 11351])).
% 1.95/2.19 tff(11354,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11353, 271, 1326, 1195, 2449, 542])).
% 1.95/2.19 tff(11355,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(11356,plain,
% 1.95/2.19 (~b(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11355, 11347, 1326, 11340])).
% 1.95/2.19 tff(11357,plain,
% 1.95/2.19 (~b(s(s(s(z))), z)),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11356, 11344])).
% 1.95/2.19 tff(11358,plain,
% 1.95/2.19 (r(s(s(s(z))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1155, 11357])).
% 1.95/2.19 tff(11359,plain,
% 1.95/2.19 (~b(s(z), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3576, 1222, 317])).
% 1.95/2.19 tff(11360,plain,
% 1.95/2.19 (~(s(s(s(z))) = s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4929, 11359, 3871])).
% 1.95/2.19 tff(11361,plain,
% 1.95/2.19 (~(s(elem!1) = s(s(elem!1)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11360, 7915])).
% 1.95/2.19 tff(11362,plain,
% 1.95/2.19 (r(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[392, 317, 11210])).
% 1.95/2.19 tff(11363,plain,
% 1.95/2.19 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[4963, 5621])).
% 1.95/2.19 tff(11364,plain,
% 1.95/2.19 (~b(z, s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2222, 542, 1326, 588])).
% 1.95/2.19 tff(11365,plain,
% 1.95/2.19 (r(z, s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2106, 11364])).
% 1.95/2.19 tff(11366,plain,
% 1.95/2.19 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[3060])).
% 1.95/2.19 tff(11367,plain,
% 1.95/2.19 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[3058, 11366])).
% 1.95/2.19 tff(11368,plain,
% 1.95/2.19 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11367])).
% 1.95/2.19 tff(11369,plain,
% 1.95/2.19 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5949, 271, 588, 5606, 542])).
% 1.95/2.19 tff(11370,plain,
% 1.95/2.19 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11369, 11368])).
% 1.95/2.19 tff(11371,plain,
% 1.95/2.19 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1733, 11370])).
% 1.95/2.19 tff(11372,plain,
% 1.95/2.19 ((~b(z, s(s(s(s(elem!1)))))) <=> (~b(z, s(s(s(s(s(z)))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[5603])).
% 1.95/2.19 tff(11373,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11374,plain,
% 1.95/2.19 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11375,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11374])).
% 1.95/2.19 tff(11376,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[11375, 11373])).
% 1.95/2.19 tff(11377,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11378,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11377, 11376])).
% 1.95/2.19 tff(11379,plain,
% 1.95/2.19 (~b(z, s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11378, 271, 1326, 588, 5606])).
% 1.95/2.19 tff(11380,plain,
% 1.95/2.19 (~b(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11379, 11372])).
% 1.95/2.19 tff(11381,plain,
% 1.95/2.19 (r(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1658, 11380])).
% 1.95/2.19 tff(11382,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5135, 11381, 11371, 1477, 109])).
% 1.95/2.19 tff(11383,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(11384,plain,
% 1.95/2.19 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11383, 1477, 109, 223, 1326, 588, 542])).
% 1.95/2.19 tff(11385,plain,
% 1.95/2.19 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[8096, 11384, 223])).
% 1.95/2.19 tff(11386,plain,
% 1.95/2.19 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[840, 11385, 7890])).
% 1.95/2.19 tff(11387,plain,
% 1.95/2.19 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11386, 3080])).
% 1.95/2.19 tff(11388,plain,
% 1.95/2.19 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[4982])).
% 1.95/2.19 tff(11389,plain,
% 1.95/2.19 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[1477, 11388])).
% 1.95/2.19 tff(11390,plain,
% 1.95/2.19 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[3057])).
% 1.95/2.19 tff(11391,plain,
% 1.95/2.19 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[11390])).
% 1.95/2.19 tff(11392,plain,
% 1.95/2.19 (r(z, s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[1661, 11391])).
% 1.95/2.19 tff(11393,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11394,plain,
% 1.95/2.19 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11395,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11394])).
% 1.95/2.19 tff(11396,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[11395, 11393])).
% 1.95/2.19 tff(11397,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11398,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11397, 11396])).
% 1.95/2.19 tff(11399,plain,
% 1.95/2.19 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11398, 121, 2088, 10184])).
% 1.95/2.19 tff(11400,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11399, 11392, 11389])).
% 1.95/2.19 tff(11401,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(11402,plain,
% 1.95/2.19 (~r(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11401, 11387, 11365, 223, 1477])).
% 1.95/2.19 tff(11403,plain,
% 1.95/2.19 (b(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1658, 11402])).
% 1.95/2.19 tff(11404,plain,
% 1.95/2.19 (b(z, s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11403, 5604])).
% 1.95/2.19 tff(11405,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11406,plain,
% 1.95/2.19 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(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(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11407,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11406])).
% 1.95/2.19 tff(11408,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[11407, 11405])).
% 1.95/2.19 tff(11409,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11410,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11409, 11408])).
% 1.95/2.19 tff(11411,plain,
% 1.95/2.19 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11410, 121, 379, 622, 11387])).
% 1.95/2.19 tff(11412,plain,
% 1.95/2.19 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5634, 21, 11411])).
% 1.95/2.19 tff(11413,plain,
% 1.95/2.19 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11412, 11363])).
% 1.95/2.19 tff(11414,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11415,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[11414, 5880])).
% 1.95/2.19 tff(11416,plain,
% 1.95/2.19 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11415, 121, 379, 622, 11387])).
% 1.95/2.19 tff(11417,plain,
% 1.95/2.19 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3112, 21, 4963, 11416])).
% 1.95/2.19 tff(11418,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11419,plain,
% 1.95/2.19 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(11420,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[11419])).
% 1.95/2.19 tff(11421,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[11420, 11418])).
% 1.95/2.19 tff(11422,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(11423,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[11422, 11421])).
% 1.95/2.20 tff(11424,plain,
% 1.95/2.20 (~b(z, s(s(s(s(elem!1)))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[11423, 271, 394, 11417, 11413])).
% 1.95/2.20 tff(11425,plain,
% 1.95/2.20 ($false),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[11424, 11404])).
% 1.95/2.20 tff(11426,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.20 tff(11427,plain,
% 1.95/2.20 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[11426, 622, 394, 379, 223, 109, 1326, 588, 542])).
% 1.95/2.20 tff(11428,plain,
% 1.95/2.20 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1494, 11427])).
% 1.95/2.20 tff(11429,plain,
% 1.95/2.20 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[7865, 11428, 223])).
% 1.95/2.20 tff(11430,plain,
% 1.95/2.20 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[11429, 4980])).
% 1.95/2.20 tff(11431,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.95/2.20 inference(rewrite,[status(thm)],[])).
% 1.95/2.20 tff(11432,plain,
% 1.95/2.20 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.95/2.20 inference(rewrite,[status(thm)],[])).
% 1.95/2.20 tff(11433,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.95/2.20 inference(monotonicity,[status(thm)],[11432])).
% 1.95/2.20 tff(11434,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.95/2.20 inference(transitivity,[status(thm)],[11433, 11431])).
% 1.95/2.20 tff(11435,plain,
% 1.95/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.95/2.20 inference(quant_inst,[status(thm)],[])).
% 1.95/2.20 tff(11436,plain,
% 1.95/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[11435, 11434])).
% 1.95/2.20 tff(11437,plain,
% 1.95/2.20 ($false),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[11436, 271, 588, 5606, 542, 5021])).
% 1.95/2.20 tff(11438,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.20 tff(11439,plain,
% 1.95/2.20 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11438, 11430, 542, 588])).
% 2.03/2.20 tff(11440,plain,
% 2.03/2.20 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[8096, 11439, 223])).
% 2.03/2.20 tff(11441,plain,
% 2.03/2.20 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[840, 11440, 7890])).
% 2.03/2.20 tff(11442,plain,
% 2.03/2.20 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11441, 3080])).
% 2.03/2.20 tff(11443,plain,
% 2.03/2.20 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11410, 121, 379, 622, 11442])).
% 2.03/2.20 tff(11444,plain,
% 2.03/2.20 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[5634, 21, 11443])).
% 2.03/2.20 tff(11445,plain,
% 2.03/2.20 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11444, 11363])).
% 2.03/2.20 tff(11446,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11415, 121, 379, 622, 11442])).
% 2.03/2.20 tff(11447,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3112, 21, 4963, 11446])).
% 2.03/2.20 tff(11448,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11449,plain,
% 2.03/2.20 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11450,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[11449])).
% 2.03/2.20 tff(11451,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[11450, 11448])).
% 2.03/2.20 tff(11452,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(11453,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11452, 11451])).
% 2.03/2.20 tff(11454,plain,
% 2.03/2.20 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11453, 271, 11447, 11430, 11445])).
% 2.03/2.20 tff(11455,plain,
% 2.03/2.20 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[526, 11454, 216])).
% 2.03/2.20 tff(11456,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11457,plain,
% 2.03/2.20 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11458,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[11457])).
% 2.03/2.20 tff(11459,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.03/2.20 inference(transitivity,[status(thm)],[11458, 11456])).
% 2.03/2.20 tff(11460,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(11461,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11460, 11459])).
% 2.03/2.20 tff(11462,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11461, 121, 379, 684, 627, 139])).
% 2.03/2.20 tff(11463,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(11464,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11463, 139, 379, 627])).
% 2.03/2.20 tff(11465,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[1373, 3057])).
% 2.03/2.20 tff(11466,plain,
% 2.03/2.20 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(symmetry,[status(thm)],[11465])).
% 2.03/2.20 tff(11467,plain,
% 2.03/2.20 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[6891])).
% 2.03/2.20 tff(11468,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11469,plain,
% 2.03/2.20 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11470,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[11469])).
% 2.03/2.20 tff(11471,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[11470, 11468])).
% 2.03/2.20 tff(11472,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(11473,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11472, 11471])).
% 2.03/2.20 tff(11474,plain,
% 2.03/2.20 ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11473, 121, 379, 139])).
% 2.03/2.20 tff(11475,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11474, 10184])).
% 2.03/2.20 tff(11476,plain,
% 2.03/2.20 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11475, 11467])).
% 2.03/2.20 tff(11477,plain,
% 2.03/2.20 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1776, 11476, 4035])).
% 2.03/2.20 tff(11478,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11477, 11466])).
% 2.03/2.20 tff(11479,plain,
% 2.03/2.20 ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11415, 121, 379, 622])).
% 2.03/2.20 tff(11480,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11479, 10184])).
% 2.03/2.20 tff(11481,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3112, 21, 3109, 11480])).
% 2.03/2.20 tff(11482,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11483,plain,
% 2.03/2.20 (((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11484,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[11483])).
% 2.03/2.20 tff(11485,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[11484, 11482])).
% 2.03/2.20 tff(11486,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(11487,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11486, 11485])).
% 2.03/2.20 tff(11488,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11487, 271, 394, 638, 11481])).
% 2.03/2.20 tff(11489,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11488, 11478])).
% 2.03/2.20 tff(11490,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(11491,plain,
% 2.03/2.20 ((~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11490, 1772])).
% 2.03/2.20 tff(11492,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11491, 139, 394, 622, 4963, 379, 10184, 223])).
% 2.03/2.20 tff(11493,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[681, 11492, 11464, 6656])).
% 2.03/2.20 tff(11494,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(11495,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11494, 622, 394, 379, 11442, 223, 11455])).
% 2.03/2.20 tff(11496,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[486, 11495, 5087])).
% 2.03/2.20 tff(11497,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[592, 271, 588, 11496, 542])).
% 2.03/2.20 tff(11498,plain,
% 2.03/2.20 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[586, 11497, 6943])).
% 2.03/2.20 tff(11499,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11500,plain,
% 2.03/2.20 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11501,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[11500])).
% 2.03/2.20 tff(11502,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.20 inference(transitivity,[status(thm)],[11501, 11499])).
% 2.03/2.20 tff(11503,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(11504,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[11503, 11502])).
% 2.03/2.20 tff(11505,plain,
% 2.03/2.20 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[11504, 271, 588, 11496, 542])).
% 2.03/2.20 tff(11506,plain,
% 2.03/2.20 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[556, 11505, 1])).
% 2.03/2.20 tff(11507,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11508,plain,
% 2.03/2.20 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(11509,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[11508])).
% 2.03/2.20 tff(11510,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11509, 11507])).
% 2.03/2.21 tff(11511,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11512,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11511, 11510])).
% 2.03/2.21 tff(11513,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11512, 121, 623, 573, 2088])).
% 2.03/2.21 tff(11514,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1904, 21, 30, 11513])).
% 2.03/2.21 tff(11515,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4506, 121, 623, 627, 573])).
% 2.03/2.21 tff(11516,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[679, 21, 11515, 82])).
% 2.03/2.21 tff(11517,plain,
% 2.03/2.21 (~r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6876, 121, 623, 627, 2088])).
% 2.03/2.21 tff(11518,plain,
% 2.03/2.21 (b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1437, 21, 11517, 1433])).
% 2.03/2.21 tff(11519,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2695, 271, 394, 11518, 11516, 11514])).
% 2.03/2.21 tff(11520,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11521,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11520, 11506, 11498, 394, 6656, 11365, 11455])).
% 2.03/2.21 tff(11522,plain,((~r(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11523,plain,
% 2.03/2.21 (~r(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11522, 5095, 394, 5082, 11341, 11347, 11362, 223, 11361, 11358, 1326])).
% 2.03/2.21 tff(11524,plain,
% 2.03/2.21 (b(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2243, 11523, 2564])).
% 2.03/2.21 tff(11525,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11526,plain,
% 2.03/2.21 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11527,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11526])).
% 2.03/2.21 tff(11528,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11527, 11525])).
% 2.03/2.21 tff(11529,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11530,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11529, 11528])).
% 2.03/2.21 tff(11531,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11530, 271, 11524, 1326, 394, 11341])).
% 2.03/2.21 tff(11532,plain,((~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = elem!1) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11533,plain,
% 2.03/2.21 (~(s(z) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11532, 317, 394, 2564, 11339, 221, 3871, 1326])).
% 2.03/2.21 tff(11534,plain,
% 2.03/2.21 (b(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[236, 11533, 232])).
% 2.03/2.21 tff(11535,plain,
% 2.03/2.21 (b(elem!1, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9270, 11533, 1326, 11210, 11338, 232, 220, 394, 11362])).
% 2.03/2.21 tff(11536,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4817, 11535, 11534, 220, 1326])).
% 2.03/2.21 tff(11537,plain,(b(elem!1, s(elem!1)) | (~b(z, s(z))) | (~b(z, elem!1)) | r(s(z), elem!1) | (~b(s(elem!1), z)) | (s(elem!1) = elem!1) | r(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11538,plain,
% 2.03/2.21 (b(elem!1, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11537, 232, 1326, 220, 394, 2564, 221, 3871])).
% 2.03/2.21 tff(11539,plain,
% 2.03/2.21 (~b(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9079, 11538, 1326, 220])).
% 2.03/2.21 tff(11540,plain,
% 2.03/2.21 (s(z) = elem!1),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[236, 11539, 232])).
% 2.03/2.21 tff(11541,plain,
% 2.03/2.21 (s(s(z)) = s(elem!1)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11540])).
% 2.03/2.21 tff(11542,plain,
% 2.03/2.21 (s(s(s(z))) = s(s(elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11541])).
% 2.03/2.21 tff(11543,plain,
% 2.03/2.21 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11542])).
% 2.03/2.21 tff(11544,plain,
% 2.03/2.21 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[11543])).
% 2.03/2.21 tff(11545,plain,
% 2.03/2.21 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11542])).
% 2.03/2.21 tff(11546,plain,
% 2.03/2.21 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11540])).
% 2.03/2.21 tff(11547,plain,
% 2.03/2.21 (b(elem!1, s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[3871, 11546])).
% 2.03/2.21 tff(11548,plain,
% 2.03/2.21 (b(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11547, 11545])).
% 2.03/2.21 tff(11549,plain,
% 2.03/2.21 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11540])).
% 2.03/2.21 tff(11550,plain,
% 2.03/2.21 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.03/2.21 inference(transitivity,[status(thm)],[11549, 2212])).
% 2.03/2.21 tff(11551,plain,
% 2.03/2.21 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11550])).
% 2.03/2.21 tff(11552,plain,
% 2.03/2.21 (~(s(s(elem!1)) = elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[2137, 11551])).
% 2.03/2.21 tff(11553,plain,
% 2.03/2.21 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11542])).
% 2.03/2.21 tff(11554,plain,
% 2.03/2.21 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11553])).
% 2.03/2.21 tff(11555,plain,
% 2.03/2.21 (~r(s(s(elem!1)), elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[221, 11554])).
% 2.03/2.21 tff(11556,plain,
% 2.03/2.21 (b(s(s(elem!1)), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[540, 21, 11555, 11552])).
% 2.03/2.21 tff(11557,plain,
% 2.03/2.21 (~b(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2222, 11556, 1326, 11548])).
% 2.03/2.21 tff(11558,plain,
% 2.03/2.21 (r(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2106, 11557])).
% 2.03/2.21 tff(11559,plain,
% 2.03/2.21 (r(z, s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11558, 11544])).
% 2.03/2.21 tff(11560,plain,
% 2.03/2.21 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11541])).
% 2.03/2.21 tff(11561,plain,
% 2.03/2.21 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11560, 3535])).
% 2.03/2.21 tff(11562,plain,
% 2.03/2.21 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11561])).
% 2.03/2.21 tff(11563,plain,
% 2.03/2.21 (~(s(s(s(z))) = s(elem!1))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[1136, 11562])).
% 2.03/2.21 tff(11564,plain,
% 2.03/2.21 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1811, 11547, 394, 11538])).
% 2.03/2.21 tff(11565,plain,
% 2.03/2.21 (r(s(s(s(z))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1816, 11564, 11563])).
% 2.03/2.21 tff(11566,plain,
% 2.03/2.21 (b(s(z), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1276, 11540, 11538])).
% 2.03/2.21 tff(11567,plain,
% 2.03/2.21 (~b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9030, 11566, 220, 394])).
% 2.03/2.21 tff(11568,plain,
% 2.03/2.21 (r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1439, 11567])).
% 2.03/2.21 tff(11569,plain,
% 2.03/2.21 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11561, 3547])).
% 2.03/2.21 tff(11570,plain,
% 2.03/2.21 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11569])).
% 2.03/2.21 tff(11571,plain,
% 2.03/2.21 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[1136, 11570])).
% 2.03/2.21 tff(11572,plain,
% 2.03/2.21 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11540])).
% 2.03/2.21 tff(11573,plain,
% 2.03/2.21 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11572, 159])).
% 2.03/2.21 tff(11574,plain,
% 2.03/2.21 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.21 inference(transitivity,[status(thm)],[11573, 160])).
% 2.03/2.21 tff(11575,plain,
% 2.03/2.21 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11574])).
% 2.03/2.21 tff(11576,plain,
% 2.03/2.21 (~(s(s(s(z))) = elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[97, 11575])).
% 2.03/2.21 tff(11577,plain,
% 2.03/2.21 (b(s(s(s(z))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[255, 11576, 221])).
% 2.03/2.21 tff(11578,plain,
% 2.03/2.21 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3879, 11577, 11566, 3871])).
% 2.03/2.21 tff(11579,plain,
% 2.03/2.21 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2044, 11578, 11571])).
% 2.03/2.21 tff(11580,plain,
% 2.03/2.21 (~r(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10701, 11579, 11568, 11565])).
% 2.03/2.21 tff(11581,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11580, 11559])).
% 2.03/2.21 tff(11582,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | r(s(s(s(z))), elem!1) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11583,plain,
% 2.03/2.21 (r(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11582, 11334, 3871, 221, 11211, 220, 2564])).
% 2.03/2.21 tff(11584,plain,
% 2.03/2.21 (~r(elem!1, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11276, 10994, 220, 3871, 11583, 11334, 11336, 2564])).
% 2.03/2.21 tff(11585,plain,
% 2.03/2.21 (elem!1 = s(z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[299, 11584, 11335])).
% 2.03/2.21 tff(11586,plain,
% 2.03/2.21 (r(s(z), elem!1) <=> r(s(z), s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11585])).
% 2.03/2.21 tff(11587,plain,
% 2.03/2.21 (r(s(z), s(z)) <=> r(s(z), elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[11586])).
% 2.03/2.21 tff(11588,plain,
% 2.03/2.21 ((~r(s(z), s(z))) <=> (~r(s(z), elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11587])).
% 2.03/2.21 tff(11589,plain,
% 2.03/2.21 ((~![X: $i] : (~r(X, X))) | (~r(s(z), s(z)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11590,plain,
% 2.03/2.21 (~r(s(z), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11589, 177])).
% 2.03/2.21 tff(11591,plain,
% 2.03/2.21 (~r(s(z), elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11590, 11588])).
% 2.03/2.21 tff(11592,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11583, 11591])).
% 2.03/2.21 tff(11593,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = elem!1) | r(s(s(s(z))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11594,plain,
% 2.03/2.21 (r(s(s(s(z))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11593, 220, 3500, 3871, 10994, 1391])).
% 2.03/2.21 tff(11595,plain,
% 2.03/2.21 (r(s(s(s(z))), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11594, 11332])).
% 2.03/2.21 tff(11596,plain,
% 2.03/2.21 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11323])).
% 2.03/2.21 tff(11597,plain,
% 2.03/2.21 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11283])).
% 2.03/2.21 tff(11598,plain,
% 2.03/2.21 (b(elem!1, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11114, 11283, 3871])).
% 2.03/2.21 tff(11599,plain,
% 2.03/2.21 (~b(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9291, 11598, 1326, 394])).
% 2.03/2.21 tff(11600,plain,
% 2.03/2.21 (r(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2243, 11599, 3500])).
% 2.03/2.21 tff(11601,plain,
% 2.03/2.21 (r(s(elem!1), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11600, 11597])).
% 2.03/2.21 tff(11602,plain,
% 2.03/2.21 (r(s(s(z)), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11601, 11596])).
% 2.03/2.21 tff(11603,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11604,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11605,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11604, 11603])).
% 2.03/2.21 tff(11606,plain,
% 2.03/2.21 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11605, 121, 110, 11602, 11595])).
% 2.03/2.21 tff(11607,plain,
% 2.03/2.21 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10458, 11606, 11283])).
% 2.03/2.21 tff(11608,plain,
% 2.03/2.21 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1816, 11607, 11331])).
% 2.03/2.21 tff(11609,plain,
% 2.03/2.21 (~b(s(s(s(z))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1956, 11608, 1326, 394])).
% 2.03/2.21 tff(11610,plain,
% 2.03/2.21 (r(s(s(s(z))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1155, 11609])).
% 2.03/2.21 tff(11611,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11612,plain,
% 2.03/2.21 (((~r(s(s(s(s(z)))), z)) | (~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))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11613,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11612])).
% 2.03/2.21 tff(11614,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11613, 11611])).
% 2.03/2.21 tff(11615,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11616,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11615, 11614])).
% 2.03/2.21 tff(11617,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11616, 121, 11610, 11329, 11327, 11322])).
% 2.03/2.21 tff(11618,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(elem!1))), s(z)) | b(elem!1, s(elem!1)) | r(s(elem!1), z) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11619,plain,
% 2.03/2.21 (r(z, elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11618, 11199, 394, 110, 111, 3871, 38, 317, 10994, 348, 377, 1326])).
% 2.03/2.21 tff(11620,plain,
% 2.03/2.21 (r(z, s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11619, 11282])).
% 2.03/2.21 tff(11621,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[899, 11620])).
% 2.03/2.21 tff(11622,plain,(r(z, s(z)) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(elem!1))), s(z)) | b(elem!1, s(elem!1)) | r(s(elem!1), z) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11623,plain,
% 2.03/2.21 (r(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11622, 317, 110, 111, 3871, 38, 394, 11198, 348, 219, 10587, 11197])).
% 2.03/2.21 tff(11624,plain,
% 2.03/2.21 (b(z, elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10586, 317, 110, 79, 1, 111, 3871, 503, 348, 394])).
% 2.03/2.21 tff(11625,plain,
% 2.03/2.21 (~(s(z) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11532, 221, 2207, 3871, 394, 11624, 9149, 317])).
% 2.03/2.21 tff(11626,plain,
% 2.03/2.21 (~(elem!1 = s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[242, 11625])).
% 2.03/2.21 tff(11627,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11628,plain,
% 2.03/2.21 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11629,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11628])).
% 2.03/2.21 tff(11630,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11629, 11627])).
% 2.03/2.21 tff(11631,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11632,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11631, 11630])).
% 2.03/2.21 tff(11633,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11632, 271, 2618, 1326, 394, 261])).
% 2.03/2.21 tff(11634,plain,((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11635,plain,
% 2.03/2.21 (~b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11634, 2618, 1326, 394])).
% 2.03/2.21 tff(11636,plain,
% 2.03/2.21 (r(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[284, 11635, 259])).
% 2.03/2.21 tff(11637,plain,
% 2.03/2.21 (~r(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1343, 121, 111, 110, 11636])).
% 2.03/2.21 tff(11638,plain,
% 2.03/2.21 (b(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[236, 11637, 231])).
% 2.03/2.21 tff(11639,plain,
% 2.03/2.21 (~r(elem!1, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[291, 121, 111, 110, 11636])).
% 2.03/2.21 tff(11640,plain,
% 2.03/2.21 (b(elem!1, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[299, 11639, 258])).
% 2.03/2.21 tff(11641,plain,
% 2.03/2.21 (~b(s(s(s(z))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4827, 11640, 1326, 11638])).
% 2.03/2.21 tff(11642,plain,
% 2.03/2.21 (s(s(s(z))) = elem!1),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[255, 11641, 221])).
% 2.03/2.21 tff(11643,plain,
% 2.03/2.21 (b(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6548, 11642, 1326])).
% 2.03/2.21 tff(11644,plain,
% 2.03/2.21 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11642])).
% 2.03/2.21 tff(11645,plain,
% 2.03/2.21 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[11644])).
% 2.03/2.21 tff(11646,plain,
% 2.03/2.21 (b(s(elem!1), s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[2618, 11645])).
% 2.03/2.21 tff(11647,plain,
% 2.03/2.21 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11642])).
% 2.03/2.21 tff(11648,plain,
% 2.03/2.21 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 2.03/2.21 inference(symmetry,[status(thm)],[11647])).
% 2.03/2.21 tff(11649,plain,
% 2.03/2.21 (b(s(s(s(z))), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11640, 11648])).
% 2.03/2.21 tff(11650,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2029, 11649, 11646, 11643, 394])).
% 2.03/2.21 tff(11651,plain,((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | r(s(s(s(z))), elem!1) | (s(z) = elem!1) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11652,plain,
% 2.03/2.21 (~b(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11651, 11626, 11624, 394, 11625, 221, 111, 110, 9298])).
% 2.03/2.21 tff(11653,plain,
% 2.03/2.21 (r(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2243, 11652, 2207])).
% 2.03/2.21 tff(11654,plain,
% 2.03/2.21 (~b(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11278, 11626, 10951, 379, 348, 3871, 219, 394, 11624])).
% 2.03/2.21 tff(11655,plain,
% 2.03/2.21 (r(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[904, 11654])).
% 2.03/2.21 tff(11656,plain,
% 2.03/2.21 (~r(z, elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10336, 11626, 394, 111, 110, 3871, 348, 379, 503, 2207])).
% 2.03/2.21 tff(11657,plain,
% 2.03/2.21 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11073, 11656, 111])).
% 2.03/2.21 tff(11658,plain,
% 2.03/2.21 (~b(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1334, 257, 1326, 261])).
% 2.03/2.21 tff(11659,plain,
% 2.03/2.21 (r(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1214, 11658])).
% 2.03/2.21 tff(11660,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 2.03/2.21 tff(11661,plain,
% 2.03/2.21 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[11660])).
% 2.03/2.21 tff(11662,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2065, 11661])).
% 2.03/2.21 tff(11663,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(11664,plain,
% 2.03/2.21 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11663, 2065])).
% 2.03/2.21 tff(11665,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 2.03/2.21 tff(11666,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8229, 7311])).
% 2.03/2.21 tff(11667,plain,
% 2.03/2.21 (~b(s(s(s(z))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1947, 257, 1326, 261])).
% 2.03/2.21 tff(11668,plain,
% 2.03/2.21 (r(s(s(s(z))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1155, 11667])).
% 2.03/2.21 tff(11669,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11670,plain,
% 2.03/2.21 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(11671,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[11670])).
% 2.03/2.21 tff(11672,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[11671, 11669])).
% 2.03/2.21 tff(11673,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(11674,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[11673, 11672])).
% 2.03/2.21 tff(11675,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11674, 121, 6842, 109, 1140, 7792])).
% 2.03/2.22 tff(11676,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11677,plain,
% 2.03/2.22 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11676, 11668, 11666, 11659])).
% 2.03/2.22 tff(11678,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11679,plain,
% 2.03/2.22 (((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11680,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11679])).
% 2.03/2.22 tff(11681,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.03/2.22 inference(transitivity,[status(thm)],[11680, 11678])).
% 2.03/2.22 tff(11682,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11683,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11682, 11681])).
% 2.03/2.22 tff(11684,plain,
% 2.03/2.22 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11683, 271, 261, 257, 504])).
% 2.03/2.22 tff(11685,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6237, 21, 11684, 11677, 11665])).
% 2.03/2.22 tff(11686,plain,((~b(s(s(s(z))), elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11687,plain,
% 2.03/2.22 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11686, 257, 261, 11664, 1326])).
% 2.03/2.22 tff(11688,plain,
% 2.03/2.22 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[486, 11687, 481])).
% 2.03/2.22 tff(11689,plain,
% 2.03/2.22 (~r(s(s(s(z))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11100, 1140, 909, 110])).
% 2.03/2.22 tff(11690,plain,
% 2.03/2.22 (b(s(s(s(z))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2325, 11689])).
% 2.03/2.22 tff(11691,plain,
% 2.03/2.22 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2081, 11690, 10953, 503])).
% 2.03/2.22 tff(11692,plain,
% 2.03/2.22 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2071, 11691, 2065])).
% 2.03/2.22 tff(11693,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11694,plain,
% 2.03/2.22 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11695,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11694])).
% 2.03/2.22 tff(11696,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[11695, 11693])).
% 2.03/2.22 tff(11697,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11698,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11697, 11696])).
% 2.03/2.22 tff(11699,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11698, 121, 111, 139, 1140, 11692])).
% 2.03/2.22 tff(11700,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11701,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11700, 11688, 11659, 111, 2065, 503, 909, 110])).
% 2.03/2.22 tff(11702,plain,((~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11703,plain,
% 2.03/2.22 (~b(s(s(s(z))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11702, 261, 9149, 503, 909, 110, 481, 111, 1326])).
% 2.03/2.22 tff(11704,plain,
% 2.03/2.22 (s(s(s(z))) = elem!1),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[255, 11703, 221])).
% 2.03/2.22 tff(11705,plain,
% 2.03/2.22 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6165, 11704, 317])).
% 2.03/2.22 tff(11706,plain,
% 2.03/2.22 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[486, 479, 481])).
% 2.03/2.22 tff(11707,plain,
% 2.03/2.22 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3520, 121, 379, 622, 11706])).
% 2.03/2.22 tff(11708,plain,
% 2.03/2.22 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[681, 11707, 79])).
% 2.03/2.22 tff(11709,plain,
% 2.03/2.22 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9184, 622, 11706, 379])).
% 2.03/2.22 tff(11710,plain,
% 2.03/2.22 (b(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2293, 21, 11709, 85])).
% 2.03/2.22 tff(11711,plain,
% 2.03/2.22 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10632, 11706, 110, 111])).
% 2.03/2.22 tff(11712,plain,
% 2.03/2.22 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[760, 11711])).
% 2.03/2.22 tff(11713,plain,
% 2.03/2.22 (~b(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10967, 271, 11712, 11710, 11708])).
% 2.03/2.22 tff(11714,plain,
% 2.03/2.22 (r(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[429, 11713, 2282])).
% 2.03/2.22 tff(11715,plain,
% 2.03/2.22 (~r(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8953, 11714, 110, 379])).
% 2.03/2.22 tff(11716,plain,
% 2.03/2.22 (b(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[299, 11715, 258])).
% 2.03/2.22 tff(11717,plain,
% 2.03/2.22 (~r(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9637, 11708, 348, 11706, 379, 622])).
% 2.03/2.22 tff(11718,plain,
% 2.03/2.22 (b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[236, 11717, 231])).
% 2.03/2.22 tff(11719,plain,
% 2.03/2.22 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10934, 271, 11718, 11716, 503])).
% 2.03/2.22 tff(11720,plain,
% 2.03/2.22 (~r(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3425, 623, 111, 11706])).
% 2.03/2.22 tff(11721,plain,
% 2.03/2.22 (b(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2106, 11720])).
% 2.03/2.22 tff(11722,plain,
% 2.03/2.22 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[671, 623, 481, 479, 657])).
% 2.03/2.22 tff(11723,plain,
% 2.03/2.22 (b(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[599, 11722, 68])).
% 2.03/2.22 tff(11724,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2238, 11723, 11721, 1326, 379, 622, 68])).
% 2.03/2.22 tff(11725,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11726,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11725, 622, 379, 1326, 68, 481, 479, 11719, 111])).
% 2.03/2.22 tff(11727,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[556, 11726, 1])).
% 2.03/2.22 tff(11728,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5254, 11727, 11710, 11708])).
% 2.03/2.22 tff(11729,plain,
% 2.03/2.22 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[701, 11728, 3313])).
% 2.03/2.22 tff(11730,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11731,plain,
% 2.03/2.22 (((~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(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11732,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11731])).
% 2.03/2.22 tff(11733,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[11732, 11730])).
% 2.03/2.22 tff(11734,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11735,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11734, 11733])).
% 2.03/2.22 tff(11736,plain,
% 2.03/2.22 (~b(s(z), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11735, 271, 11712, 11710, 11708])).
% 2.03/2.22 tff(11737,plain,
% 2.03/2.22 (r(s(z), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[444, 11736, 348])).
% 2.03/2.22 tff(11738,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11739,plain,
% 2.03/2.22 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11740,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11739])).
% 2.03/2.22 tff(11741,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[11740, 11738])).
% 2.03/2.22 tff(11742,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11743,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11742, 11741])).
% 2.03/2.22 tff(11744,plain,
% 2.03/2.22 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11743, 121, 379, 622, 683])).
% 2.03/2.22 tff(11745,plain,
% 2.03/2.22 (b(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[599, 11744, 68])).
% 2.03/2.22 tff(11746,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11747,plain,
% 2.03/2.22 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11748,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11747])).
% 2.03/2.22 tff(11749,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[11748, 11746])).
% 2.03/2.22 tff(11750,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11751,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11750, 11749])).
% 2.03/2.22 tff(11752,plain,
% 2.03/2.22 (~b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11751, 271, 543, 505, 11745])).
% 2.03/2.22 tff(11753,plain,
% 2.03/2.22 (r(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[236, 11752, 231])).
% 2.03/2.22 tff(11754,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9622, 121, 379, 622, 11753, 431])).
% 2.03/2.22 tff(11755,plain,((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (s(z) = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11756,plain,
% 2.03/2.22 (~b(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11755, 11729, 231, 11737, 11727, 622, 379, 68])).
% 2.03/2.22 tff(11757,plain,
% 2.03/2.22 (r(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2167, 11756])).
% 2.03/2.22 tff(11758,plain,
% 2.03/2.22 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3275, 11757, 11737, 11729])).
% 2.03/2.22 tff(11759,plain,
% 2.03/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[526, 11758, 211])).
% 2.03/2.22 tff(11760,plain,
% 2.03/2.22 (~(s(s(s(z))) = s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4929, 11736, 3871])).
% 2.03/2.22 tff(11761,plain,
% 2.03/2.22 (r(s(s(s(z))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1816, 11760, 3506])).
% 2.03/2.22 tff(11762,plain,
% 2.03/2.22 (~b(s(s(s(z))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9017, 11737, 258, 622, 11761, 379, 11718])).
% 2.03/2.22 tff(11763,plain,
% 2.03/2.22 (s(s(s(z))) = elem!1),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[255, 11762, 221])).
% 2.03/2.22 tff(11764,plain,
% 2.03/2.22 (s(elem!1) = s(s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2605, 11763])).
% 2.03/2.22 tff(11765,plain,
% 2.03/2.22 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11764])).
% 2.03/2.22 tff(11766,plain,
% 2.03/2.22 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 2.03/2.22 inference(symmetry,[status(thm)],[11765])).
% 2.03/2.22 tff(11767,plain,
% 2.03/2.22 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(elem!1)))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11766])).
% 2.03/2.22 tff(11768,plain,
% 2.03/2.22 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11764])).
% 2.03/2.22 tff(11769,plain,
% 2.03/2.22 (r(s(s(s(s(z)))), s(z))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11714, 11768])).
% 2.03/2.22 tff(11770,plain,
% 2.03/2.22 (~r(z, s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1109, 121, 110, 909, 11769])).
% 2.03/2.22 tff(11771,plain,
% 2.03/2.22 (~r(z, s(elem!1))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11770, 11767])).
% 2.03/2.22 tff(11772,plain,
% 2.03/2.22 (b(z, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1439, 11771])).
% 2.03/2.22 tff(11773,plain,
% 2.03/2.22 (~b(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8781, 11759, 11727, 11772])).
% 2.03/2.22 tff(11774,plain,
% 2.03/2.22 (r(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2106, 11773])).
% 2.03/2.22 tff(11775,plain,
% 2.03/2.22 (~b(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10869, 11774, 11708, 11727, 563, 11759])).
% 2.03/2.22 tff(11776,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11777,plain,
% 2.03/2.22 (((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11778,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[11777])).
% 2.03/2.22 tff(11779,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[11778, 11776])).
% 2.03/2.22 tff(11780,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11781,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[11780, 11779])).
% 2.03/2.22 tff(11782,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11781, 121, 1625, 2088, 110, 2417])).
% 2.03/2.22 tff(11783,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11784,plain,
% 2.03/2.22 (~r(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11783, 11774, 110, 11757])).
% 2.03/2.22 tff(11785,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2430, 11784, 11775])).
% 2.03/2.22 tff(11786,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | r(s(s(s(z))), elem!1) | (elem!1 = s(z)) | b(s(s(s(z))), s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(11787,plain,
% 2.03/2.22 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11786, 11705, 379, 231, 68, 1, 1326, 481, 110, 111, 503, 909, 221, 243, 622, 348, 3871])).
% 2.03/2.22 tff(11788,plain,
% 2.03/2.22 (b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10599, 11704, 3871])).
% 2.03/2.22 tff(11789,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(11790,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(11791,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11790, 11789])).
% 2.03/2.23 tff(11792,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11791, 271, 11788, 261, 11787, 503])).
% 2.03/2.23 tff(11793,plain,((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(elem!1))) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | r(s(s(s(z))), elem!1) | (~r(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11794,plain,
% 2.03/2.23 (~b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11793, 11625, 379, 503, 68, 1, 11624, 11657, 110, 111, 11655, 221, 11653, 348, 3871, 317])).
% 2.03/2.23 tff(11795,plain,
% 2.03/2.23 (r(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[284, 11794, 9298])).
% 2.03/2.23 tff(11796,plain,
% 2.03/2.23 (~r(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[291, 121, 111, 110, 11795])).
% 2.03/2.23 tff(11797,plain,
% 2.03/2.23 (b(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[299, 11796, 11626])).
% 2.03/2.23 tff(11798,plain,
% 2.03/2.23 (~r(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1343, 121, 111, 110, 11795])).
% 2.03/2.23 tff(11799,plain,
% 2.03/2.23 (b(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[236, 11798, 11625])).
% 2.03/2.23 tff(11800,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8132, 504, 448, 260])).
% 2.03/2.23 tff(11801,plain,
% 2.03/2.23 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[66, 21, 11800])).
% 2.03/2.23 tff(11802,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11801, 2861])).
% 2.03/2.23 tff(11803,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11804,plain,
% 2.03/2.23 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11805,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[11804])).
% 2.03/2.23 tff(11806,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[11805, 11803])).
% 2.03/2.23 tff(11807,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(11808,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11807, 11806])).
% 2.03/2.23 tff(11809,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11808, 121, 110, 909, 11802])).
% 2.03/2.23 tff(11810,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1904, 21, 30, 11809])).
% 2.03/2.23 tff(11811,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11812,plain,
% 2.03/2.23 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11813,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[11812])).
% 2.03/2.23 tff(11814,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[11813, 11811])).
% 2.03/2.23 tff(11815,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(11816,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11815, 11814])).
% 2.03/2.23 tff(11817,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11816, 271, 1326, 448, 504, 11810])).
% 2.03/2.23 tff(11818,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11819,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11818, 11799, 110, 11624, 11797, 11655])).
% 2.03/2.23 tff(11820,plain,
% 2.03/2.23 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11786, 11819, 379, 11625, 68, 1, 11624, 11657, 110, 111, 503, 11655, 221, 11626, 11653, 348, 3871])).
% 2.03/2.23 tff(11821,plain,
% 2.03/2.23 (~b(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4827, 11799, 11624, 11797])).
% 2.03/2.23 tff(11822,plain,
% 2.03/2.23 (s(s(s(z))) = elem!1),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[255, 11821, 221])).
% 2.03/2.23 tff(11823,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6165, 11822, 11820, 317])).
% 2.03/2.23 tff(11824,plain,(r(s(s(s(z))), elem!1) | b(elem!1, s(elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11825,plain,
% 2.03/2.23 (r(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11824, 317, 11197, 68, 1, 110, 111, 67, 348, 3871, 394])).
% 2.03/2.23 tff(11826,plain,
% 2.03/2.23 (~r(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[10336, 243, 394, 111, 110, 3871, 348, 379, 503, 2207])).
% 2.03/2.23 tff(11827,plain,
% 2.03/2.23 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11073, 11826, 111])).
% 2.03/2.23 tff(11828,plain,
% 2.03/2.23 (~r(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9121, 121, 110, 909, 3456])).
% 2.03/2.23 tff(11829,plain,
% 2.03/2.23 (b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[284, 11828, 259])).
% 2.03/2.23 tff(11830,plain,
% 2.03/2.23 (~b(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11634, 11829, 1326, 394])).
% 2.03/2.23 tff(11831,plain,
% 2.03/2.23 (r(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2243, 11830, 2207])).
% 2.03/2.23 tff(11832,plain,
% 2.03/2.23 (~r(s(elem!1), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6290, 121, 379, 11831, 145])).
% 2.03/2.23 tff(11833,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3888, 139, 3456, 622])).
% 2.03/2.23 tff(11834,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[681, 11833, 82])).
% 2.03/2.23 tff(11835,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[10977, 11834, 10953, 110, 422, 3456, 622, 2280, 139])).
% 2.03/2.23 tff(11836,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11837,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11836, 3456, 422, 110, 11831, 79, 111])).
% 2.03/2.23 tff(11838,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[486, 11837, 481])).
% 2.03/2.23 tff(11839,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7080, 271, 1326, 11829, 11838])).
% 2.03/2.23 tff(11840,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8229, 11839])).
% 2.03/2.23 tff(11841,plain,
% 2.03/2.23 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6221, 121, 111, 110, 6842])).
% 2.03/2.23 tff(11842,plain,
% 2.03/2.23 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[760, 11841])).
% 2.03/2.23 tff(11843,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[486, 147, 481])).
% 2.03/2.23 tff(11844,plain,
% 2.03/2.23 (b(s(z), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4929, 1997, 3871])).
% 2.03/2.23 tff(11845,plain,
% 2.03/2.23 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[4329])).
% 2.03/2.23 tff(11846,plain,
% 2.03/2.23 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[11845])).
% 2.03/2.23 tff(11847,plain,
% 2.03/2.23 (r(z, s(s(s(s(s(z))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[111, 11846])).
% 2.03/2.23 tff(11848,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11849,plain,
% 2.03/2.23 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11850,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[11849])).
% 2.03/2.23 tff(11851,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[11850, 11848])).
% 2.03/2.23 tff(11852,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(11853,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11852, 11851])).
% 2.03/2.23 tff(11854,plain,
% 2.03/2.23 ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11853, 271, 394, 446])).
% 2.03/2.23 tff(11855,plain,
% 2.03/2.23 (~b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11854, 9894])).
% 2.03/2.23 tff(11856,plain,
% 2.03/2.23 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1754, 21, 11855])).
% 2.03/2.23 tff(11857,plain,
% 2.03/2.23 (r(s(z), s(s(s(s(s(z))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11856, 5380])).
% 2.03/2.23 tff(11858,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11859,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(11860,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11859, 11858])).
% 2.03/2.23 tff(11861,plain,
% 2.03/2.23 ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11860, 271, 394, 446])).
% 2.03/2.23 tff(11862,plain,
% 2.03/2.23 (~b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11861, 9894])).
% 2.03/2.23 tff(11863,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1680, 21, 1677, 11862])).
% 2.03/2.23 tff(11864,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5406, 121, 909, 1661, 11863, 11857])).
% 2.03/2.23 tff(11865,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11866,plain,
% 2.03/2.23 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11865, 11847, 394, 11844, 909])).
% 2.03/2.23 tff(11867,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4334, 11866, 1997])).
% 2.03/2.23 tff(11868,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[681, 11867, 79])).
% 2.03/2.23 tff(11869,plain,
% 2.03/2.23 (b(s(s(s(z))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6195, 1997, 447])).
% 2.03/2.23 tff(11870,plain,
% 2.03/2.23 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2081, 11869, 11842, 503])).
% 2.03/2.23 tff(11871,plain,
% 2.03/2.23 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2071, 11870, 2065])).
% 2.03/2.23 tff(11872,plain,
% 2.03/2.23 (r(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11871, 9653])).
% 2.03/2.23 tff(11873,plain,
% 2.03/2.23 (~r(z, s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9056, 121, 111, 11872, 6842])).
% 2.03/2.23 tff(11874,plain,
% 2.03/2.23 (b(z, s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1439, 11873])).
% 2.03/2.23 tff(11875,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2422, 2417, 110, 909])).
% 2.03/2.23 tff(11876,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2143, 11875])).
% 2.03/2.23 tff(11877,plain,
% 2.03/2.23 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[989, 11876, 504, 750])).
% 2.03/2.23 tff(11878,plain,
% 2.03/2.23 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[556, 11877, 1])).
% 2.03/2.23 tff(11879,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9803, 121, 11878, 684, 111, 2417])).
% 2.03/2.23 tff(11880,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11881,plain,
% 2.03/2.23 (~r(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11880, 11868, 111, 1, 11843, 11842, 110, 909])).
% 2.03/2.23 tff(11882,plain,
% 2.03/2.23 (b(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2430, 11881])).
% 2.03/2.23 tff(11883,plain,
% 2.03/2.23 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2853, 11882, 394, 11874])).
% 2.03/2.23 tff(11884,plain,
% 2.03/2.23 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[701, 11883, 3313])).
% 2.03/2.23 tff(11885,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3132, 11884, 11872, 11868])).
% 2.03/2.23 tff(11886,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[556, 11885, 1])).
% 2.03/2.23 tff(11887,plain,
% 2.03/2.23 (~b(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[989, 11886, 11843, 11842])).
% 2.03/2.23 tff(11888,plain,
% 2.03/2.23 (r(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2143, 11887])).
% 2.03/2.23 tff(11889,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11890,plain,
% 2.03/2.23 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11891,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[11890])).
% 2.03/2.23 tff(11892,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[11891, 11889])).
% 2.03/2.23 tff(11893,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(11894,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11893, 11892])).
% 2.03/2.23 tff(11895,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11894, 121, 622, 684, 727, 798])).
% 2.03/2.23 tff(11896,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11897,plain,
% 2.03/2.23 (~r(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11896, 11868, 622, 11872])).
% 2.03/2.23 tff(11898,plain,
% 2.03/2.23 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[660, 21, 1043])).
% 2.03/2.23 tff(11899,plain,
% 2.03/2.23 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11898, 656])).
% 2.03/2.23 tff(11900,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[486, 481, 147])).
% 2.03/2.23 tff(11901,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11902,plain,
% 2.03/2.23 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(11903,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[11902])).
% 2.03/2.23 tff(11904,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[11903, 11901])).
% 2.03/2.23 tff(11905,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(11906,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[11905, 11904])).
% 2.03/2.23 tff(11907,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11906, 271, 543, 588, 11900, 11899])).
% 2.03/2.23 tff(11908,plain,((s(s(s(elem!1))) = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(11909,plain,
% 2.03/2.23 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11908, 11886, 147, 481, 11897])).
% 2.03/2.23 tff(11910,plain,
% 2.03/2.23 (r(elem!1, s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[599, 11909, 68])).
% 2.03/2.24 tff(11911,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11912,plain,
% 2.03/2.24 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11913,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11912])).
% 2.03/2.24 tff(11914,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.24 inference(transitivity,[status(thm)],[11913, 11911])).
% 2.03/2.24 tff(11915,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(11916,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11915, 11914])).
% 2.03/2.24 tff(11917,plain,
% 2.03/2.24 (~b(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11916, 271, 11886, 11842, 11843])).
% 2.03/2.24 tff(11918,plain,
% 2.03/2.24 (r(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2167, 11917])).
% 2.03/2.24 tff(11919,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5850, 121, 11918, 11910, 11888, 3456])).
% 2.03/2.24 tff(11920,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(11921,plain,
% 2.03/2.24 (~(s(s(s(z))) = s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11920, 3456, 68, 11837, 481, 1, 394, 111, 110, 909, 11831, 11840, 2065, 503, 10234, 3871])).
% 2.03/2.24 tff(11922,plain,
% 2.03/2.24 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2035, 11921])).
% 2.03/2.24 tff(11923,plain,
% 2.03/2.24 (b(s(elem!1), s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2044, 11922, 11832])).
% 2.03/2.24 tff(11924,plain,
% 2.03/2.24 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8370, 121, 379, 11831, 145])).
% 2.03/2.24 tff(11925,plain,
% 2.03/2.24 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1816, 11921, 11924])).
% 2.03/2.24 tff(11926,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11927,plain,
% 2.03/2.24 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11928,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11927])).
% 2.03/2.24 tff(11929,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[11928, 11926])).
% 2.03/2.24 tff(11930,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(11931,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11930, 11929])).
% 2.03/2.24 tff(11932,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11931, 271, 11925, 10234, 3871, 11923])).
% 2.03/2.24 tff(11933,plain,((~r(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(11934,plain,
% 2.03/2.24 (~r(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11933, 11827, 68, 3871, 1, 394, 111, 110, 909, 9149, 503, 1326, 2282, 379, 145, 9298])).
% 2.03/2.24 tff(11935,plain,
% 2.03/2.24 (b(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[299, 11934, 243])).
% 2.03/2.24 tff(11936,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11937,plain,
% 2.03/2.24 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11938,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11937])).
% 2.03/2.24 tff(11939,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[11938, 11936])).
% 2.03/2.24 tff(11940,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(11941,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11940, 11939])).
% 2.03/2.24 tff(11942,plain,
% 2.03/2.24 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11941, 271, 11935, 3871, 503])).
% 2.03/2.24 tff(11943,plain,
% 2.03/2.24 (~(elem!1 = s(s(s(elem!1))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11827, 655])).
% 2.03/2.24 tff(11944,plain,
% 2.03/2.24 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[660, 21, 11943, 11942])).
% 2.03/2.24 tff(11945,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11946,plain,
% 2.03/2.24 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11947,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11946])).
% 2.03/2.24 tff(11948,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[11947, 11945])).
% 2.03/2.24 tff(11949,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(11950,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11949, 11948])).
% 2.03/2.24 tff(11951,plain,
% 2.03/2.24 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11950, 271, 11935, 3871, 503])).
% 2.03/2.24 tff(11952,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[486, 11951, 11827])).
% 2.03/2.24 tff(11953,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(11954,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(11955,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~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)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11954, 11953])).
% 2.03/2.24 tff(11956,plain,
% 2.03/2.24 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11955, 121, 11952, 11944, 145])).
% 2.03/2.24 tff(11957,plain,
% 2.03/2.24 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2071, 11956, 9149])).
% 2.03/2.24 tff(11958,plain,
% 2.03/2.24 (~r(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10989, 121, 111, 11952, 11944])).
% 2.03/2.24 tff(11959,plain,
% 2.03/2.24 (b(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[284, 11958, 9298])).
% 2.03/2.24 tff(11960,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11634, 11959, 1326, 394])).
% 2.03/2.24 tff(11961,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2243, 11960, 2207])).
% 2.03/2.24 tff(11962,plain,
% 2.03/2.24 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3520, 121, 379, 11961, 11952])).
% 2.03/2.24 tff(11963,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[681, 11962, 79])).
% 2.03/2.24 tff(11964,plain,
% 2.03/2.24 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10632, 11952, 110, 111])).
% 2.03/2.24 tff(11965,plain,
% 2.03/2.24 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[760, 11964])).
% 2.03/2.24 tff(11966,plain,
% 2.03/2.24 (~b(s(s(s(z))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2081, 11957, 11965, 503])).
% 2.03/2.24 tff(11967,plain,
% 2.03/2.24 (r(s(s(s(z))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2325, 11966])).
% 2.03/2.24 tff(11968,plain,
% 2.03/2.24 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11725, 11961, 379, 1326, 68, 11827, 11942, 11951, 111])).
% 2.03/2.24 tff(11969,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[556, 11968, 1])).
% 2.03/2.24 tff(11970,plain,
% 2.03/2.24 (~b(s(s(s(z))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2464, 11969, 3504, 909, 11965, 110, 11967, 503])).
% 2.03/2.24 tff(11971,plain,
% 2.03/2.24 (r(s(s(s(z))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1155, 11970])).
% 2.03/2.24 tff(11972,plain,
% 2.03/2.24 (~(s(s(s(z))) = s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11011, 11971, 10951])).
% 2.03/2.24 tff(11973,plain,
% 2.03/2.24 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8370, 121, 379, 11961, 145])).
% 2.03/2.24 tff(11974,plain,
% 2.03/2.24 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1816, 11973, 11972])).
% 2.03/2.24 tff(11975,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2114, 11974, 11963, 394, 11957])).
% 2.03/2.24 tff(11976,plain,((s(z) = elem!1) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(11977,plain,
% 2.03/2.24 (s(z) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11976, 11825, 11197, 394, 11623, 110, 67, 1, 10587, 68, 111, 3871, 348])).
% 2.03/2.24 tff(11978,plain,
% 2.03/2.24 (elem!1 = s(z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1221, 11977])).
% 2.03/2.24 tff(11979,plain,
% 2.03/2.24 (b(elem!1, s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11114, 11978, 3871])).
% 2.03/2.24 tff(11980,plain,
% 2.03/2.24 (r(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6824, 11977, 11825])).
% 2.03/2.24 tff(11981,plain,
% 2.03/2.24 (~r(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2422, 11980, 110, 11623])).
% 2.03/2.24 tff(11982,plain,
% 2.03/2.24 (b(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2430, 11981])).
% 2.03/2.24 tff(11983,plain,
% 2.03/2.24 (~b(s(s(elem!1)), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11355, 11982, 10587, 11979])).
% 2.03/2.24 tff(11984,plain,
% 2.03/2.24 (r(s(s(elem!1)), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[862, 11983, 198])).
% 2.03/2.24 tff(11985,plain,
% 2.03/2.24 (r(s(z), z) <=> r(elem!1, z)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11977])).
% 2.03/2.24 tff(11986,plain,
% 2.03/2.24 (r(elem!1, z)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[110, 11985])).
% 2.03/2.24 tff(11987,plain,
% 2.03/2.24 (b(z, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1397, 11978, 10587])).
% 2.03/2.24 tff(11988,plain,
% 2.03/2.24 (r(z, elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11618, 11987, 394, 110, 111, 3871, 38, 317, 11198, 348, 219, 10587])).
% 2.03/2.24 tff(11989,plain,
% 2.03/2.24 (~r(z, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6940, 121, 11988, 11986, 11984])).
% 2.03/2.24 tff(11990,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9291, 11979, 10587, 394])).
% 2.03/2.24 tff(11991,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2243, 11990, 2207])).
% 2.03/2.24 tff(11992,plain,
% 2.03/2.24 (s(s(z)) = s(elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11977])).
% 2.03/2.24 tff(11993,plain,
% 2.03/2.24 (s(s(s(z))) = s(s(elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11992])).
% 2.03/2.24 tff(11994,plain,
% 2.03/2.24 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[11993])).
% 2.03/2.24 tff(11995,plain,
% 2.03/2.24 (b(elem!1, s(s(elem!1)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[11979, 11994])).
% 2.03/2.24 tff(11996,plain,
% 2.03/2.24 (~b(z, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2238, 11995, 11197, 10587, 11991, 68])).
% 2.03/2.24 tff(11997,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2106, 11996, 11989])).
% 2.03/2.24 tff(11998,plain,(b(elem!1, s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(elem!1))), s(z)) | (s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(11999,plain,
% 2.03/2.24 (b(elem!1, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11998, 68, 26, 10217, 37, 9838, 38, 10218, 1])).
% 2.03/2.24 tff(12000,plain,
% 2.03/2.24 (r(elem!1, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11196, 9838, 26, 37, 10217, 1, 38, 10218, 68])).
% 2.03/2.24 tff(12001,plain,
% 2.03/2.24 (r(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[284, 10705, 9298])).
% 2.03/2.24 tff(12002,plain,
% 2.03/2.24 (~r(s(z), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1343, 121, 111, 110, 12001])).
% 2.03/2.24 tff(12003,plain,
% 2.03/2.24 (elem!1 = s(z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10336, 10219, 394, 111, 110, 3871, 348, 379, 503, 2564])).
% 2.03/2.24 tff(12004,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[242, 12003, 230])).
% 2.03/2.24 tff(12005,plain,(b(z, elem!1) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (s(elem!1) = elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(12006,plain,
% 2.03/2.24 (b(z, elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12005, 220, 111, 110, 3871, 348, 379, 503, 3500, 394])).
% 2.03/2.24 tff(12007,plain,
% 2.03/2.24 (r(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11582, 12006, 3871, 394, 12002, 220, 3500])).
% 2.03/2.24 tff(12008,plain,
% 2.03/2.24 (s(z) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11204, 12006, 379, 377, 394, 348, 12002, 220])).
% 2.03/2.24 tff(12009,plain,
% 2.03/2.24 (r(z, elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9060, 12008, 6201, 111, 110, 307, 503, 12006])).
% 2.03/2.24 tff(12010,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10721, 12009, 12007, 3871, 307, 9298, 394, 220])).
% 2.03/2.24 tff(12011,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(elem!1))) | (elem!1 = s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(12012,plain,
% 2.03/2.24 (~b(z, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12011, 3871, 307, 394, 2280, 111, 110, 503, 379, 219, 348])).
% 2.03/2.24 tff(12013,plain,
% 2.03/2.24 (r(z, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[904, 12012])).
% 2.03/2.24 tff(12014,plain,
% 2.03/2.24 (elem!1 = s(z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10336, 378, 394, 111, 110, 3871, 348, 379, 503, 2207])).
% 2.03/2.24 tff(12015,plain,
% 2.03/2.24 (b(elem!1, s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11114, 12014, 3871])).
% 2.03/2.24 tff(12016,plain,
% 2.03/2.24 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1811, 12015, 307, 394])).
% 2.03/2.24 tff(12017,plain,
% 2.03/2.24 (~(s(s(s(z))) = elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4909, 12016, 307])).
% 2.03/2.24 tff(12018,plain,
% 2.03/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1234, 12014, 10228])).
% 2.03/2.24 tff(12019,plain,
% 2.03/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[932, 12018])).
% 2.03/2.24 tff(12020,plain,
% 2.03/2.24 (~r(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11190, 12019, 3871, 307, 563, 12013, 503, 12014, 211, 394, 110])).
% 2.03/2.24 tff(12021,plain,
% 2.03/2.24 (b(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[255, 12020, 12017])).
% 2.03/2.24 tff(12022,plain,
% 2.03/2.24 (s(z) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[242, 12014])).
% 2.03/2.24 tff(12023,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12022])).
% 2.03/2.24 tff(12024,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[503, 12023])).
% 2.03/2.24 tff(12025,plain,
% 2.03/2.24 (s(s(z)) = s(elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12022])).
% 2.03/2.24 tff(12026,plain,
% 2.03/2.24 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12025])).
% 2.03/2.24 tff(12027,plain,
% 2.03/2.24 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.03/2.24 inference(transitivity,[status(thm)],[12026, 3535])).
% 2.03/2.24 tff(12028,plain,
% 2.03/2.24 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12027])).
% 2.03/2.24 tff(12029,plain,
% 2.03/2.24 (~(s(s(s(z))) = s(elem!1))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[1136, 12028])).
% 2.03/2.24 tff(12030,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10540, 12029, 12024, 110, 82, 379, 378, 12014, 12021, 394, 12013, 1, 111, 3871])).
% 2.03/2.24 tff(12031,plain,((~r(z, elem!1)) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(12032,plain,
% 2.03/2.24 (~r(z, elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12031, 79, 26, 12000, 10217, 1, 37, 9838, 67, 11999, 10218])).
% 2.03/2.24 tff(12033,plain,
% 2.03/2.24 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11073, 12032, 37])).
% 2.03/2.24 tff(12034,plain,
% 2.03/2.24 (~(z = elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[500, 10218])).
% 2.03/2.24 tff(12035,plain,
% 2.03/2.24 (b(z, elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[355, 12032, 12034])).
% 2.03/2.24 tff(12036,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4598, 12035, 11999, 10217])).
% 2.03/2.24 tff(12037,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2243, 12036, 2207])).
% 2.03/2.24 tff(12038,plain,
% 2.03/2.24 (~b(z, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12011, 9838, 11999, 10217, 85, 37, 26, 67, 12000, 219, 10218])).
% 2.03/2.24 tff(12039,plain,
% 2.03/2.24 (~(elem!1 = s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1397, 12035, 12038])).
% 2.03/2.24 tff(12040,plain,
% 2.03/2.24 (~(elem!1 = z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[333, 12034])).
% 2.03/2.24 tff(12041,plain,
% 2.03/2.24 (~r(s(elem!1), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2312, 10218, 79, 67, 37, 26])).
% 2.03/2.24 tff(12042,plain,
% 2.03/2.24 (~(s(elem!1) = s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[350, 10218])).
% 2.03/2.24 tff(12043,plain,
% 2.03/2.24 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2063, 10218])).
% 2.03/2.24 tff(12044,plain,
% 2.03/2.24 (~b(z, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9091, 12035, 11999, 10217])).
% 2.03/2.24 tff(12045,plain,
% 2.03/2.24 (r(z, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1439, 12044])).
% 2.03/2.24 tff(12046,plain,
% 2.03/2.24 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[7694, 12045, 37, 12037])).
% 2.03/2.24 tff(12047,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[681, 12046, 79])).
% 2.03/2.24 tff(12048,plain,
% 2.03/2.24 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11067, 12047, 12043, 67, 26, 37, 11999, 9838, 12035, 10217, 12042, 12041, 12040, 12039, 12037, 85])).
% 2.03/2.24 tff(12049,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[486, 12048, 12033])).
% 2.03/2.24 tff(12050,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2401, 271, 11999, 10217, 12047, 12049])).
% 2.03/2.24 tff(12051,plain,((elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z)) | b(s(z), z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(12052,plain,
% 2.03/2.24 (elem!1 = s(s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12051, 38, 1, 2, 33])).
% 2.03/2.24 tff(12053,plain,
% 2.03/2.24 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12052])).
% 2.03/2.24 tff(12054,plain,
% 2.03/2.24 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[12053])).
% 2.03/2.24 tff(12055,plain,
% 2.03/2.24 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12054])).
% 2.03/2.24 tff(12056,plain,
% 2.03/2.24 (~(s(z) = elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[2137, 12055])).
% 2.03/2.24 tff(12057,plain,
% 2.03/2.24 (~b(z, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6491, 12052, 33])).
% 2.03/2.24 tff(12058,plain,
% 2.03/2.24 (r(z, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1439, 12057])).
% 2.03/2.24 tff(12059,plain,
% 2.03/2.24 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.24 tff(12060,plain,
% 2.03/2.24 ((s(s(s(elem!1))) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[12059, 558])).
% 2.03/2.24 tff(12061,plain,
% 2.03/2.24 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[12060])).
% 2.03/2.24 tff(12062,plain,
% 2.03/2.24 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12061])).
% 2.03/2.24 tff(12063,plain,
% 2.03/2.24 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[1, 12062])).
% 2.03/2.24 tff(12064,plain,
% 2.03/2.24 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.24 tff(12065,plain,
% 2.03/2.24 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(elem!1))),
% 2.03/2.24 inference(symmetry,[status(thm)],[12064])).
% 2.03/2.24 tff(12066,plain,
% 2.03/2.24 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(z))),
% 2.03/2.24 inference(transitivity,[status(thm)],[12065, 4396])).
% 2.03/2.24 tff(12067,plain,
% 2.03/2.24 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(z)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12066])).
% 2.03/2.24 tff(12068,plain,
% 2.03/2.24 (~(s(elem!1) = s(z))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[61, 12067])).
% 2.03/2.24 tff(12069,plain,
% 2.03/2.24 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[12065])).
% 2.03/2.24 tff(12070,plain,
% 2.03/2.24 (~(s(z) = s(elem!1))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[61, 12069])).
% 2.03/2.24 tff(12071,plain,
% 2.03/2.24 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.25 tff(12072,plain,
% 2.03/2.25 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 2.03/2.25 inference(symmetry,[status(thm)],[12071])).
% 2.03/2.25 tff(12073,plain,
% 2.03/2.25 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12072, 1218])).
% 2.03/2.25 tff(12074,plain,
% 2.03/2.25 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12073])).
% 2.03/2.25 tff(12075,plain,
% 2.03/2.25 (~(elem!1 = s(z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[2137, 12074])).
% 2.03/2.25 tff(12076,plain,
% 2.03/2.25 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12072])).
% 2.03/2.25 tff(12077,plain,
% 2.03/2.25 (~(s(z) = elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[2137, 12076])).
% 2.03/2.25 tff(12078,plain,
% 2.03/2.25 ((z = elem!1) <=> (z = s(s(elem!1)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.25 tff(12079,plain,
% 2.03/2.25 ((z = elem!1) <=> (s(s(elem!1)) = z)),
% 2.03/2.25 inference(transitivity,[status(thm)],[12078, 2098])).
% 2.03/2.25 tff(12080,plain,
% 2.03/2.25 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.03/2.25 inference(symmetry,[status(thm)],[12079])).
% 2.03/2.25 tff(12081,plain,
% 2.03/2.25 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12080])).
% 2.03/2.25 tff(12082,plain,
% 2.03/2.25 (~(z = elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[59, 12081])).
% 2.03/2.25 tff(12083,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12084,plain,
% 2.03/2.25 (((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12085,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12084])).
% 2.03/2.25 tff(12086,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12085, 12083])).
% 2.03/2.25 tff(12087,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12088,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12087, 12086])).
% 2.03/2.25 tff(12089,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12088, 121, 379, 378, 1441, 412])).
% 2.03/2.25 tff(12090,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12091,plain,
% 2.03/2.25 (~r(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12090, 1243, 1441, 412])).
% 2.03/2.25 tff(12092,plain,
% 2.03/2.25 (b(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[392, 12091, 377])).
% 2.03/2.25 tff(12093,plain,
% 2.03/2.25 (~b(s(z), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8883, 12092, 258, 3500, 412, 1243, 348, 110])).
% 2.03/2.25 tff(12094,plain,
% 2.03/2.25 (r(s(z), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[236, 12093, 231])).
% 2.03/2.25 tff(12095,plain,
% 2.03/2.25 (~r(z, s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3490, 12092, 258, 108, 412, 348, 422, 1243])).
% 2.03/2.25 tff(12096,plain,
% 2.03/2.25 (b(z, s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[904, 12095])).
% 2.03/2.25 tff(12097,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[466, 12096, 12094, 110, 331, 377, 199])).
% 2.03/2.25 tff(12098,plain,(b(z, elem!1) | (~r(s(z), z)) | (z = elem!1) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (elem!1 = s(z)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12099,plain,
% 2.03/2.25 (b(z, elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12098, 412, 12082, 377, 12077, 12075, 108, 110, 12070, 12068, 1441])).
% 2.03/2.25 tff(12100,plain,
% 2.03/2.25 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.25 tff(12101,plain,
% 2.03/2.25 (r(s(s(s(elem!1))), z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[412, 12100])).
% 2.03/2.25 tff(12102,plain,
% 2.03/2.25 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6221, 121, 111, 110, 12101])).
% 2.03/2.25 tff(12103,plain,
% 2.03/2.25 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[760, 12102])).
% 2.03/2.25 tff(12104,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12105,plain,
% 2.03/2.25 (((~r(s(elem!1), z)) | (~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))) | (~r(s(elem!1), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12106,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12105])).
% 2.03/2.25 tff(12107,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12106, 12104])).
% 2.03/2.25 tff(12108,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12109,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12108, 12107])).
% 2.03/2.25 tff(12110,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12109, 121, 1441, 110, 412, 431])).
% 2.03/2.25 tff(12111,plain,((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12112,plain,
% 2.03/2.25 (~r(s(z), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12111, 412, 110, 1441])).
% 2.03/2.25 tff(12113,plain,
% 2.03/2.25 (b(s(z), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[444, 12112, 12070])).
% 2.03/2.25 tff(12114,plain,
% 2.03/2.25 (b(s(s(elem!1)), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2430, 2424])).
% 2.03/2.25 tff(12115,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12116,plain,
% 2.03/2.25 (((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12117,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12116])).
% 2.03/2.25 tff(12118,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12117, 12115])).
% 2.03/2.25 tff(12119,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12120,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12119, 12118])).
% 2.03/2.25 tff(12121,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12120, 271, 220, 446, 2449, 981])).
% 2.03/2.25 tff(12122,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12123,plain,
% 2.03/2.25 (~b(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12122, 12114, 446, 220])).
% 2.03/2.25 tff(12124,plain,
% 2.03/2.25 (r(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2143, 12123])).
% 2.03/2.25 tff(12125,plain,
% 2.03/2.25 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.25 tff(12126,plain,
% 2.03/2.25 ((~r(elem!1, s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12125])).
% 2.03/2.25 tff(12127,plain,
% 2.03/2.25 (~r(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[293, 12126])).
% 2.03/2.25 tff(12128,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2117, 12127])).
% 2.03/2.25 tff(12129,plain,(r(elem!1, s(z)) | (~r(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12130,plain,
% 2.03/2.25 (r(elem!1, s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12129, 12124, 2470])).
% 2.03/2.25 tff(12131,plain,
% 2.03/2.25 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.03/2.25 inference(transitivity,[status(thm)],[12080, 361])).
% 2.03/2.25 tff(12132,plain,
% 2.03/2.25 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12131])).
% 2.03/2.25 tff(12133,plain,
% 2.03/2.25 (~(elem!1 = z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[59, 12132])).
% 2.03/2.25 tff(12134,plain,
% 2.03/2.25 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.25 tff(12135,plain,
% 2.03/2.25 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 2.03/2.25 inference(symmetry,[status(thm)],[12134])).
% 2.03/2.25 tff(12136,plain,
% 2.03/2.25 ((~r(s(s(elem!1)), z)) <=> (~r(elem!1, z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12135])).
% 2.03/2.25 tff(12137,plain,
% 2.03/2.25 (~r(elem!1, z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[2424, 12136])).
% 2.03/2.25 tff(12138,plain,
% 2.03/2.25 (b(elem!1, z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[284, 12137, 12133])).
% 2.03/2.25 tff(12139,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12140,plain,
% 2.03/2.25 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12141,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12140])).
% 2.03/2.25 tff(12142,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12141, 12139])).
% 2.03/2.25 tff(12143,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12144,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12143, 12142])).
% 2.03/2.25 tff(12145,plain,
% 2.03/2.25 ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12144, 271])).
% 2.03/2.25 tff(12146,plain,
% 2.03/2.25 (~b(s(z), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12145, 12138, 1326, 220])).
% 2.03/2.25 tff(12147,plain,
% 2.03/2.25 (r(s(z), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[236, 12146, 12077])).
% 2.03/2.25 tff(12148,plain,
% 2.03/2.25 (~b(s(s(s(z))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1947, 12138, 1935, 1326])).
% 2.03/2.25 tff(12149,plain,
% 2.03/2.25 (r(s(s(s(z))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[255, 12148, 3907])).
% 2.03/2.25 tff(12150,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[4112, 12149, 12147, 108, 12130])).
% 2.03/2.25 tff(12151,plain,(r(s(s(elem!1)), z) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12152,plain,
% 2.03/2.25 (r(s(s(elem!1)), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12151, 220, 8458, 1326, 108, 2470, 446])).
% 2.03/2.25 tff(12153,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12154,plain,
% 2.03/2.25 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12155,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12154])).
% 2.03/2.25 tff(12156,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12155, 12153])).
% 2.03/2.25 tff(12157,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12158,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12157, 12156])).
% 2.03/2.25 tff(12159,plain,
% 2.03/2.25 (~r(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12158, 121, 111, 110, 12152])).
% 2.03/2.25 tff(12160,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2143, 12159])).
% 2.03/2.25 tff(12161,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12162,plain,
% 2.03/2.25 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12163,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12162])).
% 2.03/2.25 tff(12164,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12163, 12161])).
% 2.03/2.25 tff(12165,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12166,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12165, 12164])).
% 2.03/2.25 tff(12167,plain,
% 2.03/2.25 (~r(s(z), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12166, 121, 111, 110, 12152])).
% 2.03/2.25 tff(12168,plain,
% 2.03/2.25 (b(s(z), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2167, 12167])).
% 2.03/2.25 tff(12169,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12170,plain,
% 2.03/2.25 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(12171,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12170])).
% 2.03/2.25 tff(12172,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[12171, 12169])).
% 2.03/2.25 tff(12173,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(12174,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[12173, 12172])).
% 2.03/2.25 tff(12175,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12174, 271, 505, 1894, 220, 981])).
% 2.03/2.25 tff(12176,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12177,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12176, 12168, 12160, 3936, 220])).
% 2.03/2.25 tff(12178,plain,((~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(12179,plain,
% 2.03/2.25 (~b(z, s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[12178, 12099, 110, 111, 108, 2470, 12113])).
% 2.03/2.25 tff(12180,plain,
% 2.03/2.25 (r(z, s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[904, 12179])).
% 2.03/2.25 tff(12181,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[5502])).
% 2.03/2.25 tff(12182,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[12181])).
% 2.03/2.25 tff(12183,plain,
% 2.03/2.25 (~(elem!1 = s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1100, 3907])).
% 2.03/2.25 tff(12184,plain,
% 2.03/2.25 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1516, 12183])).
% 2.03/2.25 tff(12185,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.25 tff(12186,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.03/2.25 inference(symmetry,[status(thm)],[12185])).
% 2.03/2.25 tff(12187,plain,
% 2.03/2.25 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[12186])).
% 2.03/2.25 tff(12188,plain,
% 2.03/2.25 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.25 tff(12189,plain,
% 2.03/2.25 (~(s(s(s(z))) = s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3917, 12070, 2470])).
% 2.03/2.25 tff(12190,plain,
% 2.03/2.25 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3766, 379, 1935, 412, 1326, 909, 12082, 3907])).
% 2.03/2.25 tff(12191,plain,
% 2.03/2.25 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1816, 12190, 12189])).
% 2.03/2.26 tff(12192,plain,
% 2.03/2.26 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12191, 12188])).
% 2.03/2.26 tff(12193,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2079, 271, 750, 12192, 503])).
% 2.03/2.26 tff(12194,plain,
% 2.03/2.26 (r(s(s(s(z))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2325, 12193])).
% 2.03/2.26 tff(12195,plain,
% 2.03/2.26 (~r(s(s(s(s(z)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[919, 911, 909, 110])).
% 2.03/2.26 tff(12196,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1095, 12195])).
% 2.03/2.26 tff(12197,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(12198,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12199,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12198, 12197])).
% 2.03/2.26 tff(12200,plain,
% 2.03/2.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12199, 121, 110, 911, 2327])).
% 2.03/2.26 tff(12201,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10426, 12200])).
% 2.03/2.26 tff(12202,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(12203,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12204,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12203, 12202])).
% 2.03/2.26 tff(12205,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12204, 271, 1894, 1935, 12201, 12196])).
% 2.03/2.26 tff(12206,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12207,plain,
% 2.03/2.26 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12206, 12194, 1935, 110, 3936, 909])).
% 2.03/2.26 tff(12208,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[932, 12207])).
% 2.03/2.26 tff(12209,plain,
% 2.03/2.26 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.26 tff(12210,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1417, 379, 412, 909])).
% 2.03/2.26 tff(12211,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[284, 12210, 12133])).
% 2.03/2.26 tff(12212,plain,
% 2.03/2.26 (~b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1947, 12211, 1935, 1326])).
% 2.03/2.26 tff(12213,plain,
% 2.03/2.26 (r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[255, 12212, 3907])).
% 2.03/2.26 tff(12214,plain,
% 2.03/2.26 ((~r(elem!1, z)) <=> (~r(s(s(elem!1)), z))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12134])).
% 2.03/2.26 tff(12215,plain,
% 2.03/2.26 (~r(s(s(elem!1)), z)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12210, 12214])).
% 2.03/2.26 tff(12216,plain,
% 2.03/2.26 (b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2428, 21, 59, 12215])).
% 2.03/2.26 tff(12217,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5738, 271, 3936, 12216, 1935])).
% 2.03/2.26 tff(12218,plain,
% 2.03/2.26 (~b(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5482, 12217, 2470])).
% 2.03/2.26 tff(12219,plain,
% 2.03/2.26 (r(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1192, 12218, 12183])).
% 2.03/2.26 tff(12220,plain,
% 2.03/2.26 (~r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9831, 12219, 108, 12213])).
% 2.03/2.26 tff(12221,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[236, 12220, 12077])).
% 2.03/2.26 tff(12222,plain,
% 2.03/2.26 (b(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12221, 12209])).
% 2.03/2.26 tff(12223,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(12224,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12225,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12224, 12223])).
% 2.03/2.26 tff(12226,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12225, 271, 12222, 503, 12208])).
% 2.03/2.26 tff(12227,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12226, 12187])).
% 2.03/2.26 tff(12228,plain,
% 2.03/2.26 (r(s(s(s(s(z)))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1559, 12227, 12184])).
% 2.03/2.26 tff(12229,plain,
% 2.03/2.26 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12228, 12182])).
% 2.03/2.26 tff(12230,plain,
% 2.03/2.26 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2063, 12070])).
% 2.03/2.26 tff(12231,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 2.03/2.26 tff(12232,plain,
% 2.03/2.26 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12231])).
% 2.03/2.26 tff(12233,plain,
% 2.03/2.26 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.03/2.26 inference(transitivity,[status(thm)],[775, 12232, 604, 2471])).
% 2.03/2.26 tff(12234,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2065, 12233])).
% 2.03/2.26 tff(12235,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12236,plain,
% 2.03/2.26 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12235, 12230, 2470])).
% 2.03/2.26 tff(12237,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[5456])).
% 2.03/2.26 tff(12238,plain,
% 2.03/2.26 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12237])).
% 2.03/2.26 tff(12239,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[1184, 12238])).
% 2.03/2.26 tff(12240,assumption,(~r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 2.03/2.26 tff(12241,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12240, 12239])).
% 2.03/2.26 tff(12242,plain,(r(s(s(elem!1)), s(s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12243,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12242, 12219, 2470])).
% 2.03/2.26 tff(12244,plain,
% 2.03/2.26 (r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12213, 3908])).
% 2.03/2.26 tff(12245,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6393, 121, 12244, 108, 12243])).
% 2.03/2.26 tff(12246,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2143, 12245])).
% 2.03/2.26 tff(12247,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(12248,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12249,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12248, 12247])).
% 2.03/2.26 tff(12250,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12249, 271, 12222, 12246, 12208])).
% 2.03/2.26 tff(12251,plain,
% 2.03/2.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(12252,plain,
% 2.03/2.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12253,plain,
% 2.03/2.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12252, 12251])).
% 2.03/2.26 tff(12254,plain,
% 2.03/2.26 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12253, 21, 12250, 12236])).
% 2.03/2.26 tff(12255,plain,
% 2.03/2.26 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[5456])).
% 2.03/2.26 tff(12256,plain,
% 2.03/2.26 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[12255, 159])).
% 2.03/2.26 tff(12257,plain,
% 2.03/2.26 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12256])).
% 2.03/2.26 tff(12258,plain,
% 2.03/2.26 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12257])).
% 2.03/2.26 tff(12259,plain,
% 2.03/2.26 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12183, 12258])).
% 2.03/2.26 tff(12260,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2464, 12194, 12259, 1935, 750, 110, 909, 503])).
% 2.03/2.26 tff(12261,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.26 tff(12262,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12261])).
% 2.03/2.26 tff(12263,plain,
% 2.03/2.26 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12262])).
% 2.03/2.26 tff(12264,plain,
% 2.03/2.26 ((~![X: $i] : (~b(X, X))) | (~b(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12265,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12264, 190])).
% 2.03/2.26 tff(12266,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12265, 12263])).
% 2.03/2.26 tff(12267,plain,
% 2.03/2.26 (r(elem!1, s(s(elem!1))) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.26 tff(12268,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12267])).
% 2.03/2.26 tff(12269,plain,
% 2.03/2.26 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12268])).
% 2.03/2.26 tff(12270,plain,
% 2.03/2.26 ((~![X: $i] : (~r(X, X))) | (~r(s(s(elem!1)), s(s(elem!1))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12271,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12270, 177])).
% 2.03/2.26 tff(12272,plain,
% 2.03/2.26 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12271, 12269])).
% 2.03/2.26 tff(12273,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12125])).
% 2.03/2.26 tff(12274,plain,
% 2.03/2.26 ((~r(s(s(elem!1)), s(z))) <=> (~r(elem!1, s(z)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12273])).
% 2.03/2.26 tff(12275,plain,
% 2.03/2.26 (~r(elem!1, s(z))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12245, 12274])).
% 2.03/2.26 tff(12276,plain,
% 2.03/2.26 (b(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[299, 12275, 12075])).
% 2.03/2.26 tff(12277,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[513, 12276, 503, 12222])).
% 2.03/2.26 tff(12278,plain,
% 2.03/2.26 (~b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3790, 12277, 2470])).
% 2.03/2.26 tff(12279,plain,
% 2.03/2.26 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4488, 12278, 12272, 12266, 481, 12260])).
% 2.03/2.26 tff(12280,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.26 tff(12281,plain,
% 2.03/2.26 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[3911, 12280])).
% 2.03/2.26 tff(12282,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[379, 12281])).
% 2.03/2.26 tff(12283,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(12284,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(12285,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12284, 12283])).
% 2.03/2.26 tff(12286,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12285, 121, 12282, 12279, 12254, 12229])).
% 2.03/2.26 tff(12287,plain,((~r(elem!1, s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12288,plain,
% 2.03/2.26 (~r(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12287, 12180, 503, 8458, 110, 2470, 481, 108, 12103, 12099, 412])).
% 2.03/2.26 tff(12289,plain,
% 2.03/2.26 (b(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[392, 12288, 377])).
% 2.03/2.26 tff(12290,plain,
% 2.03/2.26 (~b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1940, 12289, 8458, 12099])).
% 2.03/2.26 tff(12291,plain,
% 2.03/2.26 (r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[255, 12290, 3907])).
% 2.03/2.26 tff(12292,plain,
% 2.03/2.26 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.26 tff(12293,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12292])).
% 2.03/2.26 tff(12294,plain,
% 2.03/2.26 (b(s(elem!1), s(z))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[503, 12293])).
% 2.03/2.26 tff(12295,plain,
% 2.03/2.26 (~b(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[456, 12289, 12294, 12113])).
% 2.03/2.26 tff(12296,plain,
% 2.03/2.26 (r(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[299, 12295, 12075])).
% 2.03/2.26 tff(12297,plain,
% 2.03/2.26 (~b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4096, 12289, 412, 12113, 12068, 12099, 12180])).
% 2.03/2.26 tff(12298,plain,
% 2.03/2.26 (r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[236, 12297, 12077])).
% 2.03/2.26 tff(12299,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4112, 12298, 12296, 108, 12291])).
% 2.03/2.26 tff(12300,plain,((~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12301,plain,
% 2.03/2.26 (~r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12300, 108, 219, 503, 110, 2470, 12063, 111, 1441])).
% 2.03/2.26 tff(12302,plain,
% 2.03/2.26 (b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[409, 12301])).
% 2.03/2.26 tff(12303,plain,
% 2.03/2.26 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.26 tff(12304,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.03/2.26 inference(symmetry,[status(thm)],[12303])).
% 2.03/2.26 tff(12305,plain,
% 2.03/2.26 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(elem!1), z))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[12304])).
% 2.03/2.26 tff(12306,plain,
% 2.03/2.26 (~b(s(elem!1), z)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[8226, 12305])).
% 2.03/2.26 tff(12307,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[394, 12306])).
% 2.03/2.26 tff(12308,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(elem!1), z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12309,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12308, 12302, 2470])).
% 2.03/2.26 tff(12310,plain,
% 2.03/2.26 (r(z, elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[355, 199, 12082])).
% 2.03/2.26 tff(12311,plain,
% 2.03/2.26 (~r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12300, 108, 377, 503, 110, 2470, 481, 111, 1441])).
% 2.03/2.26 tff(12312,plain,
% 2.03/2.26 (b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[409, 12311])).
% 2.03/2.26 tff(12313,plain,
% 2.03/2.26 (~b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8926, 220, 447, 394])).
% 2.03/2.26 tff(12314,plain,
% 2.03/2.26 (~r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[466, 220, 110, 331, 377, 199])).
% 2.03/2.26 tff(12315,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[236, 12314, 12313, 231])).
% 2.03/2.26 tff(12316,plain,((~b(z, s(z))) | (s(z) = elem!1) | (~r(s(z), z)) | (z = elem!1) | (elem!1 = s(elem!1)) | b(z, elem!1) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12317,plain,
% 2.03/2.26 (~b(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12316, 199, 110, 12082, 377, 12077, 12294, 12312])).
% 2.03/2.26 tff(12318,plain,
% 2.03/2.26 (r(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[904, 12317])).
% 2.03/2.26 tff(12319,plain,
% 2.03/2.26 (~r(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4202, 12318, 110, 12310])).
% 2.03/2.26 tff(12320,plain,
% 2.03/2.26 (b(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[299, 12319, 12075])).
% 2.03/2.26 tff(12321,plain,
% 2.03/2.26 (r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[284, 279, 12133])).
% 2.03/2.26 tff(12322,plain,
% 2.03/2.26 (~r(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3387, 12321, 12310, 1441])).
% 2.03/2.26 tff(12323,plain,
% 2.03/2.26 (b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2243, 12322, 2564])).
% 2.03/2.26 tff(12324,plain,
% 2.03/2.26 (~r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[375, 279, 12133, 199, 110])).
% 2.03/2.26 tff(12325,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[236, 12324, 12077])).
% 2.03/2.26 tff(12326,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8132, 12325, 503, 448])).
% 2.03/2.26 tff(12327,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3790, 12326, 12323, 2470])).
% 2.03/2.26 tff(12328,plain,(b(elem!1, z) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = elem!1) | (~r(z, s(elem!1))) | b(z, elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12329,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12328, 12320, 503, 2470, 3500, 1441, 199, 110])).
% 2.03/2.26 tff(12330,plain,
% 2.03/2.26 (~b(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1315, 307, 394, 261])).
% 2.03/2.26 tff(12331,plain,
% 2.03/2.26 (r(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1214, 12330])).
% 2.03/2.26 tff(12332,plain,
% 2.03/2.26 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1508, 12331, 108, 909])).
% 2.03/2.26 tff(12333,plain,
% 2.03/2.26 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1816, 12332, 2033])).
% 2.03/2.26 tff(12334,plain,
% 2.03/2.26 (~r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3375, 12331, 108, 110])).
% 2.03/2.26 tff(12335,plain,
% 2.03/2.26 (b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[255, 12334, 907])).
% 2.03/2.26 tff(12336,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3288, 12335, 12333, 394, 307])).
% 2.03/2.26 tff(12337,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(z))) = elem!1) | (s(s(s(z))) = s(elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12338,plain,
% 2.03/2.26 (~b(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12337, 12318, 3907, 12189, 108, 110, 12312, 12329])).
% 2.03/2.26 tff(12339,plain,
% 2.03/2.26 (r(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[392, 12338, 377])).
% 2.03/2.26 tff(12340,plain,
% 2.03/2.26 (~r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[387, 12339, 110, 12310])).
% 2.03/2.26 tff(12341,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[236, 12340, 12077])).
% 2.03/2.26 tff(12342,plain,
% 2.03/2.26 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10227, 12339, 12310, 111])).
% 2.03/2.26 tff(12343,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[486, 12342, 481])).
% 2.03/2.26 tff(12344,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8132, 12343, 12341, 503, 12320])).
% 2.03/2.26 tff(12345,plain,(b(z, elem!1) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = s(elem!1)) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12346,plain,
% 2.03/2.26 (b(z, elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12345, 108, 12063, 111, 110, 219, 503, 2470, 1441])).
% 2.03/2.26 tff(12347,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1956, 12346, 8458, 12302])).
% 2.03/2.26 tff(12348,plain,
% 2.03/2.26 (r(s(s(s(z))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1816, 12347, 12189])).
% 2.03/2.26 tff(12349,plain,
% 2.03/2.26 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.26 tff(12350,plain,
% 2.03/2.26 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12349])).
% 2.03/2.26 tff(12351,plain,
% 2.03/2.26 (r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[236, 12313, 12077])).
% 2.03/2.26 tff(12352,plain,
% 2.03/2.26 (~b(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9291, 2618, 1326, 394])).
% 2.03/2.26 tff(12353,plain,
% 2.03/2.26 (r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[11651, 2618, 1326, 394, 231, 258, 111, 110, 259])).
% 2.03/2.26 tff(12354,plain,
% 2.03/2.26 (~r(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9831, 12353, 108, 357])).
% 2.03/2.26 tff(12355,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1192, 12354, 12352, 1102])).
% 2.03/2.26 tff(12356,plain,((~b(s(elem!1), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12357,plain,
% 2.03/2.26 (~b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12356, 12351, 108, 12183, 1326, 394, 12077, 12075, 111, 110, 12133])).
% 2.03/2.26 tff(12358,plain,
% 2.03/2.26 (s(s(s(elem!1))) = s(elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7490, 2470])).
% 2.03/2.26 tff(12359,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7281, 12358, 2467])).
% 2.03/2.26 tff(12360,plain,
% 2.03/2.26 (s(s(s(elem!1))) = elem!1),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[486, 12359, 147])).
% 2.03/2.26 tff(12361,plain,
% 2.03/2.26 (elem!1 = s(s(s(elem!1)))),
% 2.03/2.26 inference(symmetry,[status(thm)],[12360])).
% 2.03/2.26 tff(12362,plain,
% 2.03/2.26 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.03/2.26 inference(transitivity,[status(thm)],[5456, 12361])).
% 2.03/2.26 tff(12363,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1, 12362])).
% 2.03/2.26 tff(12364,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12365,plain,
% 2.03/2.26 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12364, 12357, 1, 2470])).
% 2.03/2.26 tff(12366,plain,
% 2.03/2.26 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10632, 12365, 110, 111])).
% 2.03/2.26 tff(12367,plain,
% 2.03/2.26 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[760, 12366])).
% 2.03/2.26 tff(12368,plain,
% 2.03/2.26 (b(s(z), s(elem!1))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12367, 12350])).
% 2.03/2.26 tff(12369,plain,
% 2.03/2.26 (~b(s(z), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12178, 220, 110, 111, 108, 2470, 1326])).
% 2.03/2.26 tff(12370,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12369, 12368])).
% 2.03/2.26 tff(12371,plain,((~b(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12372,plain,
% 2.03/2.26 (~b(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12371, 108, 110, 111, 1, 2470, 12346, 12302, 12294])).
% 2.03/2.26 tff(12373,plain,
% 2.03/2.26 (r(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[904, 12372])).
% 2.03/2.26 tff(12374,plain,
% 2.03/2.26 (~r(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1508, 12373, 108, 12348])).
% 2.03/2.26 tff(12375,plain,
% 2.03/2.26 (b(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1214, 12374])).
% 2.03/2.26 tff(12376,plain,
% 2.03/2.26 (~b(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2020, 5469, 1326, 1307])).
% 2.03/2.26 tff(12377,plain,
% 2.03/2.26 (~b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[11651, 221, 1326, 394, 231, 258, 111, 110, 259])).
% 2.03/2.26 tff(12378,plain,
% 2.03/2.26 (r(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2243, 12377, 3500])).
% 2.03/2.26 tff(12379,plain,
% 2.03/2.26 (~b(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9353, 221, 1935, 394, 1326])).
% 2.03/2.26 tff(12380,plain,
% 2.03/2.26 (r(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[392, 12379, 377])).
% 2.03/2.26 tff(12381,plain,
% 2.03/2.26 (~r(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3849, 12380, 1500, 12378])).
% 2.03/2.26 tff(12382,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1192, 12381, 12376, 1101])).
% 2.03/2.26 tff(12383,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = z) | (s(s(s(z))) = elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(12384,plain,
% 2.03/2.26 (r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12383, 12348, 12346, 12375, 219, 12302, 12077, 12075, 111, 110, 12133, 3907, 8458])).
% 2.03/2.26 tff(12385,plain,
% 2.03/2.26 (r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[12384, 3908])).
% 2.03/2.26 tff(12386,plain,
% 2.03/2.27 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.27 tff(12387,plain,
% 2.03/2.27 (~b(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3790, 479, 2470])).
% 2.03/2.27 tff(12388,plain,
% 2.03/2.27 (~r(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9190, 479, 111, 110, 12230, 108, 3907, 503, 394, 1326, 12294, 379, 260])).
% 2.03/2.27 tff(12389,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2243, 12388, 12387, 2564])).
% 2.03/2.27 tff(12390,plain,(b(s(s(s(elem!1))), elem!1) | (s(elem!1) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12391,plain,
% 2.03/2.27 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12390, 260, 111, 110, 108, 503, 394, 1326, 379, 2564, 2470])).
% 2.03/2.27 tff(12392,plain,
% 2.03/2.27 (b(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7281, 12391, 12358])).
% 2.03/2.27 tff(12393,plain,
% 2.03/2.27 (~b(elem!1, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9291, 12392, 1326, 394])).
% 2.03/2.27 tff(12394,plain,
% 2.03/2.27 (r(elem!1, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1192, 12393, 12183])).
% 2.03/2.27 tff(12395,plain,
% 2.03/2.27 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12242, 12394, 2470])).
% 2.03/2.27 tff(12396,plain,
% 2.03/2.27 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.27 tff(12397,plain,
% 2.03/2.27 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12396])).
% 2.03/2.27 tff(12398,plain,
% 2.03/2.27 (~b(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8132, 12391, 503, 260])).
% 2.03/2.27 tff(12399,plain,
% 2.03/2.27 (~b(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12398, 12397])).
% 2.03/2.27 tff(12400,plain,
% 2.03/2.27 (r(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 12399])).
% 2.03/2.27 tff(12401,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[6393, 121, 12400, 7794, 108, 12395])).
% 2.03/2.27 tff(12402,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12403,plain,
% 2.03/2.27 (~b(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12402, 379, 108, 2470, 1326, 394, 503, 111, 110, 7794, 2564])).
% 2.03/2.27 tff(12404,plain,
% 2.03/2.27 (r(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[236, 12403, 12077])).
% 2.03/2.27 tff(12405,plain,
% 2.03/2.27 (r(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12404, 12386])).
% 2.03/2.27 tff(12406,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12407,plain,
% 2.03/2.27 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12408,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12407])).
% 2.03/2.27 tff(12409,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[12408, 12406])).
% 2.03/2.27 tff(12410,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(12411,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12410, 12409])).
% 2.03/2.27 tff(12412,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12411, 121, 12282, 12405, 7794, 108])).
% 2.03/2.27 tff(12413,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12414,plain,
% 2.03/2.27 (~r(elem!1, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12413, 12385, 108, 2470, 12346, 12302, 503, 111, 110, 2207])).
% 2.03/2.27 tff(12415,plain,
% 2.03/2.27 (b(elem!1, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[392, 12414, 219])).
% 2.03/2.27 tff(12416,plain,
% 2.03/2.27 (~b(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4598, 12415, 12302, 12346])).
% 2.03/2.27 tff(12417,plain,
% 2.03/2.27 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12364, 12416, 1, 2470])).
% 2.03/2.27 tff(12418,plain,
% 2.03/2.27 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10632, 12417, 110, 111])).
% 2.03/2.27 tff(12419,plain,
% 2.03/2.27 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[760, 12418])).
% 2.03/2.27 tff(12420,plain,
% 2.03/2.27 (~b(elem!1, z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1315, 12415, 12302, 12375])).
% 2.03/2.27 tff(12421,plain,
% 2.03/2.27 (r(elem!1, z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[284, 12420, 12133])).
% 2.03/2.27 tff(12422,plain,
% 2.03/2.27 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2035, 12189])).
% 2.03/2.27 tff(12423,plain,
% 2.03/2.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2479, 12415, 2470])).
% 2.03/2.27 tff(12424,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2464, 12419, 12259, 8458, 12423, 110, 12373, 503])).
% 2.03/2.27 tff(12425,plain,
% 2.03/2.27 (b(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2325, 12424])).
% 2.03/2.27 tff(12426,plain,
% 2.03/2.27 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2029, 12425, 12375, 12302])).
% 2.03/2.27 tff(12427,plain,
% 2.03/2.27 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2044, 12426, 12422])).
% 2.03/2.27 tff(12428,plain,
% 2.03/2.27 (~r(s(z), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3445, 12427, 108, 12384])).
% 2.03/2.27 tff(12429,plain,
% 2.03/2.27 (b(s(z), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[444, 12428, 12070])).
% 2.03/2.27 tff(12430,plain,
% 2.03/2.27 (~b(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[456, 12429, 12294, 12415])).
% 2.03/2.27 tff(12431,plain,
% 2.03/2.27 (r(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[299, 12430, 12075])).
% 2.03/2.27 tff(12432,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12433,plain,
% 2.03/2.27 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12434,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12433])).
% 2.03/2.27 tff(12435,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[12434, 12432])).
% 2.03/2.27 tff(12436,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(12437,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12436, 12435])).
% 2.03/2.27 tff(12438,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12437, 121, 1625, 909, 1409, 3456])).
% 2.03/2.27 tff(12439,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12440,plain,
% 2.03/2.27 (~r(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12439, 12431, 12421, 12373])).
% 2.03/2.27 tff(12441,plain,
% 2.03/2.27 (b(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2167, 12440])).
% 2.03/2.27 tff(12442,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12443,plain,
% 2.03/2.27 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12444,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12443])).
% 2.03/2.27 tff(12445,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(transitivity,[status(thm)],[12444, 12442])).
% 2.03/2.27 tff(12446,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(12447,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12446, 12445])).
% 2.03/2.27 tff(12448,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12447, 271, 12423, 12441, 12419, 12309])).
% 2.03/2.27 tff(12449,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12450,plain,
% 2.03/2.27 (~r(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12449, 67, 26, 37, 1, 12052, 12058])).
% 2.03/2.27 tff(12451,plain,
% 2.03/2.27 (b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[105, 12450])).
% 2.03/2.27 tff(12452,plain,
% 2.03/2.27 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12052])).
% 2.03/2.27 tff(12453,plain,
% 2.03/2.27 ((s(s(s(elem!1))) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[12452, 558])).
% 2.03/2.27 tff(12454,plain,
% 2.03/2.27 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.03/2.27 inference(symmetry,[status(thm)],[12453])).
% 2.03/2.27 tff(12455,plain,
% 2.03/2.27 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12454])).
% 2.03/2.27 tff(12456,plain,
% 2.03/2.27 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[1, 12455])).
% 2.03/2.27 tff(12457,plain,
% 2.03/2.27 (~r(elem!1, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12090, 412, 1441, 1243])).
% 2.03/2.27 tff(12458,plain,
% 2.03/2.27 (b(elem!1, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[392, 12457, 377])).
% 2.03/2.27 tff(12459,plain,
% 2.03/2.27 (~b(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8883, 12458, 258, 3500, 1243, 412, 348, 110])).
% 2.03/2.27 tff(12460,plain,
% 2.03/2.27 (~r(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1305, 12459, 331, 199, 412, 12458, 231])).
% 2.03/2.27 tff(12461,plain,
% 2.03/2.27 (r(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[236, 12459, 231])).
% 2.03/2.27 tff(12462,plain,
% 2.03/2.27 (~b(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[466, 12461, 110, 331, 377, 199])).
% 2.03/2.27 tff(12463,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[904, 12462, 12460])).
% 2.03/2.27 tff(12464,plain,((~r(s(elem!1), z)) | (~r(s(z), z)) | (z = elem!1) | (elem!1 = s(elem!1)) | b(z, elem!1) | (s(z) = elem!1) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12465,plain,
% 2.03/2.27 (~r(s(elem!1), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12464, 199, 12082, 377, 110, 12077, 12075, 12070, 1441])).
% 2.03/2.27 tff(12466,plain,
% 2.03/2.27 (b(s(elem!1), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[409, 12465])).
% 2.03/2.27 tff(12467,plain,
% 2.03/2.27 (~r(elem!1, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10336, 12466, 12075, 111, 110, 3871, 12070, 12310, 503, 3500])).
% 2.03/2.27 tff(12468,plain,
% 2.03/2.27 (b(elem!1, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[392, 12467, 377])).
% 2.03/2.27 tff(12469,plain,
% 2.03/2.27 (~r(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10591, 12468, 12310, 12133, 110, 12466])).
% 2.03/2.27 tff(12470,plain,
% 2.03/2.27 (b(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[299, 12469, 12075])).
% 2.03/2.27 tff(12471,plain,
% 2.03/2.27 (~r(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10703, 12470, 3871, 199, 12068, 12466, 12468, 110, 12183, 12082, 377])).
% 2.03/2.27 tff(12472,plain,
% 2.03/2.27 (b(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[236, 12471, 12077])).
% 2.03/2.27 tff(12473,plain,
% 2.03/2.27 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8132, 12472, 503, 12470])).
% 2.03/2.27 tff(12474,plain,
% 2.03/2.27 (~b(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12316, 12466, 110, 12082, 377, 12077, 12294, 199])).
% 2.03/2.27 tff(12475,plain,
% 2.03/2.27 (r(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[904, 12474])).
% 2.03/2.27 tff(12476,plain,
% 2.03/2.27 (b(elem!1, z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12328, 12470, 503, 2470, 3500, 1441, 199, 110])).
% 2.03/2.27 tff(12477,plain,
% 2.03/2.27 (~b(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1315, 12476, 12466, 12468])).
% 2.03/2.27 tff(12478,plain,
% 2.03/2.27 (r(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1214, 12477])).
% 2.03/2.27 tff(12479,plain,
% 2.03/2.27 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[11700, 12478, 111, 12230, 503, 12475, 110])).
% 2.03/2.27 tff(12480,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[486, 12479, 12473, 481])).
% 2.03/2.27 tff(12481,plain,(b(z, elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12482,plain,
% 2.03/2.27 (b(z, elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12481, 12456, 37, 67, 26, 12451, 219, 12052, 12058])).
% 2.03/2.27 tff(12483,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[5748, 271, 750, 2073, 3871, 503])).
% 2.03/2.27 tff(12484,plain,((~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(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12485,plain,
% 2.03/2.27 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12484, 12103, 3871, 503])).
% 2.03/2.27 tff(12486,plain,
% 2.03/2.27 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2071, 12485, 12230])).
% 2.03/2.27 tff(12487,plain,
% 2.03/2.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2479, 307, 2470])).
% 2.03/2.27 tff(12488,plain,
% 2.03/2.27 (~b(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2437, 271, 12487, 12103, 503])).
% 2.03/2.27 tff(12489,plain,
% 2.03/2.27 (r(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2167, 12488])).
% 2.03/2.27 tff(12490,plain,
% 2.03/2.27 (~b(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[456, 307, 12294, 446])).
% 2.03/2.27 tff(12491,plain,
% 2.03/2.27 (r(elem!1, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[299, 12490, 12075])).
% 2.03/2.27 tff(12492,plain,
% 2.03/2.27 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[2470])).
% 2.03/2.27 tff(12493,plain,
% 2.03/2.27 (b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[257, 12492])).
% 2.03/2.27 tff(12494,plain,
% 2.03/2.27 (~b(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1978, 257, 1326, 307])).
% 2.03/2.27 tff(12495,plain,
% 2.03/2.27 (r(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1214, 12494])).
% 2.03/2.27 tff(12496,plain,
% 2.03/2.27 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3879, 257, 3871, 446])).
% 2.03/2.27 tff(12497,plain,
% 2.03/2.27 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2044, 12496, 12422])).
% 2.03/2.27 tff(12498,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3865, 12497, 412, 12495])).
% 2.03/2.27 tff(12499,plain,
% 2.03/2.27 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1816, 12498, 12189])).
% 2.03/2.27 tff(12500,plain,
% 2.03/2.27 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12499, 12188])).
% 2.03/2.27 tff(12501,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12502,plain,
% 2.03/2.27 (((~b(s(s(s(elem!1))), s(z))) | (~b(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(elem!1))))) <=> ((~b(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(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12503,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(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(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12502])).
% 2.03/2.27 tff(12504,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(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(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[12503, 12501])).
% 2.03/2.27 tff(12505,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(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(elem!1)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(12506,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12505, 12504])).
% 2.03/2.27 tff(12507,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12506, 271, 12487, 12500, 12493, 503])).
% 2.03/2.27 tff(12508,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12509,plain,
% 2.03/2.27 (~b(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12508, 307, 2470, 412, 3871, 446, 1326, 503])).
% 2.03/2.27 tff(12510,plain,
% 2.03/2.27 (r(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[255, 12509, 3907])).
% 2.03/2.27 tff(12511,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12512,plain,
% 2.03/2.27 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(12513,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12512])).
% 2.03/2.27 tff(12514,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[12513, 12511])).
% 2.03/2.27 tff(12515,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(12516,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12515, 12514])).
% 2.03/2.27 tff(12517,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12516, 121, 1625, 3456, 145, 2327])).
% 2.03/2.27 tff(12518,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(12519,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12518, 12510, 12491, 12489])).
% 2.03/2.27 tff(12520,plain,
% 2.03/2.27 (b(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2325, 12519])).
% 2.03/2.27 tff(12521,plain,
% 2.03/2.27 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2081, 12520, 12103, 503])).
% 2.03/2.27 tff(12522,plain,
% 2.03/2.27 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2071, 12521, 12230])).
% 2.03/2.27 tff(12523,plain,
% 2.03/2.27 (~r(s(s(s(z))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7330, 121, 111, 12101, 12522])).
% 2.03/2.27 tff(12524,plain,
% 2.03/2.27 (b(s(s(s(z))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1155, 12523])).
% 2.03/2.27 tff(12525,plain,
% 2.03/2.27 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3622, 12520, 3871, 12294])).
% 2.03/2.27 tff(12526,plain,
% 2.03/2.27 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2044, 12525, 12422])).
% 2.03/2.27 tff(12527,plain,
% 2.03/2.27 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 2.03/2.27 inference(symmetry,[status(thm)],[12188])).
% 2.03/2.27 tff(12528,plain,
% 2.03/2.27 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12527])).
% 2.03/2.27 tff(12529,plain,
% 2.03/2.27 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12521, 12528])).
% 2.03/2.27 tff(12530,plain,
% 2.03/2.27 (r(s(s(s(z))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1816, 12529, 12189])).
% 2.03/2.27 tff(12531,plain,
% 2.03/2.27 (~r(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3865, 12530, 412, 12526])).
% 2.03/2.27 tff(12532,plain,
% 2.03/2.27 (b(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1214, 12531])).
% 2.03/2.27 tff(12533,plain,
% 2.03/2.27 (~b(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10270, 271, 12532, 3871, 12524])).
% 2.03/2.27 tff(12534,plain,
% 2.03/2.27 (r(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[904, 12533])).
% 2.03/2.27 tff(12535,plain,
% 2.03/2.27 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[11663, 12230])).
% 2.03/2.27 tff(12536,plain,
% 2.03/2.27 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[2471])).
% 2.03/2.27 tff(12537,plain,
% 2.03/2.27 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12536])).
% 2.03/2.27 tff(12538,plain,
% 2.03/2.27 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12525, 12537])).
% 2.03/2.27 tff(12539,plain,
% 2.03/2.27 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[6237, 21, 12538, 12535])).
% 2.03/2.27 tff(12540,plain,
% 2.03/2.27 (r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[12510, 3908])).
% 2.03/2.27 tff(12541,plain,
% 2.03/2.27 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[12181])).
% 2.03/2.27 tff(12542,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.03/2.27 tff(12543,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12544,plain,
% 2.03/2.28 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12545,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[12544])).
% 2.03/2.28 tff(12546,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[12545, 12543])).
% 2.03/2.28 tff(12547,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12548,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12547, 12546])).
% 2.03/2.28 tff(12549,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12548, 121, 7794, 7792, 12542])).
% 2.03/2.28 tff(12550,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12549, 12541])).
% 2.03/2.28 tff(12551,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1559, 12550, 12184])).
% 2.03/2.28 tff(12552,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12551, 12185])).
% 2.03/2.28 tff(12553,plain,
% 2.03/2.28 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[946, 12259])).
% 2.03/2.28 tff(12554,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12555,plain,
% 2.03/2.28 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12556,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[12555])).
% 2.03/2.28 tff(12557,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[12556, 12554])).
% 2.03/2.28 tff(12558,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12559,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12558, 12557])).
% 2.03/2.28 tff(12560,plain,
% 2.03/2.28 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12559, 121, 7794, 7792, 12542])).
% 2.03/2.28 tff(12561,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1014, 12560, 12553])).
% 2.03/2.28 tff(12562,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.03/2.28 tff(12563,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12564,plain,
% 2.03/2.28 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12565,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[12564])).
% 2.03/2.28 tff(12566,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[12565, 12563])).
% 2.03/2.28 tff(12567,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12568,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12567, 12566])).
% 2.03/2.28 tff(12569,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12568, 271, 750, 937, 1066, 12562])).
% 2.03/2.28 tff(12570,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(12571,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12570, 12561, 750, 937])).
% 2.03/2.28 tff(12572,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12571, 12552])).
% 2.03/2.28 tff(12573,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(12574,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12573, 937, 750, 2470, 7794, 7792])).
% 2.03/2.28 tff(12575,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10426, 12574])).
% 2.03/2.28 tff(12576,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12577,plain,
% 2.03/2.28 (((~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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12578,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[12577])).
% 2.03/2.28 tff(12579,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[12578, 12576])).
% 2.03/2.28 tff(12580,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12581,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12580, 12579])).
% 2.03/2.28 tff(12582,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12581, 271, 3871, 222, 937, 12575])).
% 2.03/2.28 tff(12583,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(12584,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12583, 12520, 3871, 12103, 2470, 12540, 12539])).
% 2.03/2.28 tff(12585,plain,
% 2.03/2.28 (r(s(s(s(s(z)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[932, 12584])).
% 2.03/2.28 tff(12586,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[919, 12585, 12534, 110])).
% 2.03/2.28 tff(12587,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1095, 12586])).
% 2.03/2.28 tff(12588,plain,
% 2.03/2.28 (~b(s(s(elem!1)), s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12490, 12397])).
% 2.03/2.28 tff(12589,plain,
% 2.03/2.28 (r(s(s(elem!1)), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 12588])).
% 2.03/2.28 tff(12590,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12591,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12592,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12591, 12590])).
% 2.03/2.28 tff(12593,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12592, 121, 12489, 12589, 12585])).
% 2.03/2.28 tff(12594,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12253, 21, 12236, 12593])).
% 2.03/2.28 tff(12595,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12596,plain,
% 2.03/2.28 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12597,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[12596])).
% 2.03/2.28 tff(12598,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[12597, 12595])).
% 2.03/2.28 tff(12599,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12600,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12599, 12598])).
% 2.03/2.28 tff(12601,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12600, 271, 12487, 3936, 12594, 12587])).
% 2.03/2.28 tff(12602,plain,((~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(12603,plain,
% 2.03/2.28 (~b(elem!1, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12602, 412, 3871, 2470, 111, 110, 503, 12113, 1326])).
% 2.03/2.28 tff(12604,plain,
% 2.03/2.28 (r(elem!1, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[392, 12603, 377])).
% 2.03/2.28 tff(12605,plain,
% 2.03/2.28 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12604, 12281])).
% 2.03/2.28 tff(12606,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12607,plain,
% 2.03/2.28 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(12608,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[12607])).
% 2.03/2.28 tff(12609,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[12608, 12606])).
% 2.03/2.28 tff(12610,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(12611,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[12610, 12609])).
% 2.03/2.28 tff(12612,plain,
% 2.03/2.28 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12611, 121, 12605, 12101, 12486])).
% 2.03/2.29 tff(12613,plain,
% 2.03/2.29 (~r(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12612, 3910])).
% 2.03/2.29 tff(12614,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12615,plain,
% 2.03/2.29 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12616,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12615])).
% 2.03/2.29 tff(12617,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 2.03/2.29 inference(transitivity,[status(thm)],[12616, 12614])).
% 2.03/2.29 tff(12618,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12619,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12618, 12617])).
% 2.03/2.29 tff(12620,plain,
% 2.03/2.29 (~r(s(s(elem!1)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12619, 121, 12605, 111, 12101])).
% 2.03/2.29 tff(12621,plain,
% 2.03/2.29 (~r(elem!1, z)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12620, 12136])).
% 2.03/2.29 tff(12622,plain,
% 2.03/2.29 (b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[284, 12621, 12133])).
% 2.03/2.29 tff(12623,plain,
% 2.03/2.29 (~r(s(s(s(z))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7330, 121, 111, 12101, 12486])).
% 2.03/2.29 tff(12624,plain,
% 2.03/2.29 (b(s(s(s(z))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1155, 12623])).
% 2.03/2.29 tff(12625,plain,
% 2.03/2.29 (~b(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1947, 12624, 12622, 1326])).
% 2.03/2.29 tff(12626,plain,
% 2.03/2.29 (r(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[255, 12625, 3907])).
% 2.03/2.29 tff(12627,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12626, 12613])).
% 2.03/2.29 tff(12628,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(s(elem!1)))) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(elem!1)) | (~r(s(z), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12629,plain,
% 2.03/2.29 (~r(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12628, 12052, 12482, 37, 12451, 67, 219, 26, 12058])).
% 2.03/2.29 tff(12630,plain,
% 2.03/2.29 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[2476, 2472])).
% 2.03/2.29 tff(12631,plain,
% 2.03/2.29 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12630])).
% 2.03/2.29 tff(12632,plain,
% 2.03/2.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[317, 12631])).
% 2.03/2.29 tff(12633,plain,
% 2.03/2.29 (b(s(elem!1), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[4488, 8688, 12272, 12266, 481, 2469])).
% 2.03/2.29 tff(12634,plain,
% 2.03/2.29 (~b(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9291, 12633, 1326, 394])).
% 2.03/2.29 tff(12635,plain,
% 2.03/2.29 (r(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1192, 12634, 12183])).
% 2.03/2.29 tff(12636,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3622, 222, 3871, 12294])).
% 2.03/2.29 tff(12637,plain,
% 2.03/2.29 (b(s(s(s(z))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9295, 12636, 379, 12189, 1184])).
% 2.03/2.29 tff(12638,plain,
% 2.03/2.29 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12637, 12188])).
% 2.03/2.29 tff(12639,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12640,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12641,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12640, 12639])).
% 2.03/2.29 tff(12642,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12641, 271, 12638, 3871, 222, 503])).
% 2.03/2.29 tff(12643,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12644,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12643, 12635, 503, 2470, 379, 3871])).
% 2.03/2.29 tff(12645,plain,
% 2.03/2.29 (r(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2325, 12644])).
% 2.03/2.29 tff(12646,plain,
% 2.03/2.29 (r(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[11651, 12633, 1326, 394, 12077, 12075, 111, 110, 12133])).
% 2.03/2.29 tff(12647,plain,
% 2.03/2.29 (r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12646, 3908])).
% 2.03/2.29 tff(12648,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10632, 572, 110, 111])).
% 2.03/2.29 tff(12649,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[486, 12648, 481])).
% 2.03/2.29 tff(12650,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12651,plain,
% 2.03/2.29 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12652,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12651])).
% 2.03/2.29 tff(12653,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[12652, 12650])).
% 2.03/2.29 tff(12654,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12655,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12654, 12653])).
% 2.03/2.29 tff(12656,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12655, 121, 572, 3456, 145, 2327])).
% 2.03/2.29 tff(12657,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12658,plain,
% 2.03/2.29 (~r(elem!1, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12657, 12645, 572, 12646])).
% 2.03/2.29 tff(12659,plain,
% 2.03/2.29 (b(elem!1, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[299, 12658, 12075])).
% 2.03/2.29 tff(12660,plain,
% 2.03/2.29 (~b(s(z), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[513, 12659, 503, 12649])).
% 2.03/2.29 tff(12661,plain,
% 2.03/2.29 (r(s(z), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2167, 12660])).
% 2.03/2.29 tff(12662,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12663,plain,
% 2.03/2.29 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12664,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12663])).
% 2.03/2.29 tff(12665,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[12664, 12662])).
% 2.03/2.29 tff(12666,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12667,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12666, 12665])).
% 2.03/2.29 tff(12668,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12667, 121, 12282, 12661, 12647, 12645])).
% 2.03/2.29 tff(12669,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(elem!1))) = elem!1) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12670,plain,
% 2.03/2.29 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12669, 9983, 2470, 67, 3871, 1326, 11211, 111, 110, 12063, 12632])).
% 2.03/2.29 tff(12671,plain,
% 2.03/2.29 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[760, 12670])).
% 2.03/2.29 tff(12672,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12484, 12671, 3871, 67])).
% 2.03/2.29 tff(12673,plain,
% 2.03/2.29 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2071, 12672, 12230])).
% 2.03/2.29 tff(12674,plain,
% 2.03/2.29 (b(s(z), s(elem!1))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12671, 12350])).
% 2.03/2.29 tff(12675,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12672, 12528])).
% 2.03/2.29 tff(12676,plain,
% 2.03/2.29 (r(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[11622, 317, 110, 111, 3871, 38, 11211, 10994, 12070, 219, 1326, 9983])).
% 2.03/2.29 tff(12677,plain,
% 2.03/2.29 (b(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[255, 221, 3907])).
% 2.03/2.29 tff(12678,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3879, 12677, 3871, 446])).
% 2.03/2.29 tff(12679,plain,
% 2.03/2.29 (~r(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9295, 12678, 379, 12189, 3506])).
% 2.03/2.29 tff(12680,plain,
% 2.03/2.29 (b(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1192, 12679, 12183])).
% 2.03/2.29 tff(12681,plain,
% 2.03/2.29 (~b(s(elem!1), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[11651, 221, 1326, 394, 12077, 12075, 111, 110, 12133])).
% 2.03/2.29 tff(12682,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12364, 12681, 1, 2470])).
% 2.03/2.29 tff(12683,plain,
% 2.03/2.29 (~r(z, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[11700, 12682, 111, 12230, 503, 909, 110])).
% 2.03/2.29 tff(12684,plain,
% 2.03/2.29 (b(z, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1214, 12683])).
% 2.03/2.29 tff(12685,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2020, 12684, 12680, 1326, 12677])).
% 2.03/2.29 tff(12686,plain,(r(s(s(s(z))), elem!1) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12687,plain,
% 2.03/2.29 (r(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12686, 12676, 111, 67, 1326, 110, 9983, 12675, 1, 2470, 3871, 12674, 11211])).
% 2.03/2.29 tff(12688,plain,
% 2.03/2.29 (r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12687, 3908])).
% 2.03/2.29 tff(12689,plain,
% 2.03/2.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[9983, 12281])).
% 2.03/2.29 tff(12690,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12691,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12692,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12691, 12690])).
% 2.03/2.29 tff(12693,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12692, 121, 623, 573, 7794, 5499])).
% 2.03/2.29 tff(12694,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12695,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12694, 12689, 12688, 12673])).
% 2.03/2.29 tff(12696,plain,
% 2.03/2.29 (b(s(elem!1), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[4488, 12695, 12272, 12266, 12063, 12632])).
% 2.03/2.29 tff(12697,plain,
% 2.03/2.29 (~b(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9291, 12696, 1326, 11211])).
% 2.03/2.29 tff(12698,plain,
% 2.03/2.29 (r(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1192, 12697, 12183])).
% 2.03/2.29 tff(12699,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12643, 12698, 67, 2470, 9983, 3871])).
% 2.03/2.29 tff(12700,plain,
% 2.03/2.29 (r(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2325, 12699])).
% 2.03/2.29 tff(12701,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3790, 12696, 2470])).
% 2.03/2.29 tff(12702,plain,
% 2.03/2.29 (~b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[11634, 12696, 1326, 11211])).
% 2.03/2.29 tff(12703,plain,
% 2.03/2.29 (r(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[284, 12702, 12133])).
% 2.03/2.29 tff(12704,plain,
% 2.03/2.29 (b(s(elem!1), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9295, 12698, 9983, 12189, 12675])).
% 2.03/2.29 tff(12705,plain,
% 2.03/2.29 (~b(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3879, 12704, 3871, 12674])).
% 2.03/2.29 tff(12706,plain,
% 2.03/2.29 (r(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[255, 10600, 2346])).
% 2.03/2.29 tff(12707,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12708,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12709,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12708, 12707])).
% 2.03/2.29 tff(12710,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12709, 121, 10603, 1409, 12706, 2327])).
% 2.03/2.29 tff(12711,plain,(b(s(z), elem!1) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | (s(z) = elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12712,plain,
% 2.03/2.29 (b(s(z), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12711, 12705, 3871, 12077, 12703, 12700])).
% 2.03/2.29 tff(12713,plain,
% 2.03/2.29 (~b(elem!1, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8132, 12712, 67, 12701])).
% 2.03/2.29 tff(12714,plain,
% 2.03/2.29 (~b(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12713, 12397])).
% 2.03/2.29 tff(12715,plain,
% 2.03/2.29 (r(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 12714])).
% 2.03/2.29 tff(12716,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12717,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(12718,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12717, 12716])).
% 2.03/2.29 tff(12719,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12718, 121, 110, 12715, 12688, 12700])).
% 2.03/2.29 tff(12720,plain,(b(elem!1, s(elem!1)) | (~r(s(z), z)) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12721,plain,
% 2.03/2.29 (b(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12720, 12052, 26, 12451, 12482, 37, 1, 38, 12629])).
% 2.03/2.29 tff(12722,plain,
% 2.03/2.29 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12052])).
% 2.03/2.29 tff(12723,plain,
% 2.03/2.29 ((~b(elem!1, z)) <=> (~b(s(s(elem!1)), z))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12722])).
% 2.03/2.29 tff(12724,plain,
% 2.03/2.29 (b(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[409, 12629])).
% 2.03/2.29 tff(12725,plain,
% 2.03/2.29 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12052])).
% 2.03/2.29 tff(12726,plain,
% 2.03/2.29 (b(z, s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12482, 12725])).
% 2.03/2.29 tff(12727,plain,
% 2.03/2.29 (~b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3404, 12721, 12726, 12724])).
% 2.03/2.29 tff(12728,plain,
% 2.03/2.29 (~b(s(s(elem!1)), z)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12727, 12723])).
% 2.03/2.29 tff(12729,plain,
% 2.03/2.29 (r(s(s(elem!1)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2428, 21, 59, 12728])).
% 2.03/2.29 tff(12730,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12308, 12724, 12052])).
% 2.03/2.29 tff(12731,plain,
% 2.03/2.29 (~b(s(elem!1), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[4598, 12721, 12482, 12724])).
% 2.03/2.29 tff(12732,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12364, 12731, 1, 12052])).
% 2.03/2.29 tff(12733,plain,
% 2.03/2.29 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10632, 12732, 26, 37])).
% 2.03/2.29 tff(12734,plain,
% 2.03/2.29 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[760, 12733])).
% 2.03/2.29 tff(12735,plain,
% 2.03/2.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2479, 12721, 12052])).
% 2.03/2.29 tff(12736,plain,
% 2.03/2.29 (~b(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[4727, 271, 12735, 12734, 12730])).
% 2.03/2.29 tff(12737,plain,
% 2.03/2.29 (r(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2143, 12736])).
% 2.03/2.29 tff(12738,plain,
% 2.03/2.29 (~r(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2422, 12737, 26, 12729])).
% 2.03/2.29 tff(12739,plain,
% 2.03/2.29 (b(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[904, 12738])).
% 2.03/2.29 tff(12740,plain,
% 2.03/2.29 (~b(s(z), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9079, 12739, 12721, 12482])).
% 2.03/2.29 tff(12741,plain,
% 2.03/2.29 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 2.03/2.29 inference(transitivity,[status(thm)],[12054, 1218])).
% 2.03/2.29 tff(12742,plain,
% 2.03/2.29 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12741])).
% 2.03/2.29 tff(12743,plain,
% 2.03/2.29 (~(elem!1 = s(z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[2137, 12742])).
% 2.03/2.29 tff(12744,plain,
% 2.03/2.29 (s(elem!1) = s(s(s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12052])).
% 2.03/2.29 tff(12745,plain,
% 2.03/2.29 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12744])).
% 2.03/2.29 tff(12746,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.03/2.29 inference(symmetry,[status(thm)],[12745])).
% 2.03/2.29 tff(12747,plain,
% 2.03/2.29 (b(s(elem!1), s(z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[67, 12746])).
% 2.03/2.29 tff(12748,plain,
% 2.03/2.29 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12744])).
% 2.03/2.29 tff(12749,plain,
% 2.03/2.29 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 2.03/2.29 inference(symmetry,[status(thm)],[12748])).
% 2.03/2.29 tff(12750,plain,
% 2.03/2.29 (b(s(z), s(elem!1))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[12734, 12749])).
% 2.03/2.29 tff(12751,plain,
% 2.03/2.29 (~b(elem!1, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[456, 12750, 12747, 12721])).
% 2.03/2.29 tff(12752,plain,
% 2.03/2.29 (r(elem!1, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[299, 12751, 12743])).
% 2.03/2.29 tff(12753,plain,
% 2.03/2.29 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12744])).
% 2.03/2.29 tff(12754,plain,
% 2.03/2.29 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(elem!1))),
% 2.03/2.29 inference(symmetry,[status(thm)],[12753])).
% 2.03/2.29 tff(12755,plain,
% 2.03/2.29 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12754])).
% 2.03/2.29 tff(12756,plain,
% 2.03/2.29 (~(s(z) = s(elem!1))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[61, 12755])).
% 2.03/2.29 tff(12757,plain,
% 2.03/2.29 (~r(s(z), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[11276, 12739, 2207, 12451, 12629, 12482, 12756, 12752])).
% 2.03/2.29 tff(12758,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[236, 12757, 12740, 12056])).
% 2.03/2.29 tff(12759,plain,(r(s(s(s(elem!1))), s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(12760,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[12759, 33, 1, 2])).
% 2.03/2.29 tff(12761,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.03/2.29 tff(12762,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12763,plain,
% 2.03/2.29 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(12764,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[12763])).
% 2.03/2.29 tff(12765,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[12764, 12762])).
% 2.03/2.29 tff(12766,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.03/2.30 inference(quant_inst,[status(thm)],[])).
% 2.03/2.30 tff(12767,plain,
% 2.03/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[12766, 12765])).
% 2.03/2.30 tff(12768,plain,
% 2.03/2.30 ($false),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[12767, 121, 111, 572, 110, 12761])).
% 2.03/2.30 tff(12769,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.30 tff(12770,plain,
% 2.03/2.30 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[12769, 12760, 37, 26])).
% 2.03/2.30 tff(12771,plain,
% 2.03/2.30 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[760, 12770])).
% 2.03/2.30 tff(12772,plain,
% 2.03/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.03/2.30 inference(rewrite,[status(thm)],[])).
% 2.03/2.30 tff(12773,plain,
% 2.03/2.30 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.03/2.30 inference(rewrite,[status(thm)],[])).
% 2.03/2.30 tff(12774,plain,
% 2.03/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[12773])).
% 2.03/2.30 tff(12775,plain,
% 2.03/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.03/2.30 inference(transitivity,[status(thm)],[12774, 12772])).
% 2.03/2.30 tff(12776,plain,
% 2.03/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 2.03/2.30 inference(quant_inst,[status(thm)],[])).
% 2.03/2.30 tff(12777,plain,
% 2.03/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[12776, 12775])).
% 2.03/2.30 tff(12778,plain,
% 2.03/2.30 ($false),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[12777, 121, 111, 110, 909, 12761])).
% 2.03/2.30 tff(12779,plain,((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.30 tff(12780,plain,
% 2.03/2.30 (~r(z, s(z))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[12779, 111, 110, 12761])).
% 2.03/2.30 tff(12781,plain,
% 2.03/2.30 (b(z, s(z))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[904, 12780])).
% 2.03/2.30 tff(12782,plain,
% 2.03/2.30 (~(s(z) = elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[229, 199, 12781])).
% 2.03/2.30 tff(12783,plain,
% 2.03/2.30 (~(z = elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[327, 317, 12781])).
% 2.03/2.30 tff(12784,plain,
% 2.03/2.30 (r(z, elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[355, 12783, 199])).
% 2.03/2.30 tff(12785,plain,
% 2.03/2.30 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10227, 12784, 3502, 111])).
% 2.03/2.30 tff(12786,plain,
% 2.03/2.30 (~r(s(z), elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[466, 12783, 110, 12781, 377, 199])).
% 2.03/2.30 tff(12787,plain,
% 2.03/2.30 (b(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[236, 12786, 12782])).
% 2.13/2.30 tff(12788,plain,
% 2.13/2.30 (~(s(z) = s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[343, 12783])).
% 2.13/2.30 tff(12789,plain,
% 2.13/2.30 (~(s(elem!1) = s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[350, 12788])).
% 2.13/2.30 tff(12790,plain,
% 2.13/2.30 (~r(z, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12464, 412, 199, 377, 110, 344, 337, 230, 331])).
% 2.13/2.30 tff(12791,plain,
% 2.13/2.30 (b(z, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1439, 12790])).
% 2.13/2.30 tff(12792,plain,
% 2.13/2.30 (~r(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[420, 412, 110, 356])).
% 2.13/2.30 tff(12793,plain,
% 2.13/2.30 (b(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[429, 12792, 351])).
% 2.13/2.30 tff(12794,plain,
% 2.13/2.30 (~r(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[466, 331, 110, 220, 377, 199])).
% 2.13/2.30 tff(12795,plain,
% 2.13/2.30 (b(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[236, 12794, 230])).
% 2.13/2.30 tff(12796,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12797,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(12798,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12797, 12796])).
% 2.13/2.30 tff(12799,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12798, 271, 12795, 220, 12793, 12791])).
% 2.13/2.30 tff(12800,plain,((~r(s(elem!1), z)) | (~b(z, s(z))) | (~r(s(z), z)) | b(z, elem!1) | (elem!1 = s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12801,plain,
% 2.13/2.30 (~r(s(elem!1), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12800, 12783, 110, 199, 377, 12781])).
% 2.13/2.30 tff(12802,plain,
% 2.13/2.30 (b(s(elem!1), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[409, 12801])).
% 2.13/2.30 tff(12803,plain,
% 2.13/2.30 (~r(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10236, 12802, 3502, 12789, 110, 12784, 12787])).
% 2.13/2.30 tff(12804,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[2505])).
% 2.13/2.30 tff(12805,plain,
% 2.13/2.30 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(symmetry,[status(thm)],[12804])).
% 2.13/2.30 tff(12806,plain,
% 2.13/2.30 ((~r(elem!1, s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12805])).
% 2.13/2.30 tff(12807,plain,
% 2.13/2.30 (~r(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[293, 12806])).
% 2.13/2.30 tff(12808,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12761, 12807])).
% 2.13/2.30 tff(12809,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(elem!1))), s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12810,plain,
% 2.13/2.30 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12809, 12803, 12761])).
% 2.13/2.30 tff(12811,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[486, 12810, 12785])).
% 2.13/2.30 tff(12812,plain,
% 2.13/2.30 (~(elem!1 = s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[242, 12782])).
% 2.13/2.30 tff(12813,plain,
% 2.13/2.30 (b(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[299, 12803, 12812])).
% 2.13/2.30 tff(12814,plain,
% 2.13/2.30 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12769, 12761, 111, 110])).
% 2.13/2.30 tff(12815,plain,
% 2.13/2.30 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[760, 12814])).
% 2.13/2.30 tff(12816,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12817,plain,
% 2.13/2.30 (((~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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12818,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12817])).
% 2.13/2.30 tff(12819,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[12818, 12816])).
% 2.13/2.30 tff(12820,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(12821,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12820, 12819])).
% 2.13/2.30 tff(12822,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12821, 271, 12787, 12815, 12813, 12811])).
% 2.13/2.30 tff(12823,plain,(b(elem!1, s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | b(z, elem!1) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12824,plain,
% 2.13/2.30 (b(elem!1, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12823, 199, 110, 12761, 377, 111])).
% 2.13/2.30 tff(12825,plain,
% 2.13/2.30 (~r(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[466, 331, 110, 199, 377, 220])).
% 2.13/2.30 tff(12826,plain,
% 2.13/2.30 (~b(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8883, 356, 243, 3500, 412, 307, 344, 110])).
% 2.13/2.30 tff(12827,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[236, 12826, 12825, 231])).
% 2.13/2.30 tff(12828,plain,((z = elem!1) | (s(z) = elem!1) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | b(z, elem!1) | (elem!1 = s(elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12829,plain,
% 2.13/2.30 (z = elem!1),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12828, 3501, 12781, 12824, 110, 199, 377, 12782])).
% 2.13/2.30 tff(12830,plain,
% 2.13/2.30 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12829])).
% 2.13/2.30 tff(12831,plain,
% 2.13/2.30 (r(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[111, 12830])).
% 2.13/2.30 tff(12832,plain,
% 2.13/2.30 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10028])).
% 2.13/2.30 tff(12833,plain,
% 2.13/2.30 (b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[754, 107, 750])).
% 2.13/2.30 tff(12834,plain,
% 2.13/2.30 (b(s(elem!1), s(s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12833, 12832])).
% 2.13/2.30 tff(12835,plain,
% 2.13/2.30 ((~b(s(z), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10029])).
% 2.13/2.30 tff(12836,plain,
% 2.13/2.30 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[71, 12835])).
% 2.13/2.30 tff(12837,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12836, 12834])).
% 2.13/2.30 tff(12838,plain,((~(z = elem!1)) | b(s(z), s(s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12839,plain,
% 2.13/2.30 (b(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12838, 12829, 12815])).
% 2.13/2.30 tff(12840,plain,
% 2.13/2.30 (r(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10135, 12839, 12829, 3500, 3501, 12781])).
% 2.13/2.30 tff(12841,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[149, 12840, 12829])).
% 2.13/2.30 tff(12842,plain,
% 2.13/2.30 (s(z) = s(elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12829])).
% 2.13/2.30 tff(12843,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12842])).
% 2.13/2.30 tff(12844,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12761, 12843])).
% 2.13/2.30 tff(12845,plain,
% 2.13/2.30 (~b(s(elem!1), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7069, 12829, 3498])).
% 2.13/2.30 tff(12846,plain,
% 2.13/2.30 (r(s(elem!1), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2243, 12845, 3500])).
% 2.13/2.30 tff(12847,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4476, 121, 12846, 12844, 12841, 12831])).
% 2.13/2.30 tff(12848,plain,(b(s(elem!1), z) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | b(z, elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12849,plain,
% 2.13/2.30 (b(s(elem!1), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12848, 199, 37, 26, 12761, 377])).
% 2.13/2.30 tff(12850,plain,
% 2.13/2.30 (~r(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12779, 37, 26, 12761])).
% 2.13/2.30 tff(12851,plain,
% 2.13/2.30 (b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[904, 12850])).
% 2.13/2.30 tff(12852,plain,
% 2.13/2.30 (~(s(z) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[229, 199, 12851])).
% 2.13/2.30 tff(12853,plain,
% 2.13/2.30 (b(elem!1, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12823, 199, 26, 12761, 377, 37])).
% 2.13/2.30 tff(12854,plain,
% 2.13/2.30 (~(s(z) = s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9144, 12849, 2])).
% 2.13/2.30 tff(12855,plain,
% 2.13/2.30 (~(z = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[500, 12854])).
% 2.13/2.30 tff(12856,plain,
% 2.13/2.30 (r(elem!1, z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[284, 10705, 358])).
% 2.13/2.30 tff(12857,plain,
% 2.13/2.30 (~b(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12316, 220, 110, 199, 377, 231, 394, 331])).
% 2.13/2.30 tff(12858,plain,
% 2.13/2.30 (r(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[429, 12857, 351])).
% 2.13/2.30 tff(12859,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12860,plain,
% 2.13/2.30 (((~r(s(z), z)) | (~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(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12861,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12860])).
% 2.13/2.30 tff(12862,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[12861, 12859])).
% 2.13/2.30 tff(12863,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(12864,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12863, 12862])).
% 2.13/2.30 tff(12865,plain,
% 2.13/2.30 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12864, 121, 110, 12761, 12858])).
% 2.13/2.30 tff(12866,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[681, 12865, 82])).
% 2.13/2.30 tff(12867,plain,
% 2.13/2.30 (~r(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10591, 307, 356, 358, 110, 394])).
% 2.13/2.30 tff(12868,plain,
% 2.13/2.30 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12809, 12867, 12761])).
% 2.13/2.30 tff(12869,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12870,plain,
% 2.13/2.30 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12871,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12870])).
% 2.13/2.30 tff(12872,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[12871, 12869])).
% 2.13/2.30 tff(12873,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(12874,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12873, 12872])).
% 2.13/2.30 tff(12875,plain,
% 2.13/2.30 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12874, 121, 110, 12761, 12858])).
% 2.13/2.30 tff(12876,plain,
% 2.13/2.30 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[11152, 12865, 82, 307, 12875])).
% 2.13/2.30 tff(12877,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[486, 12876, 12868])).
% 2.13/2.30 tff(12878,plain,
% 2.13/2.30 (~b(z, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3351, 12877, 394, 307, 358, 12866])).
% 2.13/2.30 tff(12879,plain,
% 2.13/2.30 (r(z, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1439, 12878])).
% 2.13/2.30 tff(12880,plain,
% 2.13/2.30 (~r(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10623, 663, 111, 378])).
% 2.13/2.30 tff(12881,plain,
% 2.13/2.30 (elem!1 = s(s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[661, 12880])).
% 2.13/2.30 tff(12882,plain,
% 2.13/2.30 (s(s(s(elem!1))) = elem!1),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12881, 653])).
% 2.13/2.30 tff(12883,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[481, 12882])).
% 2.13/2.30 tff(12884,plain,((s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12885,plain,
% 2.13/2.30 (b(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12884, 12876, 111, 356, 12868])).
% 2.13/2.30 tff(12886,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3217, 271, 307, 2618, 638, 738])).
% 2.13/2.30 tff(12887,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12888,plain,
% 2.13/2.30 (~b(s(elem!1), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12887, 12885, 307, 12866])).
% 2.13/2.30 tff(12889,plain,
% 2.13/2.30 (r(s(elem!1), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2243, 12888, 3500])).
% 2.13/2.30 tff(12890,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3387, 12889, 12879, 356, 12856])).
% 2.13/2.30 tff(12891,plain,((~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | b(z, elem!1) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12892,plain,
% 2.13/2.30 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12891, 12855, 12851, 37, 12853, 26, 12761, 199, 377, 12852, 12849])).
% 2.13/2.30 tff(12893,plain,
% 2.13/2.30 (elem!1 = s(s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[78, 12892])).
% 2.13/2.30 tff(12894,plain,
% 2.13/2.30 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12769, 12761, 37, 26])).
% 2.13/2.30 tff(12895,plain,
% 2.13/2.30 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[760, 12894])).
% 2.13/2.30 tff(12896,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2479, 12893, 12853])).
% 2.13/2.30 tff(12897,plain,
% 2.13/2.30 (~(elem!1 = z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[333, 12855])).
% 2.13/2.30 tff(12898,plain,
% 2.13/2.30 (r(z, elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[355, 12855, 199])).
% 2.13/2.30 tff(12899,plain,
% 2.13/2.30 (~r(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10591, 12898, 12853, 12897, 26, 12849])).
% 2.13/2.30 tff(12900,plain,
% 2.13/2.30 (~r(s(s(elem!1)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12129, 12893, 12899])).
% 2.13/2.30 tff(12901,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2143, 12900])).
% 2.13/2.30 tff(12902,plain,
% 2.13/2.30 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[989, 12901, 12896, 12895])).
% 2.13/2.30 tff(12903,plain,
% 2.13/2.30 (~b(elem!1, z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[402, 12849, 12851, 12853])).
% 2.13/2.30 tff(12904,plain,
% 2.13/2.30 (r(elem!1, z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[284, 12897, 12903])).
% 2.13/2.30 tff(12905,plain,
% 2.13/2.30 (~b(z, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6491, 12893, 33])).
% 2.13/2.30 tff(12906,plain,
% 2.13/2.30 (r(z, s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1439, 12905])).
% 2.13/2.30 tff(12907,plain,
% 2.13/2.30 (~r(s(elem!1), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3387, 12906, 12898, 12904])).
% 2.13/2.30 tff(12908,plain,
% 2.13/2.30 (b(s(elem!1), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2243, 12907, 3500])).
% 2.13/2.30 tff(12909,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3790, 12908, 12902, 12893])).
% 2.13/2.30 tff(12910,plain,(b(z, elem!1) | b(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(elem!1)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12911,plain,
% 2.13/2.30 (b(z, elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12910, 33, 12760, 219, 2])).
% 2.13/2.30 tff(12912,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12913,plain,
% 2.13/2.30 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12914,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[12913])).
% 2.13/2.30 tff(12915,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[12914, 12912])).
% 2.13/2.30 tff(12916,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(12917,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[12916, 12915])).
% 2.13/2.30 tff(12918,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12917, 271, 1326, 750, 448, 220])).
% 2.13/2.30 tff(12919,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(12920,plain,
% 2.13/2.30 (~b(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12919, 1326, 12815, 12781])).
% 2.13/2.30 tff(12921,plain,
% 2.13/2.30 (~(z = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[324, 12920, 12781])).
% 2.13/2.30 tff(12922,plain,
% 2.13/2.30 (~(s(z) = s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[343, 12921])).
% 2.13/2.30 tff(12923,plain,
% 2.13/2.30 (~(s(elem!1) = s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[350, 12922])).
% 2.13/2.30 tff(12924,plain,
% 2.13/2.30 (~(elem!1 = z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[333, 12921])).
% 2.13/2.30 tff(12925,plain,
% 2.13/2.30 (b(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[429, 9126, 422])).
% 2.13/2.30 tff(12926,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12927,plain,
% 2.13/2.30 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(12928,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[12927])).
% 2.13/2.31 tff(12929,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[12928, 12926])).
% 2.13/2.31 tff(12930,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(12931,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[12930, 12929])).
% 2.13/2.31 tff(12932,plain,
% 2.13/2.31 (~b(z, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12931, 271, 12815, 12781, 12925])).
% 2.13/2.31 tff(12933,plain,
% 2.13/2.31 (r(z, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1439, 12932])).
% 2.13/2.31 tff(12934,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(12935,plain,
% 2.13/2.31 (((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(12936,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[12935])).
% 2.13/2.31 tff(12937,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[12936, 12934])).
% 2.13/2.31 tff(12938,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(12939,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[12938, 12937])).
% 2.13/2.31 tff(12940,plain,
% 2.13/2.31 (~r(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12939, 121, 379, 12933, 3501])).
% 2.13/2.31 tff(12941,plain,
% 2.13/2.31 (b(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[284, 12940, 259])).
% 2.13/2.31 tff(12942,plain,
% 2.13/2.31 (~b(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12145, 12941, 1326, 12781])).
% 2.13/2.31 tff(12943,plain,
% 2.13/2.31 (r(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[236, 12942, 231])).
% 2.13/2.31 tff(12944,plain,
% 2.13/2.31 (~r(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12090, 12933, 3501, 379])).
% 2.13/2.31 tff(12945,plain,
% 2.13/2.31 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11073, 12944, 111])).
% 2.13/2.31 tff(12946,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(12947,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(12948,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[12947, 12946])).
% 2.13/2.31 tff(12949,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12948, 121, 1441, 110, 12761, 6842])).
% 2.13/2.31 tff(12950,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(12951,plain,
% 2.13/2.31 (~r(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12950, 12933, 110, 12761])).
% 2.13/2.31 tff(12952,plain,
% 2.13/2.31 (b(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8229, 12951])).
% 2.13/2.31 tff(12953,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(12954,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(12955,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[12954, 12953])).
% 2.13/2.31 tff(12956,plain,
% 2.13/2.31 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12955, 271, 1326, 12941, 12952])).
% 2.13/2.31 tff(12957,plain,
% 2.13/2.31 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[486, 12956, 12945])).
% 2.13/2.31 tff(12958,plain,
% 2.13/2.31 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3823, 12957, 12943, 3501, 12925, 379])).
% 2.13/2.31 tff(12959,plain,
% 2.13/2.31 (elem!1 = s(s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[78, 12958])).
% 2.13/2.31 tff(12960,plain,
% 2.13/2.31 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[12959])).
% 2.13/2.31 tff(12961,plain,
% 2.13/2.31 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[12960])).
% 2.13/2.31 tff(12962,plain,
% 2.13/2.31 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.13/2.31 inference(symmetry,[status(thm)],[12961])).
% 2.13/2.31 tff(12963,plain,
% 2.13/2.31 (b(s(elem!1), z)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[12952, 12962])).
% 2.13/2.31 tff(12964,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3498, 12963])).
% 2.13/2.31 tff(12965,plain,(b(s(elem!1), z) | (~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(z) = elem!1) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(12966,plain,
% 2.13/2.31 (~r(elem!1, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12965, 3498, 1326, 110, 12761, 231, 12924, 111, 12923])).
% 2.13/2.31 tff(12967,plain,
% 2.13/2.31 (b(elem!1, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[392, 12966, 377])).
% 2.13/2.31 tff(12968,plain,
% 2.13/2.31 (b(s(elem!1), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[429, 9126, 12923])).
% 2.13/2.31 tff(12969,plain,
% 2.13/2.31 (~b(z, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4122, 12968, 1326, 12967])).
% 2.13/2.31 tff(12970,plain,
% 2.13/2.31 (r(elem!1, s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[299, 243, 12920])).
% 2.13/2.31 tff(12971,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(12972,plain,
% 2.13/2.31 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(12973,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[12972])).
% 2.13/2.31 tff(12974,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[12973, 12971])).
% 2.13/2.31 tff(12975,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(12976,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[12975, 12974])).
% 2.13/2.31 tff(12977,plain,
% 2.13/2.31 (~r(s(s(s(elem!1))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12976, 121, 110, 12761, 12970])).
% 2.13/2.31 tff(12978,plain,
% 2.13/2.31 (~b(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9079, 12967, 1326, 12781])).
% 2.13/2.31 tff(12979,plain,
% 2.13/2.31 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2562, 12978, 12815])).
% 2.13/2.31 tff(12980,plain,
% 2.13/2.31 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[486, 12979, 12977])).
% 2.13/2.31 tff(12981,plain,
% 2.13/2.31 (~b(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7702, 271, 12967, 1326, 12980])).
% 2.13/2.31 tff(12982,plain,
% 2.13/2.31 (r(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8229, 12981])).
% 2.13/2.31 tff(12983,plain,
% 2.13/2.31 (~r(z, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12950, 12982, 110, 12761])).
% 2.13/2.31 tff(12984,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1439, 12983, 12969])).
% 2.13/2.31 tff(12985,plain,(b(s(elem!1), z) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(12986,plain,
% 2.13/2.31 (b(s(elem!1), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12985, 231, 12761, 1326, 111, 377, 110])).
% 2.13/2.31 tff(12987,plain,
% 2.13/2.31 (~b(elem!1, s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12919, 1326, 750, 220])).
% 2.13/2.31 tff(12988,plain,
% 2.13/2.31 (r(elem!1, s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[299, 243, 12987])).
% 2.13/2.31 tff(12989,plain,
% 2.13/2.31 (~(z = elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[324, 12987, 220])).
% 2.13/2.31 tff(12990,plain,
% 2.13/2.31 (~(s(z) = s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[343, 12989])).
% 2.13/2.31 tff(12991,plain,
% 2.13/2.31 (r(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11204, 379, 1326, 377, 220, 394, 12990, 231])).
% 2.13/2.31 tff(12992,plain,
% 2.13/2.31 (~r(s(elem!1), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11229, 12991, 220, 12988, 394, 12990])).
% 2.13/2.31 tff(12993,plain,
% 2.13/2.31 (b(s(elem!1), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2243, 12992, 3500])).
% 2.13/2.31 tff(12994,plain,
% 2.13/2.31 (~b(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9291, 12993, 1326, 394])).
% 2.13/2.31 tff(12995,plain,
% 2.13/2.31 (~(s(elem!1) = s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[350, 12990])).
% 2.13/2.31 tff(12996,plain,
% 2.13/2.31 (~r(s(elem!1), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8953, 379, 110, 12988])).
% 2.13/2.31 tff(12997,plain,
% 2.13/2.31 (b(s(elem!1), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[429, 12996, 12995])).
% 2.13/2.31 tff(12998,plain,
% 2.13/2.31 (~b(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8926, 12997, 220, 394])).
% 2.13/2.31 tff(12999,plain,
% 2.13/2.31 (~(elem!1 = z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[333, 12989])).
% 2.13/2.31 tff(13000,plain,
% 2.13/2.31 (elem!1 = s(s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12356, 2618, 357, 108, 1326, 394, 231, 243, 111, 110, 259])).
% 2.13/2.31 tff(13001,plain,
% 2.13/2.31 (s(s(s(z))) = elem!1),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1100, 13000])).
% 2.13/2.31 tff(13002,plain,
% 2.13/2.31 (r(s(s(s(z))), elem!1) <=> r(elem!1, elem!1)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[13001])).
% 2.13/2.31 tff(13003,plain,
% 2.13/2.31 (r(elem!1, elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(symmetry,[status(thm)],[13002])).
% 2.13/2.31 tff(13004,plain,
% 2.13/2.31 ((~r(elem!1, elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[13003])).
% 2.13/2.31 tff(13005,plain,
% 2.13/2.31 (~r(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[9971, 13004])).
% 2.13/2.31 tff(13006,plain,
% 2.13/2.31 (r(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11651, 2618, 1326, 394, 231, 243, 111, 110, 259])).
% 2.13/2.31 tff(13007,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13006, 13005])).
% 2.13/2.31 tff(13008,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(13009,plain,
% 2.13/2.31 (~r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13008, 12993, 12991, 1326, 394, 231, 111, 110, 12999])).
% 2.13/2.31 tff(13010,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[105, 13009])).
% 2.13/2.31 tff(13011,plain,
% 2.13/2.31 (~(s(s(s(z))) = elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10599, 13010, 12998])).
% 2.13/2.31 tff(13012,plain,
% 2.13/2.31 (~(elem!1 = s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1100, 13011])).
% 2.13/2.31 tff(13013,plain,
% 2.13/2.31 (r(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1192, 13012, 12994])).
% 2.13/2.31 tff(13014,plain,
% 2.13/2.31 (~r(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11254, 13013, 12991, 12988])).
% 2.13/2.31 tff(13015,plain,
% 2.13/2.31 (b(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2325, 13014])).
% 2.13/2.31 tff(13016,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(13017,plain,
% 2.13/2.31 (((~b(s(z), s(s(s(elem!1))))) | (~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(elem!1))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(13018,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[13017])).
% 2.13/2.31 tff(13019,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[13018, 13016])).
% 2.13/2.31 tff(13020,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(13021,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[13020, 13019])).
% 2.13/2.31 tff(13022,plain,
% 2.13/2.31 (~b(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13021, 271, 750, 220, 13015])).
% 2.13/2.31 tff(13023,plain,
% 2.13/2.31 (r(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1214, 13022])).
% 2.13/2.31 tff(13024,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(13025,plain,
% 2.13/2.31 (((~b(s(z), s(s(s(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(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(13026,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(z))), z))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[13025])).
% 2.13/2.31 tff(13027,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[13026, 13024])).
% 2.13/2.31 tff(13028,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(13029,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(elem!1))))) | (~b(s(s(s(z))), z))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[13028, 13027])).
% 2.13/2.31 tff(13030,plain,
% 2.13/2.31 (~b(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13029, 271, 750, 220, 13015])).
% 2.13/2.31 tff(13031,plain,
% 2.13/2.31 (r(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1155, 13030])).
% 2.13/2.31 tff(13032,plain,
% 2.13/2.31 (~b(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11634, 12993, 1326, 394])).
% 2.13/2.31 tff(13033,plain,
% 2.13/2.31 (r(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[284, 13032, 12999])).
% 2.13/2.31 tff(13034,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(13035,plain,
% 2.13/2.31 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(13036,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[13035])).
% 2.13/2.31 tff(13037,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[13036, 13034])).
% 2.13/2.31 tff(13038,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(13039,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[13038, 13037])).
% 2.13/2.31 tff(13040,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13039, 121, 13013, 13033, 13031, 13023])).
% 2.13/2.31 tff(13041,plain,((~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(13042,plain,
% 2.13/2.31 (~r(elem!1, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13041, 12986, 12781, 1326, 12815, 231, 111, 110, 377])).
% 2.13/2.31 tff(13043,plain,
% 2.13/2.31 (b(elem!1, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[392, 13042, 377])).
% 2.13/2.31 tff(13044,plain,
% 2.13/2.31 (~b(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9079, 13043, 1326, 12781])).
% 2.13/2.31 tff(13045,plain,
% 2.13/2.31 (r(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[236, 13044, 231])).
% 2.13/2.31 tff(13046,plain,
% 2.13/2.31 (~b(s(elem!1), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4598, 13043, 1326, 12986])).
% 2.13/2.31 tff(13047,plain,
% 2.13/2.31 (r(s(elem!1), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2243, 13046, 3500])).
% 2.13/2.31 tff(13048,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11229, 13047, 13045, 12781, 12970, 12986, 12922])).
% 2.13/2.31 tff(13049,plain,((s(z) = elem!1) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(13050,plain,
% 2.13/2.31 (s(z) = elem!1),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[13049, 12911, 219, 37, 26, 12760])).
% 2.13/2.31 tff(13051,plain,
% 2.13/2.31 (b(elem!1, s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8233, 13050, 12771])).
% 2.13/2.31 tff(13052,plain,
% 2.13/2.31 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[13050])).
% 2.13/2.31 tff(13053,plain,
% 2.13/2.31 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13052])).
% 2.13/2.32 tff(13054,plain,
% 2.13/2.32 (~(elem!1 = s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[2137, 13053])).
% 2.13/2.32 tff(13055,plain,
% 2.13/2.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[78, 13054])).
% 2.13/2.32 tff(13056,plain,
% 2.13/2.32 (~r(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[12779, 37, 26, 12760])).
% 2.13/2.32 tff(13057,plain,
% 2.13/2.32 (b(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[904, 13056])).
% 2.13/2.32 tff(13058,plain,
% 2.13/2.32 (~b(elem!1, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[12919, 12911, 12771, 13057])).
% 2.13/2.32 tff(13059,plain,
% 2.13/2.32 (~(z = elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[324, 13058, 13057])).
% 2.13/2.32 tff(13060,plain,
% 2.13/2.32 (~(s(z) = s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[343, 13059])).
% 2.13/2.32 tff(13061,plain,
% 2.13/2.32 (~(s(elem!1) = s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[350, 13060])).
% 2.13/2.32 tff(13062,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13050])).
% 2.13/2.32 tff(13063,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[12760, 13062])).
% 2.13/2.32 tff(13064,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13065,plain,
% 2.13/2.32 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13066,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13065])).
% 2.13/2.32 tff(13067,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13066, 13064])).
% 2.13/2.32 tff(13068,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13069,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13068, 13067])).
% 2.13/2.32 tff(13070,plain,
% 2.13/2.32 (~r(elem!1, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13069, 121, 111, 1408, 412])).
% 2.13/2.32 tff(13071,plain,
% 2.13/2.32 (b(elem!1, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[392, 13070, 377])).
% 2.13/2.32 tff(13072,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13073,plain,
% 2.13/2.32 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13074,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13073])).
% 2.13/2.32 tff(13075,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13074, 13072])).
% 2.13/2.32 tff(13076,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13077,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13076, 13075])).
% 2.13/2.32 tff(13078,plain,
% 2.13/2.32 (~r(s(elem!1), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13077, 121, 111, 1408, 412])).
% 2.13/2.32 tff(13079,plain,
% 2.13/2.32 (b(s(elem!1), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2243, 13078, 3500])).
% 2.13/2.32 tff(13080,plain,
% 2.13/2.32 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[1038])).
% 2.13/2.32 tff(13081,plain,
% 2.13/2.32 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[13080])).
% 2.13/2.32 tff(13082,plain,
% 2.13/2.32 (r(z, s(s(s(s(z)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[111, 13081])).
% 2.13/2.32 tff(13083,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13084,plain,
% 2.13/2.32 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13085,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13084])).
% 2.13/2.32 tff(13086,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13085, 13083])).
% 2.13/2.32 tff(13087,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13088,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13087, 13086])).
% 2.13/2.32 tff(13089,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13088, 121, 110, 412, 411, 1518])).
% 2.13/2.32 tff(13090,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13091,plain,
% 2.13/2.32 (~r(s(elem!1), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13090, 412, 110, 13082])).
% 2.13/2.32 tff(13092,plain,
% 2.13/2.32 (b(s(elem!1), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[429, 13091, 422])).
% 2.13/2.32 tff(13093,plain,
% 2.13/2.32 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[84, 6656])).
% 2.13/2.32 tff(13094,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13095,plain,
% 2.13/2.32 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13096,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13095])).
% 2.13/2.32 tff(13097,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13096, 13094])).
% 2.13/2.32 tff(13098,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13099,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13098, 13097])).
% 2.13/2.32 tff(13100,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13099, 121, 111, 139, 412, 798])).
% 2.13/2.32 tff(13101,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13102,plain,
% 2.13/2.32 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13101, 412, 139, 111])).
% 2.13/2.32 tff(13103,plain,
% 2.13/2.32 (b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2293, 21, 13102, 13093])).
% 2.13/2.32 tff(13104,plain,
% 2.13/2.32 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6230, 13103, 13092, 750])).
% 2.13/2.32 tff(13105,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[1037])).
% 2.13/2.32 tff(13106,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[13105])).
% 2.13/2.32 tff(13107,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[589, 13106])).
% 2.13/2.32 tff(13108,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.32 tff(13109,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13108, 13107])).
% 2.13/2.32 tff(13110,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13111,plain,
% 2.13/2.32 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13110, 13104, 223])).
% 2.13/2.32 tff(13112,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[586, 13111, 6943])).
% 2.13/2.32 tff(13113,plain,
% 2.13/2.32 (~b(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1940, 2343, 1326, 307])).
% 2.13/2.32 tff(13114,plain,
% 2.13/2.32 (r(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[255, 13113, 6655])).
% 2.13/2.32 tff(13115,plain,
% 2.13/2.32 (r(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13114, 4949])).
% 2.13/2.32 tff(13116,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13117,plain,
% 2.13/2.32 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13118,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13117])).
% 2.13/2.32 tff(13119,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13118, 13116])).
% 2.13/2.32 tff(13120,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13121,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13120, 13119])).
% 2.13/2.32 tff(13122,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13121, 121, 573, 6714, 139, 13115])).
% 2.13/2.32 tff(13123,plain,(b(s(z), s(s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13124,plain,
% 2.13/2.32 (b(s(z), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13123, 13112, 139, 223, 1326, 13071, 110, 111])).
% 2.13/2.32 tff(13125,plain,
% 2.13/2.32 (b(elem!1, s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11114, 13124, 1222])).
% 2.13/2.32 tff(13126,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13127,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13128,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13127, 13126])).
% 2.13/2.32 tff(13129,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13128, 271, 307, 2618, 257])).
% 2.13/2.32 tff(13130,plain,
% 2.13/2.32 (r(s(s(s(z))), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1816, 13129, 2033])).
% 2.13/2.32 tff(13131,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13132,plain,
% 2.13/2.32 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13133,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13132])).
% 2.13/2.32 tff(13134,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13133, 13131])).
% 2.13/2.32 tff(13135,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13136,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13135, 13134])).
% 2.13/2.32 tff(13137,plain,
% 2.13/2.32 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13136, 271, 307, 2618, 257])).
% 2.13/2.32 tff(13138,plain,
% 2.13/2.32 (r(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2044, 13137, 6284])).
% 2.13/2.32 tff(13139,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[3865, 13138, 13130, 412, 1140])).
% 2.13/2.32 tff(13140,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13141,plain,
% 2.13/2.32 (~r(z, s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13140, 257, 412, 2618, 307, 2033])).
% 2.13/2.32 tff(13142,plain,
% 2.13/2.32 (~b(z, s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2020, 257, 1326, 1195])).
% 2.13/2.32 tff(13143,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1214, 13142, 13141])).
% 2.13/2.32 tff(13144,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13145,plain,
% 2.13/2.32 (~b(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13144, 13125, 1326, 412, 13079, 13071, 7853])).
% 2.13/2.32 tff(13146,plain,
% 2.13/2.32 (r(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[255, 13145, 6655])).
% 2.13/2.32 tff(13147,plain,
% 2.13/2.32 (r(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[13146, 4949])).
% 2.13/2.32 tff(13148,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6946, 121, 13112, 1408, 139, 13147])).
% 2.13/2.32 tff(13149,plain,((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(13150,plain,
% 2.13/2.32 (~r(s(elem!1), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13149, 13063, 13050, 12911, 26, 37, 563, 12771, 219, 13061])).
% 2.13/2.32 tff(13151,plain,
% 2.13/2.32 (b(s(elem!1), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[409, 13150])).
% 2.13/2.32 tff(13152,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13153,plain,
% 2.13/2.32 (((~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(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(13154,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[13153])).
% 2.13/2.32 tff(13155,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[13154, 13152])).
% 2.13/2.32 tff(13156,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(13157,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13156, 13155])).
% 2.13/2.33 tff(13158,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13157, 271, 2618, 1326, 394, 738])).
% 2.13/2.33 tff(13159,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13160,plain,
% 2.13/2.33 (~b(s(elem!1), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13159, 12911, 13151, 13051])).
% 2.13/2.33 tff(13161,plain,
% 2.13/2.33 (r(s(elem!1), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2243, 13160, 2207])).
% 2.13/2.33 tff(13162,plain,
% 2.13/2.33 (r(z, s(z)) <=> r(z, elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13050])).
% 2.13/2.33 tff(13163,plain,
% 2.13/2.33 ((~r(z, s(z))) <=> (~r(z, elem!1))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13162])).
% 2.13/2.33 tff(13164,plain,
% 2.13/2.33 (~r(z, elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13056, 13163])).
% 2.13/2.33 tff(13165,plain,
% 2.13/2.33 (~b(s(s(s(z))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1956, 2343, 1326, 394])).
% 2.13/2.33 tff(13166,plain,
% 2.13/2.33 (r(s(s(s(z))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1816, 13165, 7853])).
% 2.13/2.33 tff(13167,plain,
% 2.13/2.33 (~r(elem!1, s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3849, 13166, 379, 622])).
% 2.13/2.33 tff(13168,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13167, 6715])).
% 2.13/2.33 tff(13169,plain,(b(s(z), s(s(s(z)))) | (~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13170,plain,
% 2.13/2.33 (b(s(z), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13169, 622, 379, 223, 1326, 11211, 110, 111])).
% 2.13/2.33 tff(13171,plain,
% 2.13/2.33 (r(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11593, 13170, 2207, 220, 10994, 1391])).
% 2.13/2.33 tff(13172,plain,
% 2.13/2.33 (r(s(s(elem!1)), elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13171, 4949])).
% 2.13/2.33 tff(13173,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13174,plain,
% 2.13/2.33 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13175,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13174])).
% 2.13/2.33 tff(13176,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[13175, 13173])).
% 2.13/2.33 tff(13177,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(13178,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13177, 13176])).
% 2.13/2.33 tff(13179,plain,
% 2.13/2.33 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13178, 121, 379, 139, 13172])).
% 2.13/2.33 tff(13180,plain,
% 2.13/2.33 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3520, 121, 379, 622, 139])).
% 2.13/2.33 tff(13181,plain,
% 2.13/2.33 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[681, 13180, 6656])).
% 2.13/2.33 tff(13182,plain,
% 2.13/2.33 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[7868, 7870])).
% 2.13/2.33 tff(13183,plain,
% 2.13/2.33 (b(elem!1, s(s(elem!1)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13170, 13182])).
% 2.13/2.33 tff(13184,plain,
% 2.13/2.33 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6906, 13183, 13181, 738])).
% 2.13/2.33 tff(13185,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[556, 13184, 13179, 1])).
% 2.13/2.33 tff(13186,plain,((~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(z, s(z))) | r(s(elem!1), z) | r(z, elem!1) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13187,plain,
% 2.13/2.33 (~r(elem!1, s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13186, 13161, 13051, 1, 13063, 13050, 13057, 13150, 13164, 12911, 26, 37])).
% 2.13/2.33 tff(13188,plain,
% 2.13/2.33 (b(elem!1, s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[392, 13187, 219])).
% 2.13/2.33 tff(13189,plain,
% 2.13/2.33 (~b(z, s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9091, 13188, 12911, 13151])).
% 2.13/2.33 tff(13190,plain,
% 2.13/2.33 (r(z, s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1439, 13189])).
% 2.13/2.33 tff(13191,plain,
% 2.13/2.33 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7694, 13190, 37, 13161])).
% 2.13/2.33 tff(13192,plain,
% 2.13/2.33 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[681, 13191, 13055])).
% 2.13/2.33 tff(13193,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13194,plain,
% 2.13/2.33 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13195,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13194])).
% 2.13/2.33 tff(13196,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[13195, 13193])).
% 2.13/2.33 tff(13197,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(13198,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13197, 13196])).
% 2.13/2.33 tff(13199,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13198, 271, 13188, 13151, 13192, 13051])).
% 2.13/2.33 tff(13200,plain,(b(z, s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13201,plain,
% 2.13/2.33 (b(z, s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13200, 1, 2])).
% 2.13/2.33 tff(13202,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 2.13/2.33 tff(13203,plain,
% 2.13/2.33 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13202])).
% 2.13/2.33 tff(13204,plain,
% 2.13/2.33 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 2.13/2.33 inference(symmetry,[status(thm)],[13203])).
% 2.13/2.33 tff(13205,plain,
% 2.13/2.33 (b(z, elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[3407, 13204])).
% 2.13/2.33 tff(13206,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[199, 13205])).
% 2.13/2.33 tff(13207,plain,((~(elem!1 = s(s(s(elem!1))))) | b(z, elem!1) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13208,plain,
% 2.13/2.33 (~(elem!1 = s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13207, 199, 3407])).
% 2.13/2.33 tff(13209,plain,
% 2.13/2.33 (~r(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[387, 9983, 110, 1243])).
% 2.13/2.33 tff(13210,plain,
% 2.13/2.33 (b(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[236, 13209, 231])).
% 2.13/2.33 tff(13211,plain,
% 2.13/2.33 (~b(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[12800, 412, 110, 331, 377, 199])).
% 2.13/2.33 tff(13212,plain,
% 2.13/2.33 (r(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[904, 13211])).
% 2.13/2.33 tff(13213,plain,
% 2.13/2.33 (r(elem!1, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3700, 13212, 3500, 199, 317, 258, 3502, 412])).
% 2.13/2.33 tff(13214,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4202, 13213, 13212, 110, 1243])).
% 2.13/2.33 tff(13215,plain,((~r(s(elem!1), z)) | (~r(s(z), z)) | b(z, elem!1) | b(elem!1, s(elem!1)) | (elem!1 = s(z)) | (z = elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13216,plain,
% 2.13/2.33 (~r(s(elem!1), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13215, 317, 199, 110, 243, 331, 219])).
% 2.13/2.33 tff(13217,plain,
% 2.13/2.33 (b(s(elem!1), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[409, 13216])).
% 2.13/2.33 tff(13218,plain,
% 2.13/2.33 (~r(elem!1, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10236, 394, 378, 2282, 110, 260, 379])).
% 2.13/2.33 tff(13219,plain,
% 2.13/2.33 (b(elem!1, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[299, 13218, 258])).
% 2.13/2.33 tff(13220,plain,
% 2.13/2.33 (elem!1 = s(s(s(elem!1)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[2505, 654])).
% 2.13/2.33 tff(13221,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4358, 13220])).
% 2.13/2.33 tff(13222,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(13223,plain,
% 2.13/2.33 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13222, 4358])).
% 2.13/2.33 tff(13224,plain,
% 2.13/2.33 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[486, 147, 13223])).
% 2.13/2.33 tff(13225,plain,
% 2.13/2.33 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8132, 13224, 260, 448])).
% 2.13/2.33 tff(13226,plain,
% 2.13/2.33 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[66, 21, 13225, 63])).
% 2.13/2.33 tff(13227,plain,
% 2.13/2.33 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[12821, 271, 260, 448, 13224])).
% 2.13/2.33 tff(13228,plain,
% 2.13/2.33 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[760, 13227])).
% 2.13/2.33 tff(13229,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13230,plain,
% 2.13/2.33 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13231,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13230])).
% 2.13/2.33 tff(13232,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[13231, 13229])).
% 2.13/2.33 tff(13233,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(13234,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13233, 13232])).
% 2.13/2.33 tff(13235,plain,
% 2.13/2.33 (~r(s(s(s(elem!1))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13234, 121, 572, 909, 12761])).
% 2.13/2.33 tff(13236,plain,
% 2.13/2.33 (b(s(s(s(elem!1))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8229, 13235])).
% 2.13/2.33 tff(13237,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13238,plain,
% 2.13/2.33 (((~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(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13239,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13238])).
% 2.13/2.33 tff(13240,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[13239, 13237])).
% 2.13/2.33 tff(13241,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(13242,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13241, 13240])).
% 2.13/2.33 tff(13243,plain,
% 2.13/2.33 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13242, 271, 394, 3407, 13236])).
% 2.13/2.33 tff(13244,plain,
% 2.13/2.33 (~b(s(elem!1), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3691, 271, 2618, 260, 448])).
% 2.13/2.33 tff(13245,plain,
% 2.13/2.33 (r(s(elem!1), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[429, 13244, 2282])).
% 2.13/2.33 tff(13246,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13247,plain,
% 2.13/2.33 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13248,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13247])).
% 2.13/2.33 tff(13249,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[13248, 13246])).
% 2.13/2.33 tff(13250,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(13251,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13250, 13249])).
% 2.13/2.33 tff(13252,plain,
% 2.13/2.33 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13251, 121, 572, 12761, 13245])).
% 2.13/2.33 tff(13253,plain,
% 2.13/2.33 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[681, 13252, 13243])).
% 2.13/2.33 tff(13254,plain,
% 2.13/2.33 (elem!1 = s(s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[78, 13253])).
% 2.13/2.33 tff(13255,plain,
% 2.13/2.33 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13254])).
% 2.13/2.33 tff(13256,plain,
% 2.13/2.33 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(symmetry,[status(thm)],[13255])).
% 2.13/2.33 tff(13257,plain,
% 2.13/2.33 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13256])).
% 2.13/2.33 tff(13258,plain,
% 2.13/2.33 (~r(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[12129, 13254, 293])).
% 2.13/2.33 tff(13259,plain,
% 2.13/2.33 (b(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2143, 13258])).
% 2.13/2.33 tff(13260,plain,
% 2.13/2.33 (~b(s(z), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3696, 271, 2618, 260, 448])).
% 2.13/2.33 tff(13261,plain,
% 2.13/2.33 (r(s(z), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[444, 13260, 348])).
% 2.13/2.33 tff(13262,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13263,plain,
% 2.13/2.33 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13264,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[13263])).
% 2.13/2.33 tff(13265,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[13264, 13262])).
% 2.13/2.33 tff(13266,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(13267,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[13266, 13265])).
% 2.13/2.33 tff(13268,plain,
% 2.13/2.33 (~r(z, s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13267, 121, 572, 909, 13245])).
% 2.13/2.33 tff(13269,plain,
% 2.13/2.33 (b(z, s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1439, 13268])).
% 2.13/2.33 tff(13270,plain,
% 2.13/2.33 (~(s(s(s(z))) = s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3917, 13254, 348])).
% 2.13/2.33 tff(13271,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13272,plain,
% 2.13/2.33 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(13273,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13272])).
% 2.13/2.34 tff(13274,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13273, 13271])).
% 2.13/2.34 tff(13275,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13276,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13275, 13274])).
% 2.13/2.34 tff(13277,plain,
% 2.13/2.34 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13276, 121, 572, 12761, 13245])).
% 2.13/2.34 tff(13278,plain,
% 2.13/2.34 (((~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), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13279,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13278])).
% 2.13/2.34 tff(13280,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13279, 3149])).
% 2.13/2.34 tff(13281,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13282,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13281, 13280])).
% 2.13/2.34 tff(13283,plain,
% 2.13/2.34 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13282, 271, 394, 3407, 13236])).
% 2.13/2.34 tff(13284,plain,
% 2.13/2.34 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2293, 21, 13283])).
% 2.13/2.34 tff(13285,plain,
% 2.13/2.34 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13284, 13277])).
% 2.13/2.34 tff(13286,plain,
% 2.13/2.34 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13254])).
% 2.13/2.34 tff(13287,plain,
% 2.13/2.34 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13285])).
% 2.13/2.34 tff(13288,plain,
% 2.13/2.34 (r(elem!1, s(s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[379, 13287])).
% 2.13/2.34 tff(13289,plain,
% 2.13/2.34 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13288, 13286])).
% 2.13/2.34 tff(13290,plain,
% 2.13/2.34 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13291,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13290])).
% 2.13/2.34 tff(13292,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13291, 2876])).
% 2.13/2.34 tff(13293,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13294,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13293, 13292])).
% 2.13/2.34 tff(13295,plain,
% 2.13/2.34 (~r(s(s(elem!1)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13294, 121, 623, 572, 12761])).
% 2.13/2.34 tff(13296,plain,
% 2.13/2.34 (b(s(s(elem!1)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2143, 13295])).
% 2.13/2.34 tff(13297,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13298,plain,
% 2.13/2.34 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13299,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13298])).
% 2.13/2.34 tff(13300,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13299, 13297])).
% 2.13/2.34 tff(13301,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13302,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13301, 13300])).
% 2.13/2.34 tff(13303,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13302, 121, 623, 12761, 5499])).
% 2.13/2.34 tff(13304,plain,
% 2.13/2.34 (b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2462, 21, 13303, 944])).
% 2.13/2.34 tff(13305,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13306,plain,
% 2.13/2.34 (((~r(s(s(s(elem!1))), s(z))) | (~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(z), s(s(s(elem!1))))) | (~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))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13307,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13306])).
% 2.13/2.34 tff(13308,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13307, 13305])).
% 2.13/2.34 tff(13309,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13310,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~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)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13309, 13308])).
% 2.13/2.34 tff(13311,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13310, 121, 572, 12761, 5499])).
% 2.13/2.34 tff(13312,plain,
% 2.13/2.34 (b(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2325, 13311])).
% 2.13/2.34 tff(13313,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13314,plain,
% 2.13/2.34 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13315,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13314])).
% 2.13/2.34 tff(13316,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13315, 13313])).
% 2.13/2.34 tff(13317,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13318,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13317, 13316])).
% 2.13/2.34 tff(13319,plain,
% 2.13/2.34 (~r(s(z), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13318, 121, 623, 572, 12761])).
% 2.13/2.34 tff(13320,plain,
% 2.13/2.34 (b(s(z), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2167, 13319])).
% 2.13/2.34 tff(13321,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13322,plain,
% 2.13/2.34 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13323,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13322])).
% 2.13/2.34 tff(13324,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13323, 13321])).
% 2.13/2.34 tff(13325,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13326,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13325, 13324])).
% 2.13/2.34 tff(13327,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13326, 271, 13320, 13312, 13304, 13296])).
% 2.13/2.34 tff(13328,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(13329,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13328, 13289, 944, 572, 12761])).
% 2.13/2.34 tff(13330,plain,
% 2.13/2.34 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[80])).
% 2.13/2.34 tff(13331,plain,
% 2.13/2.34 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[1500, 13330])).
% 2.13/2.34 tff(13332,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[906, 13331])).
% 2.13/2.34 tff(13333,plain,((~r(s(s(s(z))), s(elem!1))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(13334,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13333, 13329, 13285])).
% 2.13/2.34 tff(13335,plain,
% 2.13/2.34 (b(s(s(s(z))), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1816, 13334, 13270])).
% 2.13/2.34 tff(13336,plain,
% 2.13/2.34 (r(s(s(s(z))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1427, 13335, 394, 13269])).
% 2.13/2.34 tff(13337,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10317, 13336, 909, 13261])).
% 2.13/2.34 tff(13338,plain,
% 2.13/2.34 (b(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2325, 13337])).
% 2.13/2.34 tff(13339,plain,
% 2.13/2.34 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13254])).
% 2.13/2.34 tff(13340,plain,
% 2.13/2.34 (b(s(z), s(s(elem!1)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[260, 13339])).
% 2.13/2.34 tff(13341,plain,
% 2.13/2.34 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[5237, 271, 13340, 13338, 13259])).
% 2.13/2.34 tff(13342,plain,
% 2.13/2.34 (~b(s(s(s(z))), elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13341, 13257])).
% 2.13/2.34 tff(13343,plain,
% 2.13/2.34 (~(s(s(s(z))) = elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3906, 13254])).
% 2.13/2.34 tff(13344,plain,
% 2.13/2.34 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2071, 13329, 9149])).
% 2.13/2.34 tff(13345,plain,
% 2.13/2.34 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13285])).
% 2.13/2.34 tff(13346,plain,
% 2.13/2.34 (b(s(elem!1), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3787, 13254, 2618])).
% 2.13/2.34 tff(13347,plain,
% 2.13/2.34 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13346, 13345])).
% 2.13/2.34 tff(13348,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13349,plain,
% 2.13/2.34 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13350,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13349])).
% 2.13/2.34 tff(13351,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[13350, 13348])).
% 2.13/2.34 tff(13352,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(13353,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[13352, 13351])).
% 2.13/2.34 tff(13354,plain,
% 2.13/2.34 (~b(z, s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[13353, 271, 13347, 3407, 13344])).
% 2.13/2.34 tff(13355,plain,
% 2.13/2.34 (r(z, s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1214, 13354])).
% 2.13/2.34 tff(13356,plain,
% 2.13/2.34 (~(elem!1 = s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1100, 13343])).
% 2.13/2.34 tff(13357,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13358,plain,
% 2.13/2.34 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(13359,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[13358])).
% 2.13/2.34 tff(13360,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13359, 13357])).
% 2.13/2.35 tff(13361,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13362,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13361, 13360])).
% 2.13/2.35 tff(13363,plain,
% 2.13/2.35 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13362, 271, 13340, 13338, 13259])).
% 2.13/2.35 tff(13364,plain,
% 2.13/2.35 (~b(elem!1, s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[5482, 13363, 13254])).
% 2.13/2.35 tff(13365,plain,
% 2.13/2.35 (r(elem!1, s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1192, 13364, 13356])).
% 2.13/2.35 tff(13366,plain,
% 2.13/2.35 (~r(s(s(s(z))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[6723, 13365, 378, 13355])).
% 2.13/2.35 tff(13367,plain,
% 2.13/2.35 (b(s(s(s(z))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[255, 13366, 13343])).
% 2.13/2.35 tff(13368,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13367, 13342])).
% 2.13/2.35 tff(13369,plain,((~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | r(elem!1, s(z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(13370,plain,
% 2.13/2.35 (~b(s(elem!1), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13369, 13228, 3407, 909, 394, 944, 378, 13226, 260, 379, 293, 348, 448])).
% 2.13/2.35 tff(13371,plain,
% 2.13/2.35 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[7281, 13370, 13224])).
% 2.13/2.35 tff(13372,plain,
% 2.13/2.35 (~r(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13234, 121, 13228, 909, 13226])).
% 2.13/2.35 tff(13373,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8229, 13372])).
% 2.13/2.35 tff(13374,plain,
% 2.13/2.35 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13282, 271, 394, 3407, 13373])).
% 2.13/2.35 tff(13375,plain,
% 2.13/2.35 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13242, 271, 394, 3407, 13373])).
% 2.13/2.35 tff(13376,plain,
% 2.13/2.35 (r(s(elem!1), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2243, 13370, 2207])).
% 2.13/2.35 tff(13377,plain,
% 2.13/2.35 (r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[681, 13371, 13375])).
% 2.13/2.35 tff(13378,plain,
% 2.13/2.35 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[84, 13371])).
% 2.13/2.35 tff(13379,plain,
% 2.13/2.35 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2293, 21, 13374])).
% 2.13/2.35 tff(13380,plain,
% 2.13/2.35 (r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13379, 13378])).
% 2.13/2.35 tff(13381,plain,
% 2.13/2.35 (~r(elem!1, s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11896, 13380, 13377, 13376])).
% 2.13/2.35 tff(13382,plain,
% 2.13/2.35 (b(elem!1, s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[660, 21, 13381, 4358])).
% 2.13/2.35 tff(13383,plain,
% 2.13/2.35 (~(elem!1 = s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[12364, 13370, 1, 147])).
% 2.13/2.35 tff(13384,plain,
% 2.13/2.35 (~(s(s(elem!1)) = elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[197, 13383])).
% 2.13/2.35 tff(13385,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13386,plain,
% 2.13/2.35 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13387,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13386])).
% 2.13/2.35 tff(13388,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13387, 13385])).
% 2.13/2.35 tff(13389,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13390,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13389, 13388])).
% 2.13/2.35 tff(13391,plain,
% 2.13/2.35 (~b(s(s(elem!1)), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13390, 271, 543, 3407, 504])).
% 2.13/2.35 tff(13392,plain,
% 2.13/2.35 (r(s(s(elem!1)), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2430, 13391])).
% 2.13/2.35 tff(13393,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13394,plain,
% 2.13/2.35 (((~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(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13395,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13394])).
% 2.13/2.35 tff(13396,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13395, 13393])).
% 2.13/2.35 tff(13397,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13398,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13397, 13396])).
% 2.13/2.35 tff(13399,plain,
% 2.13/2.35 (~b(s(s(elem!1)), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13398, 271, 543, 504, 738])).
% 2.13/2.35 tff(13400,plain,
% 2.13/2.35 (r(s(s(elem!1)), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[862, 13399, 851])).
% 2.13/2.35 tff(13401,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8501, 13400, 13392, 378, 379])).
% 2.13/2.35 tff(13402,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = 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)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(13403,plain,
% 2.13/2.35 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13402, 13384, 379, 378, 13224, 13382, 3407])).
% 2.13/2.35 tff(13404,plain,
% 2.13/2.35 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[556, 13403, 1])).
% 2.13/2.35 tff(13405,plain,
% 2.13/2.35 (~r(s(elem!1), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3190, 13404, 13375, 13374, 13371])).
% 2.13/2.35 tff(13406,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13407,plain,
% 2.13/2.35 (((~r(s(s(s(elem!1))), s(elem!1))) | (~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(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13408,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13407])).
% 2.13/2.35 tff(13409,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13408, 13406])).
% 2.13/2.35 tff(13410,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13411,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13410, 13409])).
% 2.13/2.35 tff(13412,plain,
% 2.13/2.35 (~r(s(elem!1), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13411, 121, 13377, 13228, 13380])).
% 2.13/2.35 tff(13413,plain,
% 2.13/2.35 (b(s(elem!1), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[429, 13412, 2282])).
% 2.13/2.35 tff(13414,plain,
% 2.13/2.35 (~b(s(elem!1), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2176, 13404, 13228, 13377, 13413])).
% 2.13/2.35 tff(13415,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[526, 13414, 13405, 211])).
% 2.13/2.35 tff(13416,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), elem!1)) | r(elem!1, s(z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(13417,plain,
% 2.13/2.35 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13416, 909, 379, 378, 3407, 4358, 1, 394, 944, 260, 13218, 348, 13219])).
% 2.13/2.35 tff(13418,plain,
% 2.13/2.35 (~r(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8972, 13417, 378, 379])).
% 2.13/2.35 tff(13419,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8229, 13418])).
% 2.13/2.35 tff(13420,plain,
% 2.13/2.35 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13242, 271, 394, 3407, 13419])).
% 2.13/2.35 tff(13421,plain,
% 2.13/2.35 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13282, 271, 394, 3407, 13419])).
% 2.13/2.35 tff(13422,plain,
% 2.13/2.35 (r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3180, 2280])).
% 2.13/2.35 tff(13423,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13424,plain,
% 2.13/2.35 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13425,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13424])).
% 2.13/2.35 tff(13426,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13425, 13423])).
% 2.13/2.35 tff(13427,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13428,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13427, 13426])).
% 2.13/2.35 tff(13429,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13428, 121, 379, 4413, 139, 13422])).
% 2.13/2.35 tff(13430,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(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))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(13431,plain,
% 2.13/2.35 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13430, 13417, 379, 13421, 13420])).
% 2.13/2.35 tff(13432,plain,
% 2.13/2.35 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13431])).
% 2.13/2.35 tff(13433,plain,
% 2.13/2.35 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.35 inference(symmetry,[status(thm)],[13432])).
% 2.13/2.35 tff(13434,plain,
% 2.13/2.35 (elem!1 = s(s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[78, 13431])).
% 2.13/2.35 tff(13435,plain,
% 2.13/2.35 (~(s(s(s(z))) = elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3906, 13434])).
% 2.13/2.35 tff(13436,plain,
% 2.13/2.35 (~(elem!1 = s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1100, 13435])).
% 2.13/2.35 tff(13437,plain,
% 2.13/2.35 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1516, 13436])).
% 2.13/2.35 tff(13438,plain,
% 2.13/2.35 (~r(s(s(elem!1)), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[12129, 13434, 13218])).
% 2.13/2.35 tff(13439,plain,
% 2.13/2.35 (b(s(s(elem!1)), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2143, 13438])).
% 2.13/2.35 tff(13440,plain,
% 2.13/2.35 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13434])).
% 2.13/2.35 tff(13441,plain,
% 2.13/2.35 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13431])).
% 2.13/2.35 tff(13442,plain,
% 2.13/2.35 (b(z, s(elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[3407, 13441])).
% 2.13/2.35 tff(13443,plain,
% 2.13/2.35 (~(s(s(s(z))) = s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3917, 13434, 348])).
% 2.13/2.35 tff(13444,plain,
% 2.13/2.35 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13434])).
% 2.13/2.35 tff(13445,plain,
% 2.13/2.35 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[379, 13444])).
% 2.13/2.35 tff(13446,plain,
% 2.13/2.35 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13434])).
% 2.13/2.35 tff(13447,plain,
% 2.13/2.35 (r(z, s(s(elem!1)))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[378, 13446])).
% 2.13/2.35 tff(13448,plain,
% 2.13/2.35 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13434])).
% 2.13/2.35 tff(13449,plain,
% 2.13/2.35 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13431])).
% 2.13/2.35 tff(13450,plain,
% 2.13/2.35 (r(s(elem!1), elem!1)),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13417, 13449])).
% 2.13/2.35 tff(13451,plain,
% 2.13/2.35 (r(s(elem!1), s(s(elem!1)))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13450, 13448])).
% 2.13/2.35 tff(13452,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13453,plain,
% 2.13/2.35 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13454,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13453])).
% 2.13/2.35 tff(13455,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13454, 13452])).
% 2.13/2.35 tff(13456,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13457,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[13456, 13455])).
% 2.13/2.35 tff(13458,plain,
% 2.13/2.35 ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13457, 121, 627, 683])).
% 2.13/2.35 tff(13459,plain,
% 2.13/2.35 (~r(s(s(s(z))), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[13458, 7794])).
% 2.13/2.35 tff(13460,plain,
% 2.13/2.35 (b(s(s(s(z))), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1816, 13459, 2033])).
% 2.13/2.35 tff(13461,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13462,plain,
% 2.13/2.35 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(13463,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[13462])).
% 2.13/2.35 tff(13464,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[13463, 13461])).
% 2.13/2.35 tff(13465,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(13466,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13465, 13464])).
% 2.13/2.36 tff(13467,plain,
% 2.13/2.36 ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13466, 121, 627, 2088])).
% 2.13/2.36 tff(13468,plain,
% 2.13/2.36 (~r(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13467, 683])).
% 2.13/2.36 tff(13469,plain,
% 2.13/2.36 (b(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[409, 13468])).
% 2.13/2.36 tff(13470,plain,
% 2.13/2.36 (~b(s(s(s(z))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1425, 271, 13469, 13460, 1421])).
% 2.13/2.36 tff(13471,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13472,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13473,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13472, 13471])).
% 2.13/2.36 tff(13474,plain,
% 2.13/2.36 ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13473, 121, 2088, 683])).
% 2.13/2.36 tff(13475,plain,
% 2.13/2.36 (~r(s(s(s(z))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13474, 7794])).
% 2.13/2.36 tff(13476,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1153, 21, 166, 13475, 13470])).
% 2.13/2.36 tff(13477,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13478,plain,
% 2.13/2.36 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13477, 13451, 13447, 13445, 13443, 13442])).
% 2.13/2.36 tff(13479,plain,
% 2.13/2.36 (r(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[145, 3908])).
% 2.13/2.36 tff(13480,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.13/2.36 tff(13481,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13480, 13479])).
% 2.13/2.36 tff(13482,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13483,plain,
% 2.13/2.36 (~r(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13482, 13478, 13434])).
% 2.13/2.36 tff(13484,plain,
% 2.13/2.36 (b(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[255, 13483, 13435])).
% 2.13/2.36 tff(13485,plain,
% 2.13/2.36 (b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13484, 13440])).
% 2.13/2.36 tff(13486,plain,
% 2.13/2.36 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13434])).
% 2.13/2.36 tff(13487,plain,
% 2.13/2.36 (b(s(z), s(s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[260, 13486])).
% 2.13/2.36 tff(13488,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13489,plain,
% 2.13/2.36 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13490,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13489])).
% 2.13/2.36 tff(13491,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[13490, 13488])).
% 2.13/2.36 tff(13492,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13493,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13492, 13491])).
% 2.13/2.36 tff(13494,plain,
% 2.13/2.36 (~b(s(z), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13493, 271, 13487, 13485, 13439])).
% 2.13/2.36 tff(13495,plain,
% 2.13/2.36 (r(s(z), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[105, 13494])).
% 2.13/2.36 tff(13496,plain,
% 2.13/2.36 (~b(s(s(s(z))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13326, 271, 13487, 13485, 13439])).
% 2.13/2.36 tff(13497,plain,
% 2.13/2.36 (r(s(s(s(z))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2325, 13496])).
% 2.13/2.36 tff(13498,plain,
% 2.13/2.36 (~r(z, s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9421, 13497, 110, 13495])).
% 2.13/2.36 tff(13499,plain,
% 2.13/2.36 (b(z, s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1214, 13498])).
% 2.13/2.36 tff(13500,plain,
% 2.13/2.36 (~r(s(s(s(z))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2096, 13495, 13447, 110])).
% 2.13/2.36 tff(13501,plain,
% 2.13/2.36 (b(s(s(s(z))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1155, 13500])).
% 2.13/2.36 tff(13502,plain,
% 2.13/2.36 (~b(s(s(s(z))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1427, 13500, 394, 13442])).
% 2.13/2.36 tff(13503,plain,
% 2.13/2.36 (r(s(s(s(z))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1816, 13502, 13443])).
% 2.13/2.36 tff(13504,plain,
% 2.13/2.36 (~r(elem!1, s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[3849, 13503, 379, 13450])).
% 2.13/2.36 tff(13505,plain,
% 2.13/2.36 (b(elem!1, s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1192, 13504, 13436])).
% 2.13/2.36 tff(13506,plain,
% 2.13/2.36 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5482, 13505, 13434])).
% 2.13/2.36 tff(13507,plain,
% 2.13/2.36 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[12235, 13434, 9149])).
% 2.13/2.36 tff(13508,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.36 tff(13509,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13510,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13511,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13510, 13509])).
% 2.13/2.36 tff(13512,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13511, 271, 1307, 1935, 13508, 1103])).
% 2.13/2.36 tff(13513,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13514,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13513, 13508, 1935, 1307])).
% 2.13/2.36 tff(13515,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1095, 13514])).
% 2.13/2.36 tff(13516,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13517,plain,
% 2.13/2.36 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13518,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13517])).
% 2.13/2.36 tff(13519,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[13518, 13516])).
% 2.13/2.36 tff(13520,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13521,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13520, 13519])).
% 2.13/2.36 tff(13522,plain,
% 2.13/2.36 (~b(s(s(elem!1)), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13521, 271, 1307, 1935, 1721])).
% 2.13/2.36 tff(13523,plain,
% 2.13/2.36 (r(s(s(elem!1)), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2430, 13522])).
% 2.13/2.36 tff(13524,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13525,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13526,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13525, 13524])).
% 2.13/2.36 tff(13527,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13526, 121, 2088, 13523, 13515])).
% 2.13/2.36 tff(13528,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 2.13/2.36 tff(13529,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13530,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13531,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13530, 13529])).
% 2.13/2.36 tff(13532,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13531, 271, 2448, 13508, 1721])).
% 2.13/2.36 tff(13533,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[12253, 21, 13532, 13528, 13527])).
% 2.13/2.36 tff(13534,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13535,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13534, 13507, 13447, 13485, 13506, 13501, 13499])).
% 2.13/2.36 tff(13536,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10426, 13535])).
% 2.13/2.36 tff(13537,plain,
% 2.13/2.36 (~(s(elem!1) = s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2035, 13443])).
% 2.13/2.36 tff(13538,plain,
% 2.13/2.36 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2354, 271, 394, 13499, 13501])).
% 2.13/2.36 tff(13539,plain,
% 2.13/2.36 (r(s(elem!1), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2044, 13538, 13537])).
% 2.13/2.36 tff(13540,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13541,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13542,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13541, 13540])).
% 2.13/2.36 tff(13543,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13542, 121, 13503, 13539, 13536])).
% 2.13/2.36 tff(13544,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1559, 13543, 13437])).
% 2.13/2.36 tff(13545,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13544, 13433])).
% 2.13/2.36 tff(13546,plain,
% 2.13/2.36 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[946, 944])).
% 2.13/2.36 tff(13547,plain,
% 2.13/2.36 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13431])).
% 2.13/2.36 tff(13548,plain,
% 2.13/2.36 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.36 inference(symmetry,[status(thm)],[13547])).
% 2.13/2.36 tff(13549,plain,
% 2.13/2.36 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13539, 13548])).
% 2.13/2.36 tff(13550,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 2.13/2.36 tff(13551,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13552,plain,
% 2.13/2.36 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13553,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13552])).
% 2.13/2.36 tff(13554,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[13553, 13551])).
% 2.13/2.36 tff(13555,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13556,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13555, 13554])).
% 2.13/2.36 tff(13557,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13556, 121, 2327, 7792, 12542, 13550])).
% 2.13/2.36 tff(13558,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13559,plain,
% 2.13/2.36 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13558, 13536, 13497, 13549])).
% 2.13/2.36 tff(13560,plain,
% 2.13/2.36 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1014, 13559, 13546])).
% 2.13/2.36 tff(13561,plain,
% 2.13/2.36 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13431])).
% 2.13/2.36 tff(13562,plain,
% 2.13/2.36 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 2.13/2.36 inference(symmetry,[status(thm)],[13561])).
% 2.13/2.36 tff(13563,plain,
% 2.13/2.36 ((~r(s(z), s(elem!1))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13562])).
% 2.13/2.36 tff(13564,plain,
% 2.13/2.36 (~r(s(s(s(z))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9017, 257, 260, 258, 622, 431, 379])).
% 2.13/2.36 tff(13565,plain,
% 2.13/2.36 (b(s(s(s(z))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1816, 13564, 2033])).
% 2.13/2.36 tff(13566,plain,
% 2.13/2.36 (r(s(s(s(z))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1427, 13565, 394, 1421])).
% 2.13/2.36 tff(13567,plain,
% 2.13/2.36 (~r(s(s(s(z))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10317, 13566, 909, 431])).
% 2.13/2.36 tff(13568,plain,
% 2.13/2.36 (b(s(s(s(z))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2325, 13567])).
% 2.13/2.36 tff(13569,plain,
% 2.13/2.36 (b(s(z), s(s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[260, 12209])).
% 2.13/2.36 tff(13570,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13326, 271, 13569, 13568, 12493, 981])).
% 2.13/2.36 tff(13571,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13572,plain,
% 2.13/2.36 (~r(s(z), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13571, 13484, 13434, 909, 13439, 394, 13442, 13443, 260, 258, 13450, 379])).
% 2.13/2.36 tff(13573,plain,
% 2.13/2.36 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13572, 13563])).
% 2.13/2.36 tff(13574,plain,
% 2.13/2.36 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[760, 13573])).
% 2.13/2.36 tff(13575,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13576,plain,
% 2.13/2.36 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(13577,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[13576])).
% 2.13/2.36 tff(13578,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[13577, 13575])).
% 2.13/2.36 tff(13579,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~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))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(13580,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[13579, 13578])).
% 2.13/2.36 tff(13581,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13580, 121, 13503, 13495, 13536])).
% 2.13/2.36 tff(13582,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[932, 13581])).
% 2.13/2.36 tff(13583,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[12570, 13582, 13574, 13560])).
% 2.13/2.36 tff(13584,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13583, 13545])).
% 2.13/2.36 tff(13585,plain,((~r(z, s(z))) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (elem!1 = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(13586,plain,
% 2.13/2.36 (~r(z, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[13585, 13217, 9983, 110, 13210, 243, 1243, 3407, 344, 13208, 1, 3504])).
% 2.13/2.37 tff(13587,plain,
% 2.13/2.37 (b(z, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[904, 13586])).
% 2.13/2.37 tff(13588,plain,
% 2.13/2.37 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13222, 13208])).
% 2.13/2.37 tff(13589,plain,
% 2.13/2.37 (~r(elem!1, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10236, 13217, 1243, 351, 110, 13210, 9983])).
% 2.13/2.37 tff(13590,plain,
% 2.13/2.37 (b(elem!1, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[299, 13589, 243])).
% 2.13/2.37 tff(13591,plain,
% 2.13/2.37 (~b(s(elem!1), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[12316, 13587, 110, 331, 219, 199, 231, 13217])).
% 2.13/2.37 tff(13592,plain,
% 2.13/2.37 (r(s(elem!1), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[429, 13591, 351])).
% 2.13/2.37 tff(13593,plain,
% 2.13/2.37 (~r(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8972, 139, 378, 379])).
% 2.13/2.37 tff(13594,plain,
% 2.13/2.37 (b(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8229, 13593])).
% 2.13/2.37 tff(13595,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13596,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(13597,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13596, 13595])).
% 2.13/2.37 tff(13598,plain,
% 2.13/2.37 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13597, 271, 394, 220, 13594])).
% 2.13/2.37 tff(13599,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13600,plain,
% 2.13/2.37 (((~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(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13601,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13600])).
% 2.13/2.37 tff(13602,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[13601, 13599])).
% 2.13/2.37 tff(13603,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(13604,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13603, 13602])).
% 2.13/2.37 tff(13605,plain,
% 2.13/2.37 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13604, 271, 394, 220, 13594])).
% 2.13/2.37 tff(13606,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13430, 13605, 13598, 379, 82, 139])).
% 2.13/2.37 tff(13607,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13608,plain,
% 2.13/2.37 (~r(s(s(s(elem!1))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13607, 82, 379, 394, 220, 378])).
% 2.13/2.37 tff(13609,plain,
% 2.13/2.37 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[486, 13608, 481])).
% 2.13/2.37 tff(13610,plain,
% 2.13/2.37 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8132, 13609, 260, 448])).
% 2.13/2.37 tff(13611,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[66, 21, 13610, 63])).
% 2.13/2.37 tff(13612,plain,
% 2.13/2.37 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[12821, 271, 260, 448, 13609])).
% 2.13/2.37 tff(13613,plain,
% 2.13/2.37 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[760, 13612])).
% 2.13/2.37 tff(13614,plain,
% 2.13/2.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13251, 121, 13613, 13611, 411])).
% 2.13/2.37 tff(13615,plain,
% 2.13/2.37 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[681, 13614, 82])).
% 2.13/2.37 tff(13616,plain,
% 2.13/2.37 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13276, 121, 13613, 13611, 411])).
% 2.13/2.37 tff(13617,plain,
% 2.13/2.37 (b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2293, 21, 13616, 2280])).
% 2.13/2.37 tff(13618,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13619,plain,
% 2.13/2.37 (((~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), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13620,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13619])).
% 2.13/2.37 tff(13621,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[13620, 13618])).
% 2.13/2.37 tff(13622,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(13623,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13622, 13621])).
% 2.13/2.37 tff(13624,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13623, 271, 394, 3407, 13617, 13615])).
% 2.13/2.37 tff(13625,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13626,plain,
% 2.13/2.37 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13625, 13217, 3407, 13592, 13210, 13590, 13588, 9983, 13587, 1243])).
% 2.13/2.37 tff(13627,plain,
% 2.13/2.37 (elem!1 = s(s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[78, 13626])).
% 2.13/2.37 tff(13628,plain,
% 2.13/2.37 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13627])).
% 2.13/2.37 tff(13629,plain,
% 2.13/2.37 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13628])).
% 2.13/2.37 tff(13630,plain,
% 2.13/2.37 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13628])).
% 2.13/2.37 tff(13631,plain,
% 2.13/2.37 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[13630])).
% 2.13/2.37 tff(13632,plain,
% 2.13/2.37 (b(z, s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[3407, 13631])).
% 2.13/2.37 tff(13633,plain,
% 2.13/2.37 (~b(s(z), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9030, 13632, 13217, 13587])).
% 2.13/2.37 tff(13634,plain,
% 2.13/2.37 (r(s(z), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[444, 13633, 344])).
% 2.13/2.37 tff(13635,plain,
% 2.13/2.37 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13634, 13629])).
% 2.13/2.37 tff(13636,plain,
% 2.13/2.37 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13627])).
% 2.13/2.37 tff(13637,plain,
% 2.13/2.37 (~b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8962, 13587, 13210, 13590])).
% 2.13/2.37 tff(13638,plain,
% 2.13/2.37 (r(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[284, 13637, 358])).
% 2.13/2.37 tff(13639,plain,
% 2.13/2.37 (r(s(s(elem!1)), z)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13638, 13636])).
% 2.13/2.37 tff(13640,plain,
% 2.13/2.37 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13628])).
% 2.13/2.37 tff(13641,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13592, 13640])).
% 2.13/2.37 tff(13642,plain,
% 2.13/2.37 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13628])).
% 2.13/2.37 tff(13643,plain,
% 2.13/2.37 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13627])).
% 2.13/2.37 tff(13644,plain,
% 2.13/2.37 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9983, 13643])).
% 2.13/2.37 tff(13645,plain,
% 2.13/2.37 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13644, 13642])).
% 2.13/2.37 tff(13646,plain,
% 2.13/2.37 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13627])).
% 2.13/2.37 tff(13647,plain,
% 2.13/2.37 (r(z, s(s(elem!1)))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[1243, 13646])).
% 2.13/2.37 tff(13648,plain,
% 2.13/2.37 (~(s(s(s(z))) = s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[3917, 13627, 344])).
% 2.13/2.37 tff(13649,plain,
% 2.13/2.37 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[2471])).
% 2.13/2.37 tff(13650,plain,
% 2.13/2.37 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[13649])).
% 2.13/2.37 tff(13651,plain,
% 2.13/2.37 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13650])).
% 2.13/2.37 tff(13652,plain,
% 2.13/2.37 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13328, 623, 572, 12761, 12259])).
% 2.13/2.37 tff(13653,plain,
% 2.13/2.37 (~r(s(s(s(z))), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13652, 13651])).
% 2.13/2.37 tff(13654,plain,
% 2.13/2.37 (b(s(s(s(z))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1816, 13653, 2033])).
% 2.13/2.37 tff(13655,plain,
% 2.13/2.37 (r(s(s(s(z))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1427, 13654, 394, 1421])).
% 2.13/2.37 tff(13656,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13657,plain,
% 2.13/2.37 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13658,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13657])).
% 2.13/2.37 tff(13659,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[13658, 13656])).
% 2.13/2.37 tff(13660,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(13661,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13660, 13659])).
% 2.13/2.37 tff(13662,plain,
% 2.13/2.37 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13661, 121, 2088, 2417, 13655])).
% 2.13/2.37 tff(13663,plain,
% 2.13/2.37 (~r(elem!1, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[12242, 13662, 2470])).
% 2.13/2.37 tff(13664,plain,
% 2.13/2.37 (b(elem!1, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1192, 13663, 12183])).
% 2.13/2.37 tff(13665,plain,
% 2.13/2.37 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[5482, 13664, 2470])).
% 2.13/2.37 tff(13666,plain,
% 2.13/2.37 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2069, 21, 2065, 13652])).
% 2.13/2.37 tff(13667,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13668,plain,
% 2.13/2.37 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13669,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13668])).
% 2.13/2.37 tff(13670,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[13669, 13667])).
% 2.13/2.37 tff(13671,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(13672,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13671, 13670])).
% 2.13/2.37 tff(13673,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13672, 271, 13666, 3871, 13296, 13665])).
% 2.13/2.37 tff(13674,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13675,plain,
% 2.13/2.37 (~b(s(z), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13674, 572, 2470, 2088, 623, 394, 1421, 2033, 2065, 2417, 12761])).
% 2.13/2.37 tff(13676,plain,
% 2.13/2.37 (r(s(z), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[105, 13675])).
% 2.13/2.37 tff(13677,plain,
% 2.13/2.37 (~r(s(s(s(z))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2096, 13676, 2088, 110])).
% 2.13/2.37 tff(13678,plain,
% 2.13/2.37 (~b(s(s(s(z))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1427, 13677, 394, 1421])).
% 2.13/2.37 tff(13679,plain,
% 2.13/2.37 (r(s(s(s(z))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1816, 13678, 2033])).
% 2.13/2.37 tff(13680,plain,
% 2.13/2.37 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13679, 13649])).
% 2.13/2.37 tff(13681,plain,
% 2.13/2.37 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13328, 572, 944, 623, 12761])).
% 2.13/2.37 tff(13682,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13681, 13680])).
% 2.13/2.37 tff(13683,plain,((~r(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13684,plain,
% 2.13/2.37 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13683, 13627, 13648, 13217, 13632, 13647, 110, 3504, 13645, 13641, 2064, 13639])).
% 2.13/2.37 tff(13685,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13684, 13635])).
% 2.13/2.37 tff(13686,plain,(b(elem!1, s(elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | b(z, elem!1) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13687,plain,
% 2.13/2.37 (b(elem!1, s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13686, 231, 3407, 331, 199, 110, 1])).
% 2.13/2.37 tff(13688,plain,
% 2.13/2.37 (~(z = elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1543, 894, 307])).
% 2.13/2.37 tff(13689,plain,
% 2.13/2.37 (~(s(z) = s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[343, 13688])).
% 2.13/2.37 tff(13690,plain,
% 2.13/2.37 (r(z, elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[355, 13688, 199])).
% 2.13/2.37 tff(13691,plain,
% 2.13/2.37 (b(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1305, 13688, 199, 412, 307, 905, 231])).
% 2.13/2.37 tff(13692,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8883, 13691, 13690, 412, 2564, 243, 307, 13689, 110])).
% 2.13/2.37 tff(13693,plain,(b(z, s(z)) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | b(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13694,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13693, 13211, 412, 3500, 307, 110, 199, 231])).
% 2.13/2.37 tff(13695,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | b(z, elem!1) | (s(z) = elem!1) | (z = elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13696,plain,
% 2.13/2.37 (~r(s(elem!1), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13695, 13687, 110, 199, 231, 331, 219])).
% 2.13/2.37 tff(13697,plain,
% 2.13/2.37 (b(s(elem!1), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[409, 13696])).
% 2.13/2.37 tff(13698,plain,
% 2.13/2.37 (~b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[3415, 13697, 3407, 13687])).
% 2.13/2.37 tff(13699,plain,
% 2.13/2.37 (~r(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[375, 13698, 358, 199, 110])).
% 2.13/2.37 tff(13700,plain,
% 2.13/2.37 (b(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[236, 13699, 231])).
% 2.13/2.37 tff(13701,plain,
% 2.13/2.37 (~r(elem!1, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10591, 13697, 13687, 358, 110, 1243])).
% 2.13/2.37 tff(13702,plain,
% 2.13/2.37 (b(elem!1, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[299, 13701, 243])).
% 2.13/2.37 tff(13703,plain,
% 2.13/2.37 (~b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[3415, 394, 3407, 307])).
% 2.13/2.37 tff(13704,plain,
% 2.13/2.37 (r(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[284, 13703, 259])).
% 2.13/2.37 tff(13705,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[681, 675, 82])).
% 2.13/2.37 tff(13706,plain,
% 2.13/2.37 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8132, 503, 260, 448])).
% 2.13/2.37 tff(13707,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[486, 13706, 13223])).
% 2.13/2.37 tff(13708,plain,
% 2.13/2.37 (~r(s(s(elem!1)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[6958, 13707, 378, 1, 563, 1409])).
% 2.13/2.37 tff(13709,plain,
% 2.13/2.37 (b(s(s(elem!1)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[862, 13708, 851])).
% 2.13/2.37 tff(13710,plain,
% 2.13/2.37 (~b(s(s(elem!1)), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[5441, 13709, 448, 260])).
% 2.13/2.37 tff(13711,plain,
% 2.13/2.37 (r(s(s(elem!1)), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2143, 13710])).
% 2.13/2.37 tff(13712,plain,
% 2.13/2.37 (~r(s(s(elem!1)), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2422, 13711, 110, 909])).
% 2.13/2.37 tff(13713,plain,
% 2.13/2.37 (b(s(s(elem!1)), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2430, 13712])).
% 2.13/2.37 tff(13714,plain,
% 2.13/2.37 (~b(elem!1, s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10934, 271, 260, 448, 503])).
% 2.13/2.37 tff(13715,plain,
% 2.13/2.37 (r(elem!1, s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[660, 21, 4358, 13714])).
% 2.13/2.37 tff(13716,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13717,plain,
% 2.13/2.37 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(13718,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[13717])).
% 2.13/2.37 tff(13719,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[13718, 13716])).
% 2.13/2.37 tff(13720,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(13721,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[13720, 13719])).
% 2.13/2.37 tff(13722,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13721, 121, 378, 139, 727, 6842])).
% 2.13/2.37 tff(13723,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(13724,plain,
% 2.13/2.37 (~r(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13723, 13715, 378, 13707])).
% 2.13/2.37 tff(13725,plain,
% 2.13/2.37 (b(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8229, 13724])).
% 2.13/2.37 tff(13726,plain,
% 2.13/2.37 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13282, 271, 394, 3407, 13725])).
% 2.13/2.37 tff(13727,plain,
% 2.13/2.37 (r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2293, 21, 13726, 6201])).
% 2.13/2.37 tff(13728,plain,
% 2.13/2.37 (~r(s(elem!1), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11896, 13727, 684, 13715])).
% 2.13/2.37 tff(13729,plain,
% 2.13/2.37 (b(s(elem!1), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2243, 13728, 2207])).
% 2.13/2.37 tff(13730,plain,
% 2.13/2.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[4719, 13729, 307, 851, 13715, 684, 3313, 13727])).
% 2.13/2.37 tff(13731,plain,
% 2.13/2.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[556, 13730, 1])).
% 2.13/2.37 tff(13732,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[4735, 271, 13731, 3407, 13725, 13713])).
% 2.13/2.37 tff(13733,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13734,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13733, 13705, 1, 307, 851, 3407, 2280, 394, 378, 13208, 260, 448, 110, 909, 1409])).
% 2.13/2.38 tff(13735,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[66, 21, 13734, 63])).
% 2.13/2.38 tff(13736,plain,
% 2.13/2.38 (~r(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11808, 121, 110, 909, 13735])).
% 2.13/2.38 tff(13737,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8229, 13736])).
% 2.13/2.38 tff(13738,plain,
% 2.13/2.38 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13282, 271, 394, 3407, 13737])).
% 2.13/2.38 tff(13739,plain,
% 2.13/2.38 (r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2293, 21, 13738, 2280])).
% 2.13/2.38 tff(13740,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13741,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13742,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13741, 13740])).
% 2.13/2.38 tff(13743,plain,
% 2.13/2.38 (~r(s(z), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13742, 121, 684, 572, 798])).
% 2.13/2.38 tff(13744,plain,
% 2.13/2.38 (b(s(z), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[444, 13743, 348])).
% 2.13/2.38 tff(13745,plain,
% 2.13/2.38 (~r(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13411, 121, 684, 572, 798])).
% 2.13/2.38 tff(13746,plain,
% 2.13/2.38 (b(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[429, 13745, 2282])).
% 2.13/2.38 tff(13747,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[456, 13746, 13744, 307, 448])).
% 2.13/2.38 tff(13748,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13749,plain,
% 2.13/2.38 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13748, 13705, 448, 348, 307, 13739])).
% 2.13/2.38 tff(13750,plain,
% 2.13/2.38 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[760, 13749])).
% 2.13/2.38 tff(13751,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2873, 271, 307, 260, 750, 504])).
% 2.13/2.38 tff(13752,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13753,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13752, 13750, 260, 307])).
% 2.13/2.38 tff(13754,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[486, 13753, 13588])).
% 2.13/2.38 tff(13755,plain,
% 2.13/2.38 (~r(s(s(elem!1)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6958, 13754, 378, 1, 563, 1409])).
% 2.13/2.38 tff(13756,plain,
% 2.13/2.38 (b(s(s(elem!1)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[862, 13755, 851])).
% 2.13/2.38 tff(13757,plain,
% 2.13/2.38 (~b(s(s(elem!1)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5441, 13756, 448, 260])).
% 2.13/2.38 tff(13758,plain,
% 2.13/2.38 (r(s(s(elem!1)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2143, 13757])).
% 2.13/2.38 tff(13759,plain,
% 2.13/2.38 (~r(s(s(elem!1)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2422, 13758, 110, 909])).
% 2.13/2.38 tff(13760,plain,
% 2.13/2.38 (b(s(s(elem!1)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2430, 13759])).
% 2.13/2.38 tff(13761,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4735, 271, 543, 3407, 1638, 2449])).
% 2.13/2.38 tff(13762,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13763,plain,
% 2.13/2.38 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13762, 13737, 3407, 13760])).
% 2.13/2.38 tff(13764,plain,
% 2.13/2.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[556, 13763, 1])).
% 2.13/2.38 tff(13765,plain,
% 2.13/2.38 (~r(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3132, 13764, 13739, 13705])).
% 2.13/2.38 tff(13766,plain,
% 2.13/2.38 (b(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3326, 13763, 1, 199, 394, 2344, 675])).
% 2.13/2.38 tff(13767,plain,
% 2.13/2.38 (~b(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6807, 13766, 307, 13756])).
% 2.13/2.38 tff(13768,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[701, 13767, 13765, 3313])).
% 2.13/2.38 tff(13769,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | (~b(s(elem!1), z)) | r(elem!1, s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13770,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13769, 909, 1, 199, 394, 2344, 3407, 110, 307, 448, 260, 851, 378, 13704, 348, 82])).
% 2.13/2.38 tff(13771,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2401, 271, 307, 394, 13770])).
% 2.13/2.38 tff(13772,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[486, 13771, 13588])).
% 2.13/2.38 tff(13773,plain,
% 2.13/2.38 (~b(z, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3351, 13772, 13770, 394, 259, 307])).
% 2.13/2.38 tff(13774,plain,
% 2.13/2.38 (r(z, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1439, 13773])).
% 2.13/2.38 tff(13775,plain,
% 2.13/2.38 (~r(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3387, 13774, 378, 13704])).
% 2.13/2.38 tff(13776,plain,
% 2.13/2.38 (b(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2243, 13775, 2207])).
% 2.13/2.38 tff(13777,plain,
% 2.13/2.38 (~b(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3247, 271, 307, 13776, 260])).
% 2.13/2.38 tff(13778,plain,
% 2.13/2.38 (r(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[429, 13777, 2282])).
% 2.13/2.38 tff(13779,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10793, 121, 13774, 110, 909, 13778])).
% 2.13/2.38 tff(13780,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13781,plain,
% 2.13/2.38 (~r(z, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13780, 198, 13687, 13700, 1243, 13697, 358, 1, 199, 2344, 3407, 13702, 110, 344, 79])).
% 2.13/2.38 tff(13782,plain,
% 2.13/2.38 (b(z, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[904, 13781])).
% 2.13/2.38 tff(13783,plain,
% 2.13/2.38 (~b(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[12316, 13782, 110, 331, 219, 199, 231, 13697])).
% 2.13/2.38 tff(13784,plain,
% 2.13/2.38 (r(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[429, 13783, 351])).
% 2.13/2.38 tff(13785,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8132, 504, 260, 448])).
% 2.13/2.38 tff(13786,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[66, 21, 13785, 63])).
% 2.13/2.38 tff(13787,plain,
% 2.13/2.38 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13752, 504, 260, 307])).
% 2.13/2.38 tff(13788,plain,
% 2.13/2.38 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[760, 13787])).
% 2.13/2.38 tff(13789,plain,
% 2.13/2.38 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13251, 121, 13788, 13786, 411])).
% 2.13/2.38 tff(13790,plain,
% 2.13/2.38 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13276, 121, 13788, 13786, 411])).
% 2.13/2.38 tff(13791,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11152, 13790, 13789, 307, 82, 504])).
% 2.13/2.38 tff(13792,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13793,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13792, 79, 13687, 13784, 13700, 13702])).
% 2.13/2.38 tff(13794,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[486, 13793, 13588])).
% 2.13/2.38 tff(13795,plain,
% 2.13/2.38 (r(elem!1, z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[284, 13698, 358])).
% 2.13/2.38 tff(13796,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13797,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13798,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13797, 13796])).
% 2.13/2.38 tff(13799,plain,
% 2.13/2.38 (~r(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13798, 121, 1243, 13795, 13794])).
% 2.13/2.38 tff(13800,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8229, 13799])).
% 2.13/2.38 tff(13801,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13597, 271, 13697, 13782, 13800])).
% 2.13/2.38 tff(13802,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[681, 13801, 79])).
% 2.13/2.38 tff(13803,plain,
% 2.13/2.38 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13604, 271, 13697, 13782, 13800])).
% 2.13/2.38 tff(13804,plain,
% 2.13/2.38 (r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2293, 21, 13803, 85])).
% 2.13/2.38 tff(13805,plain,
% 2.13/2.38 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13748, 13804, 13702, 344, 13687, 13802])).
% 2.13/2.38 tff(13806,plain,
% 2.13/2.38 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[760, 13805])).
% 2.13/2.38 tff(13807,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13808,plain,
% 2.13/2.38 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13809,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13808])).
% 2.13/2.38 tff(13810,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[13809, 13807])).
% 2.13/2.38 tff(13811,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13812,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13811, 13810])).
% 2.13/2.38 tff(13813,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13812, 271, 13806, 13782, 3407, 13800])).
% 2.13/2.38 tff(13814,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (z = elem!1) | b(z, elem!1) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13815,plain,
% 2.13/2.38 (elem!1 = s(s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13814, 2344, 110, 331, 199, 231, 1, 3407])).
% 2.13/2.38 tff(13816,plain,
% 2.13/2.38 (~(s(s(s(z))) = elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3906, 13815])).
% 2.13/2.38 tff(13817,plain,
% 2.13/2.38 (~(elem!1 = s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1100, 13816])).
% 2.13/2.38 tff(13818,plain,
% 2.13/2.38 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13815])).
% 2.13/2.38 tff(13819,plain,
% 2.13/2.38 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13818])).
% 2.13/2.38 tff(13820,plain,
% 2.13/2.38 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13818])).
% 2.13/2.38 tff(13821,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[13820])).
% 2.13/2.38 tff(13822,plain,
% 2.13/2.38 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13821])).
% 2.13/2.38 tff(13823,plain,
% 2.13/2.38 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[179, 13822])).
% 2.13/2.38 tff(13824,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13818])).
% 2.13/2.38 tff(13825,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[13824])).
% 2.13/2.38 tff(13826,plain,
% 2.13/2.38 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13825])).
% 2.13/2.38 tff(13827,plain,
% 2.13/2.38 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[179, 13826])).
% 2.13/2.38 tff(13828,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[12308, 13815, 13697])).
% 2.13/2.38 tff(13829,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2479, 13815, 13687])).
% 2.13/2.38 tff(13830,plain,
% 2.13/2.38 (~b(s(s(elem!1)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13762, 13829, 3407, 13828])).
% 2.13/2.38 tff(13831,plain,
% 2.13/2.38 (r(s(s(elem!1)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2430, 13830])).
% 2.13/2.38 tff(13832,plain,
% 2.13/2.38 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13815])).
% 2.13/2.38 tff(13833,plain,
% 2.13/2.38 (r(z, s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[1243, 13832])).
% 2.13/2.38 tff(13834,plain,
% 2.13/2.38 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13818])).
% 2.13/2.38 tff(13835,plain,
% 2.13/2.38 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[13834])).
% 2.13/2.38 tff(13836,plain,
% 2.13/2.38 (b(z, s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[3407, 13835])).
% 2.13/2.38 tff(13837,plain,
% 2.13/2.38 (~(s(s(s(z))) = s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3917, 13815, 344])).
% 2.13/2.38 tff(13838,plain,
% 2.13/2.38 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[2471])).
% 2.13/2.38 tff(13839,plain,
% 2.13/2.38 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[13838])).
% 2.13/2.38 tff(13840,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[12308, 2470, 394])).
% 2.13/2.38 tff(13841,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2479, 2470, 307])).
% 2.13/2.38 tff(13842,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[12447, 271, 543, 505, 750, 1638])).
% 2.13/2.38 tff(13843,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13844,plain,
% 2.13/2.38 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13843, 13841, 13569, 13840])).
% 2.13/2.38 tff(13845,plain,
% 2.13/2.38 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[760, 13844])).
% 2.13/2.38 tff(13846,plain,
% 2.13/2.38 (r(s(z), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13845, 13839])).
% 2.13/2.38 tff(13847,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[2471])).
% 2.13/2.38 tff(13848,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[13847])).
% 2.13/2.38 tff(13849,plain,
% 2.13/2.38 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13848])).
% 2.13/2.38 tff(13850,plain,
% 2.13/2.38 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[179, 13849])).
% 2.13/2.38 tff(13851,plain,
% 2.13/2.38 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[12280])).
% 2.13/2.38 tff(13852,plain,
% 2.13/2.38 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[3911])).
% 2.13/2.38 tff(13853,plain,
% 2.13/2.38 (~r(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[2344, 13852])).
% 2.13/2.38 tff(13854,plain,
% 2.13/2.38 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13853, 13851])).
% 2.13/2.38 tff(13855,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 2.13/2.38 tff(13856,plain,
% 2.13/2.38 (b(s(elem!1), s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[526, 4441, 13855])).
% 2.13/2.38 tff(13857,plain,
% 2.13/2.38 (~(elem!1 = s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3922, 13856, 2467])).
% 2.13/2.38 tff(13858,plain,
% 2.13/2.38 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[78, 13857])).
% 2.13/2.38 tff(13859,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[681, 13858, 676])).
% 2.13/2.38 tff(13860,plain,
% 2.13/2.38 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13858, 2840])).
% 2.13/2.38 tff(13861,plain,
% 2.13/2.38 (b(elem!1, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[392, 4442, 2344])).
% 2.13/2.38 tff(13862,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[644, 271, 13861, 13856, 13859])).
% 2.13/2.38 tff(13863,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[486, 13862, 481])).
% 2.13/2.38 tff(13864,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.13/2.38 tff(13865,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[556, 4436, 13864])).
% 2.13/2.38 tff(13866,plain,
% 2.13/2.38 (~b(elem!1, s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9687, 13861, 13865, 13856])).
% 2.13/2.38 tff(13867,plain,
% 2.13/2.38 (r(elem!1, s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[599, 13857, 13866])).
% 2.13/2.38 tff(13868,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13869,plain,
% 2.13/2.38 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13870,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13869])).
% 2.13/2.38 tff(13871,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[13870, 13868])).
% 2.13/2.38 tff(13872,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13873,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13872, 13871])).
% 2.13/2.38 tff(13874,plain,
% 2.13/2.38 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13873, 121, 4444, 13867, 13863])).
% 2.13/2.38 tff(13875,plain,
% 2.13/2.38 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2293, 21, 13874])).
% 2.13/2.38 tff(13876,plain,
% 2.13/2.38 (b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13875, 13860])).
% 2.13/2.38 tff(13877,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13878,plain,
% 2.13/2.38 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13879,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13878])).
% 2.13/2.38 tff(13880,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[13879, 13877])).
% 2.13/2.38 tff(13881,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13882,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13881, 13880])).
% 2.13/2.38 tff(13883,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13882, 271, 13865, 13856, 13876, 13859])).
% 2.13/2.38 tff(13884,plain,((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), s(elem!1)) | b(s(elem!1), elem!1) | r(elem!1, s(elem!1)) | r(s(elem!1), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13885,plain,
% 2.13/2.38 (r(s(elem!1), s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13884, 2467, 2344, 13854, 481, 13850])).
% 2.13/2.38 tff(13886,plain,
% 2.13/2.38 (~b(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3299, 13885, 307, 260, 2033, 394, 13846])).
% 2.13/2.38 tff(13887,plain,
% 2.13/2.38 (r(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[255, 13886, 3907])).
% 2.13/2.38 tff(13888,plain,
% 2.13/2.38 (r(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13482, 13887, 2470])).
% 2.13/2.38 tff(13889,plain,
% 2.13/2.38 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[2471])).
% 2.13/2.38 tff(13890,plain,
% 2.13/2.38 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[2470])).
% 2.13/2.38 tff(13891,plain,
% 2.13/2.38 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[13890, 13889])).
% 2.13/2.38 tff(13892,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[7673, 13891])).
% 2.13/2.38 tff(13893,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13894,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13895,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13894, 13893])).
% 2.13/2.38 tff(13896,plain,
% 2.13/2.38 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13895, 121, 13892, 13888, 2417])).
% 2.13/2.38 tff(13897,plain,
% 2.13/2.38 (~r(s(s(s(z))), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13896, 13651])).
% 2.13/2.38 tff(13898,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(13899,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(13900,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13899, 13898])).
% 2.13/2.38 tff(13901,plain,
% 2.13/2.38 (~r(s(s(s(z))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13900, 121, 2088, 13888, 2417])).
% 2.13/2.38 tff(13902,plain,
% 2.13/2.38 (~b(s(s(s(z))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1427, 13901, 394, 1421])).
% 2.13/2.38 tff(13903,plain,
% 2.13/2.38 (r(s(s(s(z))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1816, 13902, 2033])).
% 2.13/2.38 tff(13904,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13903, 13897])).
% 2.13/2.38 tff(13905,plain,(b(s(elem!1), elem!1) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | r(elem!1, s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(13906,plain,
% 2.13/2.38 (b(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[13905, 13815, 13837, 13697, 13836, 13833, 13831, 13687, 13700, 2344, 13588, 2207])).
% 2.13/2.38 tff(13907,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3790, 13906, 13815])).
% 2.13/2.38 tff(13908,plain,
% 2.13/2.38 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11152, 307, 504, 11148, 676])).
% 2.13/2.38 tff(13909,plain,
% 2.13/2.38 (elem!1 = s(s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[78, 13908])).
% 2.13/2.38 tff(13910,plain,
% 2.13/2.38 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13909])).
% 2.13/2.38 tff(13911,plain,
% 2.13/2.38 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[13910])).
% 2.13/2.38 tff(13912,plain,
% 2.13/2.38 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13911])).
% 2.13/2.38 tff(13913,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[13908])).
% 2.13/2.38 tff(13914,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2479, 13909, 307])).
% 2.13/2.38 tff(13915,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[13914, 13913])).
% 2.13/2.39 tff(13916,plain,
% 2.13/2.39 (~(s(s(s(z))) = s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3917, 13909, 348])).
% 2.13/2.39 tff(13917,plain,
% 2.13/2.39 (b(s(s(s(z))), s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1816, 13916, 1510])).
% 2.13/2.39 tff(13918,plain,
% 2.13/2.39 (b(s(elem!1), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7281, 13908, 504])).
% 2.13/2.39 tff(13919,plain,
% 2.13/2.39 (b(s(elem!1), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3787, 13909, 13918])).
% 2.13/2.39 tff(13920,plain,
% 2.13/2.39 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7769, 271, 13919, 13917, 13915])).
% 2.13/2.39 tff(13921,plain,
% 2.13/2.39 (~b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13920, 13912])).
% 2.13/2.39 tff(13922,plain,
% 2.13/2.39 (~(s(s(s(z))) = elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3906, 13909])).
% 2.13/2.39 tff(13923,plain,
% 2.13/2.39 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13908])).
% 2.13/2.39 tff(13924,plain,
% 2.13/2.39 (b(z, s(elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[3407, 13923])).
% 2.13/2.39 tff(13925,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13926,plain,
% 2.13/2.39 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13927,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13926])).
% 2.13/2.39 tff(13928,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[13927, 13925])).
% 2.13/2.39 tff(13929,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(13930,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13929, 13928])).
% 2.13/2.39 tff(13931,plain,
% 2.13/2.39 (~b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13930, 271, 13919, 13917, 13924])).
% 2.13/2.39 tff(13932,plain,
% 2.13/2.39 (r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1214, 13931])).
% 2.13/2.39 tff(13933,plain,
% 2.13/2.39 (~(elem!1 = s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1100, 13922])).
% 2.13/2.39 tff(13934,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13935,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(13936,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13935, 13934])).
% 2.13/2.39 tff(13937,plain,
% 2.13/2.39 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13936, 271, 13919, 13917, 13915])).
% 2.13/2.39 tff(13938,plain,
% 2.13/2.39 (~b(elem!1, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5482, 13937, 13909])).
% 2.13/2.39 tff(13939,plain,
% 2.13/2.39 (r(elem!1, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1192, 13938, 13933])).
% 2.13/2.39 tff(13940,plain,
% 2.13/2.39 (~r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6723, 13939, 13932, 378])).
% 2.13/2.39 tff(13941,plain,
% 2.13/2.39 (b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[255, 13940, 13922])).
% 2.13/2.39 tff(13942,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13941, 13921])).
% 2.13/2.39 tff(13943,plain,((~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(z))), s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(13944,plain,
% 2.13/2.39 (r(s(s(s(z))), s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13943, 13907, 3407, 13687, 13827, 344, 13823, 1243])).
% 2.13/2.39 tff(13945,plain,
% 2.13/2.39 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13944, 13819])).
% 2.13/2.39 tff(13946,plain,
% 2.13/2.39 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8132, 13907, 13700, 13702])).
% 2.13/2.39 tff(13947,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[66, 21, 13946, 63])).
% 2.13/2.39 tff(13948,plain,
% 2.13/2.39 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13815])).
% 2.13/2.39 tff(13949,plain,
% 2.13/2.39 (b(s(z), s(s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13700, 13948])).
% 2.13/2.39 tff(13950,plain,
% 2.13/2.39 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13843, 13829, 13949, 13828])).
% 2.13/2.39 tff(13951,plain,
% 2.13/2.39 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[760, 13950])).
% 2.13/2.39 tff(13952,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13953,plain,
% 2.13/2.39 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13954,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13953])).
% 2.13/2.39 tff(13955,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[13954, 13952])).
% 2.13/2.39 tff(13956,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(13957,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13956, 13955])).
% 2.13/2.39 tff(13958,plain,
% 2.13/2.39 (~r(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13957, 121, 13951, 13947, 13945])).
% 2.13/2.39 tff(13959,plain,
% 2.13/2.39 (b(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[105, 13958])).
% 2.13/2.39 tff(13960,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13310, 121, 13951, 13947, 13945])).
% 2.13/2.39 tff(13961,plain,
% 2.13/2.39 (b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2325, 13960])).
% 2.13/2.39 tff(13962,plain,
% 2.13/2.39 (~b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[312, 13961, 13687, 13700])).
% 2.13/2.39 tff(13963,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[255, 13962, 13816])).
% 2.13/2.39 tff(13964,plain,
% 2.13/2.39 (r(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13482, 13963, 13815])).
% 2.13/2.39 tff(13965,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13900, 121, 13833, 13964, 13831])).
% 2.13/2.39 tff(13966,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1155, 13965])).
% 2.13/2.39 tff(13967,plain,
% 2.13/2.39 (~b(elem!1, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11038, 13966, 13702, 13959])).
% 2.13/2.39 tff(13968,plain,
% 2.13/2.39 (r(elem!1, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1192, 13967, 13817])).
% 2.13/2.39 tff(13969,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[12242, 13968, 13815])).
% 2.13/2.39 tff(13970,plain,
% 2.13/2.39 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11663, 2064])).
% 2.13/2.39 tff(13971,plain,
% 2.13/2.39 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13818])).
% 2.13/2.39 tff(13972,plain,
% 2.13/2.39 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13971])).
% 2.13/2.39 tff(13973,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13974,plain,
% 2.13/2.39 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13975,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13974])).
% 2.13/2.39 tff(13976,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[13975, 13973])).
% 2.13/2.39 tff(13977,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(13978,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13977, 13976])).
% 2.13/2.39 tff(13979,plain,
% 2.13/2.39 (~r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13978, 121, 13833, 13964, 13831])).
% 2.13/2.39 tff(13980,plain,
% 2.13/2.39 (b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1214, 13979])).
% 2.13/2.39 tff(13981,plain,
% 2.13/2.39 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2029, 13980, 13961, 13697])).
% 2.13/2.39 tff(13982,plain,
% 2.13/2.39 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13981, 13972])).
% 2.13/2.39 tff(13983,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6237, 21, 13982, 13970])).
% 2.13/2.39 tff(13984,plain,
% 2.13/2.39 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[12235, 13815, 2064])).
% 2.13/2.39 tff(13985,plain,
% 2.13/2.39 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[13818])).
% 2.13/2.39 tff(13986,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13985])).
% 2.13/2.39 tff(13987,plain,
% 2.13/2.39 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13986])).
% 2.13/2.39 tff(13988,plain,
% 2.13/2.39 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[946, 3504])).
% 2.13/2.39 tff(13989,plain,
% 2.13/2.39 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13988, 13987])).
% 2.13/2.39 tff(13990,plain,
% 2.13/2.39 (~b(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10721, 13963, 1243, 13687, 358, 13697, 13959])).
% 2.13/2.39 tff(13991,plain,
% 2.13/2.39 (r(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[904, 13990])).
% 2.13/2.39 tff(13992,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 2.13/2.39 tff(13993,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13994,plain,
% 2.13/2.39 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(13995,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[13994])).
% 2.13/2.39 tff(13996,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[13995, 13993])).
% 2.13/2.39 tff(13997,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(13998,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[13997, 13996])).
% 2.13/2.39 tff(13999,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[13998, 121, 7794, 13992, 12542])).
% 2.13/2.39 tff(14000,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[12253, 21, 13528, 13999])).
% 2.13/2.39 tff(14001,plain,
% 2.13/2.39 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[2471])).
% 2.13/2.39 tff(14002,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[14001])).
% 2.13/2.39 tff(14003,plain,
% 2.13/2.39 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[14002])).
% 2.13/2.39 tff(14004,plain,
% 2.13/2.39 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[12560, 14003])).
% 2.13/2.39 tff(14005,assumption,(~r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 2.13/2.39 tff(14006,plain,
% 2.13/2.39 (s(elem!1) = s(s(s(s(z))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1511, 1927])).
% 2.13/2.39 tff(14007,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2603, 14006])).
% 2.13/2.39 tff(14008,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(14009,plain,
% 2.13/2.39 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[14008, 2603])).
% 2.13/2.39 tff(14010,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1559, 14009, 14005])).
% 2.13/2.39 tff(14011,assumption,(~r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.13/2.39 tff(14012,plain,
% 2.13/2.39 (b(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1995, 2603, 14011])).
% 2.13/2.39 tff(14013,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(14014,plain,
% 2.13/2.39 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(14015,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[14014])).
% 2.13/2.39 tff(14016,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[14015, 14013])).
% 2.13/2.39 tff(14017,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(14018,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[14017, 14016])).
% 2.13/2.39 tff(14019,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[14018, 271, 1421, 14012, 14010, 1157])).
% 2.13/2.39 tff(14020,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(elem!1)) | r(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(14021,plain,
% 2.13/2.39 (~b(z, s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[14020, 14004, 1421, 2603, 12550])).
% 2.13/2.39 tff(14022,plain,
% 2.13/2.39 (r(z, s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1121, 14021])).
% 2.13/2.39 tff(14023,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9490, 14022, 909, 572])).
% 2.13/2.39 tff(14024,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[932, 14023])).
% 2.13/2.39 tff(14025,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.40 inference(rewrite,[status(thm)],[])).
% 2.13/2.40 tff(14026,plain,
% 2.13/2.40 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.40 inference(rewrite,[status(thm)],[])).
% 2.13/2.40 tff(14027,plain,
% 2.13/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14026])).
% 2.13/2.40 tff(14028,plain,
% 2.13/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.13/2.40 inference(transitivity,[status(thm)],[14027, 14025])).
% 2.13/2.40 tff(14029,plain,
% 2.13/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.40 inference(quant_inst,[status(thm)],[])).
% 2.13/2.40 tff(14030,plain,
% 2.13/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[14029, 14028])).
% 2.13/2.40 tff(14031,plain,
% 2.13/2.40 ($false),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[14030, 271, 543, 505, 14024, 14000])).
% 2.13/2.40 tff(14032,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.40 tff(14033,plain,
% 2.13/2.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[14032, 13829, 13949, 13991, 13951, 13836, 13989, 13984, 13815, 13964, 13983, 13969])).
% 2.13/2.40 tff(14034,plain,
% 2.13/2.40 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[10426, 14033])).
% 2.13/2.40 tff(14035,plain,
% 2.13/2.40 (~b(s(s(s(s(z)))), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[13513, 14034, 13966, 13980])).
% 2.13/2.40 tff(14036,plain,
% 2.13/2.40 (r(s(s(s(s(z)))), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[1095, 14035])).
% 2.13/2.40 tff(14037,plain,
% 2.13/2.40 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[919, 14036, 13991, 110])).
% 2.13/2.40 tff(14038,plain,
% 2.13/2.40 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[932, 14037])).
% 2.13/2.40 tff(14039,plain,
% 2.13/2.40 ($false),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[12581, 271, 13959, 13961, 14038, 14034])).
% 2.13/2.40 tff(14040,plain,(r(elem!1, s(elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | b(z, elem!1) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.40 tff(14041,plain,
% 2.13/2.40 (r(elem!1, s(elem!1))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[14040, 231, 3407, 331, 199, 110, 1])).
% 2.13/2.40 tff(14042,plain,
% 2.13/2.40 (~r(z, s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[13585, 14041, 13697, 110, 13700, 243, 1243, 3407, 344, 13208, 1, 3504])).
% 2.13/2.40 tff(14043,plain,
% 2.13/2.40 (b(z, s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[904, 14042])).
% 2.13/2.40 tff(14044,plain,
% 2.13/2.40 (~b(s(elem!1), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[12316, 14043, 110, 331, 219, 199, 231, 13697])).
% 2.13/2.40 tff(14045,plain,
% 2.13/2.40 (r(s(elem!1), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[429, 14044, 351])).
% 2.13/2.40 tff(14046,plain,
% 2.13/2.40 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[13625, 14045, 3407, 13697, 13700, 13702, 13588, 14041, 14043, 1243])).
% 2.13/2.40 tff(14047,plain,
% 2.13/2.40 (elem!1 = s(s(elem!1))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[78, 14046])).
% 2.13/2.40 tff(14048,plain,
% 2.13/2.40 (b(s(s(s(elem!1))), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[12308, 14047, 13697])).
% 2.13/2.40 tff(14049,plain,
% 2.13/2.40 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2479, 14047, 13687])).
% 2.13/2.40 tff(14050,plain,
% 2.13/2.40 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14047])).
% 2.13/2.40 tff(14051,plain,
% 2.13/2.40 (b(s(z), s(s(elem!1)))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[13700, 14050])).
% 2.13/2.40 tff(14052,plain,
% 2.13/2.40 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[13843, 14051, 14049, 14048])).
% 2.13/2.40 tff(14053,plain,
% 2.13/2.40 (~b(s(s(elem!1)), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[13762, 14049, 3407, 14048])).
% 2.13/2.40 tff(14054,plain,
% 2.13/2.40 (r(s(s(elem!1)), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2430, 14053])).
% 2.13/2.40 tff(14055,plain,
% 2.13/2.40 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14047])).
% 2.13/2.40 tff(14056,plain,
% 2.13/2.40 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14055])).
% 2.13/2.40 tff(14057,plain,
% 2.13/2.40 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[14045, 14056])).
% 2.13/2.40 tff(14058,plain,
% 2.13/2.40 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14055])).
% 2.13/2.40 tff(14059,plain,
% 2.13/2.40 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.13/2.40 inference(symmetry,[status(thm)],[14058])).
% 2.13/2.40 tff(14060,plain,
% 2.13/2.40 (b(z, s(elem!1))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[3407, 14059])).
% 2.13/2.40 tff(14061,plain,
% 2.13/2.40 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14047])).
% 2.13/2.40 tff(14062,plain,
% 2.13/2.40 (r(z, s(s(elem!1)))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[1243, 14061])).
% 2.13/2.40 tff(14063,plain,
% 2.13/2.40 (~(s(s(s(z))) = s(elem!1))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3917, 14047, 344])).
% 2.13/2.40 tff(14064,plain,
% 2.13/2.40 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14055])).
% 2.13/2.40 tff(14065,plain,
% 2.13/2.40 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[14047])).
% 2.13/2.40 tff(14066,plain,
% 2.13/2.40 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[14041, 14065])).
% 2.13/2.40 tff(14067,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14066, 14064])).
% 2.23/2.40 tff(14068,plain,
% 2.23/2.40 (~r(s(z), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[13683, 14067, 14063, 13697, 14047, 14062, 110, 3504, 14060, 14057, 2064, 14054])).
% 2.23/2.40 tff(14069,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[760, 14068, 14052])).
% 2.23/2.40 tff(14070,plain,((s(z) = elem!1) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14071,plain,
% 2.23/2.40 (s(z) = elem!1),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14070, 199, 3407, 331, 110, 1])).
% 2.23/2.40 tff(14072,plain,
% 2.23/2.40 (s(s(z)) = s(elem!1)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.40 tff(14073,plain,
% 2.23/2.40 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14072])).
% 2.23/2.40 tff(14074,plain,
% 2.23/2.40 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14073])).
% 2.23/2.40 tff(14075,plain,
% 2.23/2.40 (s(s(s(z))) = s(s(elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14072])).
% 2.23/2.40 tff(14076,plain,
% 2.23/2.40 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14075])).
% 2.23/2.40 tff(14077,plain,
% 2.23/2.40 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14076])).
% 2.23/2.40 tff(14078,plain,
% 2.23/2.40 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14077])).
% 2.23/2.40 tff(14079,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14078])).
% 2.23/2.40 tff(14080,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[14079, 14074])).
% 2.23/2.40 tff(14081,plain,
% 2.23/2.40 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14080])).
% 2.23/2.40 tff(14082,plain,
% 2.23/2.40 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.40 tff(14083,plain,
% 2.23/2.40 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.23/2.40 inference(transitivity,[status(thm)],[14082, 2212])).
% 2.23/2.40 tff(14084,plain,
% 2.23/2.40 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14083])).
% 2.23/2.40 tff(14085,plain,
% 2.23/2.40 (~(s(s(elem!1)) = elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[2137, 14084])).
% 2.23/2.40 tff(14086,plain,
% 2.23/2.40 (r(s(z), z) <=> r(elem!1, z)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.40 tff(14087,plain,
% 2.23/2.40 (r(elem!1, z)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[110, 14086])).
% 2.23/2.40 tff(14088,plain,
% 2.23/2.40 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14082])).
% 2.23/2.40 tff(14089,plain,
% 2.23/2.40 (~(elem!1 = s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[2137, 14088])).
% 2.23/2.40 tff(14090,plain,
% 2.23/2.40 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[78, 14089])).
% 2.23/2.40 tff(14091,plain,
% 2.23/2.40 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.40 tff(14092,plain,
% 2.23/2.40 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14091])).
% 2.23/2.40 tff(14093,plain,
% 2.23/2.40 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14092])).
% 2.23/2.40 tff(14094,plain,
% 2.23/2.40 (~b(elem!1, s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[192, 14093])).
% 2.23/2.40 tff(14095,plain,
% 2.23/2.40 (~b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[229, 14071, 199])).
% 2.23/2.40 tff(14096,plain,
% 2.23/2.40 (r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[904, 14095])).
% 2.23/2.40 tff(14097,plain,
% 2.23/2.40 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.40 tff(14098,plain,
% 2.23/2.40 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 2.23/2.40 inference(symmetry,[status(thm)],[14097])).
% 2.23/2.40 tff(14099,plain,
% 2.23/2.40 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14098])).
% 2.23/2.40 tff(14100,plain,
% 2.23/2.40 (~b(s(z), elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[192, 14099])).
% 2.23/2.40 tff(14101,plain,
% 2.23/2.40 (r(s(z), s(elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3578, 317, 331, 199, 14100, 14096, 14094])).
% 2.23/2.40 tff(14102,plain,
% 2.23/2.40 (b(elem!1, s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8233, 750, 223])).
% 2.23/2.40 tff(14103,plain,
% 2.23/2.40 (~r(s(elem!1), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1417, 379, 1408, 909])).
% 2.23/2.40 tff(14104,plain,
% 2.23/2.40 (b(s(elem!1), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[409, 14103])).
% 2.23/2.40 tff(14105,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3341, 271, 394, 3407, 1421, 638])).
% 2.23/2.40 tff(14106,plain,((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14107,plain,
% 2.23/2.40 (~b(z, s(elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14106, 638, 3407, 394])).
% 2.23/2.40 tff(14108,plain,
% 2.23/2.40 (r(z, s(elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1439, 14107])).
% 2.23/2.40 tff(14109,plain,
% 2.23/2.40 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6958, 139, 378, 1, 563, 1409])).
% 2.23/2.40 tff(14110,plain,
% 2.23/2.40 (r(s(s(elem!1)), elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[145, 4949])).
% 2.23/2.40 tff(14111,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[860, 14110])).
% 2.23/2.40 tff(14112,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14113,plain,
% 2.23/2.40 (~r(s(s(s(z))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14112, 14109, 223])).
% 2.23/2.40 tff(14114,plain,
% 2.23/2.40 (b(s(s(s(z))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[255, 14113, 6655])).
% 2.23/2.40 tff(14115,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8109, 14114, 223])).
% 2.23/2.40 tff(14116,plain,
% 2.23/2.40 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.40 tff(14117,plain,
% 2.23/2.40 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14116])).
% 2.23/2.40 tff(14118,plain,
% 2.23/2.40 (~r(s(elem!1), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3387, 1441, 378, 1409])).
% 2.23/2.40 tff(14119,plain,
% 2.23/2.40 (b(s(elem!1), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2243, 14118, 8337])).
% 2.23/2.40 tff(14120,plain,
% 2.23/2.40 (b(s(elem!1), s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14119, 14117])).
% 2.23/2.40 tff(14121,plain,
% 2.23/2.40 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1449, 1441, 378, 379])).
% 2.23/2.40 tff(14122,plain,
% 2.23/2.40 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[526, 14121, 216])).
% 2.23/2.40 tff(14123,plain,
% 2.23/2.40 (b(s(elem!1), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2369, 14122, 1222])).
% 2.23/2.40 tff(14124,plain,
% 2.23/2.40 (~b(s(elem!1), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3622, 14123, 222, 3871])).
% 2.23/2.40 tff(14125,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14124, 14120])).
% 2.23/2.40 tff(14126,plain,((~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14127,plain,
% 2.23/2.40 (~b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14126, 14115, 223, 1441, 211, 378, 379, 1409])).
% 2.23/2.40 tff(14128,plain,
% 2.23/2.40 (~b(elem!1, s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6679, 14127, 1222])).
% 2.23/2.40 tff(14129,plain,
% 2.23/2.40 (r(elem!1, s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[599, 14128, 5038])).
% 2.23/2.40 tff(14130,plain,
% 2.23/2.40 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[526, 14121, 211])).
% 2.23/2.40 tff(14131,plain,
% 2.23/2.40 (b(s(elem!1), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2243, 14118, 2207])).
% 2.23/2.40 tff(14132,plain,
% 2.23/2.40 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2781, 14129, 378, 638, 14131, 139, 348, 14130])).
% 2.23/2.40 tff(14133,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[556, 14132, 1])).
% 2.23/2.40 tff(14134,plain,
% 2.23/2.40 (~b(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[13762, 14133, 3407, 13594])).
% 2.23/2.40 tff(14135,plain,
% 2.23/2.40 (r(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2430, 14134])).
% 2.23/2.40 tff(14136,plain,
% 2.23/2.40 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1459, 14133, 638, 14130])).
% 2.23/2.40 tff(14137,plain,
% 2.23/2.40 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[586, 14136, 563])).
% 2.23/2.40 tff(14138,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(14139,plain,
% 2.23/2.40 (((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(14140,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14139])).
% 2.23/2.40 tff(14141,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[14140, 14138])).
% 2.23/2.40 tff(14142,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(14143,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14142, 14141])).
% 2.23/2.40 tff(14144,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14143, 121, 573, 624, 139, 2417])).
% 2.23/2.40 tff(14145,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14146,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14145, 14137, 14135, 139, 14129])).
% 2.23/2.40 tff(14147,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~(s(z) = elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14148,plain,
% 2.23/2.40 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14147, 638, 3407, 1, 378, 348, 223, 14108, 379, 1409])).
% 2.23/2.40 tff(14149,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[486, 14148, 481])).
% 2.23/2.40 tff(14150,plain,
% 2.23/2.40 (~r(s(elem!1), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3387, 14108, 378, 1409])).
% 2.23/2.40 tff(14151,plain,
% 2.23/2.40 (b(s(elem!1), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2243, 14150, 2207])).
% 2.23/2.40 tff(14152,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(14153,plain,
% 2.23/2.40 (((~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(elem!1), 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)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(14154,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14153])).
% 2.23/2.40 tff(14155,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[14154, 14152])).
% 2.23/2.40 tff(14156,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(14157,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14156, 14155])).
% 2.23/2.40 tff(14158,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14157, 271, 14151, 638, 14149, 738])).
% 2.23/2.40 tff(14159,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14160,plain,
% 2.23/2.40 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14159, 14102, 481, 3407, 1, 378, 348, 223, 379, 1408, 14104])).
% 2.23/2.40 tff(14161,plain,
% 2.23/2.40 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[1037, 3056])).
% 2.23/2.40 tff(14162,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14161])).
% 2.23/2.40 tff(14163,plain,
% 2.23/2.40 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14162])).
% 2.23/2.40 tff(14164,plain,
% 2.23/2.40 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[3057])).
% 2.23/2.40 tff(14165,plain,
% 2.23/2.40 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.40 inference(symmetry,[status(thm)],[14164])).
% 2.23/2.40 tff(14166,plain,
% 2.23/2.40 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14165])).
% 2.23/2.40 tff(14167,plain,
% 2.23/2.40 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[7890, 14166])).
% 2.23/2.40 tff(14168,plain,
% 2.23/2.40 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8844, 14129, 378, 223, 211, 394, 379, 14115])).
% 2.23/2.40 tff(14169,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[556, 14168, 1])).
% 2.23/2.40 tff(14170,plain,
% 2.23/2.40 (b(s(elem!1), s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14131, 14117])).
% 2.23/2.40 tff(14171,plain,
% 2.23/2.40 (b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[13430, 139, 6656, 379, 675])).
% 2.23/2.40 tff(14172,plain,
% 2.23/2.40 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6230, 14171, 14170, 750])).
% 2.23/2.40 tff(14173,plain,
% 2.23/2.40 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[13110, 14172, 223])).
% 2.23/2.40 tff(14174,plain,
% 2.23/2.40 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[586, 14173, 563])).
% 2.23/2.40 tff(14175,plain,
% 2.23/2.40 (~r(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14145, 14129, 139, 14174])).
% 2.23/2.40 tff(14176,plain,
% 2.23/2.40 (b(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2430, 14175])).
% 2.23/2.40 tff(14177,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[13762, 14176, 14169, 3407, 13594])).
% 2.23/2.40 tff(14178,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14179,plain,
% 2.23/2.40 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14178, 1441, 1, 378, 223, 14104, 379, 3407, 1408, 750, 675])).
% 2.23/2.40 tff(14180,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[486, 14179, 481])).
% 2.23/2.40 tff(14181,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[13402, 14180, 6796, 378, 379, 14102, 3407])).
% 2.23/2.40 tff(14182,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[556, 14181, 1])).
% 2.23/2.40 tff(14183,plain,
% 2.23/2.40 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.40 tff(14184,plain,
% 2.23/2.40 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14183])).
% 2.23/2.40 tff(14185,plain,
% 2.23/2.40 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[6791, 14184])).
% 2.23/2.40 tff(14186,plain,
% 2.23/2.40 (b(s(z), s(s(s(s(z)))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14102, 14185])).
% 2.23/2.40 tff(14187,plain,
% 2.23/2.40 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[681, 675, 6656])).
% 2.23/2.40 tff(14188,plain,
% 2.23/2.40 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[1036])).
% 2.23/2.40 tff(14189,plain,
% 2.23/2.40 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[14188])).
% 2.23/2.40 tff(14190,plain,
% 2.23/2.40 (b(s(elem!1), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2369, 14130, 1222])).
% 2.23/2.40 tff(14191,plain,
% 2.23/2.40 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14190, 14189])).
% 2.23/2.40 tff(14192,plain,
% 2.23/2.40 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8844, 222, 378, 223, 216, 394, 379, 623])).
% 2.23/2.40 tff(14193,plain,
% 2.23/2.40 (~b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14126, 222, 223, 1441, 216, 378, 379, 1409])).
% 2.23/2.40 tff(14194,plain,
% 2.23/2.40 (~b(elem!1, s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6679, 14193, 1222])).
% 2.23/2.40 tff(14195,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[599, 14194, 14192, 5038])).
% 2.23/2.40 tff(14196,plain,((~b(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14197,plain,
% 2.23/2.40 (~b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14196, 14182, 223, 211, 14104, 379, 378, 1441, 1408])).
% 2.23/2.40 tff(14198,plain,
% 2.23/2.40 (r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2325, 14197])).
% 2.23/2.40 tff(14199,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.23/2.40 tff(14200,plain,
% 2.23/2.40 (~r(s(elem!1), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[436, 378, 431, 110])).
% 2.23/2.40 tff(14201,plain,
% 2.23/2.40 (b(s(elem!1), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[409, 14200])).
% 2.23/2.40 tff(14202,plain,
% 2.23/2.40 (b(s(s(z)), z)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14201, 11174])).
% 2.23/2.40 tff(14203,plain,
% 2.23/2.40 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[1224])).
% 2.23/2.40 tff(14204,plain,
% 2.23/2.40 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[2372])).
% 2.23/2.40 tff(14205,plain,
% 2.23/2.40 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14204])).
% 2.23/2.40 tff(14206,plain,
% 2.23/2.40 (r(z, s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[378, 3643])).
% 2.23/2.40 tff(14207,plain,
% 2.23/2.40 (~r(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10559, 121, 110, 14206, 2327])).
% 2.23/2.40 tff(14208,plain,
% 2.23/2.40 (~r(z, s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14207, 14205])).
% 2.23/2.40 tff(14209,plain,
% 2.23/2.40 (b(z, s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2106, 14208])).
% 2.23/2.40 tff(14210,plain,
% 2.23/2.40 (b(z, s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14209, 14203])).
% 2.23/2.40 tff(14211,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(14212,plain,
% 2.23/2.40 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(14213,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[14212])).
% 2.23/2.40 tff(14214,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[14213, 14211])).
% 2.23/2.40 tff(14215,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(14216,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[14215, 14214])).
% 2.23/2.40 tff(14217,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14216, 271, 14210, 14202, 1405, 14199])).
% 2.23/2.40 tff(14218,plain,((~r(z, elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(14219,plain,
% 2.23/2.40 (~b(s(s(s(z))), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14218, 14198, 110, 378, 14191, 1222, 431])).
% 2.23/2.40 tff(14220,plain,
% 2.23/2.40 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[1223])).
% 2.23/2.41 tff(14221,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[1422, 14220])).
% 2.23/2.41 tff(14222,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1363, 14221])).
% 2.23/2.41 tff(14223,plain,((~b(s(s(s(z))), s(elem!1))) | b(s(s(s(z))), s(s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(14224,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14223, 14219, 1222])).
% 2.23/2.41 tff(14225,plain,
% 2.23/2.41 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1816, 14224, 7853])).
% 2.23/2.41 tff(14226,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[2372, 1226])).
% 2.23/2.41 tff(14227,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[14226])).
% 2.23/2.41 tff(14228,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[623, 14227])).
% 2.23/2.41 tff(14229,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[1226, 1223])).
% 2.23/2.41 tff(14230,plain,
% 2.23/2.41 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.23/2.41 inference(symmetry,[status(thm)],[14229])).
% 2.23/2.41 tff(14231,plain,
% 2.23/2.41 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[1223])).
% 2.23/2.41 tff(14232,plain,
% 2.23/2.41 (r(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[684, 14231])).
% 2.23/2.41 tff(14233,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), s(elem!1))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14232, 14230])).
% 2.23/2.41 tff(14234,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14233, 2381])).
% 2.23/2.41 tff(14235,plain,
% 2.23/2.41 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[2376])).
% 2.23/2.41 tff(14236,plain,
% 2.23/2.41 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.23/2.41 inference(transitivity,[status(thm)],[14235, 5619])).
% 2.23/2.41 tff(14237,plain,
% 2.23/2.41 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[14236])).
% 2.23/2.41 tff(14238,plain,
% 2.23/2.41 ((~(s(s(s(s(elem!1)))) = s(elem!1))) <=> (~(s(s(z)) = s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[14237])).
% 2.23/2.41 tff(14239,plain,
% 2.23/2.41 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[3109, 14238])).
% 2.23/2.41 tff(14240,plain,
% 2.23/2.41 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[2383])).
% 2.23/2.41 tff(14241,plain,
% 2.23/2.41 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.23/2.41 inference(symmetry,[status(thm)],[14240])).
% 2.23/2.41 tff(14242,plain,
% 2.23/2.41 (b(s(s(z)), elem!1) <=> b(s(elem!1), s(z))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[2376, 239])).
% 2.23/2.41 tff(14243,plain,
% 2.23/2.41 (b(s(elem!1), s(z)) <=> b(s(s(z)), elem!1)),
% 2.23/2.41 inference(symmetry,[status(thm)],[14242])).
% 2.23/2.41 tff(14244,plain,
% 2.23/2.41 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[239])).
% 2.23/2.41 tff(14245,plain,
% 2.23/2.41 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.23/2.41 inference(transitivity,[status(thm)],[14244, 14243])).
% 2.23/2.41 tff(14246,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[1224])).
% 2.23/2.41 tff(14247,plain,
% 2.23/2.41 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.23/2.41 inference(symmetry,[status(thm)],[14246])).
% 2.23/2.41 tff(14248,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[1500, 14247])).
% 2.23/2.41 tff(14249,plain,
% 2.23/2.41 (~r(s(elem!1), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[692, 14248, 684, 623])).
% 2.23/2.41 tff(14250,plain,
% 2.23/2.41 (b(s(elem!1), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2243, 14249, 2564])).
% 2.23/2.41 tff(14251,plain,
% 2.23/2.41 (b(s(s(z)), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14250, 14245])).
% 2.23/2.41 tff(14252,plain,
% 2.23/2.41 (b(s(s(z)), s(z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14251, 14241])).
% 2.23/2.41 tff(14253,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 2.23/2.41 tff(14254,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14255,plain,
% 2.23/2.41 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14256,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[14255])).
% 2.23/2.41 tff(14257,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[14256, 14254])).
% 2.23/2.41 tff(14258,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(14259,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14258, 14257])).
% 2.23/2.41 tff(14260,plain,
% 2.23/2.41 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14259, 271, 1067, 14253])).
% 2.23/2.41 tff(14261,plain,
% 2.23/2.41 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14260, 14252])).
% 2.23/2.41 tff(14262,plain,
% 2.23/2.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14263,plain,
% 2.23/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(14264,plain,
% 2.23/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14263, 14262])).
% 2.23/2.41 tff(14265,plain,
% 2.23/2.41 ((s(s(z)) = s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14264, 21, 14261])).
% 2.23/2.41 tff(14266,plain,
% 2.23/2.41 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14265, 14239])).
% 2.23/2.41 tff(14267,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14268,plain,
% 2.23/2.41 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14269,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[14268])).
% 2.23/2.41 tff(14270,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[14269, 14267])).
% 2.23/2.41 tff(14271,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(14272,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14271, 14270])).
% 2.23/2.41 tff(14273,plain,
% 2.23/2.41 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14272, 121, 14266])).
% 2.23/2.41 tff(14274,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14273, 4274, 14234, 14228])).
% 2.23/2.41 tff(14275,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(14276,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14275, 14225, 1222, 14187, 5861, 14186, 2207, 14182])).
% 2.23/2.41 tff(14277,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.41 tff(14278,plain,
% 2.23/2.41 ((~b(s(s(s(s(elem!1)))), s(z))) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[14277])).
% 2.23/2.41 tff(14279,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 2.23/2.41 tff(14280,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14279, 14278])).
% 2.23/2.41 tff(14281,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5606, 14280])).
% 2.23/2.41 tff(14282,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(s(elem!1)))), s(z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(14283,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14282, 14276, 223])).
% 2.23/2.41 tff(14284,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10196, 14283, 14167])).
% 2.23/2.41 tff(14285,plain,
% 2.23/2.41 (~b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8109, 14197, 223])).
% 2.23/2.41 tff(14286,plain,
% 2.23/2.41 (r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[255, 14285, 6655])).
% 2.23/2.41 tff(14287,plain,
% 2.23/2.41 (r(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14112, 14286, 223])).
% 2.23/2.41 tff(14288,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14289,plain,
% 2.23/2.41 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14290,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[14289])).
% 2.23/2.41 tff(14291,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[14290, 14288])).
% 2.23/2.41 tff(14292,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(14293,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14292, 14291])).
% 2.23/2.41 tff(14294,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14293, 121, 379, 14287, 14284])).
% 2.23/2.41 tff(14295,plain,
% 2.23/2.41 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14294, 14163])).
% 2.23/2.41 tff(14296,plain,
% 2.23/2.41 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8096, 14283, 223])).
% 2.23/2.41 tff(14297,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[840, 14296, 7890])).
% 2.23/2.41 tff(14298,plain,
% 2.23/2.41 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3066, 14297, 1408, 14286])).
% 2.23/2.41 tff(14299,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1733, 14298])).
% 2.23/2.41 tff(14300,plain,
% 2.23/2.41 (~r(s(s(s(z))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10317, 14198, 909, 431])).
% 2.23/2.41 tff(14301,plain,
% 2.23/2.41 (b(s(s(s(z))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1155, 14300])).
% 2.23/2.41 tff(14302,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.41 tff(14303,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.41 inference(symmetry,[status(thm)],[14302])).
% 2.23/2.41 tff(14304,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14297, 14303])).
% 2.23/2.41 tff(14305,plain,
% 2.23/2.41 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1669, 14304, 110, 909])).
% 2.23/2.41 tff(14306,plain,
% 2.23/2.41 (b(z, s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1658, 14305])).
% 2.23/2.41 tff(14307,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4072, 14306, 14301, 14299])).
% 2.23/2.41 tff(14308,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1494, 14307])).
% 2.23/2.41 tff(14309,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14308, 14295])).
% 2.23/2.41 tff(14310,plain,((~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(14311,plain,
% 2.23/2.41 (~r(z, s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14310, 750, 110, 909, 379, 378, 431, 1, 3407, 481, 223, 14160])).
% 2.23/2.41 tff(14312,plain,
% 2.23/2.41 (b(z, s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1439, 14311])).
% 2.23/2.41 tff(14313,plain,
% 2.23/2.41 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[13402, 504, 6796, 378, 379, 738, 3407])).
% 2.23/2.41 tff(14314,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[556, 14313, 1])).
% 2.23/2.41 tff(14315,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[692, 8448, 14187, 623])).
% 2.23/2.41 tff(14316,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[701, 14315, 8423])).
% 2.23/2.41 tff(14317,plain,
% 2.23/2.41 (~b(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2853, 14316, 394, 1421])).
% 2.23/2.41 tff(14318,plain,
% 2.23/2.41 (r(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2430, 14317])).
% 2.23/2.41 tff(14319,plain,
% 2.23/2.41 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8501, 14318, 378, 379])).
% 2.23/2.41 tff(14320,plain,
% 2.23/2.41 (~r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14112, 14319, 223])).
% 2.23/2.41 tff(14321,plain,
% 2.23/2.41 (b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[255, 14320, 6655])).
% 2.23/2.41 tff(14322,plain,
% 2.23/2.41 (b(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8109, 14321, 223])).
% 2.23/2.41 tff(14323,plain,
% 2.23/2.41 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8844, 14322, 378, 223, 216, 394, 379, 623])).
% 2.23/2.41 tff(14324,plain,
% 2.23/2.41 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4488, 14323, 675, 2469, 481, 2467])).
% 2.23/2.41 tff(14325,plain,
% 2.23/2.41 (b(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[862, 14319, 6796])).
% 2.23/2.41 tff(14326,plain,
% 2.23/2.41 (b(elem!1, s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[599, 14323, 5038])).
% 2.23/2.41 tff(14327,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10405, 14326, 223, 504, 623, 14325, 14324])).
% 2.23/2.41 tff(14328,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10196, 14327, 14167])).
% 2.23/2.41 tff(14329,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14330,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(14331,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14330, 14329])).
% 2.23/2.41 tff(14332,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14331, 121, 379, 378, 14328])).
% 2.23/2.41 tff(14333,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3089, 21, 812, 14332])).
% 2.23/2.41 tff(14334,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11415, 121, 379, 8448, 14328])).
% 2.23/2.41 tff(14335,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3112, 21, 5861, 14334])).
% 2.23/2.41 tff(14336,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14337,plain,
% 2.23/2.41 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(14338,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[14337])).
% 2.23/2.41 tff(14339,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[14338, 14336])).
% 2.23/2.41 tff(14340,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(14341,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[14340, 14339])).
% 2.23/2.41 tff(14342,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14341, 271, 394, 1421, 14335, 14333])).
% 2.23/2.41 tff(14343,plain,(b(s(elem!1), elem!1) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(14344,plain,
% 2.23/2.41 (b(s(elem!1), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[14343, 504, 1421, 379, 378, 223, 394, 14314, 675, 14313, 481, 211])).
% 2.23/2.41 tff(14345,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14346,plain,
% 2.23/2.42 (((~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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14347,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14346])).
% 2.23/2.42 tff(14348,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[14347, 14345])).
% 2.23/2.42 tff(14349,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(14350,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14349, 14348])).
% 2.23/2.42 tff(14351,plain,
% 2.23/2.42 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14350, 271, 14344, 504, 738])).
% 2.23/2.42 tff(14352,plain,
% 2.23/2.42 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3190, 14351, 6656, 675, 14314])).
% 2.23/2.42 tff(14353,plain,
% 2.23/2.42 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[526, 14352, 211])).
% 2.23/2.42 tff(14354,plain,
% 2.23/2.42 (b(s(elem!1), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2369, 14353, 1222])).
% 2.23/2.42 tff(14355,plain,
% 2.23/2.42 (b(s(elem!1), s(z))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14344, 14117])).
% 2.23/2.42 tff(14356,plain,
% 2.23/2.42 (r(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2293, 21, 14351, 13093])).
% 2.23/2.42 tff(14357,plain,
% 2.23/2.42 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3132, 14356, 14187, 14314])).
% 2.23/2.42 tff(14358,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[701, 14357, 3313])).
% 2.23/2.42 tff(14359,plain,
% 2.23/2.42 (~b(s(s(elem!1)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2853, 14358, 394, 1421])).
% 2.23/2.42 tff(14360,plain,
% 2.23/2.42 (r(s(s(elem!1)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2430, 14359])).
% 2.23/2.42 tff(14361,plain,
% 2.23/2.42 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8501, 14360, 378, 379])).
% 2.23/2.42 tff(14362,plain,
% 2.23/2.42 (~r(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14112, 14361, 223])).
% 2.23/2.42 tff(14363,plain,
% 2.23/2.42 (b(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[255, 14362, 6655])).
% 2.23/2.42 tff(14364,plain,
% 2.23/2.42 (b(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8109, 14363, 223])).
% 2.23/2.42 tff(14365,plain,
% 2.23/2.42 (~b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3622, 14364, 14355, 14354])).
% 2.23/2.42 tff(14366,plain,
% 2.23/2.42 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8844, 14364, 378, 223, 211, 394, 379, 14314])).
% 2.23/2.42 tff(14367,plain,
% 2.23/2.42 (b(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[599, 14366, 5038])).
% 2.23/2.42 tff(14368,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6679, 14367, 14365, 1222])).
% 2.23/2.42 tff(14369,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | b(s(s(s(elem!1))), s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14370,plain,
% 2.23/2.42 (~b(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14369, 14312, 223, 14104, 379, 378, 14160, 14102, 481, 1, 3407])).
% 2.23/2.42 tff(14371,plain,
% 2.23/2.42 (r(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[486, 14370, 481])).
% 2.23/2.42 tff(14372,plain,
% 2.23/2.42 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6958, 14371, 378, 1, 563, 1408])).
% 2.23/2.42 tff(14373,plain,
% 2.23/2.42 (b(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[862, 14372, 6796])).
% 2.23/2.42 tff(14374,plain,
% 2.23/2.42 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[681, 14160, 6656])).
% 2.23/2.42 tff(14375,plain,
% 2.23/2.42 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11463, 14371, 379, 14374])).
% 2.23/2.42 tff(14376,plain,
% 2.23/2.42 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[526, 14375, 211])).
% 2.23/2.42 tff(14377,plain,
% 2.23/2.42 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.23/2.42 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.42 tff(14378,plain,
% 2.23/2.42 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14377])).
% 2.23/2.42 tff(14379,plain,
% 2.23/2.42 (~(s(s(z)) = elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[3595, 14378])).
% 2.23/2.42 tff(14380,plain,
% 2.23/2.42 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[1036])).
% 2.23/2.42 tff(14381,plain,
% 2.23/2.42 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.23/2.42 inference(symmetry,[status(thm)],[14380])).
% 2.23/2.42 tff(14382,plain,
% 2.23/2.42 (r(elem!1, s(s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[379, 14381])).
% 2.23/2.42 tff(14383,plain,
% 2.23/2.42 (r(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14374, 1372])).
% 2.23/2.42 tff(14384,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14385,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(14386,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14385, 14384])).
% 2.23/2.42 tff(14387,plain,
% 2.23/2.42 ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14386, 121])).
% 2.23/2.42 tff(14388,plain,
% 2.23/2.42 (~r(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14387, 14371, 14383, 14382])).
% 2.23/2.42 tff(14389,plain,
% 2.23/2.42 (b(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3613, 14388, 14379])).
% 2.23/2.42 tff(14390,plain,
% 2.23/2.42 (b(s(elem!1), elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14389, 6728])).
% 2.23/2.42 tff(14391,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14392,plain,
% 2.23/2.42 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14393,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14392])).
% 2.23/2.42 tff(14394,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[14393, 14391])).
% 2.23/2.42 tff(14395,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(14396,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14395, 14394])).
% 2.23/2.42 tff(14397,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14396, 271, 14390, 14376, 14373, 14102])).
% 2.23/2.42 tff(14398,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14399,plain,
% 2.23/2.42 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14398, 9983, 14071, 1243, 1, 13588, 3407, 110, 14096, 14101, 344])).
% 2.23/2.42 tff(14400,plain,
% 2.23/2.42 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[760, 14399])).
% 2.23/2.42 tff(14401,plain,
% 2.23/2.42 (~r(s(elem!1), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9617, 684, 572, 431])).
% 2.23/2.42 tff(14402,plain,
% 2.23/2.42 (b(s(elem!1), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2243, 14401, 2207])).
% 2.23/2.42 tff(14403,plain,
% 2.23/2.42 (b(s(elem!1), s(z))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14402, 14117])).
% 2.23/2.42 tff(14404,plain,
% 2.23/2.42 (r(elem!1, s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1045, 572, 223])).
% 2.23/2.42 tff(14405,plain,
% 2.23/2.42 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.42 tff(14406,plain,
% 2.23/2.42 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.23/2.42 inference(symmetry,[status(thm)],[14405])).
% 2.23/2.42 tff(14407,plain,
% 2.23/2.42 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11463, 139, 379, 684])).
% 2.23/2.42 tff(14408,plain,
% 2.23/2.42 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[526, 14407, 211])).
% 2.23/2.42 tff(14409,plain,
% 2.23/2.42 (b(s(elem!1), s(z))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[2618, 14117])).
% 2.23/2.42 tff(14410,plain,
% 2.23/2.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2176, 14408, 572, 684, 14409])).
% 2.23/2.42 tff(14411,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[556, 14410, 1])).
% 2.23/2.42 tff(14412,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14413,plain,
% 2.23/2.42 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14414,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14413])).
% 2.23/2.42 tff(14415,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[14414, 14412])).
% 2.23/2.42 tff(14416,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(14417,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14416, 14415])).
% 2.23/2.42 tff(14418,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14417, 271, 2618, 543, 517, 588])).
% 2.23/2.42 tff(14419,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14420,plain,
% 2.23/2.42 (~b(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14419, 14411, 14408, 2618])).
% 2.23/2.42 tff(14421,plain,
% 2.23/2.42 (r(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[599, 14420, 5038])).
% 2.23/2.42 tff(14422,plain,
% 2.23/2.42 (r(s(z), s(s(elem!1)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14421, 14406])).
% 2.23/2.42 tff(14423,plain,
% 2.23/2.42 (~b(s(s(elem!1)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[13762, 14411, 3407, 13594])).
% 2.23/2.42 tff(14424,plain,
% 2.23/2.42 (r(s(s(elem!1)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2430, 14423])).
% 2.23/2.42 tff(14425,plain,
% 2.23/2.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14145, 14421, 139, 14424])).
% 2.23/2.42 tff(14426,plain,
% 2.23/2.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[586, 14425, 563])).
% 2.23/2.42 tff(14427,plain,
% 2.23/2.42 (~b(z, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1921, 14426, 110, 572, 14411])).
% 2.23/2.42 tff(14428,plain,
% 2.23/2.42 (r(z, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2106, 14427])).
% 2.23/2.42 tff(14429,plain,
% 2.23/2.42 (~r(s(z), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11783, 14428, 110, 14424])).
% 2.23/2.42 tff(14430,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14429, 14422])).
% 2.23/2.42 tff(14431,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14432,plain,
% 2.23/2.42 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14431, 14402, 110, 572, 223, 3407, 1, 684, 379, 378])).
% 2.23/2.42 tff(14433,plain,
% 2.23/2.42 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[486, 14432, 481])).
% 2.23/2.42 tff(14434,plain,
% 2.23/2.42 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10103, 623, 727, 684])).
% 2.23/2.42 tff(14435,plain,
% 2.23/2.42 (b(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[862, 14434, 851])).
% 2.23/2.42 tff(14436,plain,
% 2.23/2.42 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[735, 623, 727, 684])).
% 2.23/2.42 tff(14437,plain,
% 2.23/2.42 (b(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[599, 14436, 68])).
% 2.23/2.42 tff(14438,plain,
% 2.23/2.42 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[594, 14437, 504, 14435])).
% 2.23/2.42 tff(14439,plain,
% 2.23/2.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[586, 14438, 6943])).
% 2.23/2.42 tff(14440,plain,
% 2.23/2.42 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2176, 623, 572, 684, 447])).
% 2.23/2.42 tff(14441,plain,
% 2.23/2.42 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[526, 14440, 216])).
% 2.23/2.42 tff(14442,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4506, 121, 623, 684, 14441, 14439])).
% 2.23/2.42 tff(14443,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14444,plain,
% 2.23/2.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14443, 684, 563, 14433, 5038, 6796, 211, 14404, 572, 14403])).
% 2.23/2.42 tff(14445,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[556, 14444, 1])).
% 2.23/2.42 tff(14446,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14447,plain,
% 2.23/2.42 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14448,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14447])).
% 2.23/2.42 tff(14449,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[14448, 14446])).
% 2.23/2.42 tff(14450,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(14451,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14450, 14449])).
% 2.23/2.42 tff(14452,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14451, 121, 379, 684, 627, 727])).
% 2.23/2.42 tff(14453,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14454,plain,
% 2.23/2.42 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14453, 684, 379, 14404])).
% 2.23/2.42 tff(14455,plain,
% 2.23/2.42 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[526, 14454, 211])).
% 2.23/2.42 tff(14456,plain,
% 2.23/2.42 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10076, 14455, 14433, 14445])).
% 2.23/2.42 tff(14457,plain,
% 2.23/2.42 (r(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2293, 21, 14456, 13093])).
% 2.23/2.42 tff(14458,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14459,plain,
% 2.23/2.42 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14460,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14459])).
% 2.23/2.42 tff(14461,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[14460, 14458])).
% 2.23/2.42 tff(14462,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(14463,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[14462, 14461])).
% 2.23/2.42 tff(14464,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14463, 121, 379, 684, 14404, 14457])).
% 2.23/2.42 tff(14465,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), z)) | (~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(14466,plain,
% 2.23/2.42 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14465, 9983, 1, 14400, 13588, 110, 14071, 3407, 1243, 14101])).
% 2.23/2.42 tff(14467,plain,
% 2.23/2.42 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[681, 14466, 14090])).
% 2.23/2.42 tff(14468,plain,
% 2.23/2.42 (~r(s(elem!1), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1417, 9983, 14087, 14096])).
% 2.23/2.42 tff(14469,plain,
% 2.23/2.42 (b(s(elem!1), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[409, 14468])).
% 2.23/2.42 tff(14470,plain,
% 2.23/2.42 (~b(z, s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14106, 14467, 3407, 14469])).
% 2.23/2.42 tff(14471,plain,
% 2.23/2.42 (r(z, s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1439, 14470])).
% 2.23/2.42 tff(14472,plain,
% 2.23/2.42 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14147, 14471, 3407, 1, 1243, 344, 14071, 14467, 9983, 14087])).
% 2.23/2.42 tff(14473,plain,
% 2.23/2.42 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[486, 14472, 13588])).
% 2.23/2.42 tff(14474,plain,
% 2.23/2.42 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8501, 2417, 378, 379])).
% 2.23/2.42 tff(14475,plain,
% 2.23/2.42 (~r(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14112, 14474, 223])).
% 2.23/2.42 tff(14476,plain,
% 2.23/2.42 (b(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[255, 14475, 6655])).
% 2.23/2.42 tff(14477,plain,
% 2.23/2.42 (b(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8109, 14476, 223])).
% 2.23/2.42 tff(14478,plain,
% 2.23/2.42 (~b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[14126, 1441, 223, 14477, 216, 378, 379, 1409])).
% 2.23/2.42 tff(14479,plain,
% 2.23/2.42 (~b(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6679, 14478, 1222])).
% 2.23/2.42 tff(14480,plain,
% 2.23/2.42 (r(elem!1, s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[599, 14479, 5038])).
% 2.23/2.42 tff(14481,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14482,plain,
% 2.23/2.42 (((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(14483,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[14482])).
% 2.23/2.42 tff(14484,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[14483, 14481])).
% 2.23/2.42 tff(14485,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(14486,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14485, 14484])).
% 2.23/2.43 tff(14487,plain,
% 2.23/2.43 (~r(elem!1, z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14486, 121, 2088, 624, 2417])).
% 2.23/2.43 tff(14488,plain,
% 2.23/2.43 (b(elem!1, z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[284, 14487, 358])).
% 2.23/2.43 tff(14489,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14490,plain,
% 2.23/2.43 (((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14491,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14490])).
% 2.23/2.43 tff(14492,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14491, 14489])).
% 2.23/2.43 tff(14493,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(14494,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14493, 14492])).
% 2.23/2.43 tff(14495,plain,
% 2.23/2.43 (~r(z, elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14494, 121, 2088, 624, 2417])).
% 2.23/2.43 tff(14496,plain,
% 2.23/2.43 (b(z, elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[355, 14495, 331])).
% 2.23/2.43 tff(14497,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7173, 14496, 14488, 3407, 504])).
% 2.23/2.43 tff(14498,plain,((~r(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14499,plain,
% 2.23/2.43 (~r(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14498, 14480, 3407, 331, 504, 2417])).
% 2.23/2.43 tff(14500,plain,
% 2.23/2.43 (b(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2106, 14499])).
% 2.23/2.43 tff(14501,plain,
% 2.23/2.43 (b(z, s(s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14500, 8835])).
% 2.23/2.43 tff(14502,plain,
% 2.23/2.43 (~b(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2029, 14123, 14477, 394])).
% 2.23/2.43 tff(14503,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14502, 14501])).
% 2.23/2.43 tff(14504,plain,((~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14505,plain,
% 2.23/2.43 (~r(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14504, 14473, 3407, 331, 14471, 14071, 14469, 211, 1243, 9983, 14087])).
% 2.23/2.43 tff(14506,plain,
% 2.23/2.43 (b(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2430, 14505])).
% 2.23/2.43 tff(14507,plain,
% 2.23/2.43 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5267, 14506, 3407, 14467])).
% 2.23/2.43 tff(14508,plain,
% 2.23/2.43 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[556, 14507, 1])).
% 2.23/2.43 tff(14509,plain,
% 2.23/2.43 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.43 tff(14510,plain,
% 2.23/2.43 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14509, 159])).
% 2.23/2.43 tff(14511,plain,
% 2.23/2.43 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.23/2.43 inference(transitivity,[status(thm)],[14510, 160])).
% 2.23/2.43 tff(14512,plain,
% 2.23/2.43 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14511])).
% 2.23/2.43 tff(14513,plain,
% 2.23/2.43 (~(s(s(s(z))) = elem!1)),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[97, 14512])).
% 2.23/2.43 tff(14514,plain,
% 2.23/2.43 (~b(s(s(s(z))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14196, 14508, 14071, 211, 14469, 9983, 1243, 14471, 14087])).
% 2.23/2.43 tff(14515,plain,
% 2.23/2.43 (~b(s(s(s(z))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8109, 14514, 14071])).
% 2.23/2.43 tff(14516,plain,
% 2.23/2.43 (r(s(s(s(z))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[255, 14515, 14513])).
% 2.23/2.43 tff(14517,plain,
% 2.23/2.43 (r(s(s(elem!1)), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6824, 14516, 14071])).
% 2.23/2.43 tff(14518,plain,
% 2.23/2.43 (~r(s(elem!1), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3387, 14471, 1243, 14087])).
% 2.23/2.43 tff(14519,plain,
% 2.23/2.43 (b(s(elem!1), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2243, 14518, 2207])).
% 2.23/2.43 tff(14520,plain,
% 2.23/2.43 (r(elem!1, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10472, 14473, 14090, 14466, 14519])).
% 2.23/2.43 tff(14521,plain,
% 2.23/2.43 (~r(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2502, 14508, 1243, 14520])).
% 2.23/2.43 tff(14522,plain,
% 2.23/2.43 (b(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2106, 14521])).
% 2.23/2.43 tff(14523,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14524,plain,
% 2.23/2.43 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14525,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14524])).
% 2.23/2.43 tff(14526,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14525, 14523])).
% 2.23/2.43 tff(14527,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(14528,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14527, 14526])).
% 2.23/2.43 tff(14529,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14528, 271, 589, 1894, 3407, 2449])).
% 2.23/2.43 tff(14530,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14531,plain,
% 2.23/2.43 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14530, 14522, 3407, 14506])).
% 2.23/2.43 tff(14532,plain,
% 2.23/2.43 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[586, 14531, 563])).
% 2.23/2.43 tff(14533,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14534,plain,
% 2.23/2.43 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14535,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14534])).
% 2.23/2.43 tff(14536,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14535, 14533])).
% 2.23/2.43 tff(14537,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(14538,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14537, 14536])).
% 2.23/2.43 tff(14539,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14538, 121, 623, 573, 572, 2117])).
% 2.23/2.43 tff(14540,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14541,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14540, 14532, 14517, 14400, 14508])).
% 2.23/2.43 tff(14542,plain,(b(elem!1, s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1) | (~r(s(z), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14543,plain,
% 2.23/2.43 (b(elem!1, s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14542, 199, 1, 331, 110, 3407])).
% 2.23/2.43 tff(14544,plain,
% 2.23/2.43 (elem!1 = s(z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1221, 14071])).
% 2.23/2.43 tff(14545,plain,
% 2.23/2.43 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[556, 2469, 1])).
% 2.23/2.43 tff(14546,plain,
% 2.23/2.43 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3310, 14545, 331, 199, 2344, 14085, 14090])).
% 2.23/2.43 tff(14547,plain,
% 2.23/2.43 (b(elem!1, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[599, 14546, 14089])).
% 2.23/2.43 tff(14548,plain,
% 2.23/2.43 (b(s(z), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6679, 14547, 14544])).
% 2.23/2.43 tff(14549,plain,
% 2.23/2.43 (s(s(elem!1)) = s(s(s(z)))),
% 2.23/2.43 inference(symmetry,[status(thm)],[14075])).
% 2.23/2.43 tff(14550,plain,
% 2.23/2.43 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14549])).
% 2.23/2.43 tff(14551,plain,
% 2.23/2.43 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(symmetry,[status(thm)],[14550])).
% 2.23/2.43 tff(14552,plain,
% 2.23/2.43 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14072])).
% 2.23/2.43 tff(14553,plain,
% 2.23/2.43 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14552, 3535])).
% 2.23/2.43 tff(14554,plain,
% 2.23/2.43 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14553])).
% 2.23/2.43 tff(14555,plain,
% 2.23/2.43 (~(s(s(s(z))) = s(elem!1))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[1136, 14554])).
% 2.23/2.43 tff(14556,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8078, 3498, 219, 14095])).
% 2.23/2.43 tff(14557,plain,
% 2.23/2.43 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6958, 139, 378, 1, 563, 1408])).
% 2.23/2.43 tff(14558,plain,
% 2.23/2.43 (b(s(s(elem!1)), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[862, 14557, 6796])).
% 2.23/2.43 tff(14559,plain,
% 2.23/2.43 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.43 inference(commutativity,[status(thm)],[])).
% 2.23/2.43 tff(14560,plain,
% 2.23/2.43 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[1037, 3056])).
% 2.23/2.43 tff(14561,plain,
% 2.23/2.43 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14560, 14559])).
% 2.23/2.43 tff(14562,plain,
% 2.23/2.43 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14561])).
% 2.23/2.43 tff(14563,plain,
% 2.23/2.43 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[1489, 14562])).
% 2.23/2.43 tff(14564,plain,
% 2.23/2.43 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[1038])).
% 2.23/2.43 tff(14565,plain,
% 2.23/2.43 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.23/2.43 inference(symmetry,[status(thm)],[14564])).
% 2.23/2.43 tff(14566,plain,
% 2.23/2.43 (b(z, s(s(s(s(z)))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[3407, 14565])).
% 2.23/2.43 tff(14567,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8096, 5869, 223])).
% 2.23/2.43 tff(14568,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[840, 14567, 7890])).
% 2.23/2.43 tff(14569,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14568, 14303])).
% 2.23/2.43 tff(14570,plain,
% 2.23/2.43 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1669, 14569, 110, 909])).
% 2.23/2.43 tff(14571,plain,
% 2.23/2.43 (b(z, s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1658, 14570])).
% 2.23/2.43 tff(14572,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10196, 5869, 14167])).
% 2.23/2.43 tff(14573,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14574,plain,
% 2.23/2.43 (((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14575,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14574])).
% 2.23/2.43 tff(14576,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14575, 14573])).
% 2.23/2.43 tff(14577,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(14578,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14577, 14576])).
% 2.23/2.43 tff(14579,plain,
% 2.23/2.43 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14578, 121, 1408, 139, 14572])).
% 2.23/2.43 tff(14580,plain,
% 2.23/2.43 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6896, 14579, 223])).
% 2.23/2.43 tff(14581,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1777, 14580])).
% 2.23/2.43 tff(14582,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14583,plain,
% 2.23/2.43 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(14584,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14583])).
% 2.23/2.43 tff(14585,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14584, 14582])).
% 2.23/2.43 tff(14586,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(14587,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14586, 14585])).
% 2.23/2.43 tff(14588,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14587, 271, 6068, 1639, 1157, 9894])).
% 2.23/2.43 tff(14589,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14590,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14589, 14581, 14571, 1157, 9894])).
% 2.23/2.43 tff(14591,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(14592,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14591, 139, 9894, 223, 110, 909, 14566])).
% 2.23/2.43 tff(14593,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10204, 14592, 307, 14563, 14558])).
% 2.23/2.43 tff(14594,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[1038])).
% 2.23/2.43 tff(14595,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[1037])).
% 2.23/2.43 tff(14596,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[14595, 14594])).
% 2.23/2.43 tff(14597,plain,
% 2.23/2.43 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[14596])).
% 2.23/2.43 tff(14598,plain,
% 2.23/2.43 (~r(s(elem!1), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5358, 412, 378, 1408])).
% 2.23/2.43 tff(14599,plain,
% 2.23/2.43 (b(s(elem!1), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2243, 14598, 2207])).
% 2.23/2.43 tff(14600,plain,
% 2.23/2.43 (~r(s(s(s(z))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14112, 14557, 223])).
% 2.23/2.43 tff(14601,plain,
% 2.23/2.43 (b(s(s(s(z))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[255, 14600, 6655])).
% 2.23/2.43 tff(14602,plain,
% 2.23/2.43 (~r(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[13140, 14601, 412, 14599, 307, 7853])).
% 2.23/2.43 tff(14603,plain,
% 2.23/2.43 (b(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1214, 14602])).
% 2.23/2.43 tff(14604,plain,
% 2.23/2.43 (b(s(s(z)), s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[14599, 6730])).
% 2.23/2.43 tff(14605,plain,
% 2.23/2.43 (b(elem!1, s(s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[307, 7920])).
% 2.23/2.43 tff(14606,plain,
% 2.23/2.43 (~b(s(s(s(z))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6740, 14601, 14605, 14604])).
% 2.23/2.43 tff(14607,plain,
% 2.23/2.43 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14223, 14606, 1222])).
% 2.23/2.43 tff(14608,plain,
% 2.23/2.43 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1816, 14607, 7853])).
% 2.23/2.43 tff(14609,plain,
% 2.23/2.43 (~r(s(s(s(z))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3650, 14608, 378, 412])).
% 2.23/2.43 tff(14610,plain,
% 2.23/2.43 (b(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1155, 14609])).
% 2.23/2.44 tff(14611,plain,
% 2.23/2.44 (~r(s(s(s(s(z)))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[919, 6659, 909, 110])).
% 2.23/2.44 tff(14612,plain,
% 2.23/2.44 (b(s(s(s(s(z)))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1095, 14611])).
% 2.23/2.44 tff(14613,plain,
% 2.23/2.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[13513, 14612, 14610, 14603])).
% 2.23/2.44 tff(14614,plain,
% 2.23/2.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14613, 14597])).
% 2.23/2.44 tff(14615,plain,
% 2.23/2.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[586, 14614, 563])).
% 2.23/2.44 tff(14616,plain,
% 2.23/2.44 (~b(s(s(elem!1)), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[6807, 14558, 307, 14599])).
% 2.23/2.44 tff(14617,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[701, 14616, 3313])).
% 2.23/2.44 tff(14618,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14619,plain,
% 2.23/2.44 (((~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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14620,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14619])).
% 2.23/2.44 tff(14621,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14620, 14618])).
% 2.23/2.44 tff(14622,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14623,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14622, 14621])).
% 2.23/2.44 tff(14624,plain,
% 2.23/2.44 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14623, 271, 307, 14599, 14558])).
% 2.23/2.44 tff(14625,plain,
% 2.23/2.44 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[526, 14624, 211])).
% 2.23/2.44 tff(14626,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14627,plain,
% 2.23/2.44 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14628,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14627])).
% 2.23/2.44 tff(14629,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14628, 14626])).
% 2.23/2.44 tff(14630,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14631,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14630, 14629])).
% 2.23/2.44 tff(14632,plain,
% 2.23/2.44 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14631, 121, 14625, 14615, 14617])).
% 2.23/2.44 tff(14633,plain,
% 2.23/2.44 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[681, 14632, 6656])).
% 2.23/2.44 tff(14634,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14635,plain,
% 2.23/2.44 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(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)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14636,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14635])).
% 2.23/2.44 tff(14637,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14636, 14634])).
% 2.23/2.44 tff(14638,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14639,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14638, 14637])).
% 2.23/2.44 tff(14640,plain,
% 2.23/2.44 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14639, 121, 14625, 14615, 14617])).
% 2.23/2.44 tff(14641,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2293, 21, 14640, 13093])).
% 2.23/2.44 tff(14642,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14643,plain,
% 2.23/2.44 (((~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14644,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14643])).
% 2.23/2.44 tff(14645,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14644, 14642])).
% 2.23/2.44 tff(14646,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14647,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14646, 14645])).
% 2.23/2.44 tff(14648,plain,
% 2.23/2.44 (~b(z, s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14647, 271, 3407, 14641, 14633])).
% 2.23/2.44 tff(14649,plain,
% 2.23/2.44 (r(z, s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1439, 14648])).
% 2.23/2.44 tff(14650,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14651,plain,
% 2.23/2.44 (((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14652,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14651])).
% 2.23/2.44 tff(14653,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14652, 14650])).
% 2.23/2.44 tff(14654,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14655,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14654, 14653])).
% 2.23/2.44 tff(14656,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14655, 121, 1441, 412, 683, 2417])).
% 2.23/2.44 tff(14657,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(14658,plain,
% 2.23/2.44 (~r(s(s(elem!1)), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14657, 14649, 412, 14617])).
% 2.23/2.44 tff(14659,plain,
% 2.23/2.44 (b(s(s(elem!1)), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2430, 14658])).
% 2.23/2.44 tff(14660,plain,
% 2.23/2.44 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5267, 14659, 3407, 14633])).
% 2.23/2.44 tff(14661,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[556, 14660, 1])).
% 2.23/2.44 tff(14662,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[1038])).
% 2.23/2.44 tff(14663,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.23/2.44 inference(symmetry,[status(thm)],[14662])).
% 2.23/2.44 tff(14664,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(s(z)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14641, 14663])).
% 2.23/2.44 tff(14665,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[1038])).
% 2.23/2.44 tff(14666,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.44 inference(symmetry,[status(thm)],[14665])).
% 2.23/2.44 tff(14667,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[3057])).
% 2.23/2.44 tff(14668,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14667, 14666])).
% 2.23/2.44 tff(14669,plain,
% 2.23/2.44 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14668])).
% 2.23/2.44 tff(14670,plain,
% 2.23/2.44 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[8218, 14669])).
% 2.23/2.44 tff(14671,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.44 tff(14672,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 2.23/2.44 tff(14673,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14674,plain,
% 2.23/2.44 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14675,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14674])).
% 2.23/2.44 tff(14676,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14675, 14673])).
% 2.23/2.44 tff(14677,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14678,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14677, 14676])).
% 2.23/2.44 tff(14679,plain,
% 2.23/2.44 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14678, 121, 623, 573, 14672])).
% 2.23/2.44 tff(14680,plain,
% 2.23/2.44 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[6896, 14679, 223])).
% 2.23/2.44 tff(14681,plain,
% 2.23/2.44 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1777, 14680])).
% 2.23/2.44 tff(14682,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.44 tff(14683,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14684,plain,
% 2.23/2.44 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(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(elem!1)))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(14685,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(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(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14684])).
% 2.23/2.44 tff(14686,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(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(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14685, 14683])).
% 2.23/2.44 tff(14687,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(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(elem!1))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(14688,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14687, 14686])).
% 2.23/2.44 tff(14689,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14688, 271, 6068, 14671, 14682, 9894])).
% 2.23/2.44 tff(14690,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(14691,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14690, 14681, 14671, 9894])).
% 2.23/2.44 tff(14692,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[9512, 14691])).
% 2.23/2.44 tff(14693,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14692, 14670])).
% 2.23/2.44 tff(14694,plain,(r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(14695,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14694, 14664, 223, 9894, 14661, 14615, 14593])).
% 2.23/2.44 tff(14696,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10400, 121, 14661, 14615, 14593, 14695])).
% 2.23/2.44 tff(14697,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(14698,plain,
% 2.23/2.44 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14697, 14556, 14071, 1, 3407, 3501, 14096, 110, 14543, 1243])).
% 2.23/2.44 tff(14699,plain,
% 2.23/2.44 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[486, 14698, 13588])).
% 2.23/2.44 tff(14700,plain,
% 2.23/2.44 (~r(s(elem!1), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5358, 3501, 1243, 14087])).
% 2.23/2.44 tff(14701,plain,
% 2.23/2.44 (b(s(elem!1), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2243, 14700, 2207])).
% 2.23/2.44 tff(14702,plain,
% 2.23/2.44 (~b(s(s(elem!1)), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[551, 543, 307, 504])).
% 2.23/2.44 tff(14703,plain,
% 2.23/2.44 (r(s(s(elem!1)), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[862, 14702, 851])).
% 2.23/2.44 tff(14704,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[6803, 14703, 239])).
% 2.23/2.44 tff(14705,plain,
% 2.23/2.44 (~r(s(s(elem!1)), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2422, 14704, 110, 909])).
% 2.23/2.44 tff(14706,plain,
% 2.23/2.44 (b(s(s(elem!1)), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2430, 14705])).
% 2.23/2.44 tff(14707,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[13390, 271, 543, 3407, 504, 14706])).
% 2.23/2.44 tff(14708,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~(elem!1 = s(z))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(14709,plain,
% 2.23/2.44 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14708, 14699, 3407, 110, 14096, 14544, 14085, 14543])).
% 2.23/2.44 tff(14710,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[556, 14709, 1])).
% 2.23/2.44 tff(14711,plain,
% 2.23/2.44 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[3192, 14710, 14090, 14543, 14701, 14699])).
% 2.23/2.44 tff(14712,plain,
% 2.23/2.44 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[526, 14711, 211])).
% 2.23/2.44 tff(14713,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2369, 14712, 14544])).
% 2.23/2.44 tff(14714,plain,
% 2.23/2.44 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.44 tff(14715,plain,
% 2.23/2.44 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.23/2.44 inference(symmetry,[status(thm)],[14714])).
% 2.23/2.44 tff(14716,plain,
% 2.23/2.44 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[14072])).
% 2.23/2.44 tff(14717,plain,
% 2.23/2.44 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.23/2.44 inference(symmetry,[status(thm)],[14716])).
% 2.23/2.44 tff(14718,plain,
% 2.23/2.44 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.23/2.44 inference(transitivity,[status(thm)],[14717, 14715])).
% 2.23/2.44 tff(14719,plain,
% 2.23/2.44 (b(s(z), s(s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14543, 14718])).
% 2.23/2.44 tff(14720,plain,
% 2.23/2.44 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[3310, 14710, 331, 199, 2344, 14085, 14090])).
% 2.23/2.44 tff(14721,plain,
% 2.23/2.44 (b(elem!1, s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[599, 14720, 14089])).
% 2.23/2.44 tff(14722,plain,
% 2.23/2.44 (b(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[6679, 14721, 14544])).
% 2.23/2.44 tff(14723,plain,
% 2.23/2.44 (~b(s(s(s(z))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[6772, 14722, 14544, 14719, 14713])).
% 2.23/2.44 tff(14724,plain,
% 2.23/2.44 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14223, 14723, 14544])).
% 2.23/2.44 tff(14725,plain,
% 2.23/2.44 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1816, 14724, 14555])).
% 2.23/2.44 tff(14726,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[14725, 14551])).
% 2.23/2.44 tff(14727,plain,
% 2.23/2.44 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[84, 14090])).
% 2.23/2.44 tff(14728,plain,
% 2.23/2.44 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2930, 271, 14543, 14701, 14699])).
% 2.23/2.44 tff(14729,plain,
% 2.23/2.44 (r(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2293, 21, 14728, 14727])).
% 2.23/2.44 tff(14730,plain,
% 2.23/2.44 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[3177, 271, 14543, 14701, 14699])).
% 2.23/2.44 tff(14731,plain,
% 2.23/2.44 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[681, 14730, 14090])).
% 2.23/2.44 tff(14732,plain,
% 2.23/2.44 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[3132, 14710, 14731, 14729])).
% 2.23/2.44 tff(14733,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14732, 14726])).
% 2.23/2.44 tff(14734,plain,(b(s(elem!1), z) | (z = elem!1) | b(z, elem!1) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14735,plain,
% 2.23/2.45 (b(s(elem!1), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14734, 2344, 199, 331, 1, 3407, 110])).
% 2.23/2.45 tff(14736,plain,
% 2.23/2.45 (~b(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3324, 14547, 14543, 14735])).
% 2.23/2.45 tff(14737,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[701, 14736, 3313])).
% 2.23/2.45 tff(14738,plain,
% 2.23/2.45 (b(s(z), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1276, 307, 223])).
% 2.23/2.45 tff(14739,plain,
% 2.23/2.45 (~b(s(elem!1), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3879, 14114, 14738, 3871])).
% 2.23/2.45 tff(14740,plain,
% 2.23/2.45 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2369, 14739, 1222])).
% 2.23/2.45 tff(14741,plain,
% 2.23/2.45 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[526, 14740, 211])).
% 2.23/2.45 tff(14742,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3201, 14741, 683, 623])).
% 2.23/2.45 tff(14743,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[681, 14742, 6656])).
% 2.23/2.45 tff(14744,plain,
% 2.23/2.45 (~b(z, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14106, 14743, 3407, 394])).
% 2.23/2.45 tff(14745,plain,
% 2.23/2.45 (r(z, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1439, 14744])).
% 2.23/2.45 tff(14746,plain,
% 2.23/2.45 (~r(s(elem!1), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10746, 14743, 378, 259, 307, 394, 1409, 623, 683])).
% 2.23/2.45 tff(14747,plain,
% 2.23/2.45 (b(s(elem!1), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2243, 14746, 2207])).
% 2.23/2.45 tff(14748,plain,
% 2.23/2.45 (~b(elem!1, s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12887, 14747, 307, 14743])).
% 2.23/2.45 tff(14749,plain,
% 2.23/2.45 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8233, 14748, 223])).
% 2.23/2.45 tff(14750,plain,
% 2.23/2.45 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[760, 14749])).
% 2.23/2.45 tff(14751,plain,
% 2.23/2.45 (r(elem!1, s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1045, 14750, 223])).
% 2.23/2.45 tff(14752,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[13723, 14751, 378, 139])).
% 2.23/2.45 tff(14753,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8229, 14752])).
% 2.23/2.45 tff(14754,plain,
% 2.23/2.45 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[1036])).
% 2.23/2.45 tff(14755,plain,
% 2.23/2.45 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.23/2.45 inference(symmetry,[status(thm)],[14754])).
% 2.23/2.45 tff(14756,plain,
% 2.23/2.45 (b(s(s(z)), z)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[394, 14755])).
% 2.23/2.45 tff(14757,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[1036])).
% 2.23/2.45 tff(14758,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.45 inference(symmetry,[status(thm)],[14757])).
% 2.23/2.45 tff(14759,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14743, 14758])).
% 2.23/2.45 tff(14760,plain,
% 2.23/2.45 (~b(z, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1648, 14759, 14756, 14753])).
% 2.23/2.45 tff(14761,plain,
% 2.23/2.45 (r(z, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1658, 14760])).
% 2.23/2.45 tff(14762,plain,
% 2.23/2.45 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[6368, 14761, 14741, 14745])).
% 2.23/2.45 tff(14763,plain,
% 2.23/2.45 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11865, 14761, 14738, 394, 909])).
% 2.23/2.45 tff(14764,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4138, 14763, 14762, 4962])).
% 2.23/2.45 tff(14765,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14766,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14765, 14545, 14096, 14071, 1243, 14543, 3407, 358, 14087, 14735, 14737, 14548, 1])).
% 2.23/2.45 tff(14767,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[486, 14766, 13588])).
% 2.23/2.45 tff(14768,plain,
% 2.23/2.45 (~b(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11154, 14767, 14544, 14090, 14543, 1, 14737, 14548])).
% 2.23/2.45 tff(14769,plain,
% 2.23/2.45 (r(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[255, 14768, 14513])).
% 2.23/2.45 tff(14770,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[6824, 14769, 14071])).
% 2.23/2.45 tff(14771,plain,
% 2.23/2.45 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14072])).
% 2.23/2.45 tff(14772,plain,
% 2.23/2.45 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.45 tff(14773,plain,
% 2.23/2.45 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.23/2.45 inference(transitivity,[status(thm)],[14772, 14771])).
% 2.23/2.45 tff(14774,plain,
% 2.23/2.45 ((~r(s(s(z)), s(z))) <=> (~r(s(elem!1), elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14773])).
% 2.23/2.45 tff(14775,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[1224])).
% 2.23/2.45 tff(14776,plain,
% 2.23/2.45 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(symmetry,[status(thm)],[14775])).
% 2.23/2.45 tff(14777,plain,
% 2.23/2.45 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), s(elem!1)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[4272])).
% 2.23/2.45 tff(14778,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 2.23/2.45 tff(14779,plain,
% 2.23/2.45 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11605, 121, 110, 14778])).
% 2.23/2.45 tff(14780,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14779, 2386])).
% 2.23/2.45 tff(14781,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14780, 14777])).
% 2.23/2.45 tff(14782,plain,
% 2.23/2.45 (b(s(s(s(z))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1816, 14781, 2033])).
% 2.23/2.45 tff(14783,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14782, 14776])).
% 2.23/2.45 tff(14784,plain,
% 2.23/2.45 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.23/2.45 inference(symmetry,[status(thm)],[4275])).
% 2.23/2.45 tff(14785,plain,
% 2.23/2.45 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14784])).
% 2.23/2.45 tff(14786,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(14787,plain,
% 2.23/2.45 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(14788,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14787])).
% 2.23/2.45 tff(14789,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[14788, 14786])).
% 2.23/2.45 tff(14790,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(14791,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14790, 14789])).
% 2.23/2.45 tff(14792,plain,
% 2.23/2.45 (~r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14791, 121, 110, 909, 14778])).
% 2.23/2.45 tff(14793,plain,
% 2.23/2.45 (~r(s(elem!1), z)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14792, 14785])).
% 2.23/2.45 tff(14794,plain,
% 2.23/2.45 (b(s(elem!1), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[409, 14793])).
% 2.23/2.45 tff(14795,plain,
% 2.23/2.45 (~b(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3324, 14794, 588, 307])).
% 2.23/2.45 tff(14796,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14795, 14783])).
% 2.23/2.45 tff(14797,plain,((~r(s(z), z)) | (~(elem!1 = s(z))) | (s(s(s(z))) = s(elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14798,plain,
% 2.23/2.45 (~r(s(s(z)), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14797, 14769, 110, 14544, 14096, 14555, 14543, 14547])).
% 2.23/2.45 tff(14799,plain,
% 2.23/2.45 (~r(s(elem!1), elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14798, 14774])).
% 2.23/2.45 tff(14800,plain,
% 2.23/2.45 (b(s(elem!1), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2243, 14799, 2207])).
% 2.23/2.45 tff(14801,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10472, 14800, 14090, 14546, 14767])).
% 2.23/2.45 tff(14802,plain,
% 2.23/2.45 (~r(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2125, 14801, 14770, 14545])).
% 2.23/2.45 tff(14803,plain,
% 2.23/2.45 (~(elem!1 = s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2479, 2469, 307])).
% 2.23/2.45 tff(14804,plain,
% 2.23/2.45 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[78, 14803])).
% 2.23/2.45 tff(14805,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[681, 14804, 675])).
% 2.23/2.45 tff(14806,plain,
% 2.23/2.45 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[614, 14804])).
% 2.23/2.45 tff(14807,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[556, 14806, 2469])).
% 2.23/2.45 tff(14808,plain,
% 2.23/2.45 (~(s(elem!1) = s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[210, 14806])).
% 2.23/2.45 tff(14809,plain,
% 2.23/2.45 (~(s(s(elem!1)) = s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[620, 14808])).
% 2.23/2.45 tff(14810,plain,
% 2.23/2.45 (~(s(s(elem!1)) = elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[197, 14803])).
% 2.23/2.45 tff(14811,plain,
% 2.23/2.45 (~b(z, elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4598, 2618, 394, 307])).
% 2.23/2.45 tff(14812,plain,
% 2.23/2.45 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3310, 14807, 14811, 331, 14810, 2344, 14804])).
% 2.23/2.45 tff(14813,plain,
% 2.23/2.45 (b(elem!1, s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[599, 14812, 14803])).
% 2.23/2.45 tff(14814,plain,
% 2.23/2.45 (~b(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3324, 14813, 307, 394])).
% 2.23/2.45 tff(14815,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[701, 14814, 14809])).
% 2.23/2.45 tff(14816,plain,
% 2.23/2.45 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3132, 14815, 14807, 14805])).
% 2.23/2.45 tff(14817,plain,
% 2.23/2.45 (~(s(s(s(elem!1))) = elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2830, 14805, 2344])).
% 2.23/2.45 tff(14818,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[486, 14817, 147])).
% 2.23/2.45 tff(14819,plain,
% 2.23/2.45 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2930, 271, 307, 2618, 14818])).
% 2.23/2.45 tff(14820,plain,
% 2.23/2.45 (s(elem!1) = s(s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2293, 21, 14819, 14816])).
% 2.23/2.45 tff(14821,plain,
% 2.23/2.45 (s(s(s(elem!1))) = s(elem!1)),
% 2.23/2.45 inference(symmetry,[status(thm)],[14820])).
% 2.23/2.45 tff(14822,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14804, 14821])).
% 2.23/2.45 tff(14823,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | (z = elem!1) | r(elem!1, s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14824,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14823, 14800, 14543, 331, 14735, 2469, 2344, 14766])).
% 2.23/2.45 tff(14825,plain,
% 2.23/2.45 (~b(elem!1, s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12887, 14824, 14543, 14800])).
% 2.23/2.45 tff(14826,plain,
% 2.23/2.45 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8233, 14825, 14071])).
% 2.23/2.45 tff(14827,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[760, 14826, 14802])).
% 2.23/2.45 tff(14828,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (z = elem!1) | r(elem!1, s(elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14829,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14828, 2344, 331, 110, 1, 3407, 199])).
% 2.23/2.45 tff(14830,plain,
% 2.23/2.45 (~b(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14708, 14829, 3407, 110, 14096, 14544, 14085, 14543])).
% 2.23/2.45 tff(14831,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[486, 14830, 13588])).
% 2.23/2.45 tff(14832,plain,
% 2.23/2.45 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[6958, 14831, 1243, 1, 563, 14087])).
% 2.23/2.45 tff(14833,plain,
% 2.23/2.45 (b(s(s(elem!1)), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[862, 14832, 14085])).
% 2.23/2.45 tff(14834,plain,
% 2.23/2.45 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14075, 14077])).
% 2.23/2.45 tff(14835,plain,
% 2.23/2.45 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.45 inference(transitivity,[status(thm)],[14834, 14559])).
% 2.23/2.45 tff(14836,plain,
% 2.23/2.45 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14835])).
% 2.23/2.45 tff(14837,plain,
% 2.23/2.45 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[1489, 14836])).
% 2.23/2.45 tff(14838,plain,
% 2.23/2.45 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14078])).
% 2.23/2.45 tff(14839,plain,
% 2.23/2.45 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.45 inference(symmetry,[status(thm)],[14838])).
% 2.23/2.45 tff(14840,plain,
% 2.23/2.45 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14839])).
% 2.23/2.45 tff(14841,plain,
% 2.23/2.45 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3049, 14071])).
% 2.23/2.45 tff(14842,plain,
% 2.23/2.45 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14841, 14840])).
% 2.23/2.45 tff(14843,plain,
% 2.23/2.45 (~r(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14112, 14832, 14071])).
% 2.23/2.45 tff(14844,plain,
% 2.23/2.45 (b(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[255, 14843, 14513])).
% 2.23/2.45 tff(14845,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3288, 14844, 14543, 14735])).
% 2.23/2.45 tff(14846,plain,
% 2.23/2.45 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1816, 14845, 14555])).
% 2.23/2.45 tff(14847,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14846, 14551])).
% 2.23/2.45 tff(14848,plain,
% 2.23/2.45 (b(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8109, 257, 223])).
% 2.23/2.45 tff(14849,plain,
% 2.23/2.45 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[3547])).
% 2.23/2.45 tff(14850,plain,
% 2.23/2.45 (~(s(elem!1) = s(s(s(z))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[2033, 14849])).
% 2.23/2.45 tff(14851,plain,
% 2.23/2.45 (~r(s(elem!1), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10701, 3290, 1441, 1140])).
% 2.23/2.45 tff(14852,plain,
% 2.23/2.45 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2042, 21, 14851])).
% 2.23/2.45 tff(14853,plain,
% 2.23/2.45 (b(s(elem!1), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14852, 14850])).
% 2.23/2.45 tff(14854,plain,
% 2.23/2.45 (~r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1508, 3290, 909, 1140])).
% 2.23/2.45 tff(14855,plain,
% 2.23/2.45 (b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[105, 14854])).
% 2.23/2.45 tff(14856,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3877, 271, 14855, 14853, 446, 257])).
% 2.23/2.45 tff(14857,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~r(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14858,plain,
% 2.23/2.45 (~r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14857, 14108, 307, 394, 257, 14738, 7853, 909])).
% 2.23/2.45 tff(14859,plain,
% 2.23/2.45 (b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1214, 14858])).
% 2.23/2.45 tff(14860,plain,
% 2.23/2.45 (~b(s(elem!1), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2029, 14859, 394, 14848])).
% 2.23/2.45 tff(14861,plain,
% 2.23/2.45 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2369, 14860, 1222])).
% 2.23/2.45 tff(14862,plain,
% 2.23/2.45 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[526, 14861, 216])).
% 2.23/2.45 tff(14863,plain,
% 2.23/2.45 (b(s(elem!1), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2243, 14150, 8337])).
% 2.23/2.45 tff(14864,plain,
% 2.23/2.45 (~b(elem!1, s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12887, 14863, 307, 638])).
% 2.23/2.45 tff(14865,plain,
% 2.23/2.45 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8233, 14864, 223])).
% 2.23/2.45 tff(14866,plain,
% 2.23/2.45 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[760, 14865])).
% 2.23/2.45 tff(14867,plain,
% 2.23/2.45 (r(elem!1, s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1045, 14866, 223])).
% 2.23/2.45 tff(14868,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[13723, 14867, 378, 139])).
% 2.23/2.45 tff(14869,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8229, 14868])).
% 2.23/2.45 tff(14870,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[638, 14758])).
% 2.23/2.45 tff(14871,plain,
% 2.23/2.45 (~b(z, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1648, 14870, 14756, 14869])).
% 2.23/2.45 tff(14872,plain,
% 2.23/2.45 (r(z, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1658, 14871])).
% 2.23/2.45 tff(14873,plain,
% 2.23/2.45 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[6368, 14872, 14862, 14108])).
% 2.23/2.45 tff(14874,plain,
% 2.23/2.45 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11865, 14872, 14738, 394, 909])).
% 2.23/2.45 tff(14875,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4138, 14874, 14873, 4962])).
% 2.23/2.45 tff(14876,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14877,plain,
% 2.23/2.45 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14876, 14735, 14096, 14071, 1243, 14831, 211, 14543, 14844, 14087, 3407])).
% 2.23/2.45 tff(14878,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[681, 14877, 14090])).
% 2.23/2.45 tff(14879,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14075, 14076])).
% 2.23/2.45 tff(14880,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[14879])).
% 2.23/2.45 tff(14881,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14829, 14880])).
% 2.23/2.45 tff(14882,plain,
% 2.23/2.45 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[1038, 1037])).
% 2.23/2.45 tff(14883,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[14882])).
% 2.23/2.45 tff(14884,plain,
% 2.23/2.45 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14883])).
% 2.23/2.45 tff(14885,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(14886,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(14887,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14886, 14885])).
% 2.23/2.45 tff(14888,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14887, 121, 622, 684, 683])).
% 2.23/2.45 tff(14889,plain,
% 2.23/2.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14888, 14884])).
% 2.23/2.45 tff(14890,plain,
% 2.23/2.45 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2697, 622, 378, 139, 6656])).
% 2.23/2.45 tff(14891,plain,
% 2.23/2.45 (b(elem!1, s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[599, 14890, 5038])).
% 2.23/2.45 tff(14892,plain,
% 2.23/2.45 (b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[6679, 14891, 1222])).
% 2.23/2.45 tff(14893,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.45 tff(14894,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[684, 1372])).
% 2.23/2.45 tff(14895,plain,
% 2.23/2.45 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[223])).
% 2.23/2.45 tff(14896,plain,
% 2.23/2.45 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.23/2.45 inference(symmetry,[status(thm)],[14895])).
% 2.23/2.45 tff(14897,plain,
% 2.23/2.45 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[1036])).
% 2.23/2.45 tff(14898,plain,
% 2.23/2.45 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.23/2.45 inference(symmetry,[status(thm)],[14897])).
% 2.23/2.45 tff(14899,plain,
% 2.23/2.45 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.23/2.45 inference(transitivity,[status(thm)],[14898, 14896])).
% 2.23/2.45 tff(14900,plain,
% 2.23/2.45 (r(s(s(z)), s(z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[622, 14899])).
% 2.23/2.45 tff(14901,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4675, 14900, 110, 14894])).
% 2.23/2.45 tff(14902,plain,
% 2.23/2.45 (~r(s(s(s(s(z)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1238, 14901, 223])).
% 2.23/2.45 tff(14903,plain,
% 2.23/2.45 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[932, 14902])).
% 2.23/2.45 tff(14904,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(14905,plain,
% 2.23/2.45 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(14906,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[14905])).
% 2.23/2.45 tff(14907,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[14906, 14904])).
% 2.23/2.45 tff(14908,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(14909,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14908, 14907])).
% 2.23/2.45 tff(14910,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14909, 271, 3871, 937, 13508, 14893])).
% 2.23/2.45 tff(14911,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14912,plain,
% 2.23/2.45 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14911, 14903, 14893, 14892])).
% 2.23/2.45 tff(14913,plain,
% 2.23/2.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10426, 14912])).
% 2.23/2.45 tff(14914,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14913, 14889])).
% 2.23/2.45 tff(14915,plain,((~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(14916,plain,
% 2.23/2.45 (~r(s(elem!1), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14915, 14881, 14071, 110, 14878, 14847, 1243, 14831])).
% 2.23/2.45 tff(14917,plain,
% 2.23/2.45 (b(s(elem!1), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2243, 14916, 2207])).
% 2.23/2.45 tff(14918,plain,
% 2.23/2.45 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14623, 271, 14543, 14917, 14833])).
% 2.23/2.45 tff(14919,plain,
% 2.23/2.45 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[526, 14918, 211])).
% 2.23/2.45 tff(14920,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(14921,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(14922,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[14921, 14920])).
% 2.23/2.45 tff(14923,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14922, 121, 14878, 14919, 14847])).
% 2.23/2.46 tff(14924,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[586, 14923, 563])).
% 2.23/2.46 tff(14925,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14926,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14927,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14926, 14925])).
% 2.23/2.46 tff(14928,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14927, 121, 378, 1409, 10184])).
% 2.23/2.46 tff(14929,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[3089, 21, 812, 14928])).
% 2.23/2.46 tff(14930,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14931,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(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))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14932,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(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)))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14931, 14930])).
% 2.23/2.46 tff(14933,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14932, 121, 1409, 139, 10184])).
% 2.23/2.46 tff(14934,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8221, 14933, 1591])).
% 2.23/2.46 tff(14935,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14936,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14937,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14936, 14935])).
% 2.23/2.46 tff(14938,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14937, 271, 589, 3407, 14934, 14929])).
% 2.23/2.46 tff(14939,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(14940,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14939, 14924, 3407, 1577, 14087, 14831, 1243])).
% 2.23/2.46 tff(14941,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10196, 14940, 14842])).
% 2.23/2.46 tff(14942,plain,
% 2.23/2.46 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10204, 14941, 14543, 14837, 14833])).
% 2.23/2.46 tff(14943,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14944,plain,
% 2.23/2.46 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14945,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14944])).
% 2.23/2.46 tff(14946,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[14945, 14943])).
% 2.23/2.46 tff(14947,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14948,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14947, 14946])).
% 2.23/2.46 tff(14949,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14948, 121, 14919, 14847, 14942])).
% 2.23/2.46 tff(14950,plain,
% 2.23/2.46 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14949, 14081])).
% 2.23/2.46 tff(14951,plain,
% 2.23/2.46 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14072])).
% 2.23/2.46 tff(14952,plain,
% 2.23/2.46 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14951])).
% 2.23/2.46 tff(14953,plain,
% 2.23/2.46 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[877, 14952])).
% 2.23/2.46 tff(14954,plain,
% 2.23/2.46 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.46 tff(14955,plain,
% 2.23/2.46 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.23/2.46 inference(symmetry,[status(thm)],[14954])).
% 2.23/2.46 tff(14956,plain,
% 2.23/2.46 (b(s(elem!1), s(z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14917, 14955])).
% 2.23/2.46 tff(14957,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14075])).
% 2.23/2.46 tff(14958,plain,
% 2.23/2.46 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[14957])).
% 2.23/2.46 tff(14959,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14829, 14958])).
% 2.23/2.46 tff(14960,plain,
% 2.23/2.46 (b(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8109, 14844, 14071])).
% 2.23/2.46 tff(14961,plain,
% 2.23/2.46 (~r(s(s(s(elem!1))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[13798, 121, 1243, 14087, 14831])).
% 2.23/2.46 tff(14962,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8229, 14961])).
% 2.23/2.46 tff(14963,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14964,plain,
% 2.23/2.46 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14965,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14964])).
% 2.23/2.46 tff(14966,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.23/2.46 inference(transitivity,[status(thm)],[14965, 14963])).
% 2.23/2.46 tff(14967,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14968,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14967, 14966])).
% 2.23/2.46 tff(14969,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14968, 271, 750, 2073, 222, 1638])).
% 2.23/2.46 tff(14970,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(14971,plain,
% 2.23/2.46 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14970, 14962, 14960, 14959])).
% 2.23/2.46 tff(14972,plain,
% 2.23/2.46 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[760, 14971])).
% 2.23/2.46 tff(14973,plain,
% 2.23/2.46 (~b(z, s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1921, 14924, 110, 14829, 14972])).
% 2.23/2.46 tff(14974,plain,
% 2.23/2.46 (r(z, s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2106, 14973])).
% 2.23/2.46 tff(14975,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14976,plain,
% 2.23/2.46 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14977,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14976])).
% 2.23/2.46 tff(14978,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[14977, 14975])).
% 2.23/2.46 tff(14979,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14980,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14979, 14978])).
% 2.23/2.46 tff(14981,plain,
% 2.23/2.46 (~r(z, s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14980, 121, 14919, 14974, 14847])).
% 2.23/2.46 tff(14982,plain,
% 2.23/2.46 (b(z, s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1439, 14981])).
% 2.23/2.46 tff(14983,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14984,plain,
% 2.23/2.46 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14985,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14984])).
% 2.23/2.46 tff(14986,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[14985, 14983])).
% 2.23/2.46 tff(14987,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14988,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14987, 14986])).
% 2.23/2.46 tff(14989,plain,
% 2.23/2.46 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14988, 121, 2088, 683])).
% 2.23/2.46 tff(14990,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14989, 11392, 14672])).
% 2.23/2.46 tff(14991,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(14992,plain,
% 2.23/2.46 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14991, 14942, 14071, 14847, 14974])).
% 2.23/2.46 tff(14993,plain,
% 2.23/2.46 (b(z, s(s(s(s(s(z))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1658, 14992])).
% 2.23/2.46 tff(14994,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14995,plain,
% 2.23/2.46 (((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(14996,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14995])).
% 2.23/2.46 tff(14997,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[14996, 14994])).
% 2.23/2.46 tff(14998,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(14999,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[14998, 14997])).
% 2.23/2.46 tff(15000,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14999, 271, 447, 1421, 1639, 9894])).
% 2.23/2.46 tff(15001,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(15002,plain,
% 2.23/2.46 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[15001, 14993, 14982, 14956])).
% 2.23/2.46 tff(15003,plain,
% 2.23/2.46 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[4138, 15002, 14953])).
% 2.23/2.46 tff(15004,plain,
% 2.23/2.46 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[4270, 15003, 14544])).
% 2.23/2.46 tff(15005,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[15004, 14950])).
% 2.23/2.46 tff(15006,plain,(r(elem!1, s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(15007,plain,
% 2.23/2.46 (r(elem!1, s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[15006, 199, 110, 1, 331, 3407])).
% 2.23/2.46 tff(15008,plain,
% 2.23/2.46 (~r(s(elem!1), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1417, 15007, 14087, 14096])).
% 2.23/2.46 tff(15009,plain,
% 2.23/2.46 (b(s(elem!1), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[409, 15008])).
% 2.23/2.46 tff(15010,plain,
% 2.23/2.46 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[14071])).
% 2.23/2.46 tff(15011,plain,
% 2.23/2.46 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.23/2.46 inference(symmetry,[status(thm)],[15010])).
% 2.23/2.46 tff(15012,plain,
% 2.23/2.46 (r(s(z), s(elem!1))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[15007, 15011])).
% 2.23/2.46 tff(15013,plain,
% 2.23/2.46 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14398, 15012, 14071, 1243, 1, 13588, 3407, 110, 14096, 15007, 344])).
% 2.23/2.46 tff(15014,plain,
% 2.23/2.46 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[760, 15013])).
% 2.23/2.46 tff(15015,plain,
% 2.23/2.46 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14465, 15014, 1, 15007, 13588, 110, 14071, 3407, 1243, 15012])).
% 2.23/2.46 tff(15016,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[681, 15015, 14090])).
% 2.23/2.46 tff(15017,plain,
% 2.23/2.46 (~b(z, s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14106, 15016, 3407, 15009])).
% 2.23/2.46 tff(15018,plain,
% 2.23/2.46 (r(z, s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1439, 15017])).
% 2.23/2.46 tff(15019,plain,
% 2.23/2.46 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1449, 15018, 1243, 15007])).
% 2.23/2.46 tff(15020,plain,
% 2.23/2.46 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[526, 15019, 211])).
% 2.23/2.46 tff(15021,plain,
% 2.23/2.46 (~r(s(elem!1), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[3387, 15018, 1243, 14087])).
% 2.23/2.46 tff(15022,plain,
% 2.23/2.46 (b(s(elem!1), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2243, 15021, 2207])).
% 2.23/2.46 tff(15023,plain,
% 2.23/2.46 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14147, 15018, 3407, 1, 1243, 344, 14071, 15007, 15016, 14087])).
% 2.23/2.46 tff(15024,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[486, 15023, 13588])).
% 2.23/2.46 tff(15025,plain,
% 2.23/2.46 (r(elem!1, s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10472, 15024, 14090, 15015, 15022])).
% 2.23/2.46 tff(15026,plain,
% 2.23/2.46 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14708, 15024, 3407, 110, 14096, 14544, 14085, 14543])).
% 2.23/2.46 tff(15027,plain,
% 2.23/2.46 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[556, 15026, 1])).
% 2.23/2.46 tff(15028,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[673, 15027, 15025, 14543, 15016, 13588, 15020])).
% 2.23/2.46 tff(15029,plain,(b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(15030,plain,
% 2.23/2.46 (b(z, elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[15029, 331, 3407, 110, 1])).
% 2.23/2.47 tff(15031,plain,
% 2.23/2.47 (~b(s(s(s(elem!1))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[7173, 261, 3407, 15030])).
% 2.23/2.47 tff(15032,plain,
% 2.23/2.47 (s(s(s(elem!1))) = elem!1),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[486, 15031, 147])).
% 2.23/2.47 tff(15033,plain,
% 2.23/2.47 (~b(s(elem!1), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11634, 2618, 15030, 261])).
% 2.23/2.47 tff(15034,plain,
% 2.23/2.47 (r(s(elem!1), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[409, 15033])).
% 2.23/2.47 tff(15035,plain,
% 2.23/2.47 (~b(z, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3747, 271, 2618, 15030, 261])).
% 2.23/2.47 tff(15036,plain,
% 2.23/2.47 (r(z, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1439, 15035])).
% 2.23/2.47 tff(15037,plain,
% 2.23/2.47 (~r(s(z), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12111, 15036, 110, 15034])).
% 2.23/2.47 tff(15038,plain,
% 2.23/2.47 (b(s(z), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[444, 15037, 344])).
% 2.23/2.47 tff(15039,plain,
% 2.23/2.47 (~r(elem!1, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[7179, 676, 2505])).
% 2.23/2.47 tff(15040,plain,
% 2.23/2.47 (b(elem!1, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[392, 15039, 219])).
% 2.23/2.47 tff(15041,plain,
% 2.23/2.47 (~b(s(elem!1), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3415, 15040, 3407, 261])).
% 2.23/2.47 tff(15042,plain,
% 2.23/2.47 (r(s(elem!1), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[409, 15041])).
% 2.23/2.47 tff(15043,plain,
% 2.23/2.47 (~b(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[9079, 260, 1326, 307])).
% 2.23/2.47 tff(15044,plain,
% 2.23/2.47 (~r(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5323, 260, 1326, 412, 307, 348])).
% 2.23/2.47 tff(15045,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[904, 15044, 15043])).
% 2.23/2.47 tff(15046,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(15047,plain,
% 2.23/2.47 (~b(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15046, 15042, 1326, 15040, 348])).
% 2.23/2.47 tff(15048,plain,
% 2.23/2.47 (r(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[236, 15047, 231])).
% 2.23/2.47 tff(15049,plain,
% 2.23/2.47 ((s(s(s(elem!1))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[2505])).
% 2.23/2.47 tff(15050,plain,
% 2.23/2.47 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.23/2.47 inference(symmetry,[status(thm)],[15049])).
% 2.23/2.47 tff(15051,plain,
% 2.23/2.47 ((~(elem!1 = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15050])).
% 2.23/2.47 tff(15052,plain,
% 2.23/2.47 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[219, 15051])).
% 2.23/2.47 tff(15053,plain,
% 2.23/2.47 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[681, 676, 15052])).
% 2.23/2.47 tff(15054,plain,
% 2.23/2.47 (b(s(s(elem!1)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8592, 543, 2505])).
% 2.23/2.47 tff(15055,plain,
% 2.23/2.47 (~b(z, s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5277, 271, 307, 1326, 15054])).
% 2.23/2.47 tff(15056,plain,
% 2.23/2.47 (r(z, s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2106, 15055])).
% 2.23/2.47 tff(15057,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15058,plain,
% 2.23/2.47 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15059,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15058])).
% 2.23/2.47 tff(15060,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15059, 15057])).
% 2.23/2.47 tff(15061,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15062,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15061, 15060])).
% 2.23/2.47 tff(15063,plain,
% 2.23/2.47 (~r(s(elem!1), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15062, 121, 15056, 110, 412])).
% 2.23/2.47 tff(15064,plain,
% 2.23/2.47 (b(s(elem!1), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[429, 15063, 422])).
% 2.23/2.47 tff(15065,plain,
% 2.23/2.47 (~b(s(s(elem!1)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5267, 543, 3407, 638])).
% 2.23/2.47 tff(15066,plain,
% 2.23/2.47 (r(s(s(elem!1)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2430, 15065])).
% 2.23/2.47 tff(15067,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15068,plain,
% 2.23/2.47 (((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15069,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15068])).
% 2.23/2.47 tff(15070,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15069, 15067])).
% 2.23/2.47 tff(15071,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15072,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15071, 15070])).
% 2.23/2.47 tff(15073,plain,
% 2.23/2.47 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15072, 121, 15056, 412, 15066])).
% 2.23/2.47 tff(15074,plain,
% 2.23/2.47 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[526, 15073, 216])).
% 2.23/2.47 tff(15075,plain,
% 2.23/2.47 (~r(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11783, 15056, 110, 15066])).
% 2.23/2.47 tff(15076,plain,
% 2.23/2.47 (b(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2167, 15075])).
% 2.23/2.47 tff(15077,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15078,plain,
% 2.23/2.47 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15079,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15078])).
% 2.23/2.47 tff(15080,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15079, 15077])).
% 2.23/2.47 tff(15081,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15082,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15081, 15080])).
% 2.23/2.47 tff(15083,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15082, 271, 15076, 15074, 15064, 15054])).
% 2.23/2.47 tff(15084,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(15085,plain,
% 2.23/2.47 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15084, 15042, 211, 2282, 110, 15040, 1326, 2505, 3407, 15053])).
% 2.23/2.47 tff(15086,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[556, 15085, 1])).
% 2.23/2.47 tff(15087,plain,
% 2.23/2.47 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[2505])).
% 2.23/2.47 tff(15088,plain,
% 2.23/2.47 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[15087])).
% 2.23/2.47 tff(15089,plain,
% 2.23/2.47 (b(elem!1, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[392, 2344, 8336])).
% 2.23/2.47 tff(15090,plain,
% 2.23/2.47 (r(s(s(elem!1)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2511, 623, 2505])).
% 2.23/2.47 tff(15091,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 2.23/2.47 tff(15092,plain,
% 2.23/2.47 (b(s(elem!1), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2243, 15091, 8337])).
% 2.23/2.47 tff(15093,plain,
% 2.23/2.47 (b(s(elem!1), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2243, 3500, 15091])).
% 2.23/2.47 tff(15094,plain,
% 2.23/2.47 (b(elem!1, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[392, 377, 2344])).
% 2.23/2.47 tff(15095,plain,
% 2.23/2.47 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15096,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15095])).
% 2.23/2.47 tff(15097,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15096, 4601])).
% 2.23/2.47 tff(15098,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15099,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15098, 15097])).
% 2.23/2.47 tff(15100,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15099, 271, 15094, 15093, 1326, 1421])).
% 2.23/2.47 tff(15101,plain,((elem!1 = s(elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(15102,plain,
% 2.23/2.47 (~b(z, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15101, 15091, 8336, 1326, 2344])).
% 2.23/2.47 tff(15103,plain,
% 2.23/2.47 (r(z, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1439, 15102])).
% 2.23/2.47 tff(15104,plain,
% 2.23/2.47 (~r(s(z), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12111, 15103, 110, 412])).
% 2.23/2.47 tff(15105,plain,
% 2.23/2.47 (b(s(z), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[444, 15104, 348])).
% 2.23/2.47 tff(15106,plain,
% 2.23/2.47 (~b(elem!1, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3019, 15105, 15089, 15092])).
% 2.23/2.47 tff(15107,plain,
% 2.23/2.47 (r(elem!1, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[299, 15106, 243])).
% 2.23/2.47 tff(15108,plain,
% 2.23/2.47 (~b(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[4613, 15092, 1326, 15089, 348])).
% 2.23/2.47 tff(15109,plain,
% 2.23/2.47 (r(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[236, 15108, 231])).
% 2.23/2.47 tff(15110,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15111,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15112,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15111, 15110])).
% 2.23/2.47 tff(15113,plain,
% 2.23/2.47 (~r(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15112, 121, 15109, 15107, 15090])).
% 2.23/2.47 tff(15114,plain,
% 2.23/2.47 (b(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2143, 15113])).
% 2.23/2.47 tff(15115,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15116,plain,
% 2.23/2.47 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15117,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15116])).
% 2.23/2.47 tff(15118,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15117, 15115])).
% 2.23/2.47 tff(15119,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15120,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15119, 15118])).
% 2.23/2.47 tff(15121,plain,
% 2.23/2.47 (~r(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15120, 121, 15109, 15107, 15090])).
% 2.23/2.47 tff(15122,plain,
% 2.23/2.47 (b(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2167, 15121])).
% 2.23/2.47 tff(15123,plain,
% 2.23/2.47 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2562, 15108, 2505])).
% 2.23/2.47 tff(15124,plain,
% 2.23/2.47 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[760, 15123])).
% 2.23/2.47 tff(15125,plain,
% 2.23/2.47 (r(s(s(s(elem!1))), s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[15107, 12805])).
% 2.23/2.47 tff(15126,plain,
% 2.23/2.47 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[13328, 15125, 3504, 15124, 623])).
% 2.23/2.47 tff(15127,plain,
% 2.23/2.47 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15087])).
% 2.23/2.47 tff(15128,plain,
% 2.23/2.47 (~r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[906, 15127])).
% 2.23/2.47 tff(15129,plain,
% 2.23/2.47 (b(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[255, 15128, 907])).
% 2.23/2.47 tff(15130,plain,
% 2.23/2.47 (~b(s(elem!1), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[13140, 15129, 412, 1140, 307, 2033])).
% 2.23/2.47 tff(15131,plain,
% 2.23/2.47 (r(s(elem!1), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2243, 15130, 8337])).
% 2.23/2.47 tff(15132,plain,
% 2.23/2.47 (~r(s(elem!1), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11219, 121, 15131, 357, 3456])).
% 2.23/2.47 tff(15133,plain,
% 2.23/2.47 (b(s(elem!1), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[429, 15132, 422])).
% 2.23/2.47 tff(15134,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15135,plain,
% 2.23/2.47 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15136,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15135])).
% 2.23/2.47 tff(15137,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15136, 15134])).
% 2.23/2.47 tff(15138,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15139,plain,
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% 2.23/2.47 inference(modus_ponens,[status(thm)],[15138, 15137])).
% 2.23/2.47 tff(15140,plain,
% 2.23/2.47 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[15139, 121, 15131, 3456, 2512])).
% 2.23/2.47 tff(15141,plain,
% 2.23/2.47 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[526, 15140, 216])).
% 2.23/2.47 tff(15142,plain,
% 2.23/2.47 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(15143,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15142])).
% 2.23/2.47 tff(15144,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[15143, 2169])).
% 2.23/2.47 tff(15145,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(15146,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15145, 15144])).
% 2.23/2.48 tff(15147,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15146, 271, 505, 15141, 15133, 981])).
% 2.23/2.48 tff(15148,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15149,plain,
% 2.23/2.48 (~r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15148, 15126, 2505, 216, 2282, 412, 15109, 15122, 15107, 15089, 2597, 2612, 15114, 623])).
% 2.23/2.48 tff(15150,plain,
% 2.23/2.48 (b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1214, 15149])).
% 2.23/2.48 tff(15151,plain,
% 2.23/2.48 (~b(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1978, 15150, 1326, 15089])).
% 2.23/2.48 tff(15152,plain,
% 2.23/2.48 (r(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[255, 15151, 2612])).
% 2.23/2.48 tff(15153,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15152, 15088])).
% 2.23/2.48 tff(15154,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15126, 15153])).
% 2.23/2.48 tff(15155,plain,(r(s(elem!1), elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (s(z) = elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15156,plain,
% 2.23/2.48 (r(s(elem!1), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15155, 15042, 1326, 211, 2505, 15086, 348, 110, 231, 15039])).
% 2.23/2.48 tff(15157,plain,
% 2.23/2.48 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15088])).
% 2.23/2.48 tff(15158,plain,
% 2.23/2.48 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(elem!1, s(z)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12804])).
% 2.23/2.48 tff(15159,plain,
% 2.23/2.48 (~b(s(z), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12145, 220, 1326, 261])).
% 2.23/2.48 tff(15160,plain,
% 2.23/2.48 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2562, 15159, 2505])).
% 2.23/2.48 tff(15161,plain,
% 2.23/2.48 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[760, 15160])).
% 2.23/2.48 tff(15162,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[145, 15088])).
% 2.23/2.48 tff(15163,plain,
% 2.23/2.48 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13328, 15162, 944, 15161, 623])).
% 2.23/2.48 tff(15164,plain,
% 2.23/2.48 (~r(elem!1, s(z))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15163, 15158])).
% 2.23/2.48 tff(15165,plain,
% 2.23/2.48 (b(elem!1, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[297, 21, 15164, 258])).
% 2.23/2.48 tff(15166,plain,
% 2.23/2.48 (~b(s(elem!1), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3415, 307, 3407, 261])).
% 2.23/2.48 tff(15167,plain,
% 2.23/2.48 (r(s(elem!1), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[409, 15166])).
% 2.23/2.48 tff(15168,plain,
% 2.23/2.48 (~b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11002, 15165, 1326, 220])).
% 2.23/2.48 tff(15169,plain,
% 2.23/2.48 (r(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[105, 15168])).
% 2.23/2.48 tff(15170,plain,
% 2.23/2.48 (~r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3375, 15169, 145, 110])).
% 2.23/2.48 tff(15171,plain,
% 2.23/2.48 (b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1214, 15170])).
% 2.23/2.48 tff(15172,plain,
% 2.23/2.48 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[5677])).
% 2.23/2.48 tff(15173,plain,
% 2.23/2.48 (~r(elem!1, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9831, 15169, 357, 145])).
% 2.23/2.48 tff(15174,plain,
% 2.23/2.48 (b(elem!1, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1192, 15173, 11082])).
% 2.23/2.48 tff(15175,plain,
% 2.23/2.48 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15174, 15172])).
% 2.23/2.48 tff(15176,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5687, 15175, 3407, 15171])).
% 2.23/2.48 tff(15177,plain,
% 2.23/2.48 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1816, 15176, 2597])).
% 2.23/2.48 tff(15178,plain,
% 2.23/2.48 (s(s(s(s(s(z))))) = elem!1),
% 2.23/2.48 inference(symmetry,[status(thm)],[4998])).
% 2.23/2.48 tff(15179,plain,
% 2.23/2.48 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[15178, 2590])).
% 2.23/2.48 tff(15180,plain,
% 2.23/2.48 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15179])).
% 2.23/2.48 tff(15181,plain,
% 2.23/2.48 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.23/2.48 inference(transitivity,[status(thm)],[872, 15180, 55])).
% 2.23/2.48 tff(15182,plain,
% 2.23/2.48 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15181])).
% 2.23/2.48 tff(15183,plain,
% 2.23/2.48 (s(s(s(z))) = s(elem!1)),
% 2.23/2.48 inference(transitivity,[status(thm)],[775, 15182, 604])).
% 2.23/2.48 tff(15184,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2033, 15183])).
% 2.23/2.48 tff(15185,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (s(s(s(z))) = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15186,plain,
% 2.23/2.48 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15185, 2505, 2597])).
% 2.23/2.48 tff(15187,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15188,plain,
% 2.23/2.48 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15189,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15188])).
% 2.23/2.48 tff(15190,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[15189, 15187])).
% 2.23/2.48 tff(15191,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(15192,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15191, 15190])).
% 2.23/2.48 tff(15193,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15192, 121, 622, 1826, 145, 1500])).
% 2.23/2.48 tff(15194,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15195,plain,
% 2.23/2.48 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15194, 145, 622, 15177])).
% 2.23/2.48 tff(15196,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1847, 15195, 15186])).
% 2.23/2.48 tff(15197,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15198,plain,
% 2.23/2.48 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15199,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15198])).
% 2.23/2.48 tff(15200,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[15199, 15197])).
% 2.23/2.48 tff(15201,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(15202,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15201, 15200])).
% 2.23/2.48 tff(15203,plain,
% 2.23/2.48 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15202, 121, 1500, 1736, 108])).
% 2.23/2.48 tff(15204,plain,
% 2.23/2.48 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1756, 15203])).
% 2.23/2.48 tff(15205,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~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))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15206,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~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))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(15207,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~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)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15206, 15205])).
% 2.23/2.48 tff(15208,plain,
% 2.23/2.48 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15207, 121, 1500, 1736, 108])).
% 2.23/2.48 tff(15209,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1682, 15208])).
% 2.23/2.48 tff(15210,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15211,plain,
% 2.23/2.48 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15212,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15211])).
% 2.23/2.48 tff(15213,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[15212, 15210])).
% 2.23/2.48 tff(15214,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(15215,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15214, 15213])).
% 2.23/2.48 tff(15216,plain,
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% 2.23/2.48 inference(unit_resolution,[status(thm)],[15215, 271, 448, 1849, 15209, 15204])).
% 2.23/2.48 tff(15217,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15218,plain,
% 2.23/2.48 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15217, 1849, 448, 108, 1500])).
% 2.23/2.48 tff(15219,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1733, 15218])).
% 2.23/2.48 tff(15220,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15221,plain,
% 2.23/2.48 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15222,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15221])).
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% 2.23/2.48 inference(transitivity,[status(thm)],[15222, 15220])).
% 2.23/2.48 tff(15224,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
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% 2.23/2.48 inference(modus_ponens,[status(thm)],[15224, 15223])).
% 2.23/2.48 tff(15226,plain,
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% 2.23/2.48 inference(unit_resolution,[status(thm)],[15225, 271, 261, 1849, 1639, 15219])).
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% 2.23/2.48 tff(15228,plain,
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% 2.23/2.48 tff(15229,plain,
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% 2.23/2.48 inference(unit_resolution,[status(thm)],[1658, 15228])).
% 2.23/2.48 tff(15230,plain,
% 2.23/2.48 (~r(s(z), s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[4785, 15229, 110, 15167])).
% 2.23/2.48 tff(15231,plain,
% 2.23/2.48 (b(s(z), s(elem!1))),
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% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15233,plain,
% 2.23/2.48 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
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% 2.23/2.48 inference(monotonicity,[status(thm)],[15233])).
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% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[15234, 15232])).
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% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
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% 2.23/2.48 inference(modus_ponens,[status(thm)],[15236, 15235])).
% 2.23/2.48 tff(15238,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15237, 121, 110, 412, 1661, 411])).
% 2.23/2.48 tff(15239,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15240,plain,
% 2.23/2.48 (~r(s(elem!1), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15239, 15229, 15167, 110])).
% 2.23/2.48 tff(15241,plain,
% 2.23/2.48 (b(s(elem!1), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[429, 15240, 2282])).
% 2.23/2.48 tff(15242,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[456, 15241, 15231, 307, 15165])).
% 2.23/2.48 tff(15243,plain,((~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(15244,plain,
% 2.23/2.48 (~r(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[15243, 623, 348, 110, 261, 622, 3407, 2505, 357, 1326, 220, 258, 944, 307])).
% 2.23/2.48 tff(15245,plain,
% 2.23/2.48 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15244, 15157])).
% 2.23/2.48 tff(15246,plain,
% 2.23/2.48 (b(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[255, 15244, 2612])).
% 2.23/2.48 tff(15247,plain,
% 2.23/2.48 (~b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1978, 15246, 1326, 307])).
% 2.23/2.48 tff(15248,plain,
% 2.23/2.48 (r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1214, 15247])).
% 2.23/2.48 tff(15249,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15250,plain,
% 2.23/2.48 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(15251,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15250])).
% 2.23/2.48 tff(15252,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[15251, 15249])).
% 2.23/2.48 tff(15253,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(15254,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[15253, 15252])).
% 2.23/2.48 tff(15255,plain,
% 2.23/2.48 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15254, 121, 110, 412, 411, 1140])).
% 2.23/2.49 tff(15256,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15257,plain,
% 2.23/2.49 (~r(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15256, 15248, 110, 15167])).
% 2.23/2.49 tff(15258,plain,
% 2.23/2.49 (b(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[429, 15257, 2282])).
% 2.23/2.49 tff(15259,plain,
% 2.23/2.49 (~b(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[4122, 15258, 1326, 307])).
% 2.23/2.49 tff(15260,plain,
% 2.23/2.49 (r(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1439, 15259])).
% 2.23/2.49 tff(15261,plain,
% 2.23/2.49 (~r(s(z), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12111, 15260, 110, 15167])).
% 2.23/2.49 tff(15262,plain,
% 2.23/2.49 (b(s(z), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[444, 15261, 348])).
% 2.23/2.49 tff(15263,plain,
% 2.23/2.49 (~b(elem!1, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[456, 15262, 307, 15258])).
% 2.23/2.49 tff(15264,plain,
% 2.23/2.49 (r(elem!1, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[299, 15263, 258])).
% 2.23/2.49 tff(15265,plain,
% 2.23/2.49 (~r(s(s(elem!1)), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15112, 121, 357, 15264, 15090])).
% 2.23/2.49 tff(15266,plain,
% 2.23/2.49 (b(s(s(elem!1)), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2143, 15265])).
% 2.23/2.49 tff(15267,plain,
% 2.23/2.49 (~r(s(z), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15120, 121, 357, 15264, 15090])).
% 2.23/2.49 tff(15268,plain,
% 2.23/2.49 (b(s(z), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2167, 15267])).
% 2.23/2.49 tff(15269,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15148, 15268, 15266, 2505, 216, 2282, 15167, 357, 15264, 15248, 307, 2597, 2612, 15245, 623])).
% 2.23/2.49 tff(15270,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15271,plain,
% 2.23/2.49 (~b(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15270, 15048, 211, 15086, 15040, 243, 348, 110, 1326, 261, 2505, 3407, 15156, 3504])).
% 2.23/2.49 tff(15272,plain,
% 2.23/2.49 (r(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[904, 15271])).
% 2.23/2.49 tff(15273,plain,
% 2.23/2.49 (~b(elem!1, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[9537, 15272, 348, 2282, 15040, 15042, 15048, 110])).
% 2.23/2.49 tff(15274,plain,
% 2.23/2.49 (r(elem!1, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[299, 15273, 243])).
% 2.23/2.49 tff(15275,plain,
% 2.23/2.49 (~r(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1254, 15272, 15042, 15048])).
% 2.23/2.49 tff(15276,plain,
% 2.23/2.49 (b(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[429, 15275, 2282])).
% 2.23/2.49 tff(15277,plain,
% 2.23/2.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[2505])).
% 2.23/2.49 tff(15278,plain,
% 2.23/2.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(elem!1)))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15277, 2211])).
% 2.23/2.49 tff(15279,plain,
% 2.23/2.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = elem!1)),
% 2.23/2.49 inference(transitivity,[status(thm)],[15278, 2212])).
% 2.23/2.49 tff(15280,plain,
% 2.23/2.49 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15279])).
% 2.23/2.49 tff(15281,plain,
% 2.23/2.49 (~(s(s(elem!1)) = elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[1, 15280])).
% 2.23/2.49 tff(15282,plain,
% 2.23/2.49 (~r(s(z), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1300, 15272, 110, 15042])).
% 2.23/2.49 tff(15283,plain,
% 2.23/2.49 (b(s(z), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[444, 15282, 348])).
% 2.23/2.49 tff(15284,plain,
% 2.23/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[5698, 15283, 2505, 1326, 15048, 15272, 9149, 15276])).
% 2.23/2.49 tff(15285,plain,
% 2.23/2.49 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1816, 15284, 2597])).
% 2.23/2.49 tff(15286,plain,
% 2.23/2.49 (~b(s(s(s(z))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[5286, 15285, 2207, 2505, 15042, 1, 1326, 261, 15281, 3504, 15040, 15048, 3841, 15276, 15274, 2612])).
% 2.23/2.49 tff(15287,plain,
% 2.23/2.49 (~r(s(s(s(z))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[5155, 15285, 15042, 15272])).
% 2.23/2.49 tff(15288,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1155, 15287, 15286])).
% 2.23/2.49 tff(15289,plain,(r(s(s(s(elem!1))), s(elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15290,plain,
% 2.23/2.49 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15289, 2505, 1, 15030, 261, 344, 110, 3407, 231])).
% 2.23/2.49 tff(15291,plain,
% 2.23/2.49 (r(elem!1, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2830, 15290, 2505])).
% 2.23/2.49 tff(15292,plain,
% 2.23/2.49 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[2505])).
% 2.23/2.49 tff(15293,plain,
% 2.23/2.49 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 2.23/2.49 inference(symmetry,[status(thm)],[15292])).
% 2.23/2.49 tff(15294,plain,
% 2.23/2.49 (b(s(s(s(elem!1))), z)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[261, 15293])).
% 2.23/2.49 tff(15295,plain,
% 2.23/2.49 (~b(s(s(elem!1)), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13762, 543, 3407, 15294])).
% 2.23/2.49 tff(15296,plain,
% 2.23/2.49 (r(s(s(elem!1)), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2430, 15295])).
% 2.23/2.49 tff(15297,plain,
% 2.23/2.49 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[14657, 15296, 412, 1441])).
% 2.23/2.49 tff(15298,plain,
% 2.23/2.49 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[701, 15297, 694])).
% 2.23/2.49 tff(15299,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15300,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(15301,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15300, 15299])).
% 2.23/2.49 tff(15302,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15301, 271, 2618, 261, 15054, 15298])).
% 2.23/2.49 tff(15303,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15304,plain,
% 2.23/2.49 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15303, 2618, 261, 3313, 15034, 15036, 3407, 2505])).
% 2.23/2.49 tff(15305,plain,
% 2.23/2.49 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[556, 15304, 1])).
% 2.23/2.49 tff(15306,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3722, 271, 2618, 260, 261, 446])).
% 2.23/2.49 tff(15307,plain,((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15308,plain,
% 2.23/2.49 (~b(s(z), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15307, 2618, 261, 15038])).
% 2.23/2.49 tff(15309,plain,
% 2.23/2.49 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2562, 15308, 2505])).
% 2.23/2.49 tff(15310,plain,
% 2.23/2.49 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[760, 15309])).
% 2.23/2.49 tff(15311,plain,
% 2.23/2.49 (~r(s(s(elem!1)), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2125, 15310, 15290, 15305])).
% 2.23/2.49 tff(15312,plain,
% 2.23/2.49 (b(s(s(elem!1)), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2143, 15311])).
% 2.23/2.49 tff(15313,plain,
% 2.23/2.49 (r(s(s(elem!1)), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2511, 15305, 2505])).
% 2.23/2.49 tff(15314,plain,
% 2.23/2.49 (r(s(z), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[236, 15308, 231])).
% 2.23/2.49 tff(15315,plain,
% 2.23/2.49 (~r(s(z), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1633, 15314, 15291, 15313])).
% 2.23/2.49 tff(15316,plain,
% 2.23/2.49 (b(s(z), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2167, 15315])).
% 2.23/2.49 tff(15317,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15318,plain,
% 2.23/2.49 (((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15319,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15318])).
% 2.23/2.49 tff(15320,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15319, 15317])).
% 2.23/2.49 tff(15321,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(15322,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15321, 15320])).
% 2.23/2.49 tff(15323,plain,
% 2.23/2.49 (~r(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15322, 121, 15036, 110, 15034])).
% 2.23/2.49 tff(15324,plain,
% 2.23/2.49 (b(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[429, 15323, 351])).
% 2.23/2.49 tff(15325,plain,
% 2.23/2.49 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2176, 15310, 15290, 15305, 15324])).
% 2.23/2.49 tff(15326,plain,
% 2.23/2.49 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[526, 15325, 211])).
% 2.23/2.49 tff(15327,plain,
% 2.23/2.49 (~r(z, s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[6878, 15326, 15305, 15036])).
% 2.23/2.49 tff(15328,plain,
% 2.23/2.49 (b(z, s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2106, 15327])).
% 2.23/2.49 tff(15329,plain,
% 2.23/2.49 (~b(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12176, 15328, 15316, 15312])).
% 2.23/2.49 tff(15330,plain,
% 2.23/2.49 (r(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[904, 15329])).
% 2.23/2.49 tff(15331,plain,
% 2.23/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[5759, 15330, 15031, 331, 15291, 15034, 3504, 15314, 1391, 243])).
% 2.23/2.49 tff(15332,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3830, 15331, 15330, 15291, 2618, 15034, 15031, 15030, 231, 15038])).
% 2.23/2.49 tff(15333,plain,((~b(s(elem!1), elem!1)) | (s(z) = elem!1) | (z = elem!1) | r(z, elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15334,plain,
% 2.23/2.49 (~b(s(elem!1), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15333, 15032, 331, 1391, 231, 261, 1, 3407, 110])).
% 2.23/2.49 tff(15335,plain,
% 2.23/2.49 (r(s(elem!1), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2243, 15334, 2207])).
% 2.23/2.49 tff(15336,plain,
% 2.23/2.49 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15289, 15032, 1, 15030, 261, 344, 110, 3407, 231])).
% 2.23/2.49 tff(15337,plain,
% 2.23/2.49 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15032])).
% 2.23/2.49 tff(15338,plain,
% 2.23/2.49 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.49 inference(symmetry,[status(thm)],[15337])).
% 2.23/2.49 tff(15339,plain,
% 2.23/2.49 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15338])).
% 2.23/2.49 tff(15340,plain,
% 2.23/2.49 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15334, 15339])).
% 2.23/2.49 tff(15341,plain,
% 2.23/2.49 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[5243])).
% 2.23/2.49 tff(15342,plain,
% 2.23/2.49 (~b(elem!1, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3415, 394, 3407, 261])).
% 2.23/2.49 tff(15343,plain,
% 2.23/2.49 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15342, 15341])).
% 2.23/2.49 tff(15344,plain,
% 2.23/2.49 (r(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15289, 2505, 1, 1326, 261, 348, 110, 3407, 231])).
% 2.23/2.49 tff(15345,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15346,plain,
% 2.23/2.49 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15347,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15346])).
% 2.23/2.49 tff(15348,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15347, 15345])).
% 2.23/2.49 tff(15349,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(15350,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15349, 15348])).
% 2.23/2.49 tff(15351,plain,
% 2.23/2.49 (~b(z, s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15350, 271, 1326, 261, 15054])).
% 2.23/2.49 tff(15352,plain,
% 2.23/2.49 (r(z, s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2106, 15351])).
% 2.23/2.49 tff(15353,plain,
% 2.23/2.49 (~r(s(z), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[11783, 15352, 110, 15296])).
% 2.23/2.49 tff(15354,plain,
% 2.23/2.49 (b(s(z), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2167, 15353])).
% 2.23/2.49 tff(15355,plain,
% 2.23/2.49 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[2505])).
% 2.23/2.49 tff(15356,plain,
% 2.23/2.49 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13843, 15354, 15294, 543])).
% 2.23/2.49 tff(15357,plain,
% 2.23/2.49 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[760, 15356])).
% 2.23/2.49 tff(15358,plain,
% 2.23/2.49 (r(s(z), elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15357, 15355])).
% 2.23/2.49 tff(15359,plain,
% 2.23/2.49 (r(elem!1, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2830, 684, 2505])).
% 2.23/2.49 tff(15360,plain,
% 2.23/2.49 (~r(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[9630, 121, 15359, 622, 15358])).
% 2.23/2.49 tff(15361,plain,
% 2.23/2.49 (b(s(elem!1), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[429, 15360, 2282])).
% 2.23/2.49 tff(15362,plain,
% 2.23/2.49 (~r(s(z), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[9617, 15357, 684, 622])).
% 2.23/2.49 tff(15363,plain,
% 2.23/2.49 (b(s(z), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[444, 15362, 348])).
% 2.23/2.49 tff(15364,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15365,plain,
% 2.23/2.49 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15366,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15365])).
% 2.23/2.49 tff(15367,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15366, 15364])).
% 2.23/2.49 tff(15368,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(15369,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15368, 15367])).
% 2.23/2.49 tff(15370,plain,
% 2.23/2.49 (~r(s(s(elem!1)), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15369, 121, 15352, 110, 15296])).
% 2.23/2.49 tff(15371,plain,
% 2.23/2.49 (b(s(s(elem!1)), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2143, 15370])).
% 2.23/2.49 tff(15372,plain,
% 2.23/2.49 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2174, 271, 15354, 15361, 15371])).
% 2.23/2.49 tff(15373,plain,
% 2.23/2.49 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[526, 15372, 216])).
% 2.23/2.49 tff(15374,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15375,plain,
% 2.23/2.49 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15376,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15375])).
% 2.23/2.49 tff(15377,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15376, 15374])).
% 2.23/2.49 tff(15378,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(15379,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15378, 15377])).
% 2.23/2.49 tff(15380,plain,
% 2.23/2.49 (~r(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15379, 121, 15373, 15352, 15296])).
% 2.23/2.49 tff(15381,plain,
% 2.23/2.49 (b(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1439, 15380])).
% 2.23/2.49 tff(15382,plain,
% 2.23/2.49 (~b(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[9030, 15381, 394, 15363])).
% 2.23/2.49 tff(15383,plain,
% 2.23/2.49 (r(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[904, 15382])).
% 2.23/2.49 tff(15384,plain,
% 2.23/2.49 (~b(s(s(s(z))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[5698, 15383, 2505, 1326, 15363, 15358, 9149, 15361])).
% 2.23/2.49 tff(15385,plain,
% 2.23/2.49 (r(s(s(s(z))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1816, 15384, 2597])).
% 2.23/2.49 tff(15386,plain,
% 2.23/2.49 (~r(s(s(s(z))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3838, 121, 15359, 622, 15385])).
% 2.23/2.49 tff(15387,plain,
% 2.23/2.49 (b(s(s(s(z))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[255, 15386, 2612])).
% 2.23/2.49 tff(15388,plain,
% 2.23/2.49 (~b(z, s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1334, 15387, 1326, 261])).
% 2.23/2.49 tff(15389,plain,
% 2.23/2.49 (r(z, s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1214, 15388])).
% 2.23/2.49 tff(15390,plain,
% 2.23/2.49 (~r(s(z), s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1508, 15389, 15383, 15385])).
% 2.23/2.49 tff(15391,plain,
% 2.23/2.49 (b(s(z), s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[105, 15390])).
% 2.23/2.49 tff(15392,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15393,plain,
% 2.23/2.49 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15394,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15393])).
% 2.23/2.49 tff(15395,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15394, 15392])).
% 2.23/2.49 tff(15396,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(15397,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[15396, 15395])).
% 2.23/2.49 tff(15398,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15397, 271, 543, 505, 3871, 2448])).
% 2.23/2.49 tff(15399,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(15400,plain,
% 2.23/2.49 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[15399, 15391, 543, 15354])).
% 2.23/2.49 tff(15401,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15402,plain,
% 2.23/2.49 (((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(15403,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[15402])).
% 2.23/2.49 tff(15404,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[15403, 15401])).
% 2.23/2.49 tff(15405,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.50 tff(15406,plain,
% 2.23/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.23/2.50 inference(modus_ponens,[status(thm)],[15405, 15404])).
% 2.23/2.50 tff(15407,plain,
% 2.23/2.50 (~b(s(s(elem!1)), s(elem!1))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[15406, 271, 15354, 15361, 15371])).
% 2.23/2.50 tff(15408,plain,
% 2.23/2.50 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[701, 15407, 8423])).
% 2.23/2.50 tff(15409,plain,
% 2.23/2.50 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[13477, 15381, 15352, 15408, 2597, 15373])).
% 2.23/2.50 tff(15410,plain,
% 2.23/2.50 ($false),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[2462, 21, 15409, 15400, 944])).
% 2.23/2.50 tff(15411,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.50 tff(15412,plain,
% 2.23/2.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[15411, 394, 1326, 261, 622, 2505, 3504, 211, 110, 348, 15344, 3407])).
% 2.23/2.50 tff(15413,plain,
% 2.23/2.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[556, 15412, 1])).
% 2.23/2.50 tff(15414,plain,
% 2.23/2.50 (~r(s(elem!1), s(s(elem!1)))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[3190, 15413, 15052, 752, 15343])).
% 2.23/2.50 tff(15415,plain,
% 2.23/2.50 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[526, 15414, 211])).
% 2.23/2.50 tff(15416,plain,
% 2.23/2.50 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.50 inference(monotonicity,[status(thm)],[2505])).
% 2.23/2.50 tff(15417,plain,
% 2.23/2.50 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.23/2.50 inference(symmetry,[status(thm)],[15416])).
% 2.23/2.50 tff(15418,plain,
% 2.23/2.50 (r(s(s(elem!1)), elem!1)),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[2511, 15413, 2505])).
% 2.23/2.50 tff(15419,plain,
% 2.23/2.50 (r(elem!1, s(elem!1))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[2830, 15344, 2505])).
% 2.23/2.50 tff(15420,plain,
% 2.23/2.50 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[692, 15413, 15344, 622])).
% 2.23/2.50 tff(15421,plain,
% 2.23/2.50 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[701, 15420, 3313])).
% 2.23/2.50 tff(15422,plain,
% 2.23/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.23/2.50 inference(rewrite,[status(thm)],[])).
% 2.23/2.50 tff(15423,plain,
% 2.23/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.23/2.50 inference(quant_inst,[status(thm)],[])).
% 2.23/2.50 tff(15424,plain,
% 2.23/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.23/2.50 inference(modus_ponens,[status(thm)],[15423, 15422])).
% 2.23/2.50 tff(15425,plain,
% 2.23/2.50 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[15424, 121, 379, 145, 1624])).
% 2.23/2.50 tff(15426,plain,
% 2.23/2.50 (b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[2462, 21, 15425, 944])).
% 2.23/2.50 tff(15427,plain,
% 2.23/2.50 (b(s(s(s(z))), s(elem!1))),
% 2.23/2.50 inference(unit_resolution,[status(thm)],[1816, 8371, 2033])).
% 2.23/2.50 tff(15428,plain,
% 2.23/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15429,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(15430,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15429, 15428])).
% 2.33/2.50 tff(15431,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15430, 271, 394, 15427, 15426, 2494])).
% 2.33/2.50 tff(15432,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(15433,plain,
% 2.33/2.50 (~r(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15432, 394, 15421, 3504, 2597, 15419, 15418, 622])).
% 2.33/2.50 tff(15434,plain,
% 2.33/2.50 (b(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[255, 15433, 2612])).
% 2.33/2.50 tff(15435,plain,
% 2.33/2.50 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15434, 15417])).
% 2.33/2.50 tff(15436,plain,
% 2.33/2.50 (~b(z, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1334, 15434, 1326, 261])).
% 2.33/2.50 tff(15437,plain,
% 2.33/2.50 (r(z, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1214, 15436])).
% 2.33/2.50 tff(15438,plain,
% 2.33/2.50 (~b(s(s(s(z))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1947, 15434, 1326, 261])).
% 2.33/2.50 tff(15439,plain,
% 2.33/2.50 (r(s(s(s(z))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1155, 15438])).
% 2.33/2.50 tff(15440,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15441,plain,
% 2.33/2.50 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15442,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15441])).
% 2.33/2.50 tff(15443,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[15442, 15440])).
% 2.33/2.50 tff(15444,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(15445,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15444, 15443])).
% 2.33/2.50 tff(15446,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15445, 121, 110, 15439, 15437])).
% 2.33/2.50 tff(15447,plain,
% 2.33/2.50 (b(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2325, 15446])).
% 2.33/2.50 tff(15448,plain,
% 2.33/2.50 (~b(s(z), s(s(s(elem!1))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[14970, 15447, 15294, 15435])).
% 2.33/2.50 tff(15449,plain,
% 2.33/2.50 (r(s(z), s(s(s(elem!1))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[760, 15448])).
% 2.33/2.50 tff(15450,plain,
% 2.33/2.50 (~b(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2176, 15449, 15344, 15413, 15415])).
% 2.33/2.50 tff(15451,plain,
% 2.33/2.50 (r(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[429, 15450, 2282])).
% 2.33/2.50 tff(15452,plain,
% 2.33/2.50 (~b(s(z), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[276, 15447, 261, 15434])).
% 2.33/2.50 tff(15453,plain,
% 2.33/2.50 (r(s(z), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[236, 15452, 231])).
% 2.33/2.50 tff(15454,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[9630, 121, 15419, 622, 15453, 15451])).
% 2.33/2.50 tff(15455,plain,((~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | (~b(elem!1, z)) | (~r(s(z), z)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, elem!1)) | b(s(elem!1), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(15456,plain,
% 2.33/2.50 (~b(s(elem!1), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15455, 15335, 231, 261, 110, 15032, 15030, 15340, 1, 344, 3407])).
% 2.33/2.50 tff(15457,plain,
% 2.33/2.50 (r(s(elem!1), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[409, 15456])).
% 2.33/2.50 tff(15458,plain,
% 2.33/2.50 (r(elem!1, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2830, 15336, 15032])).
% 2.33/2.50 tff(15459,plain,
% 2.33/2.50 (~(s(s(s(z))) = elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2611, 15032])).
% 2.33/2.50 tff(15460,plain,
% 2.33/2.50 (~(elem!1 = s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1100, 15459])).
% 2.33/2.50 tff(15461,plain,
% 2.33/2.50 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15032])).
% 2.33/2.50 tff(15462,plain,
% 2.33/2.50 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15461])).
% 2.33/2.50 tff(15463,plain,
% 2.33/2.50 (~(s(s(s(z))) = s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2596, 15032])).
% 2.33/2.50 tff(15464,plain,
% 2.33/2.50 (~(s(elem!1) = s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2035, 15463])).
% 2.33/2.50 tff(15465,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15466,plain,
% 2.33/2.50 (((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15467,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15466])).
% 2.33/2.50 tff(15468,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[15467, 15465])).
% 2.33/2.50 tff(15469,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(15470,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15469, 15468])).
% 2.33/2.50 tff(15471,plain,
% 2.33/2.50 (~r(s(z), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15470, 121, 110, 412, 11659])).
% 2.33/2.50 tff(15472,plain,
% 2.33/2.50 (b(s(z), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[444, 15471, 348])).
% 2.33/2.50 tff(15473,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15474,plain,
% 2.33/2.50 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15475,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15474])).
% 2.33/2.50 tff(15476,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[15475, 15473])).
% 2.33/2.50 tff(15477,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(15478,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15477, 15476])).
% 2.33/2.50 tff(15479,plain,
% 2.33/2.50 (~r(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15478, 121, 110, 11668, 11659])).
% 2.33/2.50 tff(15480,plain,
% 2.33/2.50 (b(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[105, 15479])).
% 2.33/2.50 tff(15481,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15482,plain,
% 2.33/2.50 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(15483,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15482])).
% 2.33/2.50 tff(15484,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[15483, 15481])).
% 2.33/2.50 tff(15485,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(15486,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15485, 15484])).
% 2.33/2.50 tff(15487,plain,
% 2.33/2.50 (~r(s(elem!1), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15486, 121, 412, 11668, 11659])).
% 2.33/2.50 tff(15488,plain,
% 2.33/2.50 (b(s(elem!1), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2044, 15487, 2037])).
% 2.33/2.50 tff(15489,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[3879, 15488, 15480, 257, 15472])).
% 2.33/2.50 tff(15490,plain,((~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(15491,plain,
% 2.33/2.50 (~b(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15490, 15464, 15457, 110, 344, 15030, 261])).
% 2.33/2.50 tff(15492,plain,
% 2.33/2.50 (r(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[255, 15491, 15459])).
% 2.33/2.50 tff(15493,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8370, 121, 15458, 15335, 15492])).
% 2.33/2.50 tff(15494,plain,
% 2.33/2.50 (b(s(s(s(z))), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1816, 15493, 15463])).
% 2.33/2.50 tff(15495,plain,
% 2.33/2.50 (~r(s(elem!1), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[6290, 121, 15458, 15335, 15492])).
% 2.33/2.50 tff(15496,plain,
% 2.33/2.50 (b(s(elem!1), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2044, 15495, 15464])).
% 2.33/2.50 tff(15497,plain,
% 2.33/2.50 (~r(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15256, 1140, 110, 412])).
% 2.33/2.50 tff(15498,plain,
% 2.33/2.50 (b(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[429, 15497, 422])).
% 2.33/2.50 tff(15499,plain,
% 2.33/2.50 (~r(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[3375, 1140, 145, 110])).
% 2.33/2.50 tff(15500,plain,
% 2.33/2.50 (b(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[105, 15499])).
% 2.33/2.50 tff(15501,plain,
% 2.33/2.50 (~b(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[3622, 15500, 3870, 15498])).
% 2.33/2.50 tff(15502,plain,
% 2.33/2.50 (r(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2325, 15501])).
% 2.33/2.50 tff(15503,plain,
% 2.33/2.50 (~r(z, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11100, 15502, 1140, 110])).
% 2.33/2.50 tff(15504,plain,
% 2.33/2.50 (b(z, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[904, 15503])).
% 2.33/2.50 tff(15505,plain,
% 2.33/2.50 (~b(elem!1, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11002, 15504, 1326, 15500])).
% 2.33/2.50 tff(15506,plain,
% 2.33/2.50 (r(elem!1, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[299, 15505, 258])).
% 2.33/2.50 tff(15507,plain,
% 2.33/2.50 (~b(s(z), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12145, 15504, 1326, 261])).
% 2.33/2.50 tff(15508,plain,
% 2.33/2.50 (~b(s(z), s(s(s(elem!1))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2562, 15507, 2505])).
% 2.33/2.50 tff(15509,plain,
% 2.33/2.50 (r(s(z), s(s(s(elem!1))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[760, 15508])).
% 2.33/2.50 tff(15510,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12657, 15509, 15506, 145, 15502])).
% 2.33/2.50 tff(15511,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | (~b(s(elem!1), s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(15512,plain,
% 2.33/2.50 (~r(z, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15511, 15492, 243, 15032, 15030, 261, 110, 15496, 351, 15457])).
% 2.33/2.50 tff(15513,plain,
% 2.33/2.50 (b(z, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1214, 15512])).
% 2.33/2.50 tff(15514,plain,
% 2.33/2.50 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[5687, 15513, 3407, 15494])).
% 2.33/2.50 tff(15515,plain,
% 2.33/2.50 (~b(elem!1, s(s(s(z))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[15514, 15462])).
% 2.33/2.50 tff(15516,plain,
% 2.33/2.50 (r(elem!1, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1192, 15515, 15460])).
% 2.33/2.50 tff(15517,plain,
% 2.33/2.50 (r(s(z), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[236, 15159, 231])).
% 2.33/2.50 tff(15518,plain,
% 2.33/2.50 (~r(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[9831, 15517, 1184, 145])).
% 2.33/2.50 tff(15519,plain,
% 2.33/2.50 (b(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[105, 15518])).
% 2.33/2.50 tff(15520,plain,
% 2.33/2.50 (~b(elem!1, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11002, 15519, 1326, 220])).
% 2.33/2.50 tff(15521,plain,
% 2.33/2.50 (r(elem!1, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[299, 15520, 243])).
% 2.33/2.50 tff(15522,plain,
% 2.33/2.50 (~r(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8953, 15521, 110, 379])).
% 2.33/2.50 tff(15523,plain,
% 2.33/2.50 (b(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[429, 15522, 422])).
% 2.33/2.50 tff(15524,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12657, 15521, 145, 15161])).
% 2.33/2.50 tff(15525,plain,
% 2.33/2.50 (b(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2325, 15524])).
% 2.33/2.50 tff(15526,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[3622, 15525, 15523, 3870, 15519])).
% 2.33/2.50 tff(15527,plain,((~b(z, s(z))) | (~b(s(elem!1), s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (s(z) = elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(15528,plain,
% 2.33/2.50 (~b(z, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15527, 15496, 351, 15492, 110, 15458, 15030, 15516, 231, 15032, 261])).
% 2.33/2.50 tff(15529,plain,
% 2.33/2.50 (r(z, s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[904, 15528])).
% 2.33/2.50 tff(15530,plain,
% 2.33/2.50 (b(s(z), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[5659, 15529, 15030, 243, 331, 15458, 15457])).
% 2.33/2.50 tff(15531,plain,
% 2.33/2.50 (~r(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[3972, 121, 110, 15529, 15457])).
% 2.33/2.50 tff(15532,plain,
% 2.33/2.50 (b(s(elem!1), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[429, 15531, 351])).
% 2.33/2.50 tff(15533,plain,
% 2.33/2.50 (~b(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[5668, 271, 15494, 15532, 15530])).
% 2.33/2.50 tff(15534,plain,
% 2.33/2.50 (r(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[105, 15533])).
% 2.33/2.50 tff(15535,plain,
% 2.33/2.50 (~b(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[5673, 271, 15494, 15532, 15530])).
% 2.33/2.50 tff(15536,plain,
% 2.33/2.50 (r(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2325, 15535])).
% 2.33/2.50 tff(15537,plain,
% 2.33/2.50 (~r(s(s(s(z))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[6186, 121, 15529, 15536, 15534])).
% 2.33/2.50 tff(15538,plain,
% 2.33/2.50 (b(s(s(s(z))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1155, 15537])).
% 2.33/2.50 tff(15539,plain,
% 2.33/2.50 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.33/2.50 inference(monotonicity,[status(thm)],[15032])).
% 2.33/2.50 tff(15540,plain,
% 2.33/2.50 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 2.33/2.50 inference(symmetry,[status(thm)],[15539])).
% 2.33/2.50 tff(15541,plain,
% 2.33/2.50 (~r(s(z), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[5759, 15529, 15031, 331, 15458, 15457, 3504, 15494, 1391, 243])).
% 2.33/2.50 tff(15542,plain,
% 2.33/2.50 (b(s(z), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[236, 15541, 231])).
% 2.33/2.51 tff(15543,plain,
% 2.33/2.51 (b(s(z), s(s(s(elem!1))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15542, 15540])).
% 2.33/2.51 tff(15544,plain,
% 2.33/2.51 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15032])).
% 2.33/2.51 tff(15545,plain,
% 2.33/2.51 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.33/2.51 inference(symmetry,[status(thm)],[15544])).
% 2.33/2.51 tff(15546,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15547,plain,
% 2.33/2.51 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15548,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15547])).
% 2.33/2.51 tff(15549,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15548, 15546])).
% 2.33/2.51 tff(15550,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15551,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15550, 15549])).
% 2.33/2.51 tff(15552,plain,
% 2.33/2.51 (~r(elem!1, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15551, 121, 15516, 15492, 15534])).
% 2.33/2.51 tff(15553,plain,
% 2.33/2.51 (b(elem!1, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[299, 15552, 243])).
% 2.33/2.51 tff(15554,plain,
% 2.33/2.51 (b(s(s(s(elem!1))), s(z))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15553, 15545])).
% 2.33/2.51 tff(15555,plain,
% 2.33/2.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2464, 15554, 3504, 15543, 15536, 110, 15529, 15538])).
% 2.33/2.51 tff(15556,plain,
% 2.33/2.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[556, 15555, 1])).
% 2.33/2.51 tff(15557,plain,
% 2.33/2.51 (~r(s(s(elem!1)), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[692, 15556, 15336, 15335])).
% 2.33/2.51 tff(15558,plain,
% 2.33/2.51 (b(s(s(elem!1)), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[701, 15557, 3313])).
% 2.33/2.51 tff(15559,plain,
% 2.33/2.51 (r(s(s(elem!1)), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2511, 15556, 15032])).
% 2.33/2.51 tff(15560,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15424, 121, 15458, 15492, 15559])).
% 2.33/2.51 tff(15561,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2462, 21, 15560, 3504])).
% 2.33/2.51 tff(15562,plain,
% 2.33/2.51 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15032])).
% 2.33/2.51 tff(15563,plain,
% 2.33/2.51 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.33/2.51 inference(symmetry,[status(thm)],[15562])).
% 2.33/2.51 tff(15564,plain,
% 2.33/2.51 (r(s(elem!1), s(s(s(elem!1))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15335, 15563])).
% 2.33/2.51 tff(15565,plain,
% 2.33/2.51 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15032])).
% 2.33/2.51 tff(15566,plain,
% 2.33/2.51 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(symmetry,[status(thm)],[15565])).
% 2.33/2.51 tff(15567,plain,
% 2.33/2.51 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15032])).
% 2.33/2.51 tff(15568,plain,
% 2.33/2.51 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(elem!1))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15567])).
% 2.33/2.51 tff(15569,plain,
% 2.33/2.51 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(symmetry,[status(thm)],[15568])).
% 2.33/2.51 tff(15570,plain,
% 2.33/2.51 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15569, 15566])).
% 2.33/2.51 tff(15571,plain,
% 2.33/2.51 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15458, 15570])).
% 2.33/2.51 tff(15572,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.33/2.51 tff(15573,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15574,plain,
% 2.33/2.51 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15575,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15574])).
% 2.33/2.51 tff(15576,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15575, 15573])).
% 2.33/2.51 tff(15577,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15578,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15577, 15576])).
% 2.33/2.51 tff(15579,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15578, 121, 623, 627, 798, 15572])).
% 2.33/2.51 tff(15580,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15581,plain,
% 2.33/2.51 (~r(s(elem!1), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15580, 15556, 15571, 15564])).
% 2.33/2.51 tff(15582,plain,
% 2.33/2.51 (b(s(elem!1), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[526, 15581, 211])).
% 2.33/2.51 tff(15583,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7769, 271, 15582, 15494, 15561, 15558])).
% 2.33/2.51 tff(15584,plain,((~b(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (s(z) = elem!1) | (z = elem!1) | r(z, elem!1) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15585,plain,
% 2.33/2.51 (~b(elem!1, z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15584, 147, 110, 231, 331, 1391, 3407, 1])).
% 2.33/2.51 tff(15586,plain,
% 2.33/2.51 (r(elem!1, z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[284, 15585, 358])).
% 2.33/2.51 tff(15587,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15588,plain,
% 2.33/2.51 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15589,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15588])).
% 2.33/2.51 tff(15590,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15589, 15587])).
% 2.33/2.51 tff(15591,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15592,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15591, 15590])).
% 2.33/2.51 tff(15593,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15592, 271, 1326, 588, 3407, 504])).
% 2.33/2.51 tff(15594,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15595,plain,
% 2.33/2.51 (~b(elem!1, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15594, 504, 3407, 1326])).
% 2.33/2.51 tff(15596,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15597,plain,
% 2.33/2.51 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15598,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15597])).
% 2.33/2.51 tff(15599,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15598, 15596])).
% 2.33/2.51 tff(15600,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15601,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15600, 15599])).
% 2.33/2.51 tff(15602,plain,
% 2.33/2.51 (~b(z, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15601, 271, 543, 3407, 504])).
% 2.33/2.51 tff(15603,plain,
% 2.33/2.51 (r(z, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2106, 15602])).
% 2.33/2.51 tff(15604,plain,
% 2.33/2.51 (~r(elem!1, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[14498, 15603, 3407, 331, 504, 13392])).
% 2.33/2.51 tff(15605,plain,
% 2.33/2.51 (elem!1 = s(s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[599, 15604, 15595])).
% 2.33/2.51 tff(15606,plain,
% 2.33/2.51 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15605])).
% 2.33/2.51 tff(15607,plain,
% 2.33/2.51 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.33/2.51 inference(symmetry,[status(thm)],[15606])).
% 2.33/2.51 tff(15608,plain,
% 2.33/2.51 ((~b(z, s(s(elem!1)))) <=> (~b(z, elem!1))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15607])).
% 2.33/2.51 tff(15609,plain,
% 2.33/2.51 (~b(z, elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15602, 15608])).
% 2.33/2.51 tff(15610,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1326, 15609])).
% 2.33/2.51 tff(15611,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15612,plain,
% 2.33/2.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15611, 504, 3407, 331, 15030])).
% 2.33/2.51 tff(15613,plain,
% 2.33/2.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[556, 15612, 1])).
% 2.33/2.51 tff(15614,plain,
% 2.33/2.51 (~b(elem!1, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11818, 909, 110, 1326, 504, 260])).
% 2.33/2.51 tff(15615,plain,
% 2.33/2.51 (r(elem!1, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[299, 15614, 258])).
% 2.33/2.51 tff(15616,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[9121, 121, 110, 909, 1409, 15615])).
% 2.33/2.51 tff(15617,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15618,plain,
% 2.33/2.51 (~r(z, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15617, 260, 1409, 258, 1326, 504, 110])).
% 2.33/2.51 tff(15619,plain,
% 2.33/2.51 (b(z, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[904, 15618])).
% 2.33/2.51 tff(15620,plain,
% 2.33/2.51 (~b(elem!1, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[4817, 15619, 1326, 260])).
% 2.33/2.51 tff(15621,plain,
% 2.33/2.51 (r(elem!1, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[299, 15620, 258])).
% 2.33/2.51 tff(15622,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(elem!1)))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15623,plain,
% 2.33/2.51 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(elem!1)))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15624,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(elem!1))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15623])).
% 2.33/2.51 tff(15625,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(elem!1)))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15624, 15622])).
% 2.33/2.51 tff(15626,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15627,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(elem!1))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15626, 15625])).
% 2.33/2.51 tff(15628,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15627, 121, 2088, 110, 1409, 3456])).
% 2.33/2.51 tff(15629,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15630,plain,
% 2.33/2.51 (~r(z, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15629, 15621, 110, 1409])).
% 2.33/2.51 tff(15631,plain,
% 2.33/2.51 (b(z, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2106, 15630])).
% 2.33/2.51 tff(15632,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15633,plain,
% 2.33/2.51 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15634,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15633])).
% 2.33/2.51 tff(15635,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15634, 15632])).
% 2.33/2.51 tff(15636,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15637,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15636, 15635])).
% 2.33/2.51 tff(15638,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15637, 271, 260, 220, 3407, 503])).
% 2.33/2.51 tff(15639,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(15640,plain,
% 2.33/2.51 (~b(s(s(s(elem!1))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15639, 260, 15619, 3407])).
% 2.33/2.51 tff(15641,plain,
% 2.33/2.51 (r(s(s(s(elem!1))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[66, 21, 15640, 63])).
% 2.33/2.51 tff(15642,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15643,plain,
% 2.33/2.51 (((~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(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(15644,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[15643])).
% 2.33/2.51 tff(15645,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.51 inference(transitivity,[status(thm)],[15644, 15642])).
% 2.33/2.51 tff(15646,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(15647,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[15646, 15645])).
% 2.33/2.51 tff(15648,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15647, 271, 750, 220, 3407, 504])).
% 2.33/2.51 tff(15649,plain,((~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))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15650,plain,
% 2.33/2.52 (~b(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15649, 15619, 3407, 504])).
% 2.33/2.52 tff(15651,plain,
% 2.33/2.52 (r(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[760, 15650])).
% 2.33/2.52 tff(15652,plain,
% 2.33/2.52 (~r(s(z), s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13318, 121, 623, 15651, 15641])).
% 2.33/2.52 tff(15653,plain,
% 2.33/2.52 (b(s(z), s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2167, 15652])).
% 2.33/2.52 tff(15654,plain,
% 2.33/2.52 (~r(s(s(elem!1)), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13294, 121, 623, 15651, 15641])).
% 2.33/2.52 tff(15655,plain,
% 2.33/2.52 (b(s(s(elem!1)), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2143, 15654])).
% 2.33/2.52 tff(15656,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12176, 15655, 15653, 15619, 15631])).
% 2.33/2.52 tff(15657,plain,((~b(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (elem!1 = s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15658,plain,
% 2.33/2.52 (~b(s(z), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15657, 15613, 3407, 504, 110, 1409, 243, 15030])).
% 2.33/2.52 tff(15659,plain,
% 2.33/2.52 (~b(elem!1, s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15594, 504, 3407, 15030])).
% 2.33/2.52 tff(15660,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15661,plain,
% 2.33/2.52 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15662,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15661])).
% 2.33/2.52 tff(15663,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.33/2.52 inference(transitivity,[status(thm)],[15662, 15660])).
% 2.33/2.52 tff(15664,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(15665,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15664, 15663])).
% 2.33/2.52 tff(15666,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15665, 271, 1326, 448, 3407, 504])).
% 2.33/2.52 tff(15667,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15668,plain,
% 2.33/2.52 (~b(elem!1, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15667, 504, 3407, 15030])).
% 2.33/2.52 tff(15669,plain,
% 2.33/2.52 (r(elem!1, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[299, 15668, 243])).
% 2.33/2.52 tff(15670,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[7685, 271, 307, 1326, 3407, 504])).
% 2.33/2.52 tff(15671,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15672,plain,
% 2.33/2.52 (~b(elem!1, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15671, 504, 3407, 15030])).
% 2.33/2.52 tff(15673,plain,
% 2.33/2.52 (r(elem!1, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[392, 15672, 219])).
% 2.33/2.52 tff(15674,plain,
% 2.33/2.52 (r(s(z), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[236, 15658, 231])).
% 2.33/2.52 tff(15675,plain,
% 2.33/2.52 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.33/2.52 inference(symmetry,[status(thm)],[9439])).
% 2.33/2.52 tff(15676,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15675])).
% 2.33/2.52 tff(15677,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[15676])).
% 2.33/2.52 tff(15678,plain,
% 2.33/2.52 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[2606])).
% 2.33/2.52 tff(15679,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.33/2.52 tff(15680,plain,
% 2.33/2.52 (~(elem!1 = s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[3906, 244])).
% 2.33/2.52 tff(15681,plain,
% 2.33/2.52 (r(elem!1, s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[599, 15680, 15679])).
% 2.33/2.52 tff(15682,plain,
% 2.33/2.52 (~r(s(elem!1), s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2199, 15681, 623, 379])).
% 2.33/2.52 tff(15683,plain,
% 2.33/2.52 (b(s(elem!1), s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[526, 15682, 211])).
% 2.33/2.52 tff(15684,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15683, 15678])).
% 2.33/2.52 tff(15685,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15684, 15677])).
% 2.33/2.52 tff(15686,plain,
% 2.33/2.52 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[2606])).
% 2.33/2.52 tff(15687,plain,
% 2.33/2.52 (b(s(elem!1), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[429, 10233, 2282])).
% 2.33/2.52 tff(15688,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15687, 15686])).
% 2.33/2.52 tff(15689,plain,
% 2.33/2.52 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[9439])).
% 2.33/2.52 tff(15690,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[623, 15689])).
% 2.33/2.52 tff(15691,plain,
% 2.33/2.52 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[9439])).
% 2.33/2.52 tff(15692,plain,
% 2.33/2.52 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15681, 15691])).
% 2.33/2.52 tff(15693,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15694,plain,
% 2.33/2.52 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15695,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15694])).
% 2.33/2.52 tff(15696,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[15695, 15693])).
% 2.33/2.52 tff(15697,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(15698,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15697, 15696])).
% 2.33/2.52 tff(15699,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15698, 121, 357, 1826, 1735, 7793])).
% 2.33/2.52 tff(15700,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15701,plain,
% 2.33/2.52 (~r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15700, 15692, 357, 15690])).
% 2.33/2.52 tff(15702,plain,
% 2.33/2.52 (b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1756, 15701])).
% 2.33/2.52 tff(15703,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1785, 15702, 15688, 15685])).
% 2.33/2.52 tff(15704,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1682, 15703])).
% 2.33/2.52 tff(15705,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.52 inference(monotonicity,[status(thm)],[244])).
% 2.33/2.52 tff(15706,plain,
% 2.33/2.52 (~b(s(z), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10599, 244, 1242])).
% 2.33/2.52 tff(15707,plain,
% 2.33/2.52 (r(s(z), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[105, 15706])).
% 2.33/2.52 tff(15708,plain,
% 2.33/2.52 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[9439])).
% 2.33/2.52 tff(15709,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[15708])).
% 2.33/2.52 tff(15710,plain,
% 2.33/2.52 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15709])).
% 2.33/2.52 tff(15711,plain,
% 2.33/2.52 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[9439])).
% 2.33/2.52 tff(15712,plain,
% 2.33/2.52 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 2.33/2.52 inference(monotonicity,[status(thm)],[244])).
% 2.33/2.52 tff(15713,plain,
% 2.33/2.52 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 2.33/2.52 inference(symmetry,[status(thm)],[15712])).
% 2.33/2.52 tff(15714,plain,
% 2.33/2.52 (r(s(s(s(z))), z)),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[1409, 15713])).
% 2.33/2.52 tff(15715,plain,
% 2.33/2.52 (~r(z, s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2096, 15714, 108, 110])).
% 2.33/2.52 tff(15716,plain,
% 2.33/2.52 (b(z, s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2106, 15715])).
% 2.33/2.52 tff(15717,plain,
% 2.33/2.52 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15716, 15711])).
% 2.33/2.52 tff(15718,assumption,(b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.33/2.52 tff(15719,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15720,plain,
% 2.33/2.52 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15721,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15720])).
% 2.33/2.52 tff(15722,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[15721, 15719])).
% 2.33/2.52 tff(15723,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(15724,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15723, 15722])).
% 2.33/2.52 tff(15725,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15724, 271, 3407, 1639, 504, 15718])).
% 2.33/2.52 tff(15726,plain,((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15727,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15726, 15717, 3407, 504])).
% 2.33/2.52 tff(15728,plain,
% 2.33/2.52 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15727, 15710])).
% 2.33/2.52 tff(15729,plain,
% 2.33/2.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[556, 15728, 1])).
% 2.33/2.52 tff(15730,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15729, 15689])).
% 2.33/2.52 tff(15731,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), z)),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[394, 9479])).
% 2.33/2.52 tff(15732,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15733,plain,
% 2.33/2.52 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15734,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15733])).
% 2.33/2.52 tff(15735,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 2.33/2.52 inference(transitivity,[status(thm)],[15734, 15732])).
% 2.33/2.52 tff(15736,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(15737,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15736, 15735])).
% 2.33/2.52 tff(15738,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15737, 121, 357, 110, 909, 1409])).
% 2.33/2.52 tff(15739,plain,((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15740,plain,
% 2.33/2.52 (~r(z, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15739, 357, 110, 1409])).
% 2.33/2.52 tff(15741,plain,
% 2.33/2.52 (b(z, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[904, 15740])).
% 2.33/2.52 tff(15742,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[447, 15686])).
% 2.33/2.52 tff(15743,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15744,plain,
% 2.33/2.52 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15745,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15744])).
% 2.33/2.52 tff(15746,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[15745, 15743])).
% 2.33/2.52 tff(15747,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(15748,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15747, 15746])).
% 2.33/2.52 tff(15749,plain,
% 2.33/2.52 ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15748, 271])).
% 2.33/2.52 tff(15750,plain,
% 2.33/2.52 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15749, 15742, 15741, 15731])).
% 2.33/2.52 tff(15751,plain,
% 2.33/2.52 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1756, 15750])).
% 2.33/2.52 tff(15752,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15698, 121, 357, 15692, 15751, 15730])).
% 2.33/2.52 tff(15753,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15754,plain,
% 2.33/2.52 (~b(s(elem!1), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15753, 15707, 1, 3407, 504, 15687, 110, 357, 244, 1409, 15679])).
% 2.33/2.52 tff(15755,plain,
% 2.33/2.52 (r(s(elem!1), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[409, 15754])).
% 2.33/2.52 tff(15756,plain,
% 2.33/2.52 (~r(s(z), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[3709, 15755, 379, 3456])).
% 2.33/2.52 tff(15757,plain,
% 2.33/2.52 (b(s(z), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[444, 15756, 348])).
% 2.33/2.52 tff(15758,plain,
% 2.33/2.52 (b(s(z), s(s(s(s(z)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[9597, 15757, 2606])).
% 2.33/2.52 tff(15759,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15760,plain,
% 2.33/2.52 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(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))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(15761,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[15760])).
% 2.33/2.52 tff(15762,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[15761, 15759])).
% 2.33/2.52 tff(15763,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(15764,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[15763, 15762])).
% 2.33/2.52 tff(15765,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15764, 271, 6068, 1723, 1067, 5381])).
% 2.33/2.52 tff(15766,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(15767,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15766, 15702, 15758, 15685])).
% 2.33/2.53 tff(15768,plain,
% 2.33/2.53 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1733, 15767])).
% 2.33/2.53 tff(15769,plain,
% 2.33/2.53 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15768, 15705])).
% 2.33/2.53 tff(15770,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15771,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15772,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15771, 15770])).
% 2.33/2.53 tff(15773,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15772, 121, 357, 1409, 15769, 15704])).
% 2.33/2.53 tff(15774,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | b(elem!1, s(s(elem!1))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15775,plain,
% 2.33/2.53 (~(s(s(s(z))) = elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15774, 15674, 1409, 15613, 344, 15673, 15669, 1, 3407, 504, 110, 15659, 15658])).
% 2.33/2.53 tff(15776,plain,
% 2.33/2.53 (~(elem!1 = s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1100, 15775])).
% 2.33/2.53 tff(15777,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15778,plain,
% 2.33/2.53 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15779,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z)))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15778])).
% 2.33/2.53 tff(15780,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15779, 15777])).
% 2.33/2.53 tff(15781,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15782,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z)))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15781, 15780])).
% 2.33/2.53 tff(15783,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15782, 121, 110, 1409, 3456, 1140])).
% 2.33/2.53 tff(15784,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15785,plain,
% 2.33/2.53 (~r(z, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15784, 15669, 1409, 110])).
% 2.33/2.53 tff(15786,plain,
% 2.33/2.53 (b(z, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1214, 15785])).
% 2.33/2.53 tff(15787,plain,
% 2.33/2.53 (~r(z, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15739, 15674, 110, 1409])).
% 2.33/2.53 tff(15788,plain,
% 2.33/2.53 (b(z, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[904, 15787])).
% 2.33/2.53 tff(15789,plain,
% 2.33/2.53 (~b(s(z), s(s(s(elem!1))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15649, 15788, 3407, 504])).
% 2.33/2.53 tff(15790,plain,
% 2.33/2.53 (r(s(z), s(s(s(elem!1))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[760, 15789])).
% 2.33/2.53 tff(15791,plain,
% 2.33/2.53 (~r(z, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15629, 15669, 110, 1409])).
% 2.33/2.53 tff(15792,plain,
% 2.33/2.53 (b(z, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2106, 15791])).
% 2.33/2.53 tff(15793,plain,
% 2.33/2.53 (~r(s(elem!1), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[8953, 15669, 110, 15673])).
% 2.33/2.53 tff(15794,plain,
% 2.33/2.53 (b(s(elem!1), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[429, 15793, 351])).
% 2.33/2.53 tff(15795,plain,
% 2.33/2.53 (r(s(elem!1), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11276, 3871, 8337, 220, 3456, 1326, 348, 10603])).
% 2.33/2.53 tff(15796,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15797,plain,
% 2.33/2.53 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15798,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15797])).
% 2.33/2.53 tff(15799,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15798, 15796])).
% 2.33/2.53 tff(15800,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15801,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15800, 15799])).
% 2.33/2.53 tff(15802,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15801, 121, 379, 1409, 412, 1661])).
% 2.33/2.53 tff(15803,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15804,plain,
% 2.33/2.53 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15803, 15795, 1409, 379])).
% 2.33/2.53 tff(15805,plain,
% 2.33/2.53 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1658, 15804])).
% 2.33/2.53 tff(15806,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15807,plain,
% 2.33/2.53 (((~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))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15808,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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)))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15807])).
% 2.33/2.53 tff(15809,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15808, 15806])).
% 2.33/2.53 tff(15810,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15811,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15810, 15809])).
% 2.33/2.53 tff(15812,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15811, 271, 220, 1307, 3871, 222])).
% 2.33/2.53 tff(15813,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15814,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15813, 3871, 1307, 220])).
% 2.33/2.53 tff(15815,plain,
% 2.33/2.53 (r(s(s(s(z))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2325, 15814])).
% 2.33/2.53 tff(15816,plain,
% 2.33/2.53 (b(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12711, 15815, 231, 1409, 1242, 3871])).
% 2.33/2.53 tff(15817,plain,
% 2.33/2.53 (~r(s(z), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[3709, 15795, 379, 3456])).
% 2.33/2.53 tff(15818,plain,
% 2.33/2.53 (b(s(z), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[444, 15817, 348])).
% 2.33/2.53 tff(15819,plain,
% 2.33/2.53 (~b(s(elem!1), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[3879, 15816, 3871, 15818])).
% 2.33/2.53 tff(15820,plain,
% 2.33/2.53 (~b(elem!1, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2020, 1307, 1326, 257])).
% 2.33/2.53 tff(15821,plain,
% 2.33/2.53 (r(elem!1, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1192, 15820, 1102])).
% 2.33/2.53 tff(15822,plain,
% 2.33/2.53 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11663, 9149])).
% 2.33/2.53 tff(15823,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15824,plain,
% 2.33/2.53 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15825,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15824])).
% 2.33/2.53 tff(15826,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15825, 15823])).
% 2.33/2.53 tff(15827,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15828,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15827, 15826])).
% 2.33/2.53 tff(15829,plain,
% 2.33/2.53 (~r(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15828, 121, 623, 572, 7792])).
% 2.33/2.53 tff(15830,plain,
% 2.33/2.53 (b(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2167, 15829])).
% 2.33/2.53 tff(15831,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15832,plain,
% 2.33/2.53 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15833,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15832])).
% 2.33/2.53 tff(15834,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15833, 15831])).
% 2.33/2.53 tff(15835,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15836,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15835, 15834])).
% 2.33/2.53 tff(15837,plain,
% 2.33/2.53 (~r(s(s(elem!1)), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15836, 121, 623, 572, 7792])).
% 2.33/2.53 tff(15838,plain,
% 2.33/2.53 (b(s(s(elem!1)), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2143, 15837])).
% 2.33/2.53 tff(15839,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12176, 15838, 15830, 220, 1894])).
% 2.33/2.53 tff(15840,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15841,plain,
% 2.33/2.53 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15840, 220, 1894, 623, 572])).
% 2.33/2.53 tff(15842,plain,
% 2.33/2.53 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[6237, 21, 15841, 15822])).
% 2.33/2.53 tff(15843,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[5687, 1307, 3407, 15842])).
% 2.33/2.53 tff(15844,plain,
% 2.33/2.53 (s(s(s(z))) = s(elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[9295, 15843, 379, 2039, 15821])).
% 2.33/2.53 tff(15845,plain,
% 2.33/2.53 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15844])).
% 2.33/2.53 tff(15846,plain,
% 2.33/2.53 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 2.33/2.53 inference(symmetry,[status(thm)],[15845])).
% 2.33/2.53 tff(15847,plain,
% 2.33/2.53 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15846])).
% 2.33/2.53 tff(15848,plain,
% 2.33/2.53 (~(elem!1 = s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[3917, 15844, 348])).
% 2.33/2.53 tff(15849,plain,
% 2.33/2.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[78, 15848])).
% 2.33/2.53 tff(15850,plain,
% 2.33/2.53 (~b(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12176, 2144, 220, 1894])).
% 2.33/2.53 tff(15851,plain,
% 2.33/2.53 (r(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2167, 15850])).
% 2.33/2.53 tff(15852,plain,
% 2.33/2.53 (~r(s(s(elem!1)), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1633, 15851, 357, 379])).
% 2.33/2.53 tff(15853,plain,
% 2.33/2.53 (~b(s(elem!1), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2176, 684, 572, 447, 623])).
% 2.33/2.53 tff(15854,plain,
% 2.33/2.53 (r(s(elem!1), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[526, 15853, 216])).
% 2.33/2.53 tff(15855,plain,
% 2.33/2.53 (~r(elem!1, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2199, 15854, 379, 623])).
% 2.33/2.53 tff(15856,plain,
% 2.33/2.53 (b(elem!1, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[599, 15855, 68])).
% 2.33/2.53 tff(15857,plain,
% 2.33/2.53 (~b(s(s(elem!1)), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2222, 15856, 1326, 1894])).
% 2.33/2.53 tff(15858,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[862, 15857, 15852, 198])).
% 2.33/2.53 tff(15859,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15860,plain,
% 2.33/2.53 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15859, 15848, 1326, 623, 220, 379, 447, 1894, 216, 572, 357])).
% 2.33/2.53 tff(15861,plain,
% 2.33/2.53 (b(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[681, 15860, 15849])).
% 2.33/2.53 tff(15862,plain,
% 2.33/2.53 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[4334, 15861, 15844])).
% 2.33/2.53 tff(15863,plain,
% 2.33/2.53 (~b(z, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15001, 15862, 1639, 447])).
% 2.33/2.53 tff(15864,plain,
% 2.33/2.53 (~b(z, s(s(s(z))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15863, 15847])).
% 2.33/2.53 tff(15865,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1307, 15864])).
% 2.33/2.53 tff(15866,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (s(z) = s(elem!1)) | b(s(elem!1), s(s(s(z)))) | (elem!1 = s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15867,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15866, 15819, 15816, 447, 1326, 623, 220, 379, 1894, 216, 572, 10603, 348, 1307, 1102, 3407, 15805])).
% 2.33/2.53 tff(15868,plain,((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(elem!1, z)) | b(s(z), elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15869,plain,
% 2.33/2.53 (~b(s(z), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15868, 15794, 15030, 15613, 15788, 15673, 15792, 211, 15790, 344, 15786, 15776, 3407, 231, 1409, 15658, 15669])).
% 2.33/2.53 tff(15870,plain,
% 2.33/2.53 (r(s(z), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[105, 15869])).
% 2.33/2.53 tff(15871,plain,
% 2.33/2.53 (~r(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[4112, 15870, 15674, 15669])).
% 2.33/2.53 tff(15872,plain,
% 2.33/2.53 (b(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[255, 15871, 15775])).
% 2.33/2.53 tff(15873,plain,
% 2.33/2.53 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15840, 15788, 15792, 15613, 15790])).
% 2.33/2.53 tff(15874,plain,
% 2.33/2.53 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[6237, 21, 15873, 13970])).
% 2.33/2.53 tff(15875,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15876,plain,
% 2.33/2.53 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15877,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15876])).
% 2.33/2.53 tff(15878,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15877, 15875])).
% 2.33/2.53 tff(15879,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15880,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15879, 15878])).
% 2.33/2.53 tff(15881,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15880, 271, 3407, 15786, 15874, 15872])).
% 2.33/2.53 tff(15882,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(15883,plain,
% 2.33/2.53 (~b(s(s(s(elem!1))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15882, 15586, 231, 3407, 1, 110, 331])).
% 2.33/2.53 tff(15884,plain,
% 2.33/2.53 (s(s(s(elem!1))) = elem!1),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[486, 15883, 147])).
% 2.33/2.53 tff(15885,plain,
% 2.33/2.53 (~r(s(z), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15739, 909, 110, 1409])).
% 2.33/2.53 tff(15886,plain,
% 2.33/2.53 (b(s(z), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[236, 15885, 231])).
% 2.33/2.53 tff(15887,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(15888,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[15887, 9116])).
% 2.33/2.53 tff(15889,plain,
% 2.33/2.53 (~r(elem!1, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15888, 121, 110, 909, 1409])).
% 2.33/2.53 tff(15890,plain,
% 2.33/2.53 (b(elem!1, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[299, 15889, 243])).
% 2.33/2.53 tff(15891,plain,
% 2.33/2.53 (~b(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[4827, 15890, 1326, 15886])).
% 2.33/2.53 tff(15892,plain,
% 2.33/2.53 (r(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[255, 15891, 2612])).
% 2.33/2.53 tff(15893,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15894,plain,
% 2.33/2.53 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(15895,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[15894])).
% 2.33/2.53 tff(15896,plain,
% 2.33/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.33/2.53 inference(transitivity,[status(thm)],[15895, 15893])).
% 2.33/2.53 tff(15897,plain,
% 2.33/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(15898,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[15897, 15896])).
% 2.33/2.54 tff(15899,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15898, 121, 909, 1409, 145, 109])).
% 2.33/2.54 tff(15900,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15901,plain,
% 2.33/2.54 (~r(s(s(s(z))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15900, 909, 1409, 15892])).
% 2.33/2.54 tff(15902,plain,
% 2.33/2.54 (b(s(s(s(z))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1155, 15901])).
% 2.33/2.54 tff(15903,plain,
% 2.33/2.54 (~b(s(s(s(z))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[4827, 448, 1326, 260])).
% 2.33/2.54 tff(15904,plain,
% 2.33/2.54 (r(s(s(s(z))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[255, 15903, 2612])).
% 2.33/2.54 tff(15905,plain,
% 2.33/2.54 (b(elem!1, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[392, 2344, 377])).
% 2.33/2.54 tff(15906,plain,
% 2.33/2.54 (~r(s(elem!1), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15046, 15905, 1326, 260, 348])).
% 2.33/2.54 tff(15907,plain,
% 2.33/2.54 (b(s(elem!1), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[409, 15906])).
% 2.33/2.54 tff(15908,plain,
% 2.33/2.54 (~b(s(elem!1), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[4613, 15905, 1326, 260, 348])).
% 2.33/2.54 tff(15909,plain,
% 2.33/2.54 (r(s(elem!1), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2243, 15908, 3500])).
% 2.33/2.54 tff(15910,plain,
% 2.33/2.54 (~b(s(z), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11047, 15909, 1326, 1935, 11082, 15905, 15904, 448, 15907])).
% 2.33/2.54 tff(15911,plain,
% 2.33/2.54 (r(s(z), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[105, 15910])).
% 2.33/2.54 tff(15912,plain,
% 2.33/2.54 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[377, 15051])).
% 2.33/2.54 tff(15913,plain,
% 2.33/2.54 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2830, 2344, 2505])).
% 2.33/2.54 tff(15914,plain,
% 2.33/2.54 (b(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[681, 15913, 15912])).
% 2.33/2.54 tff(15915,plain,
% 2.33/2.54 (~b(z, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[14106, 15914, 3407, 15907])).
% 2.33/2.54 tff(15916,plain,
% 2.33/2.54 (r(z, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1439, 15915])).
% 2.33/2.54 tff(15917,plain,
% 2.33/2.54 (~r(s(elem!1), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2186, 15911, 909, 15916])).
% 2.33/2.54 tff(15918,plain,
% 2.33/2.54 (b(s(elem!1), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[429, 15917, 2282])).
% 2.33/2.54 tff(15919,plain,
% 2.33/2.54 (~b(s(z), s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[456, 15918, 448, 15905])).
% 2.33/2.54 tff(15920,plain,
% 2.33/2.54 (r(s(z), s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[444, 15919, 348])).
% 2.33/2.54 tff(15921,plain,
% 2.33/2.54 (~r(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[3445, 15920, 15911, 15904])).
% 2.33/2.54 tff(15922,plain,
% 2.33/2.54 (b(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2044, 15921, 3841])).
% 2.33/2.54 tff(15923,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[9101, 271, 1326, 15907, 15922, 1935])).
% 2.33/2.54 tff(15924,plain,(r(elem!1, s(elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15925,plain,
% 2.33/2.54 (r(elem!1, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15924, 15902, 1326, 348, 15890, 909, 3407, 15886, 2505, 377])).
% 2.33/2.54 tff(15926,plain,
% 2.33/2.54 (~r(s(elem!1), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1417, 15925, 1409, 909])).
% 2.33/2.54 tff(15927,plain,
% 2.33/2.54 (b(s(elem!1), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[409, 15926])).
% 2.33/2.54 tff(15928,plain,
% 2.33/2.54 (~b(s(s(s(z))), s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1956, 15927, 1326, 15902])).
% 2.33/2.54 tff(15929,plain,
% 2.33/2.54 (~b(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[9101, 271, 1326, 15927, 15902])).
% 2.33/2.54 tff(15930,plain,
% 2.33/2.54 (~r(elem!1, s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[9295, 15929, 2597, 15925, 15928])).
% 2.33/2.54 tff(15931,plain,
% 2.33/2.54 (b(elem!1, s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1192, 15930, 11082])).
% 2.33/2.54 tff(15932,plain,
% 2.33/2.54 (~b(s(elem!1), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[9291, 15931, 1326, 15927])).
% 2.33/2.54 tff(15933,plain,
% 2.33/2.54 (r(s(elem!1), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2243, 15932, 3500])).
% 2.33/2.54 tff(15934,plain,
% 2.33/2.54 (~b(s(z), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11038, 15931, 15890, 15902])).
% 2.33/2.54 tff(15935,plain,
% 2.33/2.54 (r(s(z), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[105, 15934])).
% 2.33/2.54 tff(15936,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[9163, 15935, 15933, 1326, 909, 15925, 2612, 15929, 2597, 15928])).
% 2.33/2.54 tff(15937,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(elem!1)) | (~r(s(z), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15938,plain,
% 2.33/2.54 (~r(z, s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15937, 15586, 15030, 344, 3407, 15884, 219, 110, 231])).
% 2.33/2.54 tff(15939,plain,
% 2.33/2.54 (b(z, s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[904, 15938])).
% 2.33/2.54 tff(15940,plain,
% 2.33/2.54 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 2.33/2.54 inference(monotonicity,[status(thm)],[2505])).
% 2.33/2.54 tff(15941,plain,
% 2.33/2.54 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 2.33/2.54 inference(symmetry,[status(thm)],[15940])).
% 2.33/2.54 tff(15942,plain,
% 2.33/2.54 (r(s(s(s(elem!1))), z)),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[1409, 15941])).
% 2.33/2.54 tff(15943,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15944,plain,
% 2.33/2.54 (((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15945,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z)))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[15944])).
% 2.33/2.54 tff(15946,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[15945, 15943])).
% 2.33/2.54 tff(15947,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(15948,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z)))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[15947, 15946])).
% 2.33/2.54 tff(15949,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15948, 121, 357, 110, 1409, 1140])).
% 2.33/2.54 tff(15950,plain,((~r(z, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15951,plain,
% 2.33/2.54 (~r(z, s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15950, 357, 110, 1409])).
% 2.33/2.54 tff(15952,plain,
% 2.33/2.54 (b(z, s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1214, 15951])).
% 2.33/2.54 tff(15953,plain,
% 2.33/2.54 (~r(s(s(s(z))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12709, 121, 357, 1409, 145])).
% 2.33/2.54 tff(15954,plain,
% 2.33/2.54 (b(s(s(s(z))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2325, 15953])).
% 2.33/2.54 tff(15955,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15956,plain,
% 2.33/2.54 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15957,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[15956])).
% 2.33/2.54 tff(15958,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[15957, 15955])).
% 2.33/2.54 tff(15959,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(15960,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[15959, 15958])).
% 2.33/2.54 tff(15961,plain,
% 2.33/2.54 (~r(s(z), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15960, 121, 357, 1409, 145])).
% 2.33/2.54 tff(15962,plain,
% 2.33/2.54 (b(s(z), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[105, 15961])).
% 2.33/2.54 tff(15963,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15813, 15962, 15954, 1307, 220])).
% 2.33/2.54 tff(15964,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15965,plain,
% 2.33/2.54 (~r(s(s(s(z))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15964, 15952, 220, 357, 1409])).
% 2.33/2.54 tff(15966,plain,
% 2.33/2.54 (b(s(s(s(z))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[255, 15965, 2612])).
% 2.33/2.54 tff(15967,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15968,plain,
% 2.33/2.54 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15969,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[15968])).
% 2.33/2.54 tff(15970,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.33/2.54 inference(transitivity,[status(thm)],[15969, 15967])).
% 2.33/2.54 tff(15971,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(15972,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[15971, 15970])).
% 2.33/2.54 tff(15973,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15972, 271, 1326, 448, 1307, 257])).
% 2.33/2.54 tff(15974,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15975,plain,
% 2.33/2.54 (~b(elem!1, s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15974, 15952, 1326, 15966])).
% 2.33/2.54 tff(15976,plain,
% 2.33/2.54 (r(elem!1, s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[299, 15975, 258])).
% 2.33/2.54 tff(15977,plain,
% 2.33/2.54 (r(s(s(s(elem!1))), s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[15976, 12805])).
% 2.33/2.54 tff(15978,plain,
% 2.33/2.54 (~r(z, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12950, 15977, 110, 15942])).
% 2.33/2.54 tff(15979,plain,
% 2.33/2.54 (b(z, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1439, 15978])).
% 2.33/2.54 tff(15980,plain,
% 2.33/2.54 (~b(elem!1, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1978, 15966, 1326, 15952])).
% 2.33/2.54 tff(15981,plain,
% 2.33/2.54 (r(elem!1, s(elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[392, 15980, 377])).
% 2.33/2.54 tff(15982,plain,
% 2.33/2.54 (~b(elem!1, s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2020, 15966, 1326, 15952])).
% 2.33/2.54 tff(15983,plain,
% 2.33/2.54 (r(elem!1, s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1192, 15982, 11082])).
% 2.33/2.54 tff(15984,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15985,plain,
% 2.33/2.54 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15986,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[15985])).
% 2.33/2.54 tff(15987,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[15986, 15984])).
% 2.33/2.54 tff(15988,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(15989,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[15988, 15987])).
% 2.33/2.54 tff(15990,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15989, 121, 110, 1409, 3456, 1661])).
% 2.33/2.54 tff(15991,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(15992,plain,
% 2.33/2.54 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[15991, 15976, 1409, 110])).
% 2.33/2.54 tff(15993,plain,
% 2.33/2.54 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1658, 15992])).
% 2.33/2.54 tff(15994,assumption,(~(elem!1 = s(s(s(s(s(z))))))), introduced(assumption)).
% 2.33/2.54 tff(15995,plain,
% 2.33/2.54 (~r(s(elem!1), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11229, 394, 3456, 357, 220, 348])).
% 2.33/2.54 tff(15996,plain,
% 2.33/2.54 (b(s(elem!1), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2243, 15995, 2564])).
% 2.33/2.54 tff(15997,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15998,plain,
% 2.33/2.54 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(15999,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[15998])).
% 2.33/2.54 tff(16000,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[15999, 15997])).
% 2.33/2.54 tff(16001,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(16002,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[16001, 16000])).
% 2.33/2.54 tff(16003,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[16002, 271, 2618, 1326, 1421, 1849])).
% 2.33/2.54 tff(16004,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(16005,plain,
% 2.33/2.54 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[16004, 15996, 1326, 1421])).
% 2.33/2.54 tff(16006,plain,
% 2.33/2.54 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1847, 16005, 15994])).
% 2.33/2.54 tff(16007,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(16008,plain,
% 2.33/2.54 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(16009,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[16008])).
% 2.33/2.54 tff(16010,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[16009, 16007])).
% 2.33/2.54 tff(16011,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(16012,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[16011, 16010])).
% 2.33/2.54 tff(16013,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[16012, 121, 357, 3456, 1826, 1660])).
% 2.33/2.54 tff(16014,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(16015,plain,
% 2.33/2.54 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[16014, 16006, 3456, 357])).
% 2.33/2.54 tff(16016,plain,
% 2.33/2.54 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1682, 16015])).
% 2.33/2.54 tff(16017,plain,
% 2.33/2.54 (~r(s(s(s(z))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11254, 3456, 357, 1184])).
% 2.33/2.54 tff(16018,plain,
% 2.33/2.54 (b(s(s(s(z))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2325, 16017])).
% 2.33/2.54 tff(16019,plain,
% 2.33/2.54 (~b(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2029, 394, 16018, 1307])).
% 2.33/2.54 tff(16020,plain,
% 2.33/2.54 (r(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2044, 16019, 2037])).
% 2.33/2.54 tff(16021,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(16022,plain,
% 2.33/2.54 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16023,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16022])).
% 2.33/2.55 tff(16024,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16023, 16021])).
% 2.33/2.55 tff(16025,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16026,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16025, 16024])).
% 2.33/2.55 tff(16027,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16026, 121, 379, 1184, 1477, 2046])).
% 2.33/2.55 tff(16028,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16029,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16028, 16020, 379, 1184])).
% 2.33/2.55 tff(16030,plain,
% 2.33/2.55 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1494, 16029])).
% 2.33/2.55 tff(16031,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16032,plain,
% 2.33/2.55 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16033,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16032])).
% 2.33/2.55 tff(16034,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16033, 16031])).
% 2.33/2.55 tff(16035,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16036,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16035, 16034])).
% 2.33/2.55 tff(16037,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16036, 271, 1307, 1639, 16030, 16016])).
% 2.33/2.55 tff(16038,plain,((~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(s(z)))) | (~b(z, s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16039,plain,
% 2.33/2.55 (~b(s(elem!1), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16038, 15952, 15993, 15976, 357, 15186, 1326, 15979, 15981, 15983, 3500, 3841, 220, 348])).
% 2.33/2.55 tff(16040,plain,
% 2.33/2.55 (r(s(elem!1), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[409, 16039])).
% 2.33/2.55 tff(16041,plain,
% 2.33/2.55 (~r(s(z), s(elem!1))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[3709, 16040, 15981, 15976])).
% 2.33/2.55 tff(16042,plain,
% 2.33/2.55 (b(s(z), s(elem!1))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[444, 16041, 348])).
% 2.33/2.55 tff(16043,plain,
% 2.33/2.55 (~r(s(elem!1), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[8953, 15976, 110, 15981])).
% 2.33/2.55 tff(16044,plain,
% 2.33/2.55 (b(s(elem!1), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[429, 16043, 2282])).
% 2.33/2.55 tff(16045,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16046,plain,
% 2.33/2.55 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16047,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16046])).
% 2.33/2.55 tff(16048,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16047, 16045])).
% 2.33/2.55 tff(16049,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16050,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16049, 16048])).
% 2.33/2.55 tff(16051,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16050, 271, 220, 16044, 16042, 15979])).
% 2.33/2.55 tff(16052,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16053,plain,
% 2.33/2.55 (~r(s(z), elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16052, 15939, 344, 15030, 15586, 110, 15884, 243, 219])).
% 2.33/2.55 tff(16054,plain,
% 2.33/2.55 (b(s(z), elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[236, 16053, 231])).
% 2.33/2.55 tff(16055,plain,
% 2.33/2.55 (~b(elem!1, s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[4817, 16054, 15030, 15939])).
% 2.33/2.55 tff(16056,plain,
% 2.33/2.55 (r(elem!1, s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[299, 16055, 243])).
% 2.33/2.55 tff(16057,plain,
% 2.33/2.55 (~(s(s(s(z))) = elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2611, 15884])).
% 2.33/2.55 tff(16058,plain,
% 2.33/2.55 (~(elem!1 = s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1100, 16057])).
% 2.33/2.55 tff(16059,plain,
% 2.33/2.55 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[15884])).
% 2.33/2.55 tff(16060,plain,
% 2.33/2.55 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16059])).
% 2.33/2.55 tff(16061,plain,
% 2.33/2.55 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.33/2.55 inference(monotonicity,[status(thm)],[15884])).
% 2.33/2.55 tff(16062,plain,
% 2.33/2.55 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 2.33/2.55 inference(symmetry,[status(thm)],[16061])).
% 2.33/2.55 tff(16063,plain,
% 2.33/2.55 (b(s(z), s(s(s(elem!1))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16054, 16062])).
% 2.33/2.55 tff(16064,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16065,plain,
% 2.33/2.55 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16066,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16065])).
% 2.33/2.55 tff(16067,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16066, 16064])).
% 2.33/2.55 tff(16068,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16069,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16068, 16067])).
% 2.33/2.55 tff(16070,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16069, 271, 750, 220, 3407, 6202])).
% 2.33/2.55 tff(16071,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16072,plain,
% 2.33/2.55 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16071, 16063, 3407, 15939])).
% 2.33/2.55 tff(16073,plain,
% 2.33/2.55 (~b(elem!1, s(s(s(z))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16072, 16060])).
% 2.33/2.55 tff(16074,plain,
% 2.33/2.55 (r(elem!1, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1192, 16073, 16058])).
% 2.33/2.55 tff(16075,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16076,plain,
% 2.33/2.55 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16077,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16076])).
% 2.33/2.55 tff(16078,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16077, 16075])).
% 2.33/2.55 tff(16079,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16080,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16079, 16078])).
% 2.33/2.55 tff(16081,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16080, 121, 110, 1184, 3456, 2327])).
% 2.33/2.55 tff(16082,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16083,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16082, 16074, 110, 16056])).
% 2.33/2.55 tff(16084,plain,
% 2.33/2.55 (b(s(s(s(z))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2325, 16083])).
% 2.33/2.55 tff(16085,plain,
% 2.33/2.55 (~r(z, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[15784, 16056, 15586, 110])).
% 2.33/2.55 tff(16086,plain,
% 2.33/2.55 (b(z, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1214, 16085])).
% 2.33/2.55 tff(16087,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16088,plain,
% 2.33/2.55 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16089,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16088])).
% 2.33/2.55 tff(16090,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16089, 16087])).
% 2.33/2.55 tff(16091,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16092,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16091, 16090])).
% 2.33/2.55 tff(16093,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16092, 271, 16054, 15939, 16086, 16084])).
% 2.33/2.55 tff(16094,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16095,plain,
% 2.33/2.55 (r(s(s(s(elem!1))), elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16094, 1391, 3407, 231, 1, 331, 110])).
% 2.33/2.55 tff(16096,plain,
% 2.33/2.55 (~b(s(s(s(z))), elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[4827, 448, 15030, 260])).
% 2.33/2.55 tff(16097,plain,
% 2.33/2.55 (~r(s(elem!1), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[15046, 307, 1326, 260, 348])).
% 2.33/2.55 tff(16098,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[409, 16097, 15166])).
% 2.33/2.55 tff(16099,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(16100,plain,
% 2.33/2.55 (~b(elem!1, s(elem!1))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16099, 261, 260, 344, 3407, 15030])).
% 2.33/2.55 tff(16101,plain,
% 2.33/2.55 (r(elem!1, s(elem!1))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[392, 16100, 219])).
% 2.33/2.55 tff(16102,plain,
% 2.33/2.55 (~(s(s(s(z))) = elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6548, 1209, 15030])).
% 2.33/2.55 tff(16103,plain,
% 2.33/2.55 (r(s(s(s(z))), elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[255, 16102, 16096])).
% 2.33/2.55 tff(16104,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16105,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16106,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~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)))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16105, 16104])).
% 2.33/2.55 tff(16107,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16106, 121, 16101, 139, 16103])).
% 2.33/2.55 tff(16108,plain,
% 2.33/2.55 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2071, 16107, 2064])).
% 2.33/2.55 tff(16109,plain,
% 2.33/2.55 (~r(s(z), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[3375, 16103, 6533, 110])).
% 2.33/2.55 tff(16110,plain,
% 2.33/2.55 (b(s(z), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[105, 16109])).
% 2.33/2.55 tff(16111,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16112,plain,
% 2.33/2.55 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16113,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[16112])).
% 2.33/2.55 tff(16114,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[16113, 16111])).
% 2.33/2.55 tff(16115,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(16116,plain,
% 2.33/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[16115, 16114])).
% 2.33/2.55 tff(16117,plain,
% 2.33/2.55 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[16116, 121, 16101, 139, 16103])).
% 2.33/2.55 tff(16118,plain,
% 2.33/2.55 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6237, 21, 16117, 13970])).
% 2.33/2.55 tff(16119,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16120,plain,
% 2.33/2.55 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(16121,plain,
% 2.33/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16120])).
% 2.33/2.56 tff(16122,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16121, 16119])).
% 2.33/2.56 tff(16123,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(16124,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16123, 16122])).
% 2.33/2.56 tff(16125,plain,
% 2.33/2.56 (~b(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16124, 271, 3407, 16118, 16108])).
% 2.33/2.56 tff(16126,plain,
% 2.33/2.56 (r(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1155, 16125])).
% 2.33/2.56 tff(16127,plain,
% 2.33/2.56 (~b(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[4817, 448, 15030, 260])).
% 2.33/2.56 tff(16128,plain,
% 2.33/2.56 (r(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[904, 16127])).
% 2.33/2.56 tff(16129,plain,
% 2.33/2.56 (~b(s(s(elem!1)), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[5441, 542, 260, 448])).
% 2.33/2.56 tff(16130,plain,
% 2.33/2.56 (r(s(s(elem!1)), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2143, 16129])).
% 2.33/2.56 tff(16131,plain,
% 2.33/2.56 (~r(s(s(elem!1)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2422, 16130, 110, 909])).
% 2.33/2.56 tff(16132,plain,
% 2.33/2.56 (b(s(s(elem!1)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2430, 16131])).
% 2.33/2.56 tff(16133,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16134,plain,
% 2.33/2.56 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16135,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16134])).
% 2.33/2.56 tff(16136,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16135, 16133])).
% 2.33/2.56 tff(16137,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(16138,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16137, 16136])).
% 2.33/2.56 tff(16139,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16138, 271, 1326, 448, 16132, 542])).
% 2.33/2.56 tff(16140,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(16141,plain,
% 2.33/2.56 (~b(s(s(elem!1)), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16140, 16128, 15030, 110, 448, 260])).
% 2.33/2.56 tff(16142,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11100, 6533, 16128, 110])).
% 2.33/2.56 tff(16143,plain,
% 2.33/2.56 (b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2325, 16142])).
% 2.33/2.56 tff(16144,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16145,plain,
% 2.33/2.56 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16146,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16145])).
% 2.33/2.56 tff(16147,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16146, 16144])).
% 2.33/2.56 tff(16148,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(16149,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16148, 16147])).
% 2.33/2.56 tff(16150,plain,
% 2.33/2.56 (~b(s(s(s(elem!1))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16149, 271, 16118, 16110, 16143])).
% 2.33/2.56 tff(16151,plain,
% 2.33/2.56 (r(s(s(s(elem!1))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[66, 21, 16150, 63])).
% 2.33/2.56 tff(16152,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16153,plain,
% 2.33/2.56 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16154,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16153])).
% 2.33/2.56 tff(16155,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16154, 16152])).
% 2.33/2.56 tff(16156,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(16157,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16156, 16155])).
% 2.33/2.56 tff(16158,plain,
% 2.33/2.56 (~b(s(z), s(s(s(elem!1))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16157, 271, 16118, 16110, 16143])).
% 2.33/2.56 tff(16159,plain,
% 2.33/2.56 (r(s(z), s(s(s(elem!1))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[760, 16158])).
% 2.33/2.56 tff(16160,plain,
% 2.33/2.56 (~r(s(s(s(elem!1))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13234, 121, 16159, 16128, 16151])).
% 2.33/2.56 tff(16161,plain,
% 2.33/2.56 (b(s(s(s(elem!1))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8229, 16160])).
% 2.33/2.56 tff(16162,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16163,plain,
% 2.33/2.56 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16164,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16163])).
% 2.33/2.56 tff(16165,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16164, 16162])).
% 2.33/2.56 tff(16166,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(16167,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16166, 16165])).
% 2.33/2.56 tff(16168,plain,
% 2.33/2.56 (~r(s(elem!1), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16167, 121, 909, 412, 109])).
% 2.33/2.56 tff(16169,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11100, 6533, 909, 110])).
% 2.33/2.56 tff(16170,plain,
% 2.33/2.56 (b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2325, 16169])).
% 2.33/2.56 tff(16171,plain,
% 2.33/2.56 (~r(s(elem!1), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[15256, 412, 110, 6533])).
% 2.33/2.56 tff(16172,plain,
% 2.33/2.56 (b(s(elem!1), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[429, 16171, 351])).
% 2.33/2.56 tff(16173,plain,
% 2.33/2.56 (~b(s(elem!1), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[3622, 16172, 16170, 3871])).
% 2.33/2.56 tff(16174,plain,
% 2.33/2.56 (s(elem!1) = s(s(s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2042, 21, 16173, 16168])).
% 2.33/2.56 tff(16175,plain,
% 2.33/2.56 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16174])).
% 2.33/2.56 tff(16176,plain,
% 2.33/2.56 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.33/2.56 inference(symmetry,[status(thm)],[16175])).
% 2.33/2.56 tff(16177,plain,
% 2.33/2.56 (s(s(z)) = elem!1),
% 2.33/2.56 inference(transitivity,[status(thm)],[92, 16176, 70])).
% 2.33/2.56 tff(16178,plain,
% 2.33/2.56 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16177])).
% 2.33/2.56 tff(16179,plain,
% 2.33/2.56 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(symmetry,[status(thm)],[16178])).
% 2.33/2.56 tff(16180,plain,
% 2.33/2.56 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16177])).
% 2.33/2.56 tff(16181,plain,
% 2.33/2.56 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16180, 1837])).
% 2.33/2.56 tff(16182,plain,
% 2.33/2.56 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16181])).
% 2.33/2.56 tff(16183,plain,
% 2.33/2.56 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[877, 16182])).
% 2.33/2.56 tff(16184,plain,
% 2.33/2.56 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16174])).
% 2.33/2.56 tff(16185,plain,
% 2.33/2.56 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16184])).
% 2.33/2.56 tff(16186,plain,
% 2.33/2.56 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.33/2.56 inference(symmetry,[status(thm)],[16185])).
% 2.33/2.56 tff(16187,plain,
% 2.33/2.56 (elem!1 = s(s(z))),
% 2.33/2.56 inference(transitivity,[status(thm)],[75, 16175, 91])).
% 2.33/2.56 tff(16188,plain,
% 2.33/2.56 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16187, 16186])).
% 2.33/2.56 tff(16189,plain,
% 2.33/2.56 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(symmetry,[status(thm)],[16188])).
% 2.33/2.56 tff(16190,plain,
% 2.33/2.56 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16189])).
% 2.33/2.56 tff(16191,plain,
% 2.33/2.56 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16187])).
% 2.33/2.56 tff(16192,plain,
% 2.33/2.56 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16191])).
% 2.33/2.56 tff(16193,plain,
% 2.33/2.56 (~b(elem!1, s(s(s(elem!1))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[4699, 271, 15030, 261, 1638])).
% 2.33/2.56 tff(16194,plain,
% 2.33/2.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16193, 16192])).
% 2.33/2.56 tff(16195,plain,
% 2.33/2.56 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16194, 16190])).
% 2.33/2.56 tff(16196,plain,
% 2.33/2.56 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1847, 16195, 16183])).
% 2.33/2.56 tff(16197,plain,
% 2.33/2.56 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16196, 16179])).
% 2.33/2.56 tff(16198,plain,
% 2.33/2.56 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16184, 16187])).
% 2.33/2.56 tff(16199,plain,
% 2.33/2.56 (s(s(s(z))) = s(elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2035, 16174])).
% 2.33/2.56 tff(16200,plain,
% 2.33/2.56 (~(elem!1 = s(s(elem!1)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[3917, 16199, 344])).
% 2.33/2.56 tff(16201,plain,
% 2.33/2.56 (~(s(s(elem!1)) = elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[197, 16200])).
% 2.33/2.56 tff(16202,plain,
% 2.33/2.56 (r(s(s(elem!1)), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[862, 16201, 859])).
% 2.33/2.56 tff(16203,plain,
% 2.33/2.56 (r(s(s(s(s(z)))), s(s(z)))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16202, 16198])).
% 2.33/2.56 tff(16204,plain,
% 2.33/2.56 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16185])).
% 2.33/2.56 tff(16205,plain,
% 2.33/2.56 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[12761, 16204])).
% 2.33/2.56 tff(16206,plain,
% 2.33/2.56 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16184, 16185])).
% 2.33/2.56 tff(16207,plain,
% 2.33/2.56 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16174])).
% 2.33/2.56 tff(16208,plain,
% 2.33/2.56 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.33/2.56 inference(symmetry,[status(thm)],[16207])).
% 2.33/2.56 tff(16209,plain,
% 2.33/2.56 (b(s(elem!1), s(s(s(elem!1))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[2073, 16208])).
% 2.33/2.56 tff(16210,plain,
% 2.33/2.56 (b(s(z), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[5659, 412, 15030, 258, 331, 909, 16101])).
% 2.33/2.56 tff(16211,plain,
% 2.33/2.56 (~b(s(elem!1), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[15307, 16210, 260, 261])).
% 2.33/2.56 tff(16212,plain,
% 2.33/2.56 (r(s(elem!1), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2243, 16211, 2207])).
% 2.33/2.56 tff(16213,plain,
% 2.33/2.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[3520, 121, 16101, 16212, 139])).
% 2.33/2.56 tff(16214,plain,
% 2.33/2.56 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[78, 16200])).
% 2.33/2.56 tff(16215,plain,
% 2.33/2.56 (b(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[681, 16214, 16213])).
% 2.33/2.56 tff(16216,plain,
% 2.33/2.56 (b(z, s(s(s(z))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[1421, 4920])).
% 2.33/2.56 tff(16217,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1209, 16216])).
% 2.33/2.56 tff(16218,plain,((~(s(s(s(z))) = s(elem!1))) | b(z, s(s(s(z)))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(16219,plain,
% 2.33/2.56 (~b(z, s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16218, 16199, 1209])).
% 2.33/2.56 tff(16220,plain,
% 2.33/2.56 (r(z, s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1439, 16219])).
% 2.33/2.56 tff(16221,plain,
% 2.33/2.56 (~b(s(s(elem!1)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13762, 543, 3407, 1638])).
% 2.33/2.56 tff(16222,plain,
% 2.33/2.56 (r(s(s(elem!1)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2430, 16221])).
% 2.33/2.56 tff(16223,plain,
% 2.33/2.56 (~b(s(s(elem!1)), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[5254, 543, 638, 739])).
% 2.33/2.56 tff(16224,plain,
% 2.33/2.56 (r(s(s(elem!1)), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[701, 16223, 694])).
% 2.33/2.56 tff(16225,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[14657, 16224, 16222, 412, 1441])).
% 2.33/2.56 tff(16226,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (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))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(16227,plain,
% 2.33/2.56 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16226, 412, 16220, 3313, 16215, 16209, 3407, 1638])).
% 2.33/2.56 tff(16228,plain,
% 2.33/2.56 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[556, 16227, 1])).
% 2.33/2.56 tff(16229,plain,
% 2.33/2.56 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16228, 16206])).
% 2.33/2.56 tff(16230,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16231,plain,
% 2.33/2.56 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(16232,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16231])).
% 2.33/2.56 tff(16233,plain,
% 2.33/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[16232, 16230])).
% 2.33/2.56 tff(16234,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(16235,plain,
% 2.33/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[16234, 16233])).
% 2.33/2.56 tff(16236,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16235, 121, 16229, 16205, 16203, 16197])).
% 2.33/2.56 tff(16237,plain,((~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(elem!1)), elem!1) | b(z, s(s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (z = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(16238,plain,
% 2.33/2.56 (~r(s(elem!1), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[16237, 16161, 3407, 1, 16151, 16108, 16141, 1209, 139, 16128, 16126, 16110, 260, 261, 258, 331, 110])).
% 2.33/2.56 tff(16239,plain,
% 2.33/2.56 (b(s(elem!1), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[409, 16238])).
% 2.33/2.56 tff(16240,plain,
% 2.33/2.56 (~(s(s(s(z))) = s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11011, 16238, 16126])).
% 2.33/2.56 tff(16241,plain,
% 2.33/2.56 (~(elem!1 = s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1100, 16102])).
% 2.33/2.56 tff(16242,plain,
% 2.33/2.56 (~b(elem!1, s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10766, 271, 260, 448, 16143])).
% 2.33/2.56 tff(16243,plain,
% 2.33/2.56 (r(elem!1, s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1192, 16242, 16241])).
% 2.33/2.56 tff(16244,plain,
% 2.33/2.56 (~b(s(elem!1), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11634, 16239, 15030, 261])).
% 2.33/2.56 tff(16245,plain,
% 2.33/2.56 (r(s(elem!1), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2243, 16244, 2207])).
% 2.33/2.56 tff(16246,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[3849, 16245, 16101, 16243])).
% 2.33/2.56 tff(16247,plain,
% 2.33/2.56 (b(s(s(s(z))), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1816, 16246, 16240])).
% 2.33/2.56 tff(16248,plain,
% 2.33/2.56 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2114, 16247, 16239, 16108])).
% 2.33/2.56 tff(16249,plain,
% 2.33/2.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[3520, 121, 16101, 16245, 139])).
% 2.33/2.56 tff(16250,plain,
% 2.33/2.56 (s(s(s(elem!1))) = s(elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[681, 16249, 16248])).
% 2.33/2.56 tff(16251,plain,
% 2.33/2.56 (elem!1 = s(s(elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[78, 16250])).
% 2.33/2.56 tff(16252,plain,
% 2.33/2.56 (s(elem!1) = s(s(s(elem!1)))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16251])).
% 2.33/2.56 tff(16253,plain,
% 2.33/2.56 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16252])).
% 2.33/2.56 tff(16254,plain,
% 2.33/2.56 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.33/2.56 inference(symmetry,[status(thm)],[16253])).
% 2.33/2.56 tff(16255,plain,
% 2.33/2.56 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16254])).
% 2.33/2.56 tff(16256,plain,
% 2.33/2.56 (s(s(s(elem!1))) = s(elem!1)),
% 2.33/2.56 inference(symmetry,[status(thm)],[16252])).
% 2.33/2.56 tff(16257,plain,
% 2.33/2.56 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16256])).
% 2.33/2.56 tff(16258,plain,
% 2.33/2.56 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16257])).
% 2.33/2.56 tff(16259,plain,
% 2.33/2.56 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[1008, 16258])).
% 2.33/2.56 tff(16260,plain,
% 2.33/2.56 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.33/2.56 inference(transitivity,[status(thm)],[3042, 2470])).
% 2.33/2.56 tff(16261,plain,
% 2.33/2.56 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[16260])).
% 2.33/2.57 tff(16262,plain,
% 2.33/2.57 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 2.33/2.57 inference(symmetry,[status(thm)],[16261])).
% 2.33/2.57 tff(16263,plain,
% 2.33/2.57 (s(elem!1) = s(s(s(s(z))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[605, 16262, 766])).
% 2.33/2.57 tff(16264,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2603, 16263])).
% 2.33/2.57 tff(16265,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16266,plain,
% 2.33/2.57 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16265, 16259, 16251])).
% 2.33/2.57 tff(16267,plain,
% 2.33/2.57 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16251])).
% 2.33/2.57 tff(16268,plain,
% 2.33/2.57 (b(z, s(s(elem!1)))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[15030, 16267])).
% 2.33/2.57 tff(16269,plain,
% 2.33/2.57 (r(s(s(elem!1)), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[12242, 16251, 16243])).
% 2.33/2.57 tff(16270,plain,
% 2.33/2.57 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16251])).
% 2.33/2.57 tff(16271,plain,
% 2.33/2.57 (b(s(s(elem!1)), z)),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[261, 16270])).
% 2.33/2.57 tff(16272,plain,
% 2.33/2.57 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[2470])).
% 2.33/2.57 tff(16273,assumption,(~r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.33/2.57 tff(16274,plain,
% 2.33/2.57 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1847, 16273, 5002])).
% 2.33/2.57 tff(16275,plain,
% 2.33/2.57 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16274, 16272])).
% 2.33/2.57 tff(16276,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16277,plain,
% 2.33/2.57 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16278,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16277])).
% 2.33/2.57 tff(16279,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[16278, 16276])).
% 2.33/2.57 tff(16280,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(16281,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16280, 16279])).
% 2.33/2.57 tff(16282,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16281, 121, 145, 1661, 1736, 1140])).
% 2.33/2.57 tff(16283,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16284,plain,
% 2.33/2.57 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16283, 1736, 145, 1140])).
% 2.33/2.57 tff(16285,plain,
% 2.33/2.57 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1658, 16284])).
% 2.33/2.57 tff(16286,plain,
% 2.33/2.57 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1847, 5002, 16273])).
% 2.33/2.57 tff(16287,plain,
% 2.33/2.57 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16286, 16272])).
% 2.33/2.57 tff(16288,plain,
% 2.33/2.57 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[2470])).
% 2.33/2.57 tff(16289,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.33/2.57 tff(16290,plain,
% 2.33/2.57 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[840, 4997, 16289])).
% 2.33/2.57 tff(16291,plain,
% 2.33/2.57 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16290, 16288])).
% 2.33/2.57 tff(16292,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16293,plain,
% 2.33/2.57 (((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16294,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16293])).
% 2.33/2.57 tff(16295,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[16294, 16292])).
% 2.33/2.57 tff(16296,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(16297,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16296, 16295])).
% 2.33/2.57 tff(16298,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16297, 271, 1894, 1639, 16291, 16287])).
% 2.33/2.57 tff(16299,plain,((s(s(s(s(s(z))))) = elem!1) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~(elem!1 = s(s(elem!1)))) | r(elem!1, s(s(s(s(s(z)))))) | r(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16300,plain,
% 2.33/2.57 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16299, 16285, 2470, 16273, 1894, 4997])).
% 2.33/2.57 tff(16301,plain,
% 2.33/2.57 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[5462, 16300, 2470])).
% 2.33/2.57 tff(16302,plain,
% 2.33/2.57 (r(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[13482, 2470, 145])).
% 2.33/2.57 tff(16303,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16304,plain,
% 2.33/2.57 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16305,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16304])).
% 2.33/2.57 tff(16306,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[16305, 16303])).
% 2.33/2.57 tff(16307,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(16308,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16307, 16306])).
% 2.33/2.57 tff(16309,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16308, 121, 1736, 16302, 16301, 13992])).
% 2.33/2.57 tff(16310,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | r(elem!1, s(s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16311,plain,
% 2.33/2.57 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16310, 16273, 2470, 13992, 1894, 4997, 145, 1140])).
% 2.33/2.57 tff(16312,plain,
% 2.33/2.57 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1733, 16311])).
% 2.33/2.57 tff(16313,plain,
% 2.33/2.57 (~r(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[3375, 145, 1140, 110])).
% 2.33/2.57 tff(16314,plain,
% 2.33/2.57 (b(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[105, 16313])).
% 2.33/2.57 tff(16315,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16316,plain,
% 2.33/2.57 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16317,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16316])).
% 2.33/2.57 tff(16318,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[16317, 16315])).
% 2.33/2.57 tff(16319,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(16320,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16319, 16318])).
% 2.33/2.57 tff(16321,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16320, 271, 2073, 3871, 1723, 5393])).
% 2.33/2.57 tff(16322,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16323,plain,
% 2.33/2.57 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16322, 16312, 16314, 2073])).
% 2.33/2.57 tff(16324,plain,
% 2.33/2.57 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1682, 16323])).
% 2.33/2.57 tff(16325,plain,
% 2.33/2.57 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1669, 16324, 110, 909])).
% 2.33/2.57 tff(16326,plain,
% 2.33/2.57 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1658, 16325])).
% 2.33/2.57 tff(16327,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16328,plain,
% 2.33/2.57 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16329,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16328])).
% 2.33/2.57 tff(16330,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[16329, 16327])).
% 2.33/2.57 tff(16331,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(16332,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16331, 16330])).
% 2.33/2.57 tff(16333,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16332, 271, 16326, 16312, 2449, 16275])).
% 2.33/2.57 tff(16334,plain,(r(elem!1, s(s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16335,plain,
% 2.33/2.57 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16334, 16271, 110, 16128, 16108, 16251, 16269, 16268, 16266, 16103, 6533])).
% 2.33/2.57 tff(16336,plain,
% 2.33/2.57 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[5456])).
% 2.33/2.57 tff(16337,plain,
% 2.33/2.57 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(symmetry,[status(thm)],[16336])).
% 2.33/2.57 tff(16338,plain,
% 2.33/2.57 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[1826, 16337])).
% 2.33/2.57 tff(16339,assumption,(~r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.33/2.57 tff(16340,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16339, 16338])).
% 2.33/2.57 tff(16341,plain,(r(s(s(elem!1)), s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(16342,plain,
% 2.33/2.57 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16341, 16335, 16251])).
% 2.33/2.57 tff(16343,plain,
% 2.33/2.57 (r(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[13482, 16251, 16103])).
% 2.33/2.57 tff(16344,assumption,(r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.33/2.57 tff(16345,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16346,plain,
% 2.33/2.57 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(16347,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[16346])).
% 2.33/2.57 tff(16348,plain,
% 2.33/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[16347, 16345])).
% 2.33/2.57 tff(16349,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(16350,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[16349, 16348])).
% 2.33/2.57 tff(16351,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[16350, 121, 1736, 7794, 13992, 16344])).
% 2.33/2.57 tff(16352,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.58 tff(16353,plain,
% 2.33/2.58 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16352, 16343, 16269, 16342])).
% 2.33/2.58 tff(16354,plain,
% 2.33/2.58 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[1733, 16353])).
% 2.33/2.58 tff(16355,plain,
% 2.33/2.58 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16322, 16354, 16110, 16108])).
% 2.33/2.58 tff(16356,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[1682, 16355])).
% 2.33/2.58 tff(16357,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16358,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(quant_inst,[status(thm)],[])).
% 2.33/2.58 tff(16359,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16358, 16357])).
% 2.33/2.58 tff(16360,plain,
% 2.33/2.58 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16359, 121, 16159, 16151, 16356])).
% 2.33/2.58 tff(16361,plain,
% 2.33/2.58 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16360, 16255])).
% 2.33/2.58 tff(16362,plain,
% 2.33/2.58 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[6358, 16251, 16240])).
% 2.33/2.58 tff(16363,plain,
% 2.33/2.58 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16252])).
% 2.33/2.58 tff(16364,plain,
% 2.33/2.58 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.33/2.58 inference(symmetry,[status(thm)],[16363])).
% 2.33/2.58 tff(16365,plain,
% 2.33/2.58 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16364])).
% 2.33/2.58 tff(16366,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16367,plain,
% 2.33/2.58 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16368,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16367])).
% 2.33/2.58 tff(16369,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16368, 16366])).
% 2.33/2.58 tff(16370,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 2.33/2.58 inference(quant_inst,[status(thm)],[])).
% 2.33/2.58 tff(16371,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16370, 16369])).
% 2.33/2.58 tff(16372,plain,
% 2.33/2.58 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16371, 271, 16118, 16108, 16354])).
% 2.33/2.58 tff(16373,plain,
% 2.33/2.58 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16372, 16365])).
% 2.33/2.58 tff(16374,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[4138, 16373, 16362])).
% 2.33/2.58 tff(16375,plain,
% 2.33/2.58 ($false),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16374, 16361])).
% 2.33/2.58 tff(16376,plain,(b(z, s(s(s(z)))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (z = elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.58 tff(16377,plain,
% 2.33/2.58 (b(z, s(s(s(z))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16376, 261, 1008, 110, 139, 3407, 1, 260, 258, 331, 448])).
% 2.33/2.58 tff(16378,plain,
% 2.33/2.58 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16106, 121, 379, 139, 145])).
% 2.33/2.58 tff(16379,plain,
% 2.33/2.58 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[2071, 16378, 2065])).
% 2.33/2.58 tff(16380,plain,
% 2.33/2.58 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16116, 121, 379, 139, 145])).
% 2.33/2.58 tff(16381,plain,
% 2.33/2.58 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[6237, 21, 16380, 11664])).
% 2.33/2.58 tff(16382,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16383,plain,
% 2.33/2.58 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16384,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16383])).
% 2.33/2.58 tff(16385,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16384, 16382])).
% 2.33/2.58 tff(16386,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.33/2.58 inference(quant_inst,[status(thm)],[])).
% 2.33/2.58 tff(16387,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16386, 16385])).
% 2.33/2.58 tff(16388,plain,
% 2.33/2.58 ($false),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16387, 271, 3407, 1307, 16381, 16379])).
% 2.33/2.58 tff(16389,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.58 tff(16390,plain,
% 2.33/2.58 (~r(s(s(s(z))), elem!1)),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16389, 16377, 3407, 2064, 16101, 139])).
% 2.33/2.58 tff(16391,plain,
% 2.33/2.58 (s(s(s(z))) = elem!1),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[255, 16390, 16096])).
% 2.33/2.58 tff(16392,plain,
% 2.33/2.58 (s(elem!1) = s(s(s(s(z))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[2605, 16391])).
% 2.33/2.58 tff(16393,plain,
% 2.33/2.58 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16392])).
% 2.33/2.58 tff(16394,plain,
% 2.33/2.58 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.33/2.58 inference(symmetry,[status(thm)],[16393])).
% 2.33/2.58 tff(16395,plain,
% 2.33/2.58 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16394])).
% 2.33/2.58 tff(16396,plain,
% 2.33/2.58 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.33/2.58 inference(symmetry,[status(thm)],[16395])).
% 2.33/2.58 tff(16397,plain,
% 2.33/2.58 (r(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16394])).
% 2.33/2.58 tff(16398,plain,
% 2.33/2.58 ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16397])).
% 2.33/2.58 tff(16399,plain,
% 2.33/2.58 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16392])).
% 2.33/2.58 tff(16400,plain,
% 2.33/2.58 (r(elem!1, s(s(s(s(z)))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16101, 16399])).
% 2.33/2.58 tff(16401,plain,
% 2.33/2.58 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16393])).
% 2.33/2.58 tff(16402,plain,
% 2.33/2.58 (~(elem!1 = s(s(elem!1)))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[3906, 16391])).
% 2.33/2.58 tff(16403,plain,
% 2.33/2.58 (~(s(s(elem!1)) = elem!1)),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[197, 16402])).
% 2.33/2.58 tff(16404,plain,
% 2.33/2.58 (r(s(s(elem!1)), elem!1)),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[862, 16403, 16141])).
% 2.33/2.58 tff(16405,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16404, 16401])).
% 2.33/2.58 tff(16406,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16407,plain,
% 2.33/2.58 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16408,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16407])).
% 2.33/2.58 tff(16409,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16408, 16406])).
% 2.33/2.58 tff(16410,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(quant_inst,[status(thm)],[])).
% 2.33/2.58 tff(16411,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16410, 16409])).
% 2.33/2.58 tff(16412,plain,
% 2.33/2.58 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16411, 121, 139, 16405, 16400])).
% 2.33/2.58 tff(16413,plain,
% 2.33/2.58 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16412, 16398])).
% 2.33/2.58 tff(16414,plain,
% 2.33/2.58 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[586, 16413, 563])).
% 2.33/2.58 tff(16415,plain,
% 2.33/2.58 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16414, 16396])).
% 2.33/2.58 tff(16416,plain,
% 2.33/2.58 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16393])).
% 2.33/2.58 tff(16417,plain,
% 2.33/2.58 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16393])).
% 2.33/2.58 tff(16418,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.58 inference(symmetry,[status(thm)],[16417])).
% 2.33/2.58 tff(16419,plain,
% 2.33/2.58 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16418])).
% 2.33/2.58 tff(16420,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16421,plain,
% 2.33/2.58 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16422,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16421])).
% 2.33/2.58 tff(16423,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16422, 16420])).
% 2.33/2.58 tff(16424,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.58 inference(quant_inst,[status(thm)],[])).
% 2.33/2.58 tff(16425,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16424, 16423])).
% 2.33/2.58 tff(16426,plain,
% 2.33/2.58 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16425, 121, 139, 16405, 16400])).
% 2.33/2.58 tff(16427,plain,
% 2.33/2.58 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16426, 16419])).
% 2.33/2.58 tff(16428,plain,
% 2.33/2.58 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[556, 16427, 1])).
% 2.33/2.58 tff(16429,plain,
% 2.33/2.58 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16428, 16416])).
% 2.33/2.58 tff(16430,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16391])).
% 2.33/2.58 tff(16431,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.58 inference(symmetry,[status(thm)],[16430])).
% 2.33/2.58 tff(16432,plain,
% 2.33/2.58 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16401, 16431])).
% 2.33/2.58 tff(16433,plain,
% 2.33/2.58 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16404, 16432])).
% 2.33/2.58 tff(16434,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16435,plain,
% 2.33/2.58 (((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16436,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16435])).
% 2.33/2.58 tff(16437,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16436, 16434])).
% 2.33/2.58 tff(16438,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(quant_inst,[status(thm)],[])).
% 2.33/2.58 tff(16439,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.33/2.58 inference(modus_ponens,[status(thm)],[16438, 16437])).
% 2.33/2.58 tff(16440,plain,
% 2.33/2.58 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16439, 271, 3407, 16429])).
% 2.33/2.58 tff(16441,plain,
% 2.33/2.58 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[16440, 16415])).
% 2.33/2.58 tff(16442,plain,
% 2.33/2.58 (r(z, s(s(s(s(s(z))))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[1658, 16441])).
% 2.33/2.58 tff(16443,plain,
% 2.33/2.58 (~r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[1744, 16442, 110, 16433])).
% 2.33/2.58 tff(16444,plain,
% 2.33/2.58 (b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.58 inference(unit_resolution,[status(thm)],[1756, 16443])).
% 2.33/2.58 tff(16445,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16446,plain,
% 2.33/2.58 (((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(rewrite,[status(thm)],[])).
% 2.33/2.58 tff(16447,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.33/2.58 inference(monotonicity,[status(thm)],[16446])).
% 2.33/2.58 tff(16448,plain,
% 2.33/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.58 inference(transitivity,[status(thm)],[16447, 16445])).
% 2.33/2.58 tff(16449,plain,
% 2.33/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16450,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16449, 16448])).
% 2.33/2.59 tff(16451,plain,
% 2.33/2.59 (~b(s(s(s(elem!1))), s(z))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16450, 271, 16444, 16429, 16415])).
% 2.33/2.59 tff(16452,plain,
% 2.33/2.59 (r(s(s(s(elem!1))), s(z))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[66, 21, 16451, 63])).
% 2.33/2.59 tff(16453,plain,
% 2.33/2.59 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1669, 16442, 110, 16128])).
% 2.33/2.59 tff(16454,plain,
% 2.33/2.59 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1682, 16453])).
% 2.33/2.59 tff(16455,plain,
% 2.33/2.59 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16393])).
% 2.33/2.59 tff(16456,plain,
% 2.33/2.59 (~r(s(z), s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[9700, 16443, 16392])).
% 2.33/2.59 tff(16457,plain,
% 2.33/2.59 (b(s(z), s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[2167, 16456])).
% 2.33/2.59 tff(16458,plain,
% 2.33/2.59 (~b(elem!1, s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[4433, 16457, 448, 16428])).
% 2.33/2.59 tff(16459,plain,
% 2.33/2.59 (r(elem!1, s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[599, 16458, 16402])).
% 2.33/2.59 tff(16460,plain,
% 2.33/2.59 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16459, 16455])).
% 2.33/2.59 tff(16461,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.33/2.59 tff(16462,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16463,plain,
% 2.33/2.59 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16464,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16463])).
% 2.33/2.59 tff(16465,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16464, 16462])).
% 2.33/2.59 tff(16466,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16467,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16466, 16465])).
% 2.33/2.59 tff(16468,plain,
% 2.33/2.59 ($false),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16467, 121, 1758, 1826, 1736, 16461])).
% 2.33/2.59 tff(16469,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.59 tff(16470,plain,
% 2.33/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16469, 16460, 16400, 16433])).
% 2.33/2.59 tff(16471,plain,
% 2.33/2.59 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1777, 16470])).
% 2.33/2.59 tff(16472,plain,
% 2.33/2.59 (~b(s(s(s(s(z)))), s(z))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1785, 16471, 16454, 16444])).
% 2.33/2.59 tff(16473,plain,
% 2.33/2.59 (r(s(s(s(s(z)))), s(z))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[932, 16472])).
% 2.33/2.59 tff(16474,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16475,plain,
% 2.33/2.59 (((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(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(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16476,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16475])).
% 2.33/2.59 tff(16477,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16476, 16474])).
% 2.33/2.59 tff(16478,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16479,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16478, 16477])).
% 2.33/2.59 tff(16480,plain,
% 2.33/2.59 (~b(s(z), s(s(s(s(z)))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16479, 271, 16471, 16444, 16429])).
% 2.33/2.59 tff(16481,plain,
% 2.33/2.59 ($false),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1064, 21, 9594, 1050, 1061])).
% 2.33/2.59 tff(16482,plain,(r(s(z), s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.59 tff(16483,plain,
% 2.33/2.59 (r(s(z), s(s(s(s(z)))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16482, 16480])).
% 2.33/2.59 tff(16484,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16485,plain,
% 2.33/2.59 (((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16486,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16485])).
% 2.33/2.59 tff(16487,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16486, 16484])).
% 2.33/2.59 tff(16488,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16489,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16488, 16487])).
% 2.33/2.59 tff(16490,plain,
% 2.33/2.59 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16489, 271, 16471, 16429, 16415])).
% 2.33/2.59 tff(16491,plain,
% 2.33/2.59 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1014, 16490, 1008])).
% 2.33/2.59 tff(16492,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16493,plain,
% 2.33/2.59 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), 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)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16494,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16493])).
% 2.33/2.59 tff(16495,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16494, 16492])).
% 2.33/2.59 tff(16496,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16497,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16496, 16495])).
% 2.33/2.59 tff(16498,plain,
% 2.33/2.59 ($false),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16497, 121, 12761, 911, 1026, 13550])).
% 2.33/2.59 tff(16499,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.59 tff(16500,plain,
% 2.33/2.59 ($false),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16499, 16491, 16483, 16473, 16452])).
% 2.33/2.59 tff(16501,plain,((~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.59 tff(16502,plain,
% 2.33/2.59 (~b(elem!1, z)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16501, 448, 1008, 110, 3407, 1, 139, 260, 258, 331])).
% 2.33/2.59 tff(16503,plain,
% 2.33/2.59 (r(elem!1, z)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[284, 16502, 358])).
% 2.33/2.59 tff(16504,plain,
% 2.33/2.59 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[244])).
% 2.33/2.59 tff(16505,plain,
% 2.33/2.59 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.59 inference(symmetry,[status(thm)],[16504])).
% 2.33/2.59 tff(16506,plain,
% 2.33/2.59 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[9439])).
% 2.33/2.59 tff(16507,plain,
% 2.33/2.59 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(elem!1)))),
% 2.33/2.59 inference(symmetry,[status(thm)],[16506])).
% 2.33/2.59 tff(16508,plain,
% 2.33/2.59 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[244])).
% 2.33/2.59 tff(16509,plain,
% 2.33/2.59 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16508, 16507, 16505])).
% 2.33/2.59 tff(16510,plain,
% 2.33/2.59 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.59 inference(symmetry,[status(thm)],[15705])).
% 2.33/2.59 tff(16511,plain,
% 2.33/2.59 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.59 inference(monotonicity,[status(thm)],[9439])).
% 2.33/2.59 tff(16512,plain,
% 2.33/2.59 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16511, 16510])).
% 2.33/2.59 tff(16513,plain,
% 2.33/2.59 (~(s(s(elem!1)) = elem!1)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[197, 15680])).
% 2.33/2.59 tff(16514,plain,
% 2.33/2.59 (r(s(s(elem!1)), elem!1)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[862, 16513, 859])).
% 2.33/2.59 tff(16515,plain,
% 2.33/2.59 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16514, 16512])).
% 2.33/2.59 tff(16516,plain,
% 2.33/2.59 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[15675])).
% 2.33/2.59 tff(16517,plain,
% 2.33/2.59 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(symmetry,[status(thm)],[16516])).
% 2.33/2.59 tff(16518,plain,
% 2.33/2.59 (r(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[15675])).
% 2.33/2.59 tff(16519,plain,
% 2.33/2.59 ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16518])).
% 2.33/2.59 tff(16520,plain,
% 2.33/2.59 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16514, 16511])).
% 2.33/2.59 tff(16521,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16522,plain,
% 2.33/2.59 (((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16523,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16522])).
% 2.33/2.59 tff(16524,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(transitivity,[status(thm)],[16523, 16521])).
% 2.33/2.59 tff(16525,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16526,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16525, 16524])).
% 2.33/2.59 tff(16527,plain,
% 2.33/2.59 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16526, 121, 1409, 139, 16520])).
% 2.33/2.59 tff(16528,plain,
% 2.33/2.59 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16527, 16519])).
% 2.33/2.59 tff(16529,plain,
% 2.33/2.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[586, 16528, 563])).
% 2.33/2.59 tff(16530,plain,
% 2.33/2.59 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16529, 16517])).
% 2.33/2.59 tff(16531,plain,
% 2.33/2.59 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.59 inference(symmetry,[status(thm)],[15689])).
% 2.33/2.59 tff(16532,plain,
% 2.33/2.59 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.33/2.59 inference(monotonicity,[status(thm)],[16531])).
% 2.33/2.59 tff(16533,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.59 inference(rewrite,[status(thm)],[])).
% 2.33/2.59 tff(16534,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.33/2.59 inference(quant_inst,[status(thm)],[])).
% 2.33/2.59 tff(16535,plain,
% 2.33/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16534, 16533])).
% 2.33/2.59 tff(16536,plain,
% 2.33/2.59 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16535, 121, 1409, 139, 16520])).
% 2.33/2.59 tff(16537,plain,
% 2.33/2.59 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16536, 16532])).
% 2.33/2.59 tff(16538,plain,
% 2.33/2.59 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[556, 16537, 1])).
% 2.33/2.59 tff(16539,plain,
% 2.33/2.59 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16538, 15708])).
% 2.33/2.59 tff(16540,plain,
% 2.33/2.59 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16439, 271, 3407, 16539])).
% 2.33/2.59 tff(16541,plain,
% 2.33/2.59 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16540, 16530])).
% 2.33/2.59 tff(16542,plain,
% 2.33/2.59 (r(z, s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1658, 16541])).
% 2.33/2.59 tff(16543,plain,
% 2.33/2.59 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[5135, 16542, 15714, 16515])).
% 2.33/2.59 tff(16544,plain,
% 2.33/2.59 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1494, 16543])).
% 2.33/2.59 tff(16545,plain,
% 2.33/2.59 (b(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.59 inference(modus_ponens,[status(thm)],[16544, 16509])).
% 2.33/2.59 tff(16546,plain,
% 2.33/2.59 (~r(s(z), s(s(s(z))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[250, 244, 232])).
% 2.33/2.59 tff(16547,plain,
% 2.33/2.59 (b(s(z), s(s(s(z))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[105, 16546])).
% 2.33/2.59 tff(16548,plain,
% 2.33/2.59 (~r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1744, 16542, 110, 16515])).
% 2.33/2.59 tff(16549,plain,
% 2.33/2.59 (~r(s(z), s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[9700, 16548, 2606])).
% 2.33/2.59 tff(16550,plain,
% 2.33/2.59 (b(s(z), s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[2167, 16549])).
% 2.33/2.59 tff(16551,plain,
% 2.33/2.59 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[15399, 16550, 16547, 16538])).
% 2.33/2.59 tff(16552,plain,
% 2.33/2.59 ($false),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16551, 16545])).
% 2.33/2.59 tff(16553,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.59 tff(16554,plain,
% 2.33/2.59 (~(s(s(s(z))) = elem!1)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[16553, 16503, 3407, 1, 110, 139, 16141, 232])).
% 2.33/2.59 tff(16555,plain,
% 2.33/2.59 (r(s(s(s(z))), elem!1)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[255, 16554, 16096])).
% 2.33/2.59 tff(16556,plain,
% 2.33/2.59 (~r(s(s(s(z))), z)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[15900, 16555, 16128, 16503])).
% 2.33/2.59 tff(16557,plain,
% 2.33/2.59 (b(s(s(s(z))), z)),
% 2.33/2.59 inference(unit_resolution,[status(thm)],[1155, 16556])).
% 2.33/2.59 tff(16558,plain,
% 2.33/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.33/2.60 inference(rewrite,[status(thm)],[])).
% 2.33/2.60 tff(16559,plain,
% 2.33/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.33/2.60 inference(quant_inst,[status(thm)],[])).
% 2.33/2.60 tff(16560,plain,
% 2.33/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.33/2.60 inference(modus_ponens,[status(thm)],[16559, 16558])).
% 2.33/2.60 tff(16561,plain,
% 2.33/2.60 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.60 inference(unit_resolution,[status(thm)],[16560, 121, 16503, 139, 16555])).
% 2.33/2.60 tff(16562,plain,
% 2.33/2.60 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.33/2.60 inference(unit_resolution,[status(thm)],[2071, 16561, 2064])).
% 2.33/2.60 tff(16563,plain,
% 2.33/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.60 inference(rewrite,[status(thm)],[])).
% 2.33/2.60 tff(16564,plain,
% 2.33/2.60 (((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.60 inference(rewrite,[status(thm)],[])).
% 2.33/2.60 tff(16565,plain,
% 2.33/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.33/2.60 inference(monotonicity,[status(thm)],[16564])).
% 2.33/2.60 tff(16566,plain,
% 2.33/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.60 inference(transitivity,[status(thm)],[16565, 16563])).
% 2.33/2.60 tff(16567,plain,
% 2.33/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.33/2.60 inference(quant_inst,[status(thm)],[])).
% 2.33/2.60 tff(16568,plain,
% 2.33/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.33/2.60 inference(modus_ponens,[status(thm)],[16567, 16566])).
% 2.33/2.60 tff(16569,plain,
% 2.33/2.60 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.60 inference(unit_resolution,[status(thm)],[16568, 121, 16503, 139, 16555])).
% 2.33/2.60 tff(16570,plain,
% 2.33/2.60 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.33/2.60 inference(unit_resolution,[status(thm)],[6237, 21, 16569, 13970])).
% 2.33/2.60 tff(16571,plain,
% 2.33/2.60 ($false),
% 2.33/2.60 inference(unit_resolution,[status(thm)],[16124, 271, 3407, 16570, 16562, 16557])).
% 2.33/2.60 tff(16572,plain,((~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | r(s(z), elem!1) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16573,plain,
% 2.43/2.60 (~b(elem!1, s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16572, 232, 139, 1, 110, 3407, 13988, 237, 243, 331])).
% 2.43/2.60 tff(16574,plain,
% 2.43/2.60 (r(elem!1, s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[299, 16573, 243])).
% 2.43/2.60 tff(16575,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[12976, 121, 110, 139, 12761, 3456])).
% 2.43/2.60 tff(16576,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16577,plain,
% 2.43/2.60 (~r(s(s(s(elem!1))), s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16576, 16574, 139, 110])).
% 2.43/2.60 tff(16578,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.43/2.60 tff(16579,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[66, 21, 38, 16578, 63])).
% 2.43/2.60 tff(16580,plain,(r(s(s(s(elem!1))), s(z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16581,plain,
% 2.43/2.60 (b(s(s(s(elem!1))), s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16580, 16577])).
% 2.43/2.60 tff(16582,plain,
% 2.43/2.60 (~b(z, s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[15639, 16581, 237, 3407])).
% 2.43/2.60 tff(16583,plain,
% 2.43/2.60 (r(z, s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[904, 16582])).
% 2.43/2.60 tff(16584,plain,
% 2.43/2.60 (~r(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[9121, 121, 110, 16583, 16574])).
% 2.43/2.60 tff(16585,plain,
% 2.43/2.60 (b(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[284, 16584, 358])).
% 2.43/2.60 tff(16586,plain,
% 2.43/2.60 (~b(elem!1, s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16099, 16585, 237, 344, 3407, 15030])).
% 2.43/2.60 tff(16587,plain,
% 2.43/2.60 (r(elem!1, s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[392, 16586, 219])).
% 2.43/2.60 tff(16588,plain,
% 2.43/2.60 (~b(s(s(s(z))), s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[276, 257, 261, 260])).
% 2.43/2.60 tff(16589,plain,
% 2.43/2.60 (r(s(s(s(z))), s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2325, 16588])).
% 2.43/2.60 tff(16590,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[11100, 16589, 11659, 909, 110])).
% 2.43/2.60 tff(16591,plain,((~b(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16592,plain,
% 2.43/2.60 (~b(s(s(s(z))), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16591, 16585, 110, 237, 16583, 15030])).
% 2.43/2.60 tff(16593,plain,
% 2.43/2.60 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[1008, 936])).
% 2.43/2.60 tff(16594,plain,
% 2.43/2.60 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[2607])).
% 2.43/2.60 tff(16595,plain,
% 2.43/2.60 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.43/2.60 inference(symmetry,[status(thm)],[16594])).
% 2.43/2.60 tff(16596,plain,
% 2.43/2.60 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[16595])).
% 2.43/2.60 tff(16597,plain,
% 2.43/2.60 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[7173, 261, 3407, 1326])).
% 2.43/2.60 tff(16598,plain,
% 2.43/2.60 (~b(s(s(s(z))), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[6165, 244, 317])).
% 2.43/2.60 tff(16599,plain,
% 2.43/2.60 (~r(s(elem!1), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[3994, 16598, 2564, 294, 894, 317, 379, 16597])).
% 2.43/2.60 tff(16600,plain,
% 2.43/2.60 (b(s(elem!1), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[409, 16599])).
% 2.43/2.60 tff(16601,plain,
% 2.43/2.60 (~b(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[11634, 16600, 1326, 261])).
% 2.43/2.60 tff(16602,plain,
% 2.43/2.60 (r(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2243, 16601, 2564])).
% 2.43/2.60 tff(16603,plain,
% 2.43/2.60 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[9184, 16602, 139, 379])).
% 2.43/2.60 tff(16604,plain,
% 2.43/2.60 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[16603, 16596])).
% 2.43/2.60 tff(16605,plain,
% 2.43/2.60 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1000, 21, 16604])).
% 2.43/2.60 tff(16606,plain,
% 2.43/2.60 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16605, 16593])).
% 2.43/2.60 tff(16607,plain,
% 2.43/2.60 (b(s(s(s(s(z)))), z)),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[16600, 9479])).
% 2.43/2.60 tff(16608,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16609,plain,
% 2.43/2.60 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16610,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[16609])).
% 2.43/2.60 tff(16611,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.43/2.60 inference(transitivity,[status(thm)],[16610, 16608])).
% 2.43/2.60 tff(16612,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(16613,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[16612, 16611])).
% 2.43/2.60 tff(16614,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16613, 271, 3407, 503, 16607, 16606])).
% 2.43/2.60 tff(16615,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | b(elem!1, s(z)) | b(z, s(z)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16616,plain,
% 2.43/2.60 (~(s(s(s(z))) = elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16615, 16581, 3407, 13988, 139, 16587, 2207, 15030, 16585, 16573, 16582, 16586])).
% 2.43/2.60 tff(16617,plain,
% 2.43/2.60 (r(s(s(s(z))), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[255, 16616, 16592])).
% 2.43/2.60 tff(16618,plain,
% 2.43/2.60 (~b(z, s(s(s(z))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16389, 16617, 3407, 2064, 16587, 139])).
% 2.43/2.60 tff(16619,plain,
% 2.43/2.60 (r(z, s(s(s(z))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1214, 16618])).
% 2.43/2.60 tff(16620,plain,
% 2.43/2.60 (~r(s(s(s(z))), s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[11100, 16619, 16583, 110])).
% 2.43/2.60 tff(16621,plain,
% 2.43/2.60 (b(s(s(s(z))), s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2325, 16620])).
% 2.43/2.60 tff(16622,plain,
% 2.43/2.60 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16106, 121, 16587, 139, 16617])).
% 2.43/2.60 tff(16623,plain,
% 2.43/2.60 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2071, 16622, 2064])).
% 2.43/2.60 tff(16624,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16625,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(16626,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[16625, 16624])).
% 2.43/2.60 tff(16627,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16626, 271, 237, 16623, 16621, 16581])).
% 2.43/2.60 tff(16628,plain,(r(s(z), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16629,plain,
% 2.43/2.60 (r(s(z), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16628, 16095, 110, 3407, 1, 331, 231])).
% 2.43/2.60 tff(16630,plain,
% 2.43/2.60 (~r(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[15739, 909, 110, 357])).
% 2.43/2.60 tff(16631,plain,
% 2.43/2.60 (b(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[284, 16630, 259])).
% 2.43/2.60 tff(16632,plain,
% 2.43/2.60 (~r(s(elem!1), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[9537, 909, 348, 2282, 357, 448, 307, 110])).
% 2.43/2.60 tff(16633,plain,
% 2.43/2.60 (b(s(elem!1), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[409, 16632])).
% 2.43/2.60 tff(16634,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[3415, 16633, 16631, 3407, 307])).
% 2.43/2.60 tff(16635,plain,((~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (elem!1 = z) | (s(z) = s(elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16636,plain,
% 2.43/2.60 (~r(z, s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16635, 448, 2345, 358, 344, 357, 3407, 110])).
% 2.43/2.60 tff(16637,plain,
% 2.43/2.60 (b(z, s(z))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[904, 16636])).
% 2.43/2.60 tff(16638,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16639,plain,
% 2.43/2.60 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16640,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[16639])).
% 2.43/2.60 tff(16641,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.43/2.60 inference(transitivity,[status(thm)],[16640, 16638])).
% 2.43/2.60 tff(16642,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(16643,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[16642, 16641])).
% 2.43/2.60 tff(16644,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16643, 271, 1326, 505, 448, 220])).
% 2.43/2.60 tff(16645,plain,((~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16646,plain,
% 2.43/2.60 (~b(s(z), s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16645, 448, 15030, 16637])).
% 2.43/2.60 tff(16647,plain,
% 2.43/2.60 (r(s(z), s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2167, 16646])).
% 2.43/2.60 tff(16648,plain,
% 2.43/2.60 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[12919, 16637, 15030, 448])).
% 2.43/2.60 tff(16649,plain,
% 2.43/2.60 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[760, 16648])).
% 2.43/2.60 tff(16650,plain,
% 2.43/2.60 (~b(s(z), s(s(s(z))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[11002, 16637, 15030, 448])).
% 2.43/2.60 tff(16651,plain,
% 2.43/2.60 (r(s(z), s(s(s(z))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[105, 16650])).
% 2.43/2.60 tff(16652,plain,
% 2.43/2.60 (~r(z, s(s(s(z))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[15950, 13704, 110, 357])).
% 2.43/2.60 tff(16653,plain,
% 2.43/2.60 (b(z, s(s(s(z))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1214, 16652])).
% 2.43/2.60 tff(16654,plain,
% 2.43/2.60 (~r(s(s(s(z))), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[15964, 16653, 357, 220, 13704])).
% 2.43/2.60 tff(16655,plain,
% 2.43/2.60 (~b(s(s(s(z))), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[9353, 16654, 1326, 307, 394])).
% 2.43/2.60 tff(16656,plain,
% 2.43/2.60 (r(s(s(s(z))), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1155, 16655])).
% 2.43/2.60 tff(16657,plain,
% 2.43/2.60 (~r(z, s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2096, 16656, 108, 110])).
% 2.43/2.60 tff(16658,plain,
% 2.43/2.60 (b(z, s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2106, 16657])).
% 2.43/2.60 tff(16659,plain,
% 2.43/2.60 (~b(s(s(s(z))), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1978, 16653, 1326, 307])).
% 2.43/2.60 tff(16660,plain,
% 2.43/2.60 (s(s(s(z))) = elem!1),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[255, 16654, 16659])).
% 2.43/2.60 tff(16661,plain,
% 2.43/2.60 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.43/2.60 inference(monotonicity,[status(thm)],[16660])).
% 2.43/2.60 tff(16662,plain,
% 2.43/2.60 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.60 inference(symmetry,[status(thm)],[16661])).
% 2.43/2.60 tff(16663,plain,
% 2.43/2.60 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[139, 16662])).
% 2.43/2.60 tff(16664,plain,
% 2.43/2.60 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[15840, 16663, 220, 572, 16658])).
% 2.43/2.60 tff(16665,plain,
% 2.43/2.60 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[556, 16664, 1])).
% 2.43/2.60 tff(16666,plain,
% 2.43/2.60 (~(elem!1 = s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[3906, 16660])).
% 2.43/2.60 tff(16667,plain,
% 2.43/2.60 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[78, 16666])).
% 2.43/2.60 tff(16668,plain,
% 2.43/2.60 (~b(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[4598, 394, 1326, 307])).
% 2.43/2.60 tff(16669,plain,
% 2.43/2.60 (r(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2243, 16668, 2207])).
% 2.43/2.60 tff(16670,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16671,plain,
% 2.43/2.60 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16672,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[16671])).
% 2.43/2.60 tff(16673,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.43/2.60 inference(transitivity,[status(thm)],[16672, 16670])).
% 2.43/2.60 tff(16674,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(16675,plain,
% 2.43/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[16674, 16673])).
% 2.43/2.60 tff(16676,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16675, 271, 1326, 543, 1894, 588])).
% 2.43/2.60 tff(16677,plain,((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16678,plain,
% 2.43/2.60 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16677, 16665, 1326, 16658])).
% 2.43/2.60 tff(16679,plain,
% 2.43/2.60 (r(elem!1, s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[599, 16678, 16666])).
% 2.43/2.60 tff(16680,plain,
% 2.43/2.60 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[720, 16679, 139, 16669])).
% 2.43/2.60 tff(16681,plain,
% 2.43/2.60 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[681, 16680, 16667])).
% 2.43/2.60 tff(16682,plain,
% 2.43/2.60 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1921, 16665, 110, 572, 16658])).
% 2.43/2.60 tff(16683,plain,
% 2.43/2.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[586, 16682, 563])).
% 2.43/2.60 tff(16684,plain,
% 2.43/2.60 (~r(s(s(elem!1)), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[14145, 16683, 139, 16679])).
% 2.43/2.60 tff(16685,plain,
% 2.43/2.60 (b(s(s(elem!1)), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2430, 16684])).
% 2.43/2.60 tff(16686,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[5267, 16685, 16681, 3407, 16665])).
% 2.43/2.60 tff(16687,plain,((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16688,plain,
% 2.43/2.60 (~b(s(elem!1), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16687, 16649, 139, 110, 3407, 15030, 1, 16637, 16651, 2345, 357, 358])).
% 2.43/2.60 tff(16689,plain,
% 2.43/2.60 (r(s(elem!1), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[409, 16688])).
% 2.43/2.60 tff(16690,plain,
% 2.43/2.60 (~b(z, s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[15101, 15091, 377, 1326, 2344])).
% 2.43/2.60 tff(16691,plain,
% 2.43/2.60 (r(z, s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1439, 16690])).
% 2.43/2.60 tff(16692,plain,
% 2.43/2.60 (b(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2243, 15091, 3500])).
% 2.43/2.60 tff(16693,plain,
% 2.43/2.60 (~b(s(z), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[3019, 16692, 15905, 448])).
% 2.43/2.60 tff(16694,plain,
% 2.43/2.60 (r(s(z), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[444, 16693, 348])).
% 2.43/2.60 tff(16695,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[12111, 16694, 16691, 110, 412])).
% 2.43/2.60 tff(16696,plain,(r(s(elem!1), elem!1) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16697,plain,
% 2.43/2.60 (r(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16696, 16689, 110, 344, 448, 219, 15030, 2344])).
% 2.43/2.60 tff(16698,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2741, 121, 623, 1625, 572, 139])).
% 2.43/2.60 tff(16699,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(16700,plain,
% 2.43/2.60 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16699, 16647, 16649, 139])).
% 2.43/2.60 tff(16701,plain,
% 2.43/2.60 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[556, 16700, 1])).
% 2.43/2.60 tff(16702,plain,
% 2.43/2.60 (~r(s(s(elem!1)), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[11783, 2088, 110, 1625])).
% 2.43/2.60 tff(16703,plain,
% 2.43/2.60 (~(s(s(elem!1)) = s(elem!1))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[2209, 4447])).
% 2.43/2.60 tff(16704,plain,
% 2.43/2.60 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[562, 2208])).
% 2.43/2.60 tff(16705,plain,
% 2.43/2.60 (r(s(z), s(s(elem!1)))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2167, 519])).
% 2.43/2.60 tff(16706,plain,
% 2.43/2.60 (~(elem!1 = s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[218, 2209])).
% 2.43/2.60 tff(16707,plain,
% 2.43/2.60 (~(s(elem!1) = elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2206, 16706])).
% 2.43/2.60 tff(16708,plain,
% 2.43/2.60 (r(s(elem!1), elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[2243, 2467, 16707])).
% 2.43/2.60 tff(16709,plain,
% 2.43/2.60 (~(s(z) = s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[521, 517, 519])).
% 2.43/2.60 tff(16710,plain,
% 2.43/2.60 (~(z = elem!1)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[500, 16709])).
% 2.43/2.60 tff(16711,plain,
% 2.43/2.60 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[10869, 517, 543, 2449, 16704, 2088])).
% 2.43/2.60 tff(16712,plain,
% 2.43/2.60 (r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[681, 16711, 79])).
% 2.43/2.60 tff(16713,plain,
% 2.43/2.60 (~r(s(s(s(elem!1))), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[6850, 412, 2088, 16712])).
% 2.43/2.60 tff(16714,plain,
% 2.43/2.60 (b(s(s(s(elem!1))), z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1904, 21, 30, 16713])).
% 2.43/2.60 tff(16715,plain,
% 2.43/2.60 (~r(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[4890, 412, 2088, 622])).
% 2.43/2.60 tff(16716,plain,
% 2.43/2.60 ((elem!1 = z) | b(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[282, 21, 16715])).
% 2.43/2.60 tff(16717,plain,
% 2.43/2.60 (b(elem!1, z)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[16716, 2886])).
% 2.43/2.60 tff(16718,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16719,plain,
% 2.43/2.60 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(16720,plain,
% 2.43/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16719])).
% 2.43/2.61 tff(16721,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[16720, 16718])).
% 2.43/2.61 tff(16722,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(16723,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16722, 16721])).
% 2.43/2.61 tff(16724,plain,
% 2.43/2.61 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16723, 271, 16717, 220, 16714])).
% 2.43/2.61 tff(16725,plain,
% 2.43/2.61 (b(elem!1, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[392, 2344, 16706])).
% 2.43/2.61 tff(16726,plain,
% 2.43/2.61 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[9687, 16725, 543, 517])).
% 2.43/2.61 tff(16727,plain,
% 2.43/2.61 (r(elem!1, s(s(elem!1)))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[599, 16726, 68])).
% 2.43/2.61 tff(16728,plain,
% 2.43/2.61 (~r(s(s(s(elem!1))), elem!1)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[720, 16727, 684, 622])).
% 2.43/2.61 tff(16729,plain,
% 2.43/2.61 (s(s(s(elem!1))) = elem!1),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[486, 16728, 479])).
% 2.43/2.61 tff(16730,plain,
% 2.43/2.61 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16729])).
% 2.43/2.61 tff(16731,plain,
% 2.43/2.61 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.61 inference(symmetry,[status(thm)],[16730])).
% 2.43/2.61 tff(16732,plain,
% 2.43/2.61 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16731])).
% 2.43/2.61 tff(16733,plain,
% 2.43/2.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[2344, 16732])).
% 2.43/2.61 tff(16734,plain,
% 2.43/2.61 ($false),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[684, 16733])).
% 2.43/2.61 tff(16735,plain,(r(elem!1, s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.61 tff(16736,plain,
% 2.43/2.61 (r(elem!1, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16735, 16724, 16712, 622, 68, 543, 517])).
% 2.43/2.61 tff(16737,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16738,plain,
% 2.43/2.61 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16739,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16738])).
% 2.43/2.61 tff(16740,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(transitivity,[status(thm)],[16739, 16737])).
% 2.43/2.61 tff(16741,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(16742,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16741, 16740])).
% 2.43/2.61 tff(16743,plain,
% 2.43/2.61 (~r(elem!1, s(s(s(elem!1))))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16742, 121, 16736, 622, 16712])).
% 2.43/2.61 tff(16744,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16745,plain,
% 2.43/2.61 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16746,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16745])).
% 2.43/2.61 tff(16747,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(transitivity,[status(thm)],[16746, 16744])).
% 2.43/2.61 tff(16748,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(16749,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16748, 16747])).
% 2.43/2.61 tff(16750,plain,
% 2.43/2.61 (~b(elem!1, s(s(s(elem!1))))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16749, 271, 16717, 220, 16714])).
% 2.43/2.61 tff(16751,plain,
% 2.43/2.61 ((elem!1 = s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[660, 21, 16750])).
% 2.43/2.61 tff(16752,plain,
% 2.43/2.61 (elem!1 = s(s(s(elem!1)))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16751, 16743])).
% 2.43/2.61 tff(16753,plain,
% 2.43/2.61 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16752])).
% 2.43/2.61 tff(16754,plain,
% 2.43/2.61 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16753])).
% 2.43/2.61 tff(16755,plain,
% 2.43/2.61 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.43/2.61 inference(symmetry,[status(thm)],[16754])).
% 2.43/2.61 tff(16756,plain,
% 2.43/2.61 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(elem!1)), z)),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16755])).
% 2.43/2.61 tff(16757,plain,
% 2.43/2.61 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 2.43/2.61 inference(symmetry,[status(thm)],[16756])).
% 2.43/2.61 tff(16758,plain,
% 2.43/2.61 (b(s(s(s(s(s(elem!1))))), z)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[2449, 16757])).
% 2.43/2.61 tff(16759,plain,
% 2.43/2.61 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16754])).
% 2.43/2.61 tff(16760,plain,
% 2.43/2.61 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[543, 16759])).
% 2.43/2.61 tff(16761,plain,
% 2.43/2.61 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16752])).
% 2.43/2.61 tff(16762,plain,
% 2.43/2.61 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16752])).
% 2.43/2.61 tff(16763,plain,
% 2.43/2.61 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 2.43/2.61 inference(symmetry,[status(thm)],[16762])).
% 2.43/2.61 tff(16764,plain,
% 2.43/2.61 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, elem!1))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16763])).
% 2.43/2.61 tff(16765,plain,
% 2.43/2.61 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16752])).
% 2.43/2.61 tff(16766,plain,
% 2.43/2.61 (r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[622, 16765])).
% 2.43/2.61 tff(16767,plain,
% 2.43/2.61 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[13202])).
% 2.43/2.61 tff(16768,plain,
% 2.43/2.61 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.43/2.61 inference(symmetry,[status(thm)],[16767])).
% 2.43/2.61 tff(16769,plain,
% 2.43/2.61 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16768])).
% 2.43/2.61 tff(16770,plain,
% 2.43/2.61 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.43/2.61 inference(symmetry,[status(thm)],[16769])).
% 2.43/2.61 tff(16771,plain,
% 2.43/2.61 (r(s(s(s(s(elem!1)))), z)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[412, 16770])).
% 2.43/2.61 tff(16772,plain,
% 2.43/2.61 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16768])).
% 2.43/2.61 tff(16773,plain,
% 2.43/2.61 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.43/2.61 inference(symmetry,[status(thm)],[16772])).
% 2.43/2.61 tff(16774,plain,
% 2.43/2.61 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[798, 16773])).
% 2.43/2.61 tff(16775,plain,
% 2.43/2.61 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16768])).
% 2.43/2.61 tff(16776,plain,
% 2.43/2.61 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.43/2.61 inference(symmetry,[status(thm)],[16775])).
% 2.43/2.61 tff(16777,plain,
% 2.43/2.61 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[684, 16776])).
% 2.43/2.61 tff(16778,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16779,plain,
% 2.43/2.61 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16780,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16779])).
% 2.43/2.61 tff(16781,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[16780, 16778])).
% 2.43/2.61 tff(16782,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(16783,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16782, 16781])).
% 2.43/2.61 tff(16784,plain,
% 2.43/2.61 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16783, 121, 111])).
% 2.43/2.61 tff(16785,plain,
% 2.43/2.61 ($false),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16784, 16777, 16774, 16771])).
% 2.43/2.61 tff(16786,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.61 tff(16787,plain,
% 2.43/2.61 (~r(z, s(s(s(elem!1))))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16786, 412, 16752, 16712, 16766])).
% 2.43/2.61 tff(16788,plain,
% 2.43/2.61 (~r(z, elem!1)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16787, 16764])).
% 2.43/2.61 tff(16789,plain,
% 2.43/2.61 (b(z, elem!1)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[355, 16788, 331])).
% 2.43/2.61 tff(16790,plain,
% 2.43/2.61 (b(z, s(s(s(elem!1))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16789, 16761])).
% 2.43/2.61 tff(16791,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16792,plain,
% 2.43/2.61 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16793,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16792])).
% 2.43/2.61 tff(16794,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[16793, 16791])).
% 2.43/2.61 tff(16795,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(16796,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16795, 16794])).
% 2.43/2.61 tff(16797,plain,
% 2.43/2.61 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16796, 271, 16790, 16760, 16714])).
% 2.43/2.61 tff(16798,plain,
% 2.43/2.61 ($false),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16797, 16758])).
% 2.43/2.61 tff(16799,plain,((~r(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (z = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.61 tff(16800,plain,
% 2.43/2.61 (~r(s(elem!1), z)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16799, 16710, 2449, 543, 16708, 68, 517, 220, 2088])).
% 2.43/2.61 tff(16801,plain,
% 2.43/2.61 (b(s(elem!1), z)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[409, 16800])).
% 2.43/2.61 tff(16802,plain,
% 2.43/2.61 (~(z = elem!1)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[2488, 394, 2467])).
% 2.43/2.61 tff(16803,plain,
% 2.43/2.61 (r(z, elem!1)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[355, 16802, 199])).
% 2.43/2.61 tff(16804,plain,
% 2.43/2.61 (b(s(s(s(elem!1))), elem!1)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16735, 2344, 684, 622, 68, 543, 517])).
% 2.43/2.61 tff(16805,plain,
% 2.43/2.61 (~r(z, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[2578, 121, 622, 378, 16727])).
% 2.43/2.61 tff(16806,plain,
% 2.43/2.61 (b(z, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1439, 16805])).
% 2.43/2.61 tff(16807,plain,
% 2.43/2.61 (~b(s(z), s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[9030, 16806, 220, 394])).
% 2.43/2.61 tff(16808,plain,
% 2.43/2.61 (r(s(z), s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[444, 16807, 348])).
% 2.43/2.61 tff(16809,plain,
% 2.43/2.61 (~r(s(z), s(s(s(elem!1))))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[9617, 16808, 684, 622])).
% 2.43/2.61 tff(16810,plain,
% 2.43/2.61 (b(s(z), s(s(s(elem!1))))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[760, 16809])).
% 2.43/2.61 tff(16811,plain,
% 2.43/2.61 (~b(s(s(elem!1)), s(z))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[989, 16810, 543, 16804])).
% 2.43/2.61 tff(16812,plain,
% 2.43/2.61 (r(s(s(elem!1)), s(z))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[2143, 16811])).
% 2.43/2.61 tff(16813,plain,
% 2.43/2.61 ($false),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[5073, 121, 378, 2088, 16727, 16812])).
% 2.43/2.61 tff(16814,plain,(r(elem!1, s(elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.61 tff(16815,plain,
% 2.43/2.61 (r(elem!1, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16814, 16803, 2088, 543, 16712, 16708, 348, 220, 394, 68, 517])).
% 2.43/2.61 tff(16816,plain,
% 2.43/2.61 (~r(z, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[8454, 121, 16815, 16708, 16803])).
% 2.43/2.61 tff(16817,plain,
% 2.43/2.61 (b(z, s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1439, 16816])).
% 2.43/2.61 tff(16818,plain,
% 2.43/2.61 (~b(s(s(elem!1)), s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[2853, 394, 16817, 2449])).
% 2.43/2.61 tff(16819,plain,
% 2.43/2.61 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[699, 21, 16818])).
% 2.43/2.61 tff(16820,plain,
% 2.43/2.61 (r(s(s(elem!1)), s(elem!1))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16819, 16703])).
% 2.43/2.61 tff(16821,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16822,plain,
% 2.43/2.61 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16823,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16822])).
% 2.43/2.61 tff(16824,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.61 inference(transitivity,[status(thm)],[16823, 16821])).
% 2.43/2.61 tff(16825,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(16826,plain,
% 2.43/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[16825, 16824])).
% 2.43/2.61 tff(16827,plain,
% 2.43/2.61 (~r(s(z), z)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[16826, 121, 1625, 2088, 16820])).
% 2.43/2.61 tff(16828,plain,
% 2.43/2.61 (b(s(z), z)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[25, 16827])).
% 2.43/2.61 tff(16829,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16830,plain,
% 2.43/2.61 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(16831,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[16830])).
% 2.43/2.61 tff(16832,plain,
% 2.43/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16831, 16829])).
% 2.43/2.62 tff(16833,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16834,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16833, 16832])).
% 2.43/2.62 tff(16835,plain,
% 2.43/2.62 (~b(s(elem!1), s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16834, 271, 394, 16828, 220])).
% 2.43/2.62 tff(16836,plain,
% 2.43/2.62 (r(s(elem!1), s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[427, 21, 16835, 9244])).
% 2.43/2.62 tff(16837,plain,
% 2.43/2.62 (~b(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[9030, 16817, 220, 394])).
% 2.43/2.62 tff(16838,plain,
% 2.43/2.62 (r(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[444, 16837, 348])).
% 2.43/2.62 tff(16839,plain,
% 2.43/2.62 (~r(s(z), s(s(s(elem!1))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[9617, 16838, 16712, 16708])).
% 2.43/2.62 tff(16840,plain,
% 2.43/2.62 (b(s(z), s(s(s(elem!1))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[760, 16839])).
% 2.43/2.62 tff(16841,plain,
% 2.43/2.62 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[989, 750, 543, 981])).
% 2.43/2.62 tff(16842,plain,
% 2.43/2.62 (r(elem!1, s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16735, 16841, 16712, 622, 68, 543, 517])).
% 2.43/2.62 tff(16843,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16844,plain,
% 2.43/2.62 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16845,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16844])).
% 2.43/2.62 tff(16846,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16845, 16843])).
% 2.43/2.62 tff(16847,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16848,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16847, 16846])).
% 2.43/2.62 tff(16849,plain,
% 2.43/2.62 (~r(s(s(s(elem!1))), elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16848, 121, 379, 622, 684])).
% 2.43/2.62 tff(16850,plain,
% 2.43/2.62 (s(s(s(elem!1))) = elem!1),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[486, 16849, 16841])).
% 2.43/2.62 tff(16851,plain,
% 2.43/2.62 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16850])).
% 2.43/2.62 tff(16852,plain,
% 2.43/2.62 (b(s(s(elem!1)), elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[543, 16851])).
% 2.43/2.62 tff(16853,plain,
% 2.43/2.62 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16850])).
% 2.43/2.62 tff(16854,plain,
% 2.43/2.62 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.43/2.62 inference(transitivity,[status(thm)],[16853, 360])).
% 2.43/2.62 tff(16855,plain,
% 2.43/2.62 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16854])).
% 2.43/2.62 tff(16856,plain,
% 2.43/2.62 (~(z = elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[30, 16855])).
% 2.43/2.62 tff(16857,plain,
% 2.43/2.62 (r(z, elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[355, 16856, 199])).
% 2.43/2.62 tff(16858,plain,
% 2.43/2.62 (~r(z, s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[8454, 121, 379, 622, 16857])).
% 2.43/2.62 tff(16859,plain,
% 2.43/2.62 (b(z, s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1439, 16858])).
% 2.43/2.62 tff(16860,plain,
% 2.43/2.62 (~r(s(elem!1), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[3681, 121, 379, 622, 16857])).
% 2.43/2.62 tff(16861,plain,
% 2.43/2.62 (b(s(elem!1), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[409, 16860])).
% 2.43/2.62 tff(16862,plain,
% 2.43/2.62 (~b(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[9030, 16861, 220, 16859])).
% 2.43/2.62 tff(16863,plain,
% 2.43/2.62 (~(s(z) = s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[343, 16856])).
% 2.43/2.62 tff(16864,plain,
% 2.43/2.62 (r(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[442, 21, 16863, 16862])).
% 2.43/2.62 tff(16865,plain,
% 2.43/2.62 (~r(elem!1, s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[9007, 121, 379, 622, 16864])).
% 2.43/2.62 tff(16866,plain,
% 2.43/2.62 (b(elem!1, s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[297, 21, 16865, 258])).
% 2.43/2.62 tff(16867,plain,
% 2.43/2.62 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16850])).
% 2.43/2.62 tff(16868,plain,
% 2.43/2.62 (b(s(z), elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[750, 16867])).
% 2.43/2.62 tff(16869,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16870,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16871,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16870, 16869])).
% 2.43/2.62 tff(16872,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16871, 271, 16868, 16866, 16852, 981])).
% 2.43/2.62 tff(16873,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (~b(z, s(z))) | b(z, elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(16874,plain,
% 2.43/2.62 (b(z, elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16873, 16842, 258, 622, 220, 981, 750, 543, 16712])).
% 2.43/2.62 tff(16875,plain,
% 2.43/2.62 (~r(s(s(s(elem!1))), elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16848, 121, 16842, 622, 16712])).
% 2.43/2.62 tff(16876,plain,
% 2.43/2.62 (s(s(s(elem!1))) = elem!1),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[486, 16875, 16841])).
% 2.43/2.62 tff(16877,plain,
% 2.43/2.62 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16876])).
% 2.43/2.62 tff(16878,plain,
% 2.43/2.62 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.43/2.62 inference(transitivity,[status(thm)],[16877, 360])).
% 2.43/2.62 tff(16879,plain,
% 2.43/2.62 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16878])).
% 2.43/2.62 tff(16880,plain,
% 2.43/2.62 (~(z = elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[30, 16879])).
% 2.43/2.62 tff(16881,plain,
% 2.43/2.62 (~(elem!1 = z)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16880, 2885])).
% 2.43/2.62 tff(16882,plain,
% 2.43/2.62 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16876])).
% 2.43/2.62 tff(16883,plain,
% 2.43/2.62 (b(s(z), elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[750, 16882])).
% 2.43/2.62 tff(16884,plain,
% 2.43/2.62 (~b(elem!1, z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[12145, 16883, 16874, 220])).
% 2.43/2.62 tff(16885,plain,
% 2.43/2.62 ((elem!1 = z) | r(elem!1, z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[282, 21, 16884])).
% 2.43/2.62 tff(16886,plain,
% 2.43/2.62 (r(elem!1, z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16885, 16881])).
% 2.43/2.62 tff(16887,plain,
% 2.43/2.62 (~r(s(elem!1), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[4890, 16886, 2088, 622])).
% 2.43/2.62 tff(16888,plain,
% 2.43/2.62 (b(s(elem!1), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[409, 16887])).
% 2.43/2.62 tff(16889,plain,
% 2.43/2.62 (~(s(s(s(z))) = s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[2596, 16876])).
% 2.43/2.62 tff(16890,plain,
% 2.43/2.62 (~(s(s(s(z))) = elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[2611, 16876])).
% 2.43/2.62 tff(16891,plain,
% 2.43/2.62 (~(elem!1 = s(s(s(z))))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16890, 5160])).
% 2.43/2.62 tff(16892,plain,
% 2.43/2.62 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16876])).
% 2.43/2.62 tff(16893,plain,
% 2.43/2.62 (b(s(s(elem!1)), elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[543, 16892])).
% 2.43/2.62 tff(16894,plain,
% 2.43/2.62 (~b(elem!1, s(s(s(z))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[11355, 16874, 2449, 16893])).
% 2.43/2.62 tff(16895,plain,
% 2.43/2.62 (r(elem!1, s(s(s(z))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1192, 16894, 16891])).
% 2.43/2.62 tff(16896,plain,
% 2.43/2.62 (~r(s(s(s(z))), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[3849, 16842, 622, 16895])).
% 2.43/2.62 tff(16897,plain,
% 2.43/2.62 (b(s(s(s(z))), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1816, 16896, 16889])).
% 2.43/2.62 tff(16898,plain,
% 2.43/2.62 (~b(s(s(s(z))), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1956, 16897, 16888, 16874])).
% 2.43/2.62 tff(16899,plain,
% 2.43/2.62 (r(s(s(s(z))), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1155, 16898])).
% 2.43/2.62 tff(16900,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16901,plain,
% 2.43/2.62 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16902,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16901])).
% 2.43/2.62 tff(16903,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16902, 16900])).
% 2.43/2.62 tff(16904,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16905,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16904, 16903])).
% 2.43/2.62 tff(16906,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16905, 121, 2088, 16895, 16886, 16899])).
% 2.43/2.62 tff(16907,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(z)) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(16908,plain,
% 2.43/2.62 (~b(s(s(elem!1)), s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16907, 16840, 16708, 2449, 220, 543, 258, 2088, 68, 517])).
% 2.43/2.62 tff(16909,plain,
% 2.43/2.62 (r(s(s(elem!1)), s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[2143, 16908])).
% 2.43/2.62 tff(16910,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16911,plain,
% 2.43/2.62 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16912,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z)))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16911])).
% 2.43/2.62 tff(16913,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16912, 16910])).
% 2.43/2.62 tff(16914,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16915,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16914, 16913])).
% 2.43/2.62 tff(16916,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16915, 121, 1625, 16909, 16836, 16820])).
% 2.43/2.62 tff(16917,plain,((~b(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(z) = s(elem!1)) | b(z, elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(16918,plain,
% 2.43/2.62 (b(z, elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16917, 16801, 220, 2088, 2449, 543, 258, 68, 517, 16709, 16705, 2467])).
% 2.43/2.62 tff(16919,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16920,plain,
% 2.43/2.62 (((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16921,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16920])).
% 2.43/2.62 tff(16922,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16921, 16919])).
% 2.43/2.62 tff(16923,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16924,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16923, 16922])).
% 2.43/2.62 tff(16925,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16924, 271, 16918, 16801, 517, 2449])).
% 2.43/2.62 tff(16926,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | b(s(elem!1), elem!1) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(16927,plain,
% 2.43/2.62 (~b(s(elem!1), s(s(elem!1)))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16926, 519, 220, 2088, 543, 258, 68, 2467, 2449])).
% 2.43/2.62 tff(16928,plain,
% 2.43/2.62 (r(s(elem!1), s(s(elem!1)))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[526, 16927, 2209])).
% 2.43/2.62 tff(16929,plain,
% 2.43/2.62 (~(s(z) = s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[343, 16802])).
% 2.43/2.62 tff(16930,plain,
% 2.43/2.62 (~(s(s(elem!1)) = s(elem!1))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[216, 4447])).
% 2.43/2.62 tff(16931,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16932,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16933,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16932, 16931])).
% 2.43/2.62 tff(16934,plain,
% 2.43/2.62 (~b(s(s(elem!1)), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16933, 271, 394, 220, 2449])).
% 2.43/2.62 tff(16935,plain,
% 2.43/2.62 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[699, 21, 16934])).
% 2.43/2.62 tff(16936,plain,
% 2.43/2.62 (r(s(s(elem!1)), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16935, 16930])).
% 2.43/2.62 tff(16937,plain,
% 2.43/2.62 (~r(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[3273, 121, 1625, 627, 16936])).
% 2.43/2.62 tff(16938,plain,
% 2.43/2.62 (b(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[444, 16937, 16929])).
% 2.43/2.62 tff(16939,plain,
% 2.43/2.62 (~r(z, s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[14980, 121, 627, 2088, 16936])).
% 2.43/2.62 tff(16940,plain,
% 2.43/2.62 (b(z, s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1439, 16939])).
% 2.43/2.62 tff(16941,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[9030, 16940, 16938, 220, 394])).
% 2.43/2.62 tff(16942,plain,((~b(s(elem!1), z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(16943,plain,
% 2.43/2.62 (~b(s(elem!1), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16942, 16928, 220, 2088, 16705, 2209, 2449, 2467])).
% 2.43/2.62 tff(16944,plain,
% 2.43/2.62 (r(s(elem!1), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[409, 16943])).
% 2.43/2.62 tff(16945,plain,
% 2.43/2.62 (~r(s(s(elem!1)), s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[5431, 16928, 2088, 16944])).
% 2.43/2.62 tff(16946,plain,
% 2.43/2.62 (b(s(s(elem!1)), s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[2143, 16945])).
% 2.43/2.62 tff(16947,plain,
% 2.43/2.62 (~b(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[12122, 16946, 220, 2449])).
% 2.43/2.62 tff(16948,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[10839, 271, 1281, 220, 2449, 981])).
% 2.43/2.62 tff(16949,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(16950,plain,
% 2.43/2.62 (~b(s(z), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16949, 16946, 2449, 220])).
% 2.43/2.62 tff(16951,plain,
% 2.43/2.62 (r(s(z), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[25, 16950])).
% 2.43/2.62 tff(16952,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16953,plain,
% 2.43/2.62 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(16954,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16953])).
% 2.43/2.62 tff(16955,plain,
% 2.43/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16954, 16952])).
% 2.43/2.62 tff(16956,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(16957,plain,
% 2.43/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16956, 16955])).
% 2.43/2.62 tff(16958,plain,
% 2.43/2.62 (~r(s(z), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[16957, 121, 2088, 16951, 16944])).
% 2.43/2.62 tff(16959,plain,
% 2.43/2.62 (s(z) = s(elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[444, 16958, 16947])).
% 2.43/2.62 tff(16960,plain,
% 2.43/2.62 (z = elem!1),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[343, 16959])).
% 2.43/2.62 tff(16961,plain,
% 2.43/2.62 (s(z) = s(elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16960])).
% 2.43/2.62 tff(16962,plain,
% 2.43/2.62 (s(s(z)) = s(s(elem!1))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16961])).
% 2.43/2.62 tff(16963,plain,
% 2.43/2.62 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16962])).
% 2.43/2.62 tff(16964,plain,
% 2.43/2.62 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16961, 16963])).
% 2.43/2.62 tff(16965,plain,
% 2.43/2.62 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.43/2.62 inference(symmetry,[status(thm)],[16964])).
% 2.43/2.62 tff(16966,plain,
% 2.43/2.62 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16961])).
% 2.43/2.62 tff(16967,plain,
% 2.43/2.62 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.43/2.62 inference(transitivity,[status(thm)],[16966, 16965])).
% 2.43/2.62 tff(16968,plain,
% 2.43/2.62 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16961])).
% 2.43/2.62 tff(16969,plain,
% 2.43/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16946, 16968])).
% 2.43/2.62 tff(16970,plain,
% 2.43/2.62 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16960])).
% 2.43/2.62 tff(16971,plain,
% 2.43/2.62 (r(elem!1, s(s(elem!1)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[2088, 16970])).
% 2.43/2.62 tff(16972,plain,
% 2.43/2.62 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16960])).
% 2.43/2.62 tff(16973,plain,
% 2.43/2.62 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16972])).
% 2.43/2.62 tff(16974,plain,
% 2.43/2.62 (~(s(s(s(elem!1))) = elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[30, 16973])).
% 2.43/2.62 tff(16975,plain,
% 2.43/2.62 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16960])).
% 2.43/2.62 tff(16976,plain,
% 2.43/2.62 (b(s(s(elem!1)), elem!1)),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[2449, 16975])).
% 2.43/2.62 tff(16977,plain,
% 2.43/2.62 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[16961])).
% 2.43/2.62 tff(16978,plain,
% 2.43/2.62 (b(elem!1, s(z))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[324, 16960, 220])).
% 2.43/2.62 tff(16979,plain,
% 2.43/2.62 (b(elem!1, s(elem!1))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16978, 16977])).
% 2.43/2.62 tff(16980,plain,
% 2.43/2.62 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[551, 16979, 543, 16976])).
% 2.43/2.62 tff(16981,plain,
% 2.43/2.62 (r(s(s(s(elem!1))), elem!1)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[486, 16980, 16974])).
% 2.43/2.62 tff(16982,plain,
% 2.43/2.62 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[720, 16981, 16971, 16708])).
% 2.43/2.62 tff(16983,plain,
% 2.43/2.62 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[681, 16982, 79])).
% 2.43/2.62 tff(16984,plain,
% 2.43/2.62 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[5254, 16983, 543, 16969])).
% 2.43/2.62 tff(16985,plain,
% 2.43/2.62 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[754, 16984, 16960])).
% 2.43/2.62 tff(16986,plain,
% 2.43/2.62 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[760, 16985])).
% 2.43/2.62 tff(16987,plain,
% 2.43/2.62 (r(s(z), s(s(s(z))))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[16986, 16967])).
% 2.43/2.62 tff(16988,plain,
% 2.43/2.62 (r(s(s(s(z))), z)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[143, 16981, 16960])).
% 2.43/2.63 tff(16989,plain,
% 2.43/2.63 (~r(s(z), s(s(s(z))))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[2096, 16988, 16951, 2088])).
% 2.43/2.63 tff(16990,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16989, 16987])).
% 2.43/2.63 tff(16991,plain,(b(s(z), s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(16992,plain,
% 2.43/2.63 (b(s(z), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16991, 2467, 2088, 2449, 220, 543, 258, 68])).
% 2.43/2.63 tff(16993,plain,
% 2.43/2.63 (r(s(s(elem!1)), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16935, 16703])).
% 2.43/2.63 tff(16994,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(16995,plain,
% 2.43/2.63 (((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(16996,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[16995])).
% 2.43/2.63 tff(16997,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[16996, 16994])).
% 2.43/2.63 tff(16998,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(16999,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[16998, 16997])).
% 2.43/2.63 tff(17000,plain,
% 2.43/2.63 (~b(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16999, 271, 394, 220, 2449])).
% 2.43/2.63 tff(17001,plain,
% 2.43/2.63 (r(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[526, 17000, 2209])).
% 2.43/2.63 tff(17002,plain,
% 2.43/2.63 (~r(z, s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[14980, 121, 17001, 2088, 16993])).
% 2.43/2.63 tff(17003,plain,
% 2.43/2.63 (b(z, s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1439, 17002])).
% 2.43/2.63 tff(17004,plain,
% 2.43/2.63 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[238])).
% 2.43/2.63 tff(17005,plain,
% 2.43/2.63 (~(s(z) = elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[258, 17004])).
% 2.43/2.63 tff(17006,plain,
% 2.43/2.63 (~b(s(z), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[9030, 17003, 220, 394])).
% 2.43/2.63 tff(17007,plain,
% 2.43/2.63 (r(s(z), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[444, 17006, 344])).
% 2.43/2.63 tff(17008,plain,
% 2.43/2.63 (~r(elem!1, s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[11755, 17007, 622, 17005, 543, 505, 68, 16993])).
% 2.43/2.63 tff(17009,plain,
% 2.43/2.63 (b(elem!1, s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[392, 17008, 16706])).
% 2.43/2.63 tff(17010,plain,
% 2.43/2.63 (~b(elem!1, z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[2892, 271, 17009, 394, 17003])).
% 2.43/2.63 tff(17011,plain,
% 2.43/2.63 ((elem!1 = z) | r(elem!1, z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[282, 21, 17010])).
% 2.43/2.63 tff(17012,plain,
% 2.43/2.63 (r(elem!1, z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17011, 2886])).
% 2.43/2.63 tff(17013,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[10847, 271, 505, 1281, 220, 2449])).
% 2.43/2.63 tff(17014,plain,((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17015,plain,
% 2.43/2.63 (~b(s(z), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17014, 505, 2449, 220])).
% 2.43/2.63 tff(17016,plain,
% 2.43/2.63 (r(s(z), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[25, 17015])).
% 2.43/2.63 tff(17017,plain,
% 2.43/2.63 (~b(z, elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[9089, 271, 17009, 394, 17003])).
% 2.43/2.63 tff(17018,plain,
% 2.43/2.63 (r(z, elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[355, 17017, 331])).
% 2.43/2.63 tff(17019,plain,
% 2.43/2.63 (~r(elem!1, s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[8900, 121, 17018, 17016, 17012])).
% 2.43/2.63 tff(17020,plain,
% 2.43/2.63 (b(elem!1, s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[297, 21, 17019, 258])).
% 2.43/2.63 tff(17021,plain,
% 2.43/2.63 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[4433, 17020, 505, 543])).
% 2.43/2.63 tff(17022,plain,
% 2.43/2.63 (r(elem!1, s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[599, 17021, 68])).
% 2.43/2.63 tff(17023,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17024,plain,
% 2.43/2.63 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17025,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17024])).
% 2.43/2.63 tff(17026,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.63 inference(transitivity,[status(thm)],[17025, 17023])).
% 2.43/2.63 tff(17027,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(17028,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17027, 17026])).
% 2.43/2.63 tff(17029,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17028, 121, 2088, 17022, 17012, 16993])).
% 2.43/2.63 tff(17030,plain,((~b(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(z)) | (z = elem!1) | (~r(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17031,plain,
% 2.43/2.63 (~b(s(elem!1), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17030, 331, 68, 505, 543, 258, 2088, 622, 220, 2449])).
% 2.43/2.63 tff(17032,plain,
% 2.43/2.63 (r(s(elem!1), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[409, 17031])).
% 2.43/2.63 tff(17033,plain,
% 2.43/2.63 (~b(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16799, 17032, 2449, 543, 622, 68, 331, 220, 2088])).
% 2.43/2.63 tff(17034,plain,
% 2.43/2.63 (r(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[526, 17033, 2209])).
% 2.43/2.63 tff(17035,plain,
% 2.43/2.63 (~r(s(s(elem!1)), s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[5431, 17034, 2088, 17032])).
% 2.43/2.63 tff(17036,plain,
% 2.43/2.63 (b(s(s(elem!1)), s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[2143, 17035])).
% 2.43/2.63 tff(17037,plain,
% 2.43/2.63 (~b(s(z), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[12122, 17036, 220, 2449])).
% 2.43/2.63 tff(17038,plain,
% 2.43/2.63 (r(s(z), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[444, 17037, 344])).
% 2.43/2.63 tff(17039,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16957, 121, 2088, 17016, 17032, 17038])).
% 2.43/2.63 tff(17040,plain,((z = elem!1) | (~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17041,plain,
% 2.43/2.63 (z = elem!1),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17040, 16708, 220, 2449, 543, 2088, 68, 16992, 258])).
% 2.43/2.63 tff(17042,plain,
% 2.43/2.63 (s(z) = s(elem!1)),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17041])).
% 2.43/2.63 tff(17043,plain,
% 2.43/2.63 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17042])).
% 2.43/2.63 tff(17044,plain,
% 2.43/2.63 (b(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[16992, 17043])).
% 2.43/2.63 tff(17045,plain,
% 2.43/2.63 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[10869, 17044, 543, 2449, 16704, 2088])).
% 2.43/2.63 tff(17046,plain,
% 2.43/2.63 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17042])).
% 2.43/2.63 tff(17047,plain,
% 2.43/2.63 (b(elem!1, s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[324, 17041, 220])).
% 2.43/2.63 tff(17048,plain,
% 2.43/2.63 (b(elem!1, s(elem!1))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17047, 17046])).
% 2.43/2.63 tff(17049,plain,
% 2.43/2.63 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17041])).
% 2.43/2.63 tff(17050,plain,
% 2.43/2.63 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 2.43/2.63 inference(symmetry,[status(thm)],[17049])).
% 2.43/2.63 tff(17051,plain,
% 2.43/2.63 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17050])).
% 2.43/2.63 tff(17052,plain,
% 2.43/2.63 (~b(z, elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[192, 17051])).
% 2.43/2.63 tff(17053,plain,
% 2.43/2.63 (~b(s(elem!1), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[2488, 17041, 2467])).
% 2.43/2.63 tff(17054,plain,
% 2.43/2.63 (r(s(elem!1), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[409, 17053])).
% 2.43/2.63 tff(17055,plain,
% 2.43/2.63 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[9687, 307, 543, 517])).
% 2.43/2.63 tff(17056,plain,
% 2.43/2.63 (r(elem!1, s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[599, 17055, 68])).
% 2.43/2.63 tff(17057,plain,
% 2.43/2.63 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.43/2.63 inference(monotonicity,[status(thm)],[779])).
% 2.43/2.63 tff(17058,plain,
% 2.43/2.63 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17057])).
% 2.43/2.63 tff(17059,plain,
% 2.43/2.63 (s(s(elem!1)) = s(s(z))),
% 2.43/2.63 inference(symmetry,[status(thm)],[134])).
% 2.43/2.63 tff(17060,plain,
% 2.43/2.63 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17059])).
% 2.43/2.63 tff(17061,plain,
% 2.43/2.63 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(symmetry,[status(thm)],[17060])).
% 2.43/2.63 tff(17062,plain,
% 2.43/2.63 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17059])).
% 2.43/2.63 tff(17063,plain,
% 2.43/2.63 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(z)), elem!1))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17062])).
% 2.43/2.63 tff(17064,plain,
% 2.43/2.63 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.43/2.63 inference(monotonicity,[status(thm)],[705])).
% 2.43/2.63 tff(17065,plain,
% 2.43/2.63 ((~b(s(s(s(s(s(elem!1))))), elem!1)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17064])).
% 2.43/2.63 tff(17066,plain,
% 2.43/2.63 (s(elem!1) = s(z)),
% 2.43/2.63 inference(symmetry,[status(thm)],[133])).
% 2.43/2.63 tff(17067,plain,
% 2.43/2.63 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17066])).
% 2.43/2.63 tff(17068,plain,
% 2.43/2.63 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.63 inference(symmetry,[status(thm)],[17067])).
% 2.43/2.63 tff(17069,plain,
% 2.43/2.63 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[10076, 504, 517, 543])).
% 2.43/2.63 tff(17070,plain,
% 2.43/2.63 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[754, 17069, 107])).
% 2.43/2.63 tff(17071,plain,
% 2.43/2.63 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[759, 17070, 11298])).
% 2.43/2.63 tff(17072,plain,
% 2.43/2.63 (r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17071, 17068])).
% 2.43/2.63 tff(17073,plain,
% 2.43/2.63 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[827, 17072, 517, 684, 307, 107, 782, 504])).
% 2.43/2.63 tff(17074,plain,
% 2.43/2.63 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17073, 17065])).
% 2.43/2.63 tff(17075,plain,
% 2.43/2.63 (r(s(s(s(s(s(z))))), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[840, 17074, 712])).
% 2.43/2.63 tff(17076,plain,
% 2.43/2.63 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17075, 707])).
% 2.43/2.63 tff(17077,plain,
% 2.43/2.63 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[848, 121, 622, 624])).
% 2.43/2.63 tff(17078,plain,
% 2.43/2.63 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17077, 17076])).
% 2.43/2.63 tff(17079,plain,
% 2.43/2.63 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[818, 21, 815, 17078])).
% 2.43/2.63 tff(17080,assumption,(b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 2.43/2.63 tff(17081,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 2.43/2.63 tff(17082,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17083,plain,
% 2.43/2.63 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17084,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17083])).
% 2.43/2.63 tff(17085,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.43/2.63 inference(transitivity,[status(thm)],[17084, 17082])).
% 2.43/2.63 tff(17086,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(17087,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17086, 17085])).
% 2.43/2.63 tff(17088,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17087, 271, 543, 517, 17081, 17080])).
% 2.43/2.63 tff(17089,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17090,plain,
% 2.43/2.63 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17089, 17079, 517, 543])).
% 2.43/2.63 tff(17091,plain,
% 2.43/2.63 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[5968, 626])).
% 2.43/2.63 tff(17092,plain,
% 2.43/2.63 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[881, 21, 17091, 17090])).
% 2.43/2.63 tff(17093,assumption,(r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 2.43/2.63 tff(17094,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 2.43/2.63 tff(17095,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[866, 121, 624, 1624, 17094, 17093])).
% 2.43/2.63 tff(17096,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17097,plain,
% 2.43/2.63 (~r(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17096, 17076, 624, 17092])).
% 2.43/2.63 tff(17098,plain,
% 2.43/2.63 (~r(s(s(z)), elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17097, 17063])).
% 2.43/2.63 tff(17099,plain,
% 2.43/2.63 (b(s(s(z)), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[3613, 17098, 10121])).
% 2.43/2.63 tff(17100,plain,
% 2.43/2.63 (b(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17099, 17061])).
% 2.43/2.63 tff(17101,plain,
% 2.43/2.63 (~b(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[549, 271, 307, 543, 504])).
% 2.43/2.63 tff(17102,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17101, 17100])).
% 2.43/2.63 tff(17103,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | (s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17104,plain,
% 2.43/2.63 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17103, 622, 307, 543, 624, 517, 107, 684, 782, 11298])).
% 2.43/2.63 tff(17105,plain,
% 2.43/2.63 (~b(s(s(s(z))), elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17104, 17058])).
% 2.43/2.63 tff(17106,plain,
% 2.43/2.63 (r(s(s(s(z))), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[255, 17105, 167])).
% 2.43/2.63 tff(17107,plain,
% 2.43/2.63 (r(s(s(s(elem!1))), elem!1)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17106, 136])).
% 2.43/2.63 tff(17108,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[718, 121, 622, 684, 624, 17107])).
% 2.43/2.63 tff(17109,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | (s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17110,plain,
% 2.43/2.63 ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17109, 778, 61])).
% 2.43/2.63 tff(17111,plain,
% 2.43/2.63 (~(z = elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17110, 17056, 622, 684, 307, 543, 517])).
% 2.43/2.63 tff(17112,plain,
% 2.43/2.63 (r(z, elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[355, 17111, 199])).
% 2.43/2.63 tff(17113,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[2690, 121, 622, 17112, 17056, 412])).
% 2.43/2.63 tff(17114,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | b(z, elem!1) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17115,plain,
% 2.43/2.63 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17114, 17044, 16708, 17054, 17052, 543, 17048, 68])).
% 2.43/2.63 tff(17116,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[681, 17115, 17045, 79])).
% 2.43/2.63 tff(17117,plain,(b(s(elem!1), elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17118,plain,
% 2.43/2.63 (b(s(elem!1), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17117, 2088, 68, 2449, 543, 220, 258])).
% 2.43/2.63 tff(17119,plain,
% 2.43/2.63 (~b(s(z), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[12122, 981, 220, 2449])).
% 2.43/2.63 tff(17120,plain,
% 2.43/2.63 (r(s(z), s(elem!1))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[444, 17119, 348])).
% 2.43/2.63 tff(17121,plain,
% 2.43/2.63 (~b(s(z), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16949, 981, 2449, 220])).
% 2.43/2.63 tff(17122,plain,
% 2.43/2.63 (r(s(z), z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[25, 17121])).
% 2.43/2.63 tff(17123,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[16957, 121, 2088, 17122, 412, 17120])).
% 2.43/2.63 tff(17124,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(17125,plain,
% 2.43/2.63 (~b(s(s(elem!1)), s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17124, 412, 2088, 344, 220, 2449])).
% 2.43/2.63 tff(17126,plain,
% 2.43/2.63 (r(s(s(elem!1)), s(z))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[2143, 17125])).
% 2.43/2.63 tff(17127,plain,
% 2.43/2.63 (~r(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[5431, 17126, 2088, 412])).
% 2.43/2.63 tff(17128,plain,
% 2.43/2.63 (b(s(elem!1), s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[526, 17127, 2209])).
% 2.43/2.63 tff(17129,plain,
% 2.43/2.63 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[14419, 17128, 543, 2618])).
% 2.43/2.63 tff(17130,plain,
% 2.43/2.63 (r(elem!1, s(s(elem!1)))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[599, 17129, 68])).
% 2.43/2.63 tff(17131,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17132,plain,
% 2.43/2.63 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17133,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17132])).
% 2.43/2.63 tff(17134,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.63 inference(transitivity,[status(thm)],[17133, 17131])).
% 2.43/2.63 tff(17135,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(17136,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[17135, 17134])).
% 2.43/2.63 tff(17137,plain,
% 2.43/2.63 (~r(elem!1, z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17136, 121, 2088, 17130, 17126])).
% 2.43/2.63 tff(17138,plain,
% 2.43/2.63 ((elem!1 = z) | b(elem!1, z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[282, 21, 17137])).
% 2.43/2.63 tff(17139,plain,
% 2.43/2.63 (b(elem!1, z)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17138, 2886])).
% 2.43/2.63 tff(17140,plain,
% 2.43/2.63 (~r(z, elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[5075, 17130, 2088, 17126])).
% 2.43/2.63 tff(17141,plain,
% 2.43/2.63 (b(z, elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[355, 17140, 331])).
% 2.43/2.63 tff(17142,plain,
% 2.43/2.63 (~b(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[4896, 271, 17141, 17139, 2449])).
% 2.43/2.63 tff(17143,plain,
% 2.43/2.63 ((s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[540, 21, 17142])).
% 2.43/2.63 tff(17144,plain,
% 2.43/2.63 (r(s(s(elem!1)), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[17143, 2214])).
% 2.43/2.63 tff(17145,plain,
% 2.43/2.63 (~b(s(z), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[12145, 17139, 17141, 220])).
% 2.43/2.63 tff(17146,plain,
% 2.43/2.63 (r(s(z), elem!1)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[236, 17145, 231])).
% 2.43/2.63 tff(17147,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17148,plain,
% 2.43/2.63 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(17149,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[17148])).
% 2.43/2.63 tff(17150,plain,
% 2.43/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[17149, 17147])).
% 2.43/2.63 tff(17151,plain,
% 2.43/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(17152,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17151, 17150])).
% 2.43/2.64 tff(17153,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17152, 121, 17146, 17130, 17126, 17144])).
% 2.43/2.64 tff(17154,plain,((~r(s(elem!1), z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (s(z) = elem!1) | (~b(z, s(z))) | (z = elem!1) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17155,plain,
% 2.43/2.64 (~r(s(elem!1), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17154, 331, 2449, 17005, 220, 68, 2088, 543, 17118])).
% 2.43/2.64 tff(17156,plain,
% 2.43/2.64 (b(s(elem!1), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[409, 17155])).
% 2.43/2.64 tff(17157,plain,
% 2.43/2.64 (~b(s(s(elem!1)), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[16933, 271, 17156, 220, 2449])).
% 2.43/2.64 tff(17158,plain,
% 2.43/2.64 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[699, 21, 17157])).
% 2.43/2.64 tff(17159,plain,
% 2.43/2.64 (r(s(s(elem!1)), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17158, 16703])).
% 2.43/2.64 tff(17160,plain,
% 2.43/2.64 (~b(s(elem!1), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[16999, 271, 17156, 220, 2449])).
% 2.43/2.64 tff(17161,plain,
% 2.43/2.64 (r(s(elem!1), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[526, 17160, 2209])).
% 2.43/2.64 tff(17162,plain,
% 2.43/2.64 (~r(z, s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[14980, 121, 17161, 2088, 17159])).
% 2.43/2.64 tff(17163,plain,
% 2.43/2.64 (b(z, s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1439, 17162])).
% 2.43/2.64 tff(17164,plain,
% 2.43/2.64 (~b(s(z), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[9030, 17163, 220, 17156])).
% 2.43/2.64 tff(17165,plain,
% 2.43/2.64 (r(s(z), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[444, 17164, 344])).
% 2.43/2.64 tff(17166,plain,
% 2.43/2.64 (~r(s(z), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[3275, 17161, 17165, 17159])).
% 2.43/2.64 tff(17167,plain,
% 2.43/2.64 (b(s(z), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2167, 17166])).
% 2.43/2.64 tff(17168,plain,
% 2.43/2.64 (~b(s(z), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17014, 17167, 2449, 220])).
% 2.43/2.64 tff(17169,plain,
% 2.43/2.64 (r(s(z), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[25, 17168])).
% 2.43/2.64 tff(17170,plain,
% 2.43/2.64 (~b(elem!1, s(z))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[4433, 588, 505, 543])).
% 2.43/2.64 tff(17171,plain,
% 2.43/2.64 (r(elem!1, s(z))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[297, 21, 17170, 258])).
% 2.43/2.64 tff(17172,plain,
% 2.43/2.64 (~b(s(z), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[11751, 271, 543, 505, 588])).
% 2.43/2.64 tff(17173,plain,
% 2.43/2.64 (r(s(z), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[236, 17172, 17005])).
% 2.43/2.64 tff(17174,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[464, 121, 378, 17173, 110, 17171])).
% 2.43/2.64 tff(17175,plain,((~b(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (elem!1 = s(z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17176,plain,
% 2.43/2.64 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17175, 378, 110, 258, 543, 505])).
% 2.43/2.64 tff(17177,plain,
% 2.43/2.64 (r(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[599, 17176, 68])).
% 2.43/2.64 tff(17178,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17179,plain,
% 2.43/2.64 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17180,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17179])).
% 2.43/2.64 tff(17181,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.64 inference(transitivity,[status(thm)],[17180, 17178])).
% 2.43/2.64 tff(17182,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(17183,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17182, 17181])).
% 2.43/2.64 tff(17184,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17183, 121, 378, 2088, 17177, 683])).
% 2.43/2.64 tff(17185,plain,((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(z), z)) | (elem!1 = s(z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17186,plain,
% 2.43/2.64 (~r(z, elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17185, 17159, 2088, 68, 17169, 258, 543, 17167])).
% 2.43/2.64 tff(17187,plain,
% 2.43/2.64 (b(z, elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[355, 17186, 331])).
% 2.43/2.64 tff(17188,plain,
% 2.43/2.64 (~b(elem!1, s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[4598, 17187, 17118, 17156])).
% 2.43/2.64 tff(17189,plain,
% 2.43/2.64 (r(elem!1, s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[392, 17188, 16706])).
% 2.43/2.64 tff(17190,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17191,plain,
% 2.43/2.64 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17192,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17191])).
% 2.43/2.64 tff(17193,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.43/2.64 inference(transitivity,[status(thm)],[17192, 17190])).
% 2.43/2.64 tff(17194,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(17195,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17194, 17193])).
% 2.43/2.64 tff(17196,plain,
% 2.43/2.64 (~r(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17195, 121, 17189, 17161, 17159])).
% 2.43/2.64 tff(17197,plain,
% 2.43/2.64 (b(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[599, 17196, 68])).
% 2.43/2.64 tff(17198,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17199,plain,
% 2.43/2.64 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17200,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17199])).
% 2.43/2.64 tff(17201,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.43/2.64 inference(transitivity,[status(thm)],[17200, 17198])).
% 2.43/2.64 tff(17202,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(17203,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17202, 17201])).
% 2.43/2.64 tff(17204,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17203, 271, 17118, 17187, 17197, 17163])).
% 2.43/2.64 tff(17205,plain,((z = elem!1) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (elem!1 = s(z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17206,plain,
% 2.43/2.64 (~b(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17205, 2088, 258, 220, 68, 331, 543])).
% 2.43/2.64 tff(17207,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2430, 17206, 16702])).
% 2.43/2.64 tff(17208,plain,((~r(z, s(s(elem!1)))) | (elem!1 = s(z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (z = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17209,plain,
% 2.43/2.64 (~r(z, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17208, 68, 220, 258, 331, 543, 110, 1625])).
% 2.43/2.64 tff(17210,plain,
% 2.43/2.64 (b(z, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2106, 17209])).
% 2.43/2.64 tff(17211,plain,
% 2.43/2.64 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[16677, 17210, 1326, 543])).
% 2.43/2.64 tff(17212,plain,
% 2.43/2.64 (r(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[599, 17211, 68])).
% 2.43/2.64 tff(17213,plain,
% 2.43/2.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[720, 17212, 139, 622])).
% 2.43/2.64 tff(17214,plain,
% 2.43/2.64 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[681, 17213, 79])).
% 2.43/2.64 tff(17215,plain,
% 2.43/2.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1921, 17210, 110, 572, 543])).
% 2.43/2.64 tff(17216,plain,
% 2.43/2.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[586, 17215, 6943])).
% 2.43/2.64 tff(17217,plain,
% 2.43/2.64 (~r(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[14145, 17216, 139, 17212])).
% 2.43/2.64 tff(17218,plain,
% 2.43/2.64 (b(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2430, 17217])).
% 2.43/2.64 tff(17219,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[5267, 17218, 17214, 3407, 543])).
% 2.43/2.64 tff(17220,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (z = elem!1) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17221,plain,
% 2.43/2.64 (elem!1 = s(s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17220, 16701, 3407, 139, 16697, 563, 110, 16649, 15030, 16637, 258, 331, 16647])).
% 2.43/2.64 tff(17222,plain,
% 2.43/2.64 (s(elem!1) = s(s(s(elem!1)))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17221])).
% 2.43/2.64 tff(17223,plain,
% 2.43/2.64 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17222])).
% 2.43/2.64 tff(17224,plain,
% 2.43/2.64 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.43/2.64 inference(symmetry,[status(thm)],[17223])).
% 2.43/2.64 tff(17225,plain,
% 2.43/2.64 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17224])).
% 2.43/2.64 tff(17226,plain,
% 2.43/2.64 (~r(z, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[4890, 1409, 412, 622])).
% 2.43/2.64 tff(17227,plain,
% 2.43/2.64 (b(z, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2106, 17226])).
% 2.43/2.64 tff(17228,plain,
% 2.43/2.64 (~r(z, s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[15950, 1409, 110, 357])).
% 2.43/2.64 tff(17229,plain,
% 2.43/2.64 (b(z, s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1214, 17228])).
% 2.43/2.64 tff(17230,plain,
% 2.43/2.64 (~b(s(s(s(z))), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1978, 17229, 1326, 307])).
% 2.43/2.64 tff(17231,plain,
% 2.43/2.64 (~r(s(s(s(z))), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[15964, 17229, 357, 220, 1409])).
% 2.43/2.64 tff(17232,plain,
% 2.43/2.64 (s(s(s(z))) = elem!1),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[255, 17231, 17230])).
% 2.43/2.64 tff(17233,plain,
% 2.43/2.64 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17232])).
% 2.43/2.64 tff(17234,plain,
% 2.43/2.64 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.64 inference(symmetry,[status(thm)],[17233])).
% 2.43/2.64 tff(17235,plain,
% 2.43/2.64 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[139, 17234])).
% 2.43/2.64 tff(17236,plain,
% 2.43/2.64 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[15840, 17235, 220, 572, 17227])).
% 2.43/2.64 tff(17237,plain,
% 2.43/2.64 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[556, 17236, 1])).
% 2.43/2.64 tff(17238,plain,
% 2.43/2.64 (~(elem!1 = s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[3906, 17232])).
% 2.43/2.64 tff(17239,plain,
% 2.43/2.64 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[78, 17238])).
% 2.43/2.64 tff(17240,plain,
% 2.43/2.64 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[16677, 17237, 1326, 17227])).
% 2.43/2.64 tff(17241,plain,
% 2.43/2.64 (r(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[599, 17240, 17238])).
% 2.43/2.64 tff(17242,plain,
% 2.43/2.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[720, 17241, 139, 622])).
% 2.43/2.64 tff(17243,plain,
% 2.43/2.64 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[681, 17242, 17239])).
% 2.43/2.64 tff(17244,plain,
% 2.43/2.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1921, 17237, 110, 572, 17227])).
% 2.43/2.64 tff(17245,plain,
% 2.43/2.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[586, 17244, 563])).
% 2.43/2.64 tff(17246,plain,
% 2.43/2.64 (~r(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[14145, 17245, 139, 17241])).
% 2.43/2.64 tff(17247,plain,
% 2.43/2.64 (b(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2430, 17246])).
% 2.43/2.64 tff(17248,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[5267, 17247, 17243, 3407, 17237])).
% 2.43/2.64 tff(17249,plain,((~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17250,plain,
% 2.43/2.64 (~r(elem!1, z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17249, 16697, 139, 3407, 110, 16649, 15030, 1, 16637, 357, 2345, 16689])).
% 2.43/2.64 tff(17251,plain,
% 2.43/2.64 (b(elem!1, z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[284, 17250, 358])).
% 2.43/2.64 tff(17252,plain,
% 2.43/2.64 (s(elem!1) = s(s(s(z)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[15490, 257, 261, 110, 348, 1326, 412])).
% 2.43/2.64 tff(17253,plain,
% 2.43/2.64 (s(s(s(z))) = s(elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2035, 17252])).
% 2.43/2.64 tff(17254,plain,
% 2.43/2.64 (~b(z, s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[16218, 17253, 12494])).
% 2.43/2.64 tff(17255,plain,
% 2.43/2.64 (~r(z, s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[3377, 17253, 110, 108, 622])).
% 2.43/2.64 tff(17256,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1439, 17255, 17254])).
% 2.43/2.64 tff(17257,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17258,plain,
% 2.43/2.64 (~b(s(s(s(z))), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17257, 16651, 110, 16697, 17251, 344, 15030, 16689, 2345])).
% 2.43/2.64 tff(17259,plain,
% 2.43/2.64 (~r(s(s(s(z))), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[3375, 6533, 108, 110])).
% 2.43/2.64 tff(17260,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[255, 17259, 6549, 2346])).
% 2.43/2.64 tff(17261,plain,(b(z, s(s(s(z)))) | b(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17262,plain,
% 2.43/2.64 (b(z, s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17261, 17258, 16651, 110, 15030])).
% 2.43/2.64 tff(17263,plain,
% 2.43/2.64 (~(s(s(s(z))) = s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[3917, 17221, 344])).
% 2.43/2.64 tff(17264,plain,
% 2.43/2.64 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17222])).
% 2.43/2.64 tff(17265,plain,
% 2.43/2.64 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 2.43/2.64 inference(symmetry,[status(thm)],[17264])).
% 2.43/2.64 tff(17266,plain,
% 2.43/2.64 (r(s(z), s(elem!1))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[16649, 17265])).
% 2.43/2.64 tff(17267,plain,
% 2.43/2.64 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[12919, 220, 15030, 448])).
% 2.43/2.64 tff(17268,plain,
% 2.43/2.64 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[760, 17267])).
% 2.43/2.64 tff(17269,plain,
% 2.43/2.64 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 2.43/2.64 inference(monotonicity,[status(thm)],[244])).
% 2.43/2.64 tff(17270,plain,
% 2.43/2.64 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.43/2.64 inference(symmetry,[status(thm)],[17269])).
% 2.43/2.64 tff(17271,plain,
% 2.43/2.64 (b(s(s(s(z))), z)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[261, 17270])).
% 2.43/2.64 tff(17272,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17273,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(17274,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17273, 17272])).
% 2.43/2.64 tff(17275,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17274, 271, 505, 220, 222, 1935])).
% 2.43/2.64 tff(17276,plain,((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17277,plain,
% 2.43/2.64 (~b(s(z), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17276, 17271, 220, 10641])).
% 2.43/2.64 tff(17278,plain,
% 2.43/2.64 (r(s(z), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2167, 17277])).
% 2.43/2.64 tff(17279,plain,
% 2.43/2.64 (r(s(z), s(s(s(s(s(z))))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[9700, 17278, 2606])).
% 2.43/2.64 tff(17280,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17281,plain,
% 2.43/2.64 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(z)))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(17282,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[17281])).
% 2.43/2.64 tff(17283,plain,
% 2.43/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.64 inference(transitivity,[status(thm)],[17282, 17280])).
% 2.43/2.64 tff(17284,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(z))))))))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(17285,plain,
% 2.43/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17284, 17283])).
% 2.43/2.64 tff(17286,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17285, 121, 572, 139, 1735, 7793])).
% 2.43/2.64 tff(17287,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17288,plain,
% 2.43/2.64 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17287, 17279, 139, 17268])).
% 2.43/2.64 tff(17289,plain,
% 2.43/2.64 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[17288, 16532])).
% 2.43/2.64 tff(17290,plain,
% 2.43/2.64 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[556, 17289, 1])).
% 2.43/2.64 tff(17291,plain,
% 2.43/2.64 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[78, 15680])).
% 2.43/2.64 tff(17292,plain,
% 2.43/2.64 (~r(z, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17208, 15680, 220, 258, 331, 17290, 110, 17278])).
% 2.43/2.64 tff(17293,plain,
% 2.43/2.64 (b(z, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2106, 17292])).
% 2.43/2.64 tff(17294,plain,
% 2.43/2.64 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[16677, 17293, 15030, 17290])).
% 2.43/2.64 tff(17295,plain,
% 2.43/2.64 (r(elem!1, s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[599, 17294, 15680])).
% 2.43/2.64 tff(17296,plain,
% 2.43/2.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[720, 17295, 139, 622])).
% 2.43/2.64 tff(17297,plain,
% 2.43/2.64 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[681, 17296, 17291])).
% 2.43/2.64 tff(17298,plain,
% 2.43/2.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1921, 17293, 110, 17268, 17290])).
% 2.43/2.64 tff(17299,plain,
% 2.43/2.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[586, 17298, 563])).
% 2.43/2.64 tff(17300,plain,
% 2.43/2.64 (~r(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[14145, 17299, 139, 17295])).
% 2.43/2.64 tff(17301,plain,
% 2.43/2.64 (b(s(s(elem!1)), z)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2430, 17300])).
% 2.43/2.64 tff(17302,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[5267, 17301, 17297, 3407, 17290])).
% 2.43/2.64 tff(17303,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(17304,plain,
% 2.43/2.64 (~(s(s(s(z))) = elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[17303, 16697, 139, 3407, 110, 16637, 258, 331, 1, 17251, 448])).
% 2.43/2.64 tff(17305,plain,
% 2.43/2.64 (~(elem!1 = s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1100, 17304])).
% 2.43/2.64 tff(17306,plain,
% 2.43/2.64 (r(s(s(s(z))), elem!1)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[255, 17304, 17258])).
% 2.43/2.64 tff(17307,plain,
% 2.43/2.64 (~r(elem!1, s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[9831, 17306, 357, 16651])).
% 2.43/2.64 tff(17308,plain,
% 2.43/2.64 (b(elem!1, s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1192, 17307, 17305])).
% 2.43/2.64 tff(17309,plain,
% 2.43/2.64 (~(s(elem!1) = s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2035, 17263])).
% 2.43/2.64 tff(17310,plain,
% 2.43/2.64 (~r(s(elem!1), s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[3445, 17266, 16651, 17306])).
% 2.43/2.64 tff(17311,plain,
% 2.43/2.64 (b(s(elem!1), s(s(s(z))))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2044, 17310, 17309])).
% 2.43/2.64 tff(17312,plain,
% 2.43/2.64 (~b(s(s(s(z))), s(z))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[10690, 17311, 2345, 17308])).
% 2.43/2.64 tff(17313,plain,
% 2.43/2.64 (r(s(s(s(z))), s(z))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2325, 17312])).
% 2.43/2.64 tff(17314,plain,
% 2.43/2.64 (~r(s(s(s(z))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[2640, 17313, 16689, 17266])).
% 2.43/2.64 tff(17315,plain,
% 2.43/2.64 (b(s(s(s(z))), s(elem!1))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1816, 17314, 17263])).
% 2.43/2.64 tff(17316,plain,
% 2.43/2.64 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[5687, 17315, 3407, 17262])).
% 2.43/2.65 tff(17317,plain,
% 2.43/2.65 (~b(s(elem!1), s(s(s(z))))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17316, 17225])).
% 2.43/2.65 tff(17318,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17311, 17317])).
% 2.43/2.65 tff(17319,plain,((~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (elem!1 = s(z)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17320,plain,
% 2.43/2.65 (~b(elem!1, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17319, 2344, 139, 110, 258, 331, 1, 357, 3407])).
% 2.43/2.65 tff(17321,plain,
% 2.43/2.65 (r(elem!1, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[299, 17320, 258])).
% 2.43/2.65 tff(17322,plain,
% 2.43/2.65 (~r(s(s(s(elem!1))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16576, 17321, 139, 110])).
% 2.43/2.65 tff(17323,plain,
% 2.43/2.65 (b(s(s(s(elem!1))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16580, 17322])).
% 2.43/2.65 tff(17324,plain,
% 2.43/2.65 (~r(s(z), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[4626, 121, 357, 139, 17321])).
% 2.43/2.65 tff(17325,plain,
% 2.43/2.65 (b(s(z), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[760, 17324])).
% 2.43/2.65 tff(17326,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17327,plain,
% 2.43/2.65 (((~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(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17328,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17327])).
% 2.43/2.65 tff(17329,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(transitivity,[status(thm)],[17328, 17326])).
% 2.43/2.65 tff(17330,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(17331,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17330, 17329])).
% 2.43/2.65 tff(17332,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17331, 271, 750, 220, 3407, 503])).
% 2.43/2.65 tff(17333,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17334,plain,
% 2.43/2.65 (~b(z, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17333, 17325, 3407, 17323])).
% 2.43/2.65 tff(17335,plain,
% 2.43/2.65 (r(z, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[904, 17334])).
% 2.43/2.65 tff(17336,plain,
% 2.43/2.65 (~r(elem!1, z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[15739, 17335, 110, 357])).
% 2.43/2.65 tff(17337,plain,
% 2.43/2.65 (b(elem!1, z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[284, 17336, 358])).
% 2.43/2.65 tff(17338,plain,
% 2.43/2.65 (~b(s(elem!1), z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3415, 17337, 3407, 2345])).
% 2.43/2.65 tff(17339,plain,
% 2.43/2.65 (r(s(elem!1), z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[409, 17338])).
% 2.43/2.65 tff(17340,plain,
% 2.43/2.65 (~r(s(elem!1), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1254, 17339, 357, 17335])).
% 2.43/2.65 tff(17341,plain,
% 2.43/2.65 (b(s(elem!1), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[429, 17340, 351])).
% 2.43/2.65 tff(17342,plain,
% 2.43/2.65 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3813, 271, 17325, 17341, 17323])).
% 2.43/2.65 tff(17343,plain,
% 2.43/2.65 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17344,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17343])).
% 2.43/2.65 tff(17345,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(transitivity,[status(thm)],[17344, 5141])).
% 2.43/2.65 tff(17346,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(17347,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17346, 17345])).
% 2.43/2.65 tff(17348,plain,
% 2.43/2.65 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17347, 271, 17325, 17341, 17323])).
% 2.43/2.65 tff(17349,plain,
% 2.43/2.65 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[84, 14804])).
% 2.43/2.65 tff(17350,plain,
% 2.43/2.65 (r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3180, 17349])).
% 2.43/2.65 tff(17351,plain,
% 2.43/2.65 (~r(s(s(elem!1)), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3132, 17350, 14545, 14805])).
% 2.43/2.65 tff(17352,plain,
% 2.43/2.65 (b(s(s(elem!1)), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[701, 17351, 3313])).
% 2.43/2.65 tff(17353,plain,
% 2.43/2.65 (~r(s(elem!1), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3888, 14805, 139, 3456])).
% 2.43/2.65 tff(17354,plain,
% 2.43/2.65 (b(s(elem!1), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2243, 17353, 2207])).
% 2.43/2.65 tff(17355,plain,
% 2.43/2.65 (~b(s(s(elem!1)), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[6807, 17354, 307, 17352])).
% 2.43/2.65 tff(17356,plain,
% 2.43/2.65 (r(s(s(elem!1)), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[862, 17355, 14810])).
% 2.43/2.65 tff(17357,plain,
% 2.43/2.65 (~r(elem!1, s(s(elem!1)))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2670, 17356, 139, 14545])).
% 2.43/2.65 tff(17358,plain,
% 2.43/2.65 (b(elem!1, s(s(elem!1)))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[599, 17357, 14803])).
% 2.43/2.65 tff(17359,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[8007, 271, 307, 17354, 17358, 17352])).
% 2.43/2.65 tff(17360,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | b(s(elem!1), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17361,plain,
% 2.43/2.65 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17360, 2345, 139, 17321, 17348, 17342, 1])).
% 2.43/2.65 tff(17362,plain,
% 2.43/2.65 (~b(s(s(elem!1)), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2414, 271, 17361, 17325, 17323])).
% 2.43/2.65 tff(17363,plain,
% 2.43/2.65 (r(s(s(elem!1)), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2143, 17362])).
% 2.43/2.65 tff(17364,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17365,plain,
% 2.43/2.65 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17366,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17365])).
% 2.43/2.65 tff(17367,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.43/2.65 inference(transitivity,[status(thm)],[17366, 17364])).
% 2.43/2.65 tff(17368,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(17369,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17368, 17367])).
% 2.43/2.65 tff(17370,plain,
% 2.43/2.65 (~b(s(s(elem!1)), z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17369, 271, 17361, 3407, 17323])).
% 2.43/2.65 tff(17371,plain,
% 2.43/2.65 (r(s(s(elem!1)), z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2430, 17370])).
% 2.43/2.65 tff(17372,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2422, 17371, 17363, 110, 17335])).
% 2.43/2.65 tff(17373,plain,(r(elem!1, s(elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17374,plain,
% 2.43/2.65 (r(elem!1, s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17373, 16095, 3407, 110, 1, 16629, 243, 331])).
% 2.43/2.65 tff(17375,plain,
% 2.43/2.65 (~r(s(s(s(elem!1))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3796, 121, 17374, 16629, 16095])).
% 2.43/2.65 tff(17376,plain,
% 2.43/2.65 (b(s(s(s(elem!1))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16580, 17375])).
% 2.43/2.65 tff(17377,plain,
% 2.43/2.65 (~r(s(z), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3805, 121, 17374, 16629, 16095])).
% 2.43/2.65 tff(17378,plain,
% 2.43/2.65 (b(s(z), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[760, 17377])).
% 2.43/2.65 tff(17379,plain,
% 2.43/2.65 (~b(z, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17333, 17378, 3407, 17376])).
% 2.43/2.65 tff(17380,plain,
% 2.43/2.65 (r(z, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[904, 17379])).
% 2.43/2.65 tff(17381,plain,
% 2.43/2.65 (~r(elem!1, z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[15739, 17380, 110, 16629])).
% 2.43/2.65 tff(17382,plain,
% 2.43/2.65 (b(elem!1, z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[284, 17381, 358])).
% 2.43/2.65 tff(17383,plain,
% 2.43/2.65 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[7173, 17382, 3407, 15030])).
% 2.43/2.65 tff(17384,plain,
% 2.43/2.65 (~b(s(elem!1), z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[11634, 2618, 1326, 261])).
% 2.43/2.65 tff(17385,plain,
% 2.43/2.65 (r(s(elem!1), z)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[409, 17384])).
% 2.43/2.65 tff(17386,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3826, 3792, 17385, 422, 139, 357, 379, 909])).
% 2.43/2.65 tff(17387,plain,((~b(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | b(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17388,plain,
% 2.43/2.65 (~b(s(elem!1), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17387, 16095, 351, 16629, 17374, 17380, 17383, 15030, 17382])).
% 2.43/2.65 tff(17389,plain,
% 2.43/2.65 (r(s(elem!1), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2243, 17388, 2207])).
% 2.43/2.65 tff(17390,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[9622, 121, 379, 622, 357, 431])).
% 2.43/2.65 tff(17391,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17392,plain,
% 2.43/2.65 (~r(s(z), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17391, 17389, 16629, 17374])).
% 2.43/2.65 tff(17393,plain,
% 2.43/2.65 (b(s(z), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[444, 17392, 344])).
% 2.43/2.65 tff(17394,plain,
% 2.43/2.65 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[9637, 17389, 16095, 344, 16629, 17374])).
% 2.43/2.65 tff(17395,plain,
% 2.43/2.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3520, 121, 17374, 17389, 16095])).
% 2.43/2.65 tff(17396,plain,
% 2.43/2.65 (s(s(s(elem!1))) = s(elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[681, 17395, 17394])).
% 2.43/2.65 tff(17397,plain,
% 2.43/2.65 (elem!1 = s(s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[78, 17396])).
% 2.43/2.65 tff(17398,plain,
% 2.43/2.65 (~r(s(elem!1), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[9630, 121, 17374, 17389, 16629])).
% 2.43/2.65 tff(17399,plain,
% 2.43/2.65 (b(s(elem!1), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[429, 17398, 351])).
% 2.43/2.65 tff(17400,plain,
% 2.43/2.65 (s(elem!1) = s(s(s(elem!1)))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17397])).
% 2.43/2.65 tff(17401,plain,
% 2.43/2.65 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17400])).
% 2.43/2.65 tff(17402,plain,
% 2.43/2.65 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.43/2.65 inference(symmetry,[status(thm)],[17401])).
% 2.43/2.65 tff(17403,plain,
% 2.43/2.65 (b(z, s(elem!1))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[3407, 17402])).
% 2.43/2.65 tff(17404,plain,
% 2.43/2.65 (~(s(s(s(z))) = s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[3917, 17397, 344])).
% 2.43/2.65 tff(17405,plain,
% 2.43/2.65 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[6358, 17397, 17404])).
% 2.43/2.65 tff(17406,plain,
% 2.43/2.65 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[2470])).
% 2.43/2.65 tff(17407,plain,
% 2.43/2.65 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[139, 17406])).
% 2.43/2.65 tff(17408,plain,
% 2.43/2.65 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[3912, 12280])).
% 2.43/2.65 tff(17409,plain,
% 2.43/2.65 (b(s(s(s(elem!1))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16580, 3797])).
% 2.43/2.65 tff(17410,plain,
% 2.43/2.65 (~b(z, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17333, 3807, 3407, 17409])).
% 2.43/2.65 tff(17411,plain,
% 2.43/2.65 (r(z, s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[904, 17410])).
% 2.43/2.65 tff(17412,plain,
% 2.43/2.65 (~r(s(s(s(z))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[6541, 11659, 357, 909])).
% 2.43/2.65 tff(17413,plain,
% 2.43/2.65 (b(s(s(s(z))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2325, 17412])).
% 2.43/2.65 tff(17414,plain,
% 2.43/2.65 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2081, 17413, 503, 750])).
% 2.43/2.65 tff(17415,plain,
% 2.43/2.65 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[2071, 17414, 2065])).
% 2.43/2.65 tff(17416,plain,
% 2.43/2.65 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[5511, 17415, 573, 4266, 2470])).
% 2.43/2.65 tff(17417,plain,
% 2.43/2.65 (s(s(s(s(z)))) = s(elem!1)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[4024, 10146])).
% 2.43/2.65 tff(17418,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1548, 17417])).
% 2.43/2.65 tff(17419,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17420,plain,
% 2.43/2.65 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17419, 12184])).
% 2.43/2.65 tff(17421,plain,
% 2.43/2.65 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16265, 17420, 2470])).
% 2.43/2.65 tff(17422,plain,
% 2.43/2.65 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[5001, 17421])).
% 2.43/2.65 tff(17423,plain,
% 2.43/2.65 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[2471])).
% 2.43/2.65 tff(17424,plain,
% 2.43/2.65 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.65 inference(symmetry,[status(thm)],[17423])).
% 2.43/2.65 tff(17425,plain,
% 2.43/2.65 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17424])).
% 2.43/2.65 tff(17426,assumption,(~r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.43/2.65 tff(17427,plain,
% 2.43/2.65 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17426, 17425])).
% 2.43/2.65 tff(17428,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[4266, 17427])).
% 2.43/2.65 tff(17429,plain,(r(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17430,plain,
% 2.43/2.65 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17429, 4266, 2470])).
% 2.43/2.65 tff(17431,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17432,plain,
% 2.43/2.65 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17433,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17432])).
% 2.43/2.65 tff(17434,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.65 inference(transitivity,[status(thm)],[17433, 17431])).
% 2.43/2.65 tff(17435,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(17436,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17435, 17434])).
% 2.43/2.65 tff(17437,plain,
% 2.43/2.65 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17436, 121, 17408, 573, 17430])).
% 2.43/2.65 tff(17438,plain,
% 2.43/2.65 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16341, 17437, 2470])).
% 2.43/2.65 tff(17439,plain,
% 2.43/2.65 (b(elem!1, s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1847, 17438, 17422])).
% 2.43/2.65 tff(17440,plain,
% 2.43/2.65 (~r(s(z), s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1148, 11668, 909, 11659])).
% 2.43/2.65 tff(17441,plain,
% 2.43/2.65 (b(s(z), s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[105, 17440])).
% 2.43/2.65 tff(17442,plain,
% 2.43/2.65 (~r(elem!1, s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[12643, 17441, 503, 2470, 379, 17413])).
% 2.43/2.65 tff(17443,plain,
% 2.43/2.65 (b(elem!1, s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1192, 17442, 12183])).
% 2.43/2.65 tff(17444,plain,
% 2.43/2.65 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1857, 17443, 17439, 257])).
% 2.43/2.65 tff(17445,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1733, 17444, 17416])).
% 2.43/2.65 tff(17446,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(17447,plain,
% 2.43/2.65 (~b(s(s(s(z))), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17446, 4266, 17407, 2470, 2065, 17409, 379, 3807, 17411, 357, 1326, 261])).
% 2.43/2.65 tff(17448,plain,
% 2.43/2.65 (r(s(s(s(z))), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[255, 17447, 3907])).
% 2.43/2.65 tff(17449,plain,
% 2.43/2.65 (r(s(s(s(z))), s(s(elem!1)))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[13482, 17448, 2470])).
% 2.43/2.65 tff(17450,plain,
% 2.43/2.65 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[12694, 17449, 17408, 17407])).
% 2.43/2.65 tff(17451,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17452,plain,
% 2.43/2.65 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(17453,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[17452])).
% 2.43/2.65 tff(17454,plain,
% 2.43/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.43/2.65 inference(transitivity,[status(thm)],[17453, 17451])).
% 2.43/2.65 tff(17455,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(17456,plain,
% 2.43/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[17455, 17454])).
% 2.43/2.65 tff(17457,plain,
% 2.43/2.65 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17456, 121, 17408, 17407, 17430])).
% 2.43/2.65 tff(17458,plain,
% 2.43/2.65 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[5462, 17457, 2470])).
% 2.43/2.65 tff(17459,plain,
% 2.43/2.65 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[17436, 121, 17408, 17407, 17430])).
% 2.43/2.65 tff(17460,plain,
% 2.43/2.65 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16341, 17459, 2470])).
% 2.43/2.65 tff(17461,plain,
% 2.43/2.65 (~b(z, s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16299, 17460, 2470, 17421, 3936, 17458])).
% 2.43/2.65 tff(17462,plain,
% 2.43/2.65 (r(z, s(s(s(s(s(z))))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1658, 17461])).
% 2.43/2.65 tff(17463,plain,
% 2.43/2.65 (~b(z, s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[16389, 17448, 3407, 2065, 379, 139])).
% 2.43/2.65 tff(17464,plain,
% 2.43/2.65 (r(z, s(s(s(z))))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1214, 17463])).
% 2.43/2.65 tff(17465,plain,
% 2.43/2.65 (~r(s(s(s(s(s(z))))), s(z))),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1669, 1661, 110, 909])).
% 2.43/2.65 tff(17466,plain,
% 2.43/2.65 (b(s(s(s(s(s(z))))), s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1682, 17465])).
% 2.43/2.66 tff(17467,plain,
% 2.43/2.66 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[16283, 1661, 145, 1140])).
% 2.43/2.66 tff(17468,plain,
% 2.43/2.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1733, 17467])).
% 2.43/2.66 tff(17469,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[16322, 17468, 17466, 16314, 2073])).
% 2.43/2.66 tff(17470,plain,((~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17471,plain,
% 2.43/2.66 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17470, 17464, 17462, 17448, 110, 17411])).
% 2.43/2.66 tff(17472,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2071, 17471, 17450, 2065])).
% 2.43/2.66 tff(17473,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~(elem!1 = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17474,plain,
% 2.43/2.66 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17473, 17397, 110, 2064, 3407, 17374, 16095, 16629, 15030, 17382])).
% 2.43/2.66 tff(17475,plain,
% 2.43/2.66 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[4138, 17474, 17405])).
% 2.43/2.66 tff(17476,plain,
% 2.43/2.66 (~r(z, s(s(s(s(s(z))))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[11865, 9894, 446, 394, 909])).
% 2.43/2.66 tff(17477,plain,
% 2.43/2.66 (~b(z, s(s(s(s(s(z))))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15001, 9894, 447, 1421])).
% 2.43/2.66 tff(17478,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1658, 17477, 17476])).
% 2.43/2.66 tff(17479,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17480,plain,
% 2.43/2.66 (~b(s(elem!1), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17479, 17475, 17403, 17393, 17399, 17380])).
% 2.43/2.66 tff(17481,plain,
% 2.43/2.66 (r(s(elem!1), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[409, 17480])).
% 2.43/2.66 tff(17482,plain,
% 2.43/2.66 (~b(s(s(s(z))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[5759, 17481, 16629, 331, 17374, 17380, 3504, 17383, 1391, 243])).
% 2.43/2.66 tff(17483,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[3952, 17482, 17481, 17380, 17397, 17374, 3504, 17388, 331, 17393, 15030, 211])).
% 2.43/2.66 tff(17484,plain,(r(z, elem!1) | (z = elem!1) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17485,plain,
% 2.43/2.66 (r(z, elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17484, 231, 110, 3407, 1, 331])).
% 2.43/2.66 tff(17486,plain,
% 2.43/2.66 (r(s(z), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[16628, 139, 110, 3407, 1, 331, 231])).
% 2.43/2.66 tff(17487,plain,
% 2.43/2.66 (r(elem!1, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17373, 139, 3407, 110, 1, 17486, 243, 331])).
% 2.43/2.66 tff(17488,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[387, 17487, 17486, 110, 17485])).
% 2.43/2.66 tff(17489,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17490,plain,
% 2.43/2.66 (~r(s(s(s(elem!1))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17489, 231, 3407, 1, 331, 110])).
% 2.43/2.66 tff(17491,plain,
% 2.43/2.66 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15882, 1409, 231, 3407, 1, 110, 331])).
% 2.43/2.66 tff(17492,plain,
% 2.43/2.66 (s(s(s(elem!1))) = elem!1),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[486, 17491, 147])).
% 2.43/2.66 tff(17493,plain,
% 2.43/2.66 (~r(z, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15937, 17492, 15030, 344, 3407, 1409, 219, 110, 231])).
% 2.43/2.66 tff(17494,plain,
% 2.43/2.66 (~r(elem!1, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[8902, 1409, 110, 17485])).
% 2.43/2.66 tff(17495,plain,
% 2.43/2.66 (b(elem!1, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[299, 17494, 243])).
% 2.43/2.66 tff(17496,plain,
% 2.43/2.66 (~b(z, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[4817, 17495, 15030, 260])).
% 2.43/2.66 tff(17497,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[904, 17496, 17493])).
% 2.43/2.66 tff(17498,plain,((~r(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(z) = elem!1) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17499,plain,
% 2.43/2.66 (~r(elem!1, z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17498, 237, 3407, 110, 231, 147, 1, 331])).
% 2.43/2.66 tff(17500,plain,
% 2.43/2.66 (b(elem!1, z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[284, 17499, 358])).
% 2.43/2.66 tff(17501,plain,
% 2.43/2.66 (~b(elem!1, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[16099, 17500, 237, 344, 3407, 15030])).
% 2.43/2.66 tff(17502,plain,
% 2.43/2.66 (r(elem!1, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[392, 17501, 219])).
% 2.43/2.66 tff(17503,plain,
% 2.43/2.66 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[7173, 17500, 3407, 15030])).
% 2.43/2.66 tff(17504,plain,
% 2.43/2.66 (s(s(s(elem!1))) = elem!1),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[486, 17503, 147])).
% 2.43/2.66 tff(17505,plain,
% 2.43/2.66 (~b(z, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[12145, 17500, 15030, 237])).
% 2.43/2.66 tff(17506,plain,
% 2.43/2.66 (r(z, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[904, 17505])).
% 2.43/2.66 tff(17507,plain,
% 2.43/2.66 (~r(elem!1, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[4202, 17506, 110, 17485])).
% 2.43/2.66 tff(17508,plain,
% 2.43/2.66 (~r(s(s(s(elem!1))), s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[12809, 17507, 17504])).
% 2.43/2.66 tff(17509,plain,
% 2.43/2.66 (b(s(s(s(elem!1))), s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[16580, 17508])).
% 2.43/2.66 tff(17510,plain,
% 2.43/2.66 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17504])).
% 2.43/2.66 tff(17511,plain,
% 2.43/2.66 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 2.43/2.66 inference(symmetry,[status(thm)],[17510])).
% 2.43/2.66 tff(17512,plain,
% 2.43/2.66 (r(z, s(s(s(elem!1))))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17485, 17511])).
% 2.43/2.66 tff(17513,plain,
% 2.43/2.66 (~(s(s(s(z))) = elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2611, 17504])).
% 2.43/2.66 tff(17514,plain,
% 2.43/2.66 (~b(s(s(s(z))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[16591, 17506, 110, 237, 17500, 15030])).
% 2.43/2.66 tff(17515,plain,
% 2.43/2.66 (r(s(s(s(z))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[255, 17514, 17513])).
% 2.43/2.66 tff(17516,plain,
% 2.43/2.66 (~r(s(s(s(z))), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[10254, 121, 17502, 17485, 17515])).
% 2.43/2.66 tff(17517,plain,
% 2.43/2.66 (b(s(elem!1), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[9345, 17516, 219, 15030, 17485, 79, 17513, 17512, 17509, 110])).
% 2.43/2.66 tff(17518,plain,
% 2.43/2.66 (~b(s(z), s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[11998, 17517, 110, 68, 17501, 17512, 17508, 344, 1])).
% 2.43/2.66 tff(17519,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[9308, 17518, 17517, 15030, 231, 232, 344, 68, 17512, 110, 17509, 17502, 1])).
% 2.43/2.66 tff(17520,plain,(r(s(z), elem!1) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17521,plain,
% 2.43/2.66 (r(s(z), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17520, 147, 68, 110, 1, 231, 3407, 331])).
% 2.43/2.66 tff(17522,plain,
% 2.43/2.66 (~r(elem!1, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[387, 17521, 110, 17485])).
% 2.43/2.66 tff(17523,plain,
% 2.43/2.66 (b(elem!1, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[392, 17522, 219])).
% 2.43/2.66 tff(17524,plain,
% 2.43/2.66 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15671, 17523, 3407, 15030])).
% 2.43/2.66 tff(17525,plain,
% 2.43/2.66 (s(s(s(elem!1))) = elem!1),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[486, 17524, 147])).
% 2.43/2.66 tff(17526,plain,
% 2.43/2.66 (~r(elem!1, z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[373, 17521, 110, 17485])).
% 2.43/2.66 tff(17527,plain,
% 2.43/2.66 (b(elem!1, z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[284, 17526, 358])).
% 2.43/2.66 tff(17528,plain,
% 2.43/2.66 (r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15289, 17525, 1, 15030, 17527, 344, 110, 3407, 231])).
% 2.43/2.66 tff(17529,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2830, 17528, 17525, 17522])).
% 2.43/2.66 tff(17530,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17531,plain,
% 2.43/2.66 (elem!1 = s(s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17530, 17490, 110, 3407, 231, 1, 331])).
% 2.43/2.66 tff(17532,plain,
% 2.43/2.66 (b(s(elem!1), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[12364, 17531, 1, 17490])).
% 2.43/2.66 tff(17533,plain,
% 2.43/2.66 (b(s(s(s(elem!1))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[3790, 17532, 17531])).
% 2.43/2.66 tff(17534,plain,
% 2.43/2.66 (~b(elem!1, z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[7173, 17533, 3407, 15030])).
% 2.43/2.66 tff(17535,plain,
% 2.43/2.66 (~r(elem!1, z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15882, 17533, 231, 3407, 1, 110, 331])).
% 2.43/2.66 tff(17536,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[284, 17535, 17534, 358])).
% 2.43/2.66 tff(17537,plain,((s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17538,plain,
% 2.43/2.66 (s(z) = elem!1),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17537, 331, 1, 110, 3407])).
% 2.43/2.66 tff(17539,plain,
% 2.43/2.66 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.66 tff(17540,plain,
% 2.43/2.66 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17539])).
% 2.43/2.66 tff(17541,plain,
% 2.43/2.66 (~(elem!1 = s(s(elem!1)))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[2137, 17540])).
% 2.43/2.66 tff(17542,plain,
% 2.43/2.66 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[78, 17541])).
% 2.43/2.66 tff(17543,plain,
% 2.43/2.66 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.66 tff(17544,plain,
% 2.43/2.66 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.43/2.66 inference(transitivity,[status(thm)],[17543, 653])).
% 2.43/2.66 tff(17545,plain,
% 2.43/2.66 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17544])).
% 2.43/2.66 tff(17546,plain,
% 2.43/2.66 (~(s(s(s(elem!1))) = elem!1)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[61, 17545])).
% 2.43/2.66 tff(17547,plain,
% 2.43/2.66 (s(s(z)) = s(elem!1)),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.66 tff(17548,plain,
% 2.43/2.66 (s(s(s(z))) = s(s(elem!1))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17547])).
% 2.43/2.66 tff(17549,plain,
% 2.43/2.66 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17548])).
% 2.43/2.66 tff(17550,plain,
% 2.43/2.66 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.43/2.66 inference(symmetry,[status(thm)],[17549])).
% 2.43/2.66 tff(17551,plain,
% 2.43/2.66 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.66 tff(17552,plain,
% 2.43/2.66 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.43/2.66 inference(symmetry,[status(thm)],[17551])).
% 2.43/2.66 tff(17553,plain,
% 2.43/2.66 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17548])).
% 2.43/2.66 tff(17554,plain,
% 2.43/2.66 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 2.43/2.66 inference(symmetry,[status(thm)],[17553])).
% 2.43/2.66 tff(17555,plain,
% 2.43/2.66 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.43/2.66 inference(transitivity,[status(thm)],[17554, 17552])).
% 2.43/2.66 tff(17556,plain,
% 2.43/2.66 (r(elem!1, s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[599, 15659, 17541])).
% 2.43/2.66 tff(17557,plain,
% 2.43/2.66 (r(s(z), s(s(s(z))))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17556, 17555])).
% 2.43/2.66 tff(17558,plain,
% 2.43/2.66 (r(s(z), z) <=> r(elem!1, z)),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.66 tff(17559,plain,
% 2.43/2.66 (r(elem!1, z)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[110, 17558])).
% 2.43/2.66 tff(17560,plain,
% 2.43/2.66 (elem!1 = s(z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1221, 17538])).
% 2.43/2.66 tff(17561,plain,
% 2.43/2.66 (~b(s(z), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[3576, 15672, 17560])).
% 2.43/2.66 tff(17562,plain,
% 2.43/2.66 (r(s(z), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[444, 17561, 344])).
% 2.43/2.66 tff(17563,plain,
% 2.43/2.66 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.66 tff(17564,plain,
% 2.43/2.66 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.43/2.66 inference(symmetry,[status(thm)],[17563])).
% 2.43/2.66 tff(17565,plain,
% 2.43/2.66 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17548])).
% 2.43/2.66 tff(17566,plain,
% 2.43/2.66 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.43/2.66 inference(transitivity,[status(thm)],[17565, 17564])).
% 2.43/2.66 tff(17567,plain,
% 2.43/2.66 (b(z, s(z))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1397, 17560, 15030])).
% 2.43/2.66 tff(17568,plain,
% 2.43/2.66 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[15649, 504, 3407, 17567])).
% 2.43/2.66 tff(17569,plain,
% 2.43/2.66 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[760, 17568])).
% 2.43/2.66 tff(17570,plain,
% 2.43/2.66 (r(s(z), s(s(s(s(z)))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1053, 17569, 17538])).
% 2.43/2.66 tff(17571,plain,
% 2.43/2.66 (r(elem!1, s(s(s(elem!1))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1045, 17569, 17538])).
% 2.43/2.66 tff(17572,plain,
% 2.43/2.66 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17548])).
% 2.43/2.66 tff(17573,plain,
% 2.43/2.66 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17572])).
% 2.43/2.66 tff(17574,plain,
% 2.43/2.66 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 2.43/2.66 inference(symmetry,[status(thm)],[17573])).
% 2.43/2.66 tff(17575,plain,
% 2.43/2.66 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(z)))), z))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17574])).
% 2.43/2.66 tff(17576,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17577,plain,
% 2.43/2.66 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17578,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17577])).
% 2.43/2.66 tff(17579,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.43/2.66 inference(transitivity,[status(thm)],[17578, 17576])).
% 2.43/2.66 tff(17580,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(17581,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17580, 17579])).
% 2.43/2.66 tff(17582,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17581, 121, 623, 624, 727, 6842])).
% 2.43/2.66 tff(17583,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17584,plain,
% 2.43/2.66 (~r(s(s(s(elem!1))), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17583, 15613, 17556, 17571])).
% 2.43/2.66 tff(17585,plain,
% 2.43/2.66 (~r(s(s(s(s(z)))), z)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17584, 17575])).
% 2.43/2.66 tff(17586,plain,
% 2.43/2.66 (b(s(s(s(s(z)))), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1095, 17585])).
% 2.43/2.66 tff(17587,plain,
% 2.43/2.66 (b(s(s(s(elem!1))), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[8229, 17584])).
% 2.43/2.66 tff(17588,plain,
% 2.43/2.66 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[735, 17571, 15613, 17556])).
% 2.43/2.66 tff(17589,plain,
% 2.43/2.66 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[681, 17588, 17542])).
% 2.43/2.66 tff(17590,plain,
% 2.43/2.66 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[223])).
% 2.43/2.66 tff(17591,plain,
% 2.43/2.66 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.43/2.66 inference(symmetry,[status(thm)],[17590])).
% 2.43/2.66 tff(17592,plain,
% 2.43/2.66 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.43/2.66 inference(transitivity,[status(thm)],[6712, 17591])).
% 2.43/2.66 tff(17593,plain,
% 2.43/2.66 (r(s(z), s(s(s(z))))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[624, 17592])).
% 2.43/2.66 tff(17594,plain,
% 2.43/2.66 (b(z, s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17261, 2346, 17593, 110, 1326])).
% 2.43/2.66 tff(17595,plain,
% 2.43/2.66 (r(s(s(s(z))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[255, 2346, 6655])).
% 2.43/2.66 tff(17596,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17597,plain,
% 2.43/2.66 (((~r(s(s(s(z))), elem!1)) | (~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(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17598,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17597])).
% 2.43/2.66 tff(17599,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.43/2.66 inference(transitivity,[status(thm)],[17598, 17596])).
% 2.43/2.66 tff(17600,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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)))))))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(17601,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17600, 17599])).
% 2.43/2.66 tff(17602,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17601, 121, 145, 108, 1026, 12542])).
% 2.43/2.66 tff(17603,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17604,plain,
% 2.43/2.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17603, 17595, 1026, 17593])).
% 2.43/2.66 tff(17605,plain,
% 2.43/2.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[10426, 17604])).
% 2.43/2.66 tff(17606,plain,
% 2.43/2.66 (~b(s(s(s(z))), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[13513, 17605, 1103, 17594])).
% 2.43/2.66 tff(17607,plain,
% 2.43/2.66 (r(s(s(s(z))), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1155, 17606])).
% 2.43/2.66 tff(17608,plain,
% 2.43/2.66 (~r(z, s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2096, 17607, 17593, 110])).
% 2.43/2.66 tff(17609,plain,
% 2.43/2.66 (b(z, s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2106, 17608])).
% 2.43/2.66 tff(17610,plain,
% 2.43/2.66 (r(elem!1, s(s(s(z))))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[624, 6712])).
% 2.43/2.66 tff(17611,plain,
% 2.43/2.66 (r(s(s(elem!1)), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[14112, 17595, 223])).
% 2.43/2.66 tff(17612,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17613,plain,
% 2.43/2.66 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17614,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17613])).
% 2.43/2.66 tff(17615,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.43/2.66 inference(transitivity,[status(thm)],[17614, 17612])).
% 2.43/2.66 tff(17616,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(17617,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17616, 17615])).
% 2.43/2.66 tff(17618,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17617, 121, 573, 624, 727, 1624])).
% 2.43/2.66 tff(17619,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17620,plain,
% 2.43/2.66 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17619, 17611, 624, 727])).
% 2.43/2.66 tff(17621,plain,
% 2.43/2.66 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[586, 17620, 6943])).
% 2.43/2.66 tff(17622,plain,
% 2.43/2.66 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[13110, 17621, 223])).
% 2.43/2.66 tff(17623,plain,
% 2.43/2.66 (~b(s(s(s(z))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[5687, 17622, 3407, 17594])).
% 2.43/2.66 tff(17624,plain,
% 2.43/2.66 (r(s(s(s(z))), s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1816, 17623, 7853])).
% 2.43/2.66 tff(17625,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[3566, 121, 379, 1184, 412, 1500])).
% 2.43/2.66 tff(17626,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17627,plain,
% 2.43/2.66 (~r(s(elem!1), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17626, 17624, 379, 17610])).
% 2.43/2.66 tff(17628,plain,
% 2.43/2.66 (b(s(elem!1), z)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[409, 17627])).
% 2.43/2.66 tff(17629,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2779, 271, 17628, 17609, 638, 1638])).
% 2.43/2.66 tff(17630,plain,(b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17631,plain,
% 2.43/2.66 (b(s(s(s(z))), elem!1)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17630, 17589, 17587, 15673, 110, 3407, 17538, 17586, 563, 17556, 17571, 17570, 15030])).
% 2.43/2.66 tff(17632,plain,
% 2.43/2.66 (b(s(s(elem!1)), s(z))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17631, 17566])).
% 2.43/2.66 tff(17633,plain,
% 2.43/2.66 (~r(s(elem!1), s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2199, 17556, 15613, 15673])).
% 2.43/2.66 tff(17634,plain,
% 2.43/2.66 (b(s(elem!1), s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[526, 17633, 211])).
% 2.43/2.66 tff(17635,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17636,plain,
% 2.43/2.66 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(17637,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[17636])).
% 2.43/2.66 tff(17638,plain,
% 2.43/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.66 inference(transitivity,[status(thm)],[17637, 17635])).
% 2.43/2.66 tff(17639,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(17640,plain,
% 2.43/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[17639, 17638])).
% 2.43/2.66 tff(17641,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17640, 121, 379, 2088, 1409, 412])).
% 2.43/2.66 tff(17642,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(17643,plain,
% 2.43/2.66 (~r(z, s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[17642, 412, 1409, 379])).
% 2.43/2.66 tff(17644,plain,
% 2.43/2.66 (b(z, s(s(elem!1)))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2106, 17643])).
% 2.43/2.66 tff(17645,plain,
% 2.43/2.66 (~r(z, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[12111, 412, 110, 431])).
% 2.43/2.66 tff(17646,plain,
% 2.43/2.66 (b(z, s(elem!1))),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1439, 17645])).
% 2.43/2.66 tff(17647,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[2152, 17646, 17644, 517, 981])).
% 2.43/2.67 tff(17648,plain,((~r(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17649,plain,
% 2.43/2.67 (~r(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17648, 17634, 17632, 110, 17562, 17559, 15673])).
% 2.43/2.67 tff(17650,plain,
% 2.43/2.67 (b(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[409, 17649])).
% 2.43/2.67 tff(17651,plain,
% 2.43/2.67 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17547])).
% 2.43/2.67 tff(17652,plain,
% 2.43/2.67 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.43/2.67 inference(transitivity,[status(thm)],[17651, 3535])).
% 2.43/2.67 tff(17653,plain,
% 2.43/2.67 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17652])).
% 2.43/2.67 tff(17654,plain,
% 2.43/2.67 (~(s(s(s(z))) = s(elem!1))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[1136, 17653])).
% 2.43/2.67 tff(17655,plain,
% 2.43/2.67 (b(s(s(s(z))), s(z))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[8109, 17631, 17538])).
% 2.43/2.67 tff(17656,plain,
% 2.43/2.67 (b(s(elem!1), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2369, 17634, 17560])).
% 2.43/2.67 tff(17657,plain,
% 2.43/2.67 (~b(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2029, 17650, 17656, 17655])).
% 2.43/2.67 tff(17658,plain,
% 2.43/2.67 (r(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1214, 17657])).
% 2.43/2.67 tff(17659,plain,
% 2.43/2.67 (~r(s(s(s(z))), s(s(z)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1356, 17658, 17557, 110])).
% 2.43/2.67 tff(17660,plain,
% 2.43/2.67 (~r(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[10458, 17659, 17560])).
% 2.43/2.67 tff(17661,plain,
% 2.43/2.67 (b(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1816, 17660, 17654])).
% 2.43/2.67 tff(17662,plain,
% 2.43/2.67 (~b(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1956, 17661, 15030, 17650])).
% 2.43/2.67 tff(17663,plain,
% 2.43/2.67 (r(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1155, 17662])).
% 2.43/2.67 tff(17664,plain,
% 2.43/2.67 (~r(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2096, 17663, 17557, 110])).
% 2.43/2.67 tff(17665,plain,
% 2.43/2.67 (b(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2106, 17664])).
% 2.43/2.67 tff(17666,plain,
% 2.43/2.67 (b(z, s(s(s(z))))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17665, 17550])).
% 2.43/2.67 tff(17667,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17657, 17666])).
% 2.43/2.67 tff(17668,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17669,plain,
% 2.43/2.67 (~b(s(s(s(elem!1))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17668, 331, 3407, 1, 110])).
% 2.43/2.67 tff(17670,plain,
% 2.43/2.67 (r(s(s(s(elem!1))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[486, 17669, 17546])).
% 2.43/2.67 tff(17671,plain,
% 2.43/2.67 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[8834])).
% 2.43/2.67 tff(17672,plain,
% 2.43/2.67 (b(z, s(z))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1397, 1222, 1326])).
% 2.43/2.67 tff(17673,plain,
% 2.43/2.67 (r(s(s(elem!1)), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[14112, 145, 223])).
% 2.43/2.67 tff(17674,plain,
% 2.43/2.67 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[6946, 121, 1408, 139, 17673])).
% 2.43/2.67 tff(17675,plain,
% 2.43/2.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[586, 17674, 563])).
% 2.43/2.67 tff(17676,plain,
% 2.43/2.67 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[6954, 121, 1408, 139, 17673])).
% 2.43/2.67 tff(17677,plain,
% 2.43/2.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[556, 17676, 1])).
% 2.43/2.67 tff(17678,plain,
% 2.43/2.67 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[13110, 17675, 223])).
% 2.43/2.67 tff(17679,plain,
% 2.43/2.67 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[16071, 17678, 3407, 220])).
% 2.43/2.67 tff(17680,plain,
% 2.43/2.67 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[760, 17679])).
% 2.43/2.67 tff(17681,plain,
% 2.43/2.67 (~b(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1921, 17680, 110, 17677, 17675])).
% 2.43/2.67 tff(17682,plain,
% 2.43/2.67 (r(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2106, 17681])).
% 2.43/2.67 tff(17683,plain,
% 2.43/2.67 (r(s(s(elem!1)), s(z))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[6824, 145, 223])).
% 2.43/2.67 tff(17684,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(17685,plain,
% 2.43/2.67 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(17686,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17685])).
% 2.43/2.67 tff(17687,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[17686, 17684])).
% 2.43/2.67 tff(17688,plain,
% 2.43/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(17689,plain,
% 2.43/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17688, 17687])).
% 2.43/2.67 tff(17690,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17689, 271, 543, 589, 3407, 2449])).
% 2.43/2.67 tff(17691,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17692,plain,
% 2.43/2.67 (~b(s(s(elem!1)), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17691, 17675, 3407, 17677])).
% 2.43/2.67 tff(17693,plain,
% 2.43/2.67 (r(s(s(elem!1)), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2430, 17692])).
% 2.43/2.67 tff(17694,plain,
% 2.43/2.67 (~r(s(z), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[11783, 17682, 110, 17693])).
% 2.43/2.67 tff(17695,plain,
% 2.43/2.67 (b(s(z), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2167, 17694])).
% 2.43/2.67 tff(17696,plain,
% 2.43/2.67 (b(elem!1, s(s(elem!1)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17695, 7872])).
% 2.43/2.67 tff(17697,plain,
% 2.43/2.67 (~b(s(elem!1), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[9687, 17696, 307, 17677])).
% 2.43/2.67 tff(17698,plain,
% 2.43/2.67 (r(s(elem!1), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[526, 17697, 211])).
% 2.43/2.67 tff(17699,plain,
% 2.43/2.67 (~r(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[5431, 17698, 17683, 17682])).
% 2.43/2.67 tff(17700,plain,
% 2.43/2.67 (~r(z, s(z))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2422, 2117, 2417, 110])).
% 2.43/2.67 tff(17701,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(17702,plain,
% 2.43/2.67 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(17703,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17702])).
% 2.43/2.67 tff(17704,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.43/2.67 inference(transitivity,[status(thm)],[17703, 17701])).
% 2.43/2.67 tff(17705,plain,
% 2.43/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(17706,plain,
% 2.43/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17705, 17704])).
% 2.43/2.67 tff(17707,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17706, 121, 1441, 627, 2088, 2117])).
% 2.43/2.67 tff(17708,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17709,plain,
% 2.43/2.67 (~r(z, s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17708, 2117, 627, 2088])).
% 2.43/2.67 tff(17710,plain,
% 2.43/2.67 (b(z, s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1439, 17709])).
% 2.43/2.67 tff(17711,plain,
% 2.43/2.67 (~b(z, s(z))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[9030, 17710, 446, 394])).
% 2.43/2.67 tff(17712,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[902, 21, 17711, 17700, 898])).
% 2.43/2.67 tff(17713,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17714,plain,
% 2.43/2.67 (~b(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17713, 17698, 17683, 17682, 110, 17693, 14738])).
% 2.43/2.67 tff(17715,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[409, 17714, 17699])).
% 2.43/2.67 tff(17716,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17717,plain,
% 2.43/2.67 (~r(s(s(s(z))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17716, 307, 110, 223, 3407, 17672, 1, 139])).
% 2.43/2.67 tff(17718,plain,
% 2.43/2.67 (b(s(s(s(z))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[255, 17717, 6655])).
% 2.43/2.67 tff(17719,plain,
% 2.43/2.67 (~b(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1978, 17718, 1326, 307])).
% 2.43/2.67 tff(17720,plain,
% 2.43/2.67 (~b(z, s(s(elem!1)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17719, 17671])).
% 2.43/2.67 tff(17721,plain,
% 2.43/2.67 (r(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2106, 17720])).
% 2.43/2.67 tff(17722,plain,
% 2.43/2.67 (r(s(z), elem!1) <=> r(elem!1, elem!1)),
% 2.43/2.67 inference(monotonicity,[status(thm)],[223])).
% 2.43/2.67 tff(17723,plain,
% 2.43/2.67 (r(elem!1, elem!1) <=> r(s(z), elem!1)),
% 2.43/2.67 inference(symmetry,[status(thm)],[17722])).
% 2.43/2.67 tff(17724,plain,
% 2.43/2.67 ((~r(elem!1, elem!1)) <=> (~r(s(z), elem!1))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17723])).
% 2.43/2.67 tff(17725,plain,
% 2.43/2.67 (~r(s(z), elem!1)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[9971, 17724])).
% 2.43/2.67 tff(17726,plain,
% 2.43/2.67 (~b(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1940, 17718, 1326, 307])).
% 2.43/2.67 tff(17727,plain,
% 2.43/2.67 (r(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1155, 17726])).
% 2.43/2.67 tff(17728,plain,
% 2.43/2.67 (~r(s(z), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2096, 17721, 17727, 110])).
% 2.43/2.67 tff(17729,plain,
% 2.43/2.67 (b(s(z), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[105, 17728])).
% 2.43/2.67 tff(17730,plain,
% 2.43/2.67 (~b(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[11582, 17729, 1326, 17672, 17725, 17717, 2207])).
% 2.43/2.67 tff(17731,plain,
% 2.43/2.67 (r(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[409, 17730])).
% 2.43/2.67 tff(17732,plain,
% 2.43/2.67 (~r(s(elem!1), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[4890, 17731, 1408, 17721])).
% 2.43/2.67 tff(17733,plain,
% 2.43/2.67 (r(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1214, 17719])).
% 2.43/2.67 tff(17734,plain,
% 2.43/2.67 (~b(s(elem!1), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[13140, 17731, 307, 17718, 7853, 17733])).
% 2.43/2.67 tff(17735,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2243, 17734, 17732, 2207])).
% 2.43/2.67 tff(17736,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17737,plain,
% 2.43/2.67 (~b(elem!1, s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17736, 15030, 110, 17538, 3407, 1, 17670])).
% 2.43/2.67 tff(17738,plain,
% 2.43/2.67 (r(elem!1, s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[392, 17737, 219])).
% 2.43/2.67 tff(17739,plain,
% 2.43/2.67 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.43/2.67 inference(transitivity,[status(thm)],[17544, 654])).
% 2.43/2.67 tff(17740,plain,
% 2.43/2.67 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17739])).
% 2.43/2.67 tff(17741,plain,
% 2.43/2.67 (~(elem!1 = s(s(s(elem!1))))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[61, 17740])).
% 2.43/2.67 tff(17742,plain,
% 2.43/2.67 (~b(elem!1, s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17736, 1326, 110, 223, 3407, 1, 139])).
% 2.43/2.67 tff(17743,plain,
% 2.43/2.67 (r(elem!1, s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[392, 17742, 219])).
% 2.43/2.67 tff(17744,plain,
% 2.43/2.67 (~b(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[16389, 17595, 3407, 2065, 139, 17743])).
% 2.43/2.67 tff(17745,plain,
% 2.43/2.67 (~r(s(z), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17261, 17744, 2346, 110, 1326])).
% 2.43/2.67 tff(17746,plain,
% 2.43/2.67 (b(s(z), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[105, 17745])).
% 2.43/2.67 tff(17747,plain,
% 2.43/2.67 (b(elem!1, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[11114, 17746, 1222])).
% 2.43/2.67 tff(17748,plain,
% 2.43/2.67 (~b(s(elem!1), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[9291, 17747, 1326, 394])).
% 2.43/2.67 tff(17749,plain,
% 2.43/2.67 (r(s(elem!1), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2243, 17748, 2207])).
% 2.43/2.67 tff(17750,plain,
% 2.43/2.67 (~r(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[4890, 1409, 2088, 622])).
% 2.43/2.67 tff(17751,plain,
% 2.43/2.67 (b(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[409, 17750])).
% 2.43/2.67 tff(17752,plain,
% 2.43/2.67 (~b(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1956, 1422, 394, 1326])).
% 2.43/2.67 tff(17753,plain,
% 2.43/2.67 (r(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1155, 17752])).
% 2.43/2.67 tff(17754,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(17755,plain,
% 2.43/2.67 (((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(17756,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17755])).
% 2.43/2.67 tff(17757,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[17756, 17754])).
% 2.43/2.67 tff(17758,plain,
% 2.43/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(17759,plain,
% 2.43/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17758, 17757])).
% 2.43/2.67 tff(17760,plain,
% 2.43/2.67 (~r(s(s(s(z))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17759, 121, 2088, 1409, 17753])).
% 2.43/2.67 tff(17761,plain,
% 2.43/2.67 (s(s(s(z))) = elem!1),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[255, 17760, 2346])).
% 2.43/2.67 tff(17762,plain,
% 2.43/2.67 (b(s(s(s(z))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17761])).
% 2.43/2.67 tff(17763,plain,
% 2.43/2.67 (b(elem!1, s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(symmetry,[status(thm)],[17762])).
% 2.43/2.67 tff(17764,plain,
% 2.43/2.67 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17763])).
% 2.43/2.67 tff(17765,plain,
% 2.43/2.67 (~b(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[317, 17764])).
% 2.43/2.67 tff(17766,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1422, 17765])).
% 2.43/2.67 tff(17767,plain,((~b(s(s(s(z))), s(elem!1))) | b(elem!1, s(elem!1)) | b(s(s(s(z))), elem!1) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17768,plain,
% 2.43/2.67 (~b(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17767, 2346, 317, 2088, 1409, 17751, 1326])).
% 2.43/2.67 tff(17769,plain,
% 2.43/2.67 (r(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1816, 17768, 2033])).
% 2.43/2.67 tff(17770,plain,
% 2.43/2.67 (r(s(s(s(z))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[255, 2346, 907])).
% 2.43/2.67 tff(17771,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[8370, 121, 379, 622, 17770, 17769])).
% 2.43/2.67 tff(17772,plain,(b(s(s(s(z))), elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = s(elem!1)) | (s(s(s(z))) = elem!1) | b(elem!1, s(elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17773,plain,
% 2.43/2.67 (~r(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17772, 17749, 1326, 17742, 1408, 17743, 6655, 7853, 2346])).
% 2.43/2.67 tff(17774,plain,
% 2.43/2.67 (b(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2106, 17773])).
% 2.43/2.67 tff(17775,plain,
% 2.43/2.67 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2238, 17774, 1326, 17743, 5038, 17749])).
% 2.43/2.67 tff(17776,plain,
% 2.43/2.67 (r(elem!1, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[599, 17775, 5038])).
% 2.43/2.67 tff(17777,plain,
% 2.43/2.67 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2670, 17776, 139, 17611])).
% 2.43/2.67 tff(17778,plain,
% 2.43/2.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[556, 17777, 1])).
% 2.43/2.67 tff(17779,plain,
% 2.43/2.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[720, 17776, 139, 17749])).
% 2.43/2.67 tff(17780,plain,
% 2.43/2.67 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[681, 17779, 6656])).
% 2.43/2.67 tff(17781,plain,
% 2.43/2.67 (~b(s(s(elem!1)), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[5267, 17780, 3407, 17778])).
% 2.43/2.67 tff(17782,plain,
% 2.43/2.67 (r(s(s(elem!1)), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2430, 17781])).
% 2.43/2.67 tff(17783,plain,
% 2.43/2.67 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[14145, 17782, 139, 17776])).
% 2.43/2.67 tff(17784,plain,
% 2.43/2.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[586, 17783, 563])).
% 2.43/2.67 tff(17785,plain,
% 2.43/2.67 (~r(s(z), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1921, 17784, 110, 17774, 17778])).
% 2.43/2.67 tff(17786,plain,
% 2.43/2.67 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[13110, 17784, 223])).
% 2.43/2.67 tff(17787,plain,
% 2.43/2.67 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[16071, 17786, 3407, 17672])).
% 2.43/2.67 tff(17788,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[760, 17787, 17785])).
% 2.43/2.67 tff(17789,plain,(b(s(s(s(z))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~(s(z) = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17790,plain,
% 2.43/2.67 (b(s(s(s(z))), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17789, 394, 110, 223, 139, 1, 1326, 3407, 2065])).
% 2.43/2.67 tff(17791,plain,
% 2.43/2.67 (b(s(s(s(z))), s(z))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[8109, 17790, 223])).
% 2.43/2.67 tff(17792,plain,
% 2.43/2.67 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.43/2.67 inference(symmetry,[status(thm)],[7872])).
% 2.43/2.67 tff(17793,plain,
% 2.43/2.67 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[7868, 7870, 17792])).
% 2.43/2.67 tff(17794,plain,
% 2.43/2.67 (b(s(elem!1), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[9295, 3506, 1184, 379, 2033])).
% 2.43/2.67 tff(17795,plain,
% 2.43/2.67 (~b(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2029, 17794, 394, 222])).
% 2.43/2.67 tff(17796,plain,
% 2.43/2.67 (r(s(s(s(z))), s(s(z)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[10458, 7114, 239])).
% 2.43/2.67 tff(17797,plain,
% 2.43/2.67 (~r(z, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1356, 17796, 108, 110])).
% 2.43/2.67 tff(17798,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1214, 17797, 17795])).
% 2.43/2.67 tff(17799,plain,(b(s(s(s(z))), s(elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~(elem!1 = s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17800,plain,
% 2.43/2.67 (b(s(s(s(z))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17799, 106, 110, 394, 222, 1222, 6715, 379, 7853])).
% 2.43/2.67 tff(17801,plain,
% 2.43/2.67 (~b(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1956, 17800, 1326, 394])).
% 2.43/2.67 tff(17802,plain,
% 2.43/2.67 (r(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1155, 17801])).
% 2.43/2.67 tff(17803,plain,
% 2.43/2.67 (~r(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2096, 17802, 106, 110])).
% 2.43/2.67 tff(17804,plain,
% 2.43/2.67 (b(z, s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2106, 17803])).
% 2.43/2.67 tff(17805,plain,
% 2.43/2.67 (b(z, s(s(s(z))))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17804, 8835])).
% 2.43/2.67 tff(17806,plain,
% 2.43/2.67 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[5687, 17805, 3407, 17800])).
% 2.43/2.67 tff(17807,plain,
% 2.43/2.67 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[13110, 17806, 223])).
% 2.43/2.67 tff(17808,plain,
% 2.43/2.67 (b(s(s(elem!1)), s(elem!1))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17800, 7849])).
% 2.43/2.67 tff(17809,plain,
% 2.43/2.67 (~b(s(s(elem!1)), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2528, 17808, 394, 17804])).
% 2.43/2.67 tff(17810,plain,
% 2.43/2.67 (r(s(s(elem!1)), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2430, 17809])).
% 2.43/2.67 tff(17811,plain,
% 2.43/2.67 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[14145, 17810, 139, 6714])).
% 2.43/2.67 tff(17812,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[586, 17811, 17807, 6943])).
% 2.43/2.67 tff(17813,plain,(b(s(z), s(s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17814,plain,
% 2.43/2.67 (b(s(z), s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17813, 394, 139, 223, 3407, 563, 110, 1326, 17791, 17743])).
% 2.43/2.67 tff(17815,plain,
% 2.43/2.67 (b(s(z), s(s(elem!1)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17814, 17793])).
% 2.43/2.67 tff(17816,plain,
% 2.43/2.67 (~b(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17276, 17815, 17672, 17791])).
% 2.43/2.67 tff(17817,plain,
% 2.43/2.67 (b(elem!1, s(s(s(z))))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[11114, 17814, 1222])).
% 2.43/2.67 tff(17818,plain,
% 2.43/2.67 (~b(s(elem!1), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[9291, 17817, 1326, 394])).
% 2.43/2.67 tff(17819,plain,
% 2.43/2.67 (r(s(elem!1), elem!1)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2243, 17818, 2207])).
% 2.43/2.67 tff(17820,plain,
% 2.43/2.67 (b(s(s(elem!1)), elem!1)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17790, 1382])).
% 2.43/2.67 tff(17821,plain,
% 2.43/2.67 (b(elem!1, s(s(elem!1)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[17814, 13182])).
% 2.43/2.67 tff(17822,plain,
% 2.43/2.67 (~r(s(s(s(z))), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[11522, 17821, 1326, 223, 17820, 17743, 1, 394, 211, 563, 17819])).
% 2.43/2.67 tff(17823,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1155, 17822, 17816])).
% 2.43/2.67 tff(17824,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(17825,plain,
% 2.43/2.67 (~b(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[17824, 15030, 17538, 1, 17670, 3407, 110, 2064])).
% 2.43/2.67 tff(17826,plain,
% 2.43/2.67 (r(s(elem!1), z)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[409, 17825])).
% 2.43/2.67 tff(17827,plain,
% 2.43/2.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[4393, 17826, 3407, 17741, 331, 17546, 17738])).
% 2.43/2.67 tff(17828,plain,
% 2.43/2.67 (b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[681, 17827, 17542])).
% 2.43/2.67 tff(17829,plain,
% 2.43/2.67 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17547])).
% 2.43/2.67 tff(17830,plain,
% 2.43/2.67 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[17829])).
% 2.43/2.67 tff(17831,plain,
% 2.43/2.67 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[877, 17830])).
% 2.43/2.67 tff(17832,plain,
% 2.43/2.67 (~b(s(z), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[3576, 17737, 17560])).
% 2.43/2.67 tff(17833,plain,
% 2.43/2.67 (r(s(z), s(elem!1))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[444, 17832, 344])).
% 2.43/2.67 tff(17834,plain,
% 2.43/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17835,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17836,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17835, 17834])).
% 2.43/2.68 tff(17837,plain,
% 2.43/2.68 (~r(s(s(s(s(s(z))))), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17836, 121, 412, 431, 4266])).
% 2.43/2.68 tff(17838,plain,
% 2.43/2.68 (b(s(s(s(s(s(z))))), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1682, 17837])).
% 2.43/2.68 tff(17839,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17840,plain,
% 2.43/2.68 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17841,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17840])).
% 2.43/2.68 tff(17842,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17841, 17839])).
% 2.43/2.68 tff(17843,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17844,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17843, 17842])).
% 2.43/2.68 tff(17845,plain,
% 2.43/2.68 ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17844, 121, 412, 431])).
% 2.43/2.68 tff(17846,plain,
% 2.43/2.68 (~r(s(z), s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17845, 4266])).
% 2.43/2.68 tff(17847,plain,
% 2.43/2.68 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1754, 21, 17846])).
% 2.43/2.68 tff(17848,plain,
% 2.43/2.68 (b(s(z), s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17847, 5380])).
% 2.43/2.68 tff(17849,plain,
% 2.43/2.68 ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17836, 121, 412, 431])).
% 2.43/2.68 tff(17850,plain,
% 2.43/2.68 (~r(s(s(s(s(s(z))))), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17849, 4266])).
% 2.43/2.68 tff(17851,plain,
% 2.43/2.68 (b(s(s(s(s(s(z))))), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1680, 21, 1677, 17850])).
% 2.43/2.68 tff(17852,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17853,plain,
% 2.43/2.68 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17854,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17853])).
% 2.43/2.68 tff(17855,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17854, 17852])).
% 2.43/2.68 tff(17856,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17857,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17856, 17855])).
% 2.43/2.68 tff(17858,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17857, 271, 220, 1639, 17851, 17848])).
% 2.43/2.68 tff(17859,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(17860,plain,
% 2.43/2.68 (~b(z, s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17859, 4266, 431, 412, 220])).
% 2.43/2.68 tff(17861,plain,
% 2.43/2.68 (r(z, s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1658, 17860])).
% 2.43/2.68 tff(17862,plain,
% 2.43/2.68 (~r(s(z), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[4785, 17861, 412, 431])).
% 2.43/2.68 tff(17863,plain,
% 2.43/2.68 (b(s(z), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[25, 17862])).
% 2.43/2.68 tff(17864,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17865,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17866,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17865, 17864])).
% 2.43/2.68 tff(17867,plain,
% 2.43/2.68 (~b(s(s(s(s(s(z))))), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17866, 271, 17863, 220, 17838])).
% 2.43/2.68 tff(17868,plain,
% 2.43/2.68 (r(s(s(s(s(s(z))))), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[6593, 21, 711, 17867])).
% 2.43/2.68 tff(17869,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17870,plain,
% 2.43/2.68 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17871,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17870])).
% 2.43/2.68 tff(17872,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17871, 17869])).
% 2.43/2.68 tff(17873,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17874,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17873, 17872])).
% 2.43/2.68 tff(17875,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17874, 121, 412, 17861, 17868, 4266])).
% 2.43/2.68 tff(17876,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(17877,plain,
% 2.43/2.68 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17876, 17826, 17833, 17567])).
% 2.43/2.68 tff(17878,plain,
% 2.43/2.68 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[4138, 17877, 17831])).
% 2.43/2.68 tff(17879,plain,
% 2.43/2.68 (~r(z, s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[15803, 17826, 17559, 17738])).
% 2.43/2.68 tff(17880,plain,
% 2.43/2.68 (b(z, s(s(s(s(s(z))))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1658, 17879])).
% 2.43/2.68 tff(17881,plain,
% 2.43/2.68 (~r(z, s(elem!1))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[12111, 17826, 110, 17833])).
% 2.43/2.68 tff(17882,plain,
% 2.43/2.68 (b(z, s(elem!1))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1439, 17881])).
% 2.43/2.68 tff(17883,plain,
% 2.43/2.68 (~b(s(elem!1), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[15001, 17882, 17880, 17878])).
% 2.43/2.68 tff(17884,plain,
% 2.43/2.68 (r(s(elem!1), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[429, 17883, 351])).
% 2.43/2.68 tff(17885,plain,
% 2.43/2.68 (~r(z, s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[15256, 17884, 110, 17826])).
% 2.43/2.68 tff(17886,plain,
% 2.43/2.68 (b(z, s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1214, 17885])).
% 2.43/2.68 tff(17887,plain,
% 2.43/2.68 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17538])).
% 2.43/2.68 tff(17888,plain,
% 2.43/2.68 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17887, 159])).
% 2.43/2.68 tff(17889,plain,
% 2.43/2.68 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.43/2.68 inference(transitivity,[status(thm)],[17888, 160])).
% 2.43/2.68 tff(17890,plain,
% 2.43/2.68 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17889])).
% 2.43/2.68 tff(17891,plain,
% 2.43/2.68 (~(s(s(s(z))) = elem!1)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[97, 17890])).
% 2.43/2.68 tff(17892,plain,
% 2.43/2.68 (~r(s(s(s(z))), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[16389, 17886, 3407, 2064, 17670, 17738])).
% 2.43/2.68 tff(17893,plain,
% 2.43/2.68 (b(s(s(s(z))), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[255, 17892, 17891])).
% 2.43/2.68 tff(17894,plain,
% 2.43/2.68 (b(s(s(s(z))), s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[8109, 17893, 17538])).
% 2.43/2.68 tff(17895,plain,
% 2.43/2.68 (~b(s(z), s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[15813, 17894, 17567, 17886])).
% 2.43/2.68 tff(17896,plain,
% 2.43/2.68 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[6679, 17895, 17560])).
% 2.43/2.68 tff(17897,plain,
% 2.43/2.68 (r(elem!1, s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[599, 17896, 17541])).
% 2.43/2.68 tff(17898,plain,
% 2.43/2.68 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17888])).
% 2.43/2.68 tff(17899,plain,
% 2.43/2.68 (~(elem!1 = s(s(s(z))))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[97, 17898])).
% 2.43/2.68 tff(17900,plain,
% 2.43/2.68 (~b(elem!1, s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2020, 17893, 15030, 17886])).
% 2.43/2.68 tff(17901,plain,
% 2.43/2.68 (r(elem!1, s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1192, 17900, 17899])).
% 2.43/2.68 tff(17902,plain,
% 2.43/2.68 (~r(s(s(s(z))), s(elem!1))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17626, 17901, 17738, 17826])).
% 2.43/2.68 tff(17903,plain,
% 2.43/2.68 (b(s(s(s(z))), s(elem!1))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1816, 17902, 17654])).
% 2.43/2.68 tff(17904,plain,
% 2.43/2.68 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[5687, 17903, 3407, 17886])).
% 2.43/2.68 tff(17905,plain,
% 2.43/2.68 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[13110, 17904, 17538])).
% 2.43/2.68 tff(17906,plain,
% 2.43/2.68 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[586, 17905, 563])).
% 2.43/2.68 tff(17907,plain,
% 2.43/2.68 (~r(s(s(elem!1)), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[14145, 17906, 17670, 17897])).
% 2.43/2.68 tff(17908,plain,
% 2.43/2.68 (b(s(s(elem!1)), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2430, 17907])).
% 2.43/2.68 tff(17909,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17910,plain,
% 2.43/2.68 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17911,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17910])).
% 2.43/2.68 tff(17912,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17911, 17909])).
% 2.43/2.68 tff(17913,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17914,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17913, 17912])).
% 2.43/2.68 tff(17915,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17914, 121, 623, 573, 624, 139])).
% 2.43/2.68 tff(17916,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(17917,plain,
% 2.43/2.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17916, 17906, 17670, 17897])).
% 2.43/2.68 tff(17918,plain,
% 2.43/2.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[556, 17917, 1])).
% 2.43/2.68 tff(17919,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[5267, 17918, 17908, 3407, 17828])).
% 2.43/2.68 tff(17920,plain,((z = elem!1) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(17921,plain,
% 2.43/2.68 (z = elem!1),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17920, 13201, 1, 26])).
% 2.43/2.68 tff(17922,plain,
% 2.43/2.68 (s(z) = s(elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[500, 17921])).
% 2.43/2.68 tff(17923,plain,
% 2.43/2.68 (~b(s(elem!1), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[9144, 17922, 2])).
% 2.43/2.68 tff(17924,plain,
% 2.43/2.68 (r(s(elem!1), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[409, 17923])).
% 2.43/2.68 tff(17925,plain,
% 2.43/2.68 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17921])).
% 2.43/2.68 tff(17926,plain,
% 2.43/2.68 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 2.43/2.68 inference(symmetry,[status(thm)],[17925])).
% 2.43/2.68 tff(17927,plain,
% 2.43/2.68 (z = elem!1),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17920, 3407, 1, 110])).
% 2.43/2.68 tff(17928,plain,
% 2.43/2.68 (s(z) = s(elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[500, 17927])).
% 2.43/2.68 tff(17929,plain,
% 2.43/2.68 (~b(s(elem!1), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[7069, 3498, 17927])).
% 2.43/2.68 tff(17930,plain,
% 2.43/2.68 (s(z) = s(elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17931,plain,
% 2.43/2.68 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17930])).
% 2.43/2.68 tff(17932,plain,
% 2.43/2.68 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17931])).
% 2.43/2.68 tff(17933,plain,
% 2.43/2.68 (b(z, s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1543, 2345, 17927])).
% 2.43/2.68 tff(17934,plain,
% 2.43/2.68 (b(elem!1, s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[324, 17933, 17927])).
% 2.43/2.68 tff(17935,plain,
% 2.43/2.68 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17936,plain,
% 2.43/2.68 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17935])).
% 2.43/2.68 tff(17937,plain,
% 2.43/2.68 (~(s(s(s(elem!1))) = elem!1)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[30, 17936])).
% 2.43/2.68 tff(17938,plain,
% 2.43/2.68 (b(s(s(s(elem!1))), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[486, 147, 17937])).
% 2.43/2.68 tff(17939,plain,
% 2.43/2.68 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17930])).
% 2.43/2.68 tff(17940,plain,
% 2.43/2.68 (~b(s(z), s(s(s(elem!1))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[15649, 17933, 3407, 17938])).
% 2.43/2.68 tff(17941,plain,
% 2.43/2.68 (r(s(z), s(s(s(elem!1))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[760, 17940])).
% 2.43/2.68 tff(17942,plain,
% 2.43/2.68 (r(s(elem!1), s(s(s(elem!1))))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17941, 17939])).
% 2.43/2.68 tff(17943,plain,
% 2.43/2.68 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17944,plain,
% 2.43/2.68 (b(elem!1, s(s(s(elem!1))))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[3407, 17943])).
% 2.43/2.68 tff(17945,plain,
% 2.43/2.68 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17946,plain,
% 2.43/2.68 (~r(s(s(s(z))), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[149, 147, 17927])).
% 2.43/2.68 tff(17947,plain,
% 2.43/2.68 (~b(s(z), s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[10135, 17933, 17927, 2207, 412, 17946])).
% 2.43/2.68 tff(17948,plain,
% 2.43/2.68 (r(s(z), s(s(s(z))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[105, 17947])).
% 2.43/2.68 tff(17949,plain,
% 2.43/2.68 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17950,plain,
% 2.43/2.68 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17949, 2211])).
% 2.43/2.68 tff(17951,plain,
% 2.43/2.68 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17950])).
% 2.43/2.68 tff(17952,plain,
% 2.43/2.68 (~(elem!1 = s(s(elem!1)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[59, 17951])).
% 2.43/2.68 tff(17953,plain,
% 2.43/2.68 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.43/2.68 inference(transitivity,[status(thm)],[17950, 2212])).
% 2.43/2.68 tff(17954,plain,
% 2.43/2.68 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17953])).
% 2.43/2.68 tff(17955,plain,
% 2.43/2.68 (~(s(s(elem!1)) = elem!1)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[59, 17954])).
% 2.43/2.68 tff(17956,plain,
% 2.43/2.68 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17930])).
% 2.43/2.68 tff(17957,plain,
% 2.43/2.68 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17956, 200])).
% 2.43/2.68 tff(17958,plain,
% 2.43/2.68 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17957])).
% 2.43/2.68 tff(17959,plain,
% 2.43/2.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[61, 17958])).
% 2.43/2.68 tff(17960,plain,
% 2.43/2.68 (~b(elem!1, s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[7550, 7548, 17927])).
% 2.43/2.68 tff(17961,plain,
% 2.43/2.68 (r(elem!1, s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[599, 17960, 17952])).
% 2.43/2.68 tff(17962,plain,
% 2.43/2.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[890, 17961, 17927, 307, 17959, 622, 17955])).
% 2.43/2.68 tff(17963,plain,
% 2.43/2.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[556, 17962, 1])).
% 2.43/2.68 tff(17964,plain,
% 2.43/2.68 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17965,plain,
% 2.43/2.68 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 2.43/2.68 inference(symmetry,[status(thm)],[17964])).
% 2.43/2.68 tff(17966,plain,
% 2.43/2.68 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17965])).
% 2.43/2.68 tff(17967,plain,
% 2.43/2.68 (~b(z, elem!1)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[192, 17966])).
% 2.43/2.68 tff(17968,plain,
% 2.43/2.68 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17930])).
% 2.43/2.68 tff(17969,plain,
% 2.43/2.68 (r(z, s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2106, 7548])).
% 2.43/2.68 tff(17970,plain,
% 2.43/2.68 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.68 tff(17971,plain,
% 2.43/2.68 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 2.43/2.68 inference(symmetry,[status(thm)],[17970])).
% 2.43/2.68 tff(17972,plain,
% 2.43/2.68 (b(s(s(s(elem!1))), z)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[504, 17971])).
% 2.43/2.68 tff(17973,plain,
% 2.43/2.68 (~b(s(s(elem!1)), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[13762, 17963, 3407, 17972])).
% 2.43/2.68 tff(17974,plain,
% 2.43/2.68 (r(s(s(elem!1)), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2430, 17973])).
% 2.43/2.68 tff(17975,plain,
% 2.43/2.68 (~r(s(z), s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[11783, 17974, 110, 17969])).
% 2.43/2.68 tff(17976,plain,
% 2.43/2.68 (b(s(z), s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2167, 17975])).
% 2.43/2.68 tff(17977,plain,
% 2.43/2.68 (b(s(elem!1), s(s(elem!1)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[17976, 17968])).
% 2.43/2.68 tff(17978,plain,
% 2.43/2.68 (s(s(z)) = s(s(elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17930])).
% 2.43/2.68 tff(17979,plain,
% 2.43/2.68 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17978])).
% 2.43/2.68 tff(17980,plain,
% 2.43/2.68 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17979])).
% 2.43/2.68 tff(17981,plain,
% 2.43/2.68 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17930])).
% 2.43/2.68 tff(17982,plain,
% 2.43/2.68 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17981, 17980])).
% 2.43/2.68 tff(17983,plain,
% 2.43/2.68 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17982])).
% 2.43/2.68 tff(17984,plain,
% 2.43/2.68 (b(z, s(z))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1543, 307, 17927])).
% 2.43/2.68 tff(17985,plain,
% 2.43/2.68 (~b(s(s(elem!1)), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[551, 17963, 504, 307])).
% 2.43/2.68 tff(17986,plain,
% 2.43/2.68 (r(s(s(elem!1)), elem!1)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[862, 17985, 17955])).
% 2.43/2.68 tff(17987,plain,
% 2.43/2.68 (~r(s(s(s(z))), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2096, 2088, 108, 110])).
% 2.43/2.68 tff(17988,plain,
% 2.43/2.68 (b(s(s(s(z))), z)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1155, 17987])).
% 2.43/2.68 tff(17989,plain,
% 2.43/2.68 (~b(s(z), s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[17276, 17988, 220, 222])).
% 2.43/2.68 tff(17990,plain,
% 2.43/2.68 (r(s(z), s(s(elem!1)))),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2167, 17989])).
% 2.43/2.68 tff(17991,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17992,plain,
% 2.43/2.68 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(17993,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[17992])).
% 2.43/2.68 tff(17994,plain,
% 2.43/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.43/2.68 inference(transitivity,[status(thm)],[17993, 17991])).
% 2.43/2.68 tff(17995,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(17996,plain,
% 2.43/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[17995, 17994])).
% 2.43/2.69 tff(17997,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[17996, 121, 17990, 2088, 110, 1624])).
% 2.43/2.69 tff(17998,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(17999,plain,
% 2.43/2.69 (~b(s(s(s(z))), s(z))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[17998, 17986, 17984, 108, 110, 17969])).
% 2.43/2.69 tff(18000,plain,
% 2.43/2.69 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[17999, 17983])).
% 2.43/2.69 tff(18001,plain,
% 2.43/2.69 (r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[679, 21, 17959, 18000])).
% 2.43/2.69 tff(18002,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[17114, 18001, 17977, 622, 412, 17967, 17963, 307, 17952])).
% 2.43/2.69 tff(18003,plain,(b(z, s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18004,plain,
% 2.43/2.69 (b(z, s(s(elem!1)))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18003, 2345, 412, 8563, 110, 17948, 3407, 17938, 1])).
% 2.43/2.69 tff(18005,plain,
% 2.43/2.69 (b(elem!1, s(s(elem!1)))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18004, 17945])).
% 2.43/2.69 tff(18006,plain,
% 2.43/2.69 (r(elem!1, s(s(s(elem!1))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[11908, 543, 481, 147, 588])).
% 2.43/2.69 tff(18007,plain,
% 2.43/2.69 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[6906, 543, 738, 588])).
% 2.43/2.69 tff(18008,plain,
% 2.43/2.69 (r(s(s(s(elem!1))), s(elem!1))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[681, 18007, 82])).
% 2.43/2.69 tff(18009,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[11896, 18008, 18006, 622, 798])).
% 2.43/2.69 tff(18010,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18011,plain,
% 2.43/2.69 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18010, 17942, 8563, 17959, 17937, 147, 18005, 17944])).
% 2.43/2.69 tff(18012,plain,
% 2.43/2.69 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[556, 18011, 1])).
% 2.43/2.69 tff(18013,plain,
% 2.43/2.69 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.43/2.69 inference(monotonicity,[status(thm)],[17927])).
% 2.43/2.69 tff(18014,plain,
% 2.43/2.69 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18013, 159])).
% 2.43/2.69 tff(18015,plain,
% 2.43/2.69 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.43/2.69 inference(transitivity,[status(thm)],[18014, 160])).
% 2.43/2.69 tff(18016,plain,
% 2.43/2.69 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18015])).
% 2.43/2.69 tff(18017,plain,
% 2.43/2.69 (~(s(s(s(z))) = elem!1)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[166, 18016])).
% 2.43/2.69 tff(18018,plain,
% 2.43/2.69 (b(s(s(s(z))), elem!1)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[255, 17946, 18017])).
% 2.43/2.69 tff(18019,plain,
% 2.43/2.69 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[17978])).
% 2.43/2.69 tff(18020,plain,
% 2.43/2.69 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.43/2.69 inference(symmetry,[status(thm)],[18019])).
% 2.43/2.69 tff(18021,plain,
% 2.43/2.69 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[17945, 18020])).
% 2.43/2.69 tff(18022,plain,
% 2.43/2.69 (b(elem!1, s(s(z)))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18004, 18021])).
% 2.43/2.69 tff(18023,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18024,plain,
% 2.43/2.69 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18025,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18024])).
% 2.43/2.69 tff(18026,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18025, 18023])).
% 2.43/2.69 tff(18027,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(18028,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18027, 18026])).
% 2.43/2.69 tff(18029,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18028, 121, 623, 627, 798, 7473])).
% 2.43/2.69 tff(18030,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18031,plain,
% 2.43/2.69 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18030, 627, 623, 798])).
% 2.43/2.69 tff(18032,plain,
% 2.43/2.69 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[7296, 18031, 107])).
% 2.43/2.69 tff(18033,plain,
% 2.43/2.69 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1494, 18032])).
% 2.43/2.69 tff(18034,plain,
% 2.43/2.69 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(symmetry,[status(thm)],[7499])).
% 2.43/2.69 tff(18035,plain,
% 2.43/2.69 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[1519, 18034])).
% 2.43/2.69 tff(18036,assumption,(~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.43/2.69 tff(18037,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18036, 18035])).
% 2.43/2.69 tff(18038,plain,(b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18039,plain,
% 2.43/2.69 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18038, 18033, 107])).
% 2.43/2.69 tff(18040,plain,
% 2.43/2.69 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.43/2.69 inference(transitivity,[status(thm)],[708, 1837])).
% 2.43/2.69 tff(18041,plain,
% 2.43/2.69 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18040])).
% 2.43/2.69 tff(18042,plain,
% 2.43/2.69 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[711, 18041])).
% 2.43/2.69 tff(18043,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.43/2.69 tff(18044,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18045,plain,
% 2.43/2.69 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18046,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18045])).
% 2.43/2.69 tff(18047,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18046, 18044])).
% 2.43/2.69 tff(18048,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(18049,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18048, 18047])).
% 2.43/2.69 tff(18050,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18049, 271, 307, 504, 785, 18043])).
% 2.43/2.69 tff(18051,plain,((~b(s(s(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(elem!1))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18052,plain,
% 2.43/2.69 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18051, 18039, 504, 307])).
% 2.43/2.69 tff(18053,plain,
% 2.43/2.69 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[835, 18052, 107])).
% 2.43/2.69 tff(18054,plain,
% 2.43/2.69 (r(s(s(s(s(s(z))))), elem!1)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[840, 18053, 712])).
% 2.43/2.69 tff(18055,plain,
% 2.43/2.69 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[9962, 18054, 1536])).
% 2.43/2.69 tff(18056,plain,
% 2.43/2.69 (b(z, s(z))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1543, 307, 107])).
% 2.43/2.69 tff(18057,plain,
% 2.43/2.69 (b(elem!1, s(z))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[324, 18056, 107])).
% 2.43/2.69 tff(18058,plain,
% 2.43/2.69 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[5833, 3512])).
% 2.43/2.69 tff(18059,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.43/2.69 tff(18060,plain,
% 2.43/2.69 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.43/2.69 inference(symmetry,[status(thm)],[18059])).
% 2.43/2.69 tff(18061,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[5951, 18060])).
% 2.43/2.69 tff(18062,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18063,plain,
% 2.43/2.69 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18062, 18058])).
% 2.43/2.69 tff(18064,plain,
% 2.43/2.69 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[11144, 627, 798, 623])).
% 2.43/2.69 tff(18065,plain,
% 2.43/2.69 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[586, 18064, 6943])).
% 2.43/2.69 tff(18066,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18067,plain,
% 2.43/2.69 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18068,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18067])).
% 2.43/2.69 tff(18069,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18068, 18066])).
% 2.43/2.69 tff(18070,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(18071,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18070, 18069])).
% 2.43/2.69 tff(18072,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18071, 271, 589, 588, 738, 5021])).
% 2.43/2.69 tff(18073,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18074,plain,
% 2.43/2.69 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18073, 18065, 738, 588])).
% 2.43/2.69 tff(18075,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.43/2.69 tff(18076,assumption,(~r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.43/2.69 tff(18077,assumption,(~b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.43/2.69 tff(18078,plain,
% 2.43/2.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18079,plain,
% 2.43/2.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(18080,plain,
% 2.43/2.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18079, 18078])).
% 2.43/2.69 tff(18081,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18080, 21, 18077, 18076, 18075])).
% 2.43/2.69 tff(18082,plain,(r(s(s(elem!1)), s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18083,plain,
% 2.43/2.69 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18082, 18074, 18063])).
% 2.43/2.69 tff(18084,plain,
% 2.43/2.69 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[134, 133])).
% 2.43/2.69 tff(18085,plain,
% 2.43/2.69 ((~b(s(s(z)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18084])).
% 2.43/2.69 tff(18086,plain,
% 2.43/2.69 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.43/2.69 inference(symmetry,[status(thm)],[1524])).
% 2.43/2.69 tff(18087,plain,
% 2.43/2.69 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.43/2.69 inference(symmetry,[status(thm)],[1522])).
% 2.43/2.69 tff(18088,plain,
% 2.43/2.69 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18087, 18086])).
% 2.43/2.69 tff(18089,plain,
% 2.43/2.69 (b(s(s(s(z))), s(s(z)))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18065, 18088])).
% 2.43/2.69 tff(18090,plain,
% 2.43/2.69 (~b(s(s(z)), s(z))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[6740, 18089, 6725, 257])).
% 2.43/2.69 tff(18091,plain,
% 2.43/2.69 (~b(s(s(elem!1)), s(elem!1))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18090, 18085])).
% 2.43/2.69 tff(18092,plain,
% 2.43/2.69 (r(s(s(elem!1)), s(elem!1))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[699, 21, 18091, 694])).
% 2.43/2.69 tff(18093,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.43/2.69 tff(18094,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[7859, 121, 622, 683, 6898, 18093])).
% 2.43/2.69 tff(18095,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18096,plain,
% 2.43/2.69 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18095, 18092, 622, 18083])).
% 2.43/2.69 tff(18097,plain,
% 2.43/2.69 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[10182, 18096, 107])).
% 2.43/2.69 tff(18098,plain,
% 2.43/2.69 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[133])).
% 2.43/2.69 tff(18099,plain,
% 2.43/2.69 (r(s(s(s(s(z)))), s(elem!1))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[911, 18098])).
% 2.43/2.69 tff(18100,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[14005, 18099])).
% 2.43/2.69 tff(18101,plain,(r(s(s(s(s(z)))), s(elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(18102,plain,
% 2.43/2.69 (~r(s(s(s(s(z)))), s(z))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18101, 18097, 107])).
% 2.43/2.69 tff(18103,plain,
% 2.43/2.69 (b(s(s(s(s(z)))), s(z))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[932, 18102])).
% 2.43/2.69 tff(18104,plain,
% 2.43/2.69 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.43/2.69 inference(monotonicity,[status(thm)],[1578])).
% 2.43/2.69 tff(18105,plain,
% 2.43/2.69 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.43/2.69 inference(symmetry,[status(thm)],[18104])).
% 2.43/2.69 tff(18106,plain,
% 2.43/2.69 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18105])).
% 2.43/2.69 tff(18107,plain,
% 2.43/2.69 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[133])).
% 2.43/2.69 tff(18108,plain,
% 2.43/2.69 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(symmetry,[status(thm)],[18107])).
% 2.43/2.69 tff(18109,plain,
% 2.43/2.69 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[705])).
% 2.43/2.69 tff(18110,plain,
% 2.43/2.69 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18109, 18108])).
% 2.43/2.69 tff(18111,plain,
% 2.43/2.69 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18110])).
% 2.43/2.69 tff(18112,plain,
% 2.43/2.69 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[705])).
% 2.43/2.69 tff(18113,plain,
% 2.43/2.69 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(symmetry,[status(thm)],[18112])).
% 2.43/2.69 tff(18114,plain,
% 2.43/2.69 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[1826, 18113])).
% 2.43/2.69 tff(18115,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18116,plain,
% 2.43/2.69 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18117,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18116])).
% 2.43/2.69 tff(18118,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[18117, 18115])).
% 2.43/2.69 tff(18119,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(18120,plain,
% 2.43/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18119, 18118])).
% 2.43/2.69 tff(18121,plain,
% 2.43/2.69 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18120, 121, 622, 17094])).
% 2.43/2.69 tff(18122,plain,
% 2.43/2.69 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[18121, 18114])).
% 2.43/2.69 tff(18123,plain,
% 2.43/2.69 (~r(s(z), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[18122, 18111])).
% 2.43/2.69 tff(18124,plain,
% 2.43/2.69 (b(s(z), s(s(s(s(s(z))))))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1756, 18123])).
% 2.43/2.69 tff(18125,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18126,plain,
% 2.43/2.69 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(18127,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[18126])).
% 2.43/2.69 tff(18128,plain,
% 2.43/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.43/2.70 inference(transitivity,[status(thm)],[18127, 18125])).
% 2.43/2.70 tff(18129,plain,
% 2.43/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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)))),
% 2.43/2.70 inference(quant_inst,[status(thm)],[])).
% 2.43/2.70 tff(18130,plain,
% 2.43/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[18129, 18128])).
% 2.43/2.70 tff(18131,plain,
% 2.43/2.70 ((~b(elem!1, 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)))), elem!1))),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[18130, 271])).
% 2.43/2.70 tff(18132,plain,
% 2.43/2.70 (~b(s(s(s(s(z)))), elem!1)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[18131, 18124, 448, 937])).
% 2.43/2.70 tff(18133,plain,
% 2.43/2.70 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[18132, 18106])).
% 2.43/2.70 tff(18134,plain,
% 2.43/2.70 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[10142, 107])).
% 2.43/2.70 tff(18135,plain,
% 2.43/2.70 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.43/2.70 inference(monotonicity,[status(thm)],[1578, 705])).
% 2.43/2.70 tff(18136,plain,
% 2.43/2.70 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.43/2.70 inference(symmetry,[status(thm)],[18135])).
% 2.43/2.70 tff(18137,plain,
% 2.43/2.70 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.70 inference(monotonicity,[status(thm)],[133])).
% 2.43/2.70 tff(18138,plain,
% 2.43/2.70 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.43/2.70 inference(symmetry,[status(thm)],[18137])).
% 2.43/2.70 tff(18139,plain,
% 2.43/2.70 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.43/2.70 inference(monotonicity,[status(thm)],[705])).
% 2.43/2.70 tff(18140,plain,
% 2.43/2.70 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.53/2.70 inference(transitivity,[status(thm)],[18139, 18138])).
% 2.53/2.70 tff(18141,plain,
% 2.53/2.70 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18140])).
% 2.53/2.70 tff(18142,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18143,plain,
% 2.53/2.70 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18144,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18143])).
% 2.53/2.70 tff(18145,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[18144, 18142])).
% 2.53/2.70 tff(18146,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(18147,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18146, 18145])).
% 2.53/2.70 tff(18148,plain,
% 2.53/2.70 ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18147, 121, 622, 17094])).
% 2.53/2.70 tff(18149,plain,
% 2.53/2.70 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18148, 18114])).
% 2.53/2.70 tff(18150,plain,
% 2.53/2.70 (~r(s(s(s(s(s(z))))), s(z))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18149, 18141])).
% 2.53/2.70 tff(18151,plain,
% 2.53/2.70 (b(s(s(s(s(s(z))))), s(z))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1682, 18150])).
% 2.53/2.70 tff(18152,plain,
% 2.53/2.70 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1785, 18124, 937, 18151])).
% 2.53/2.70 tff(18153,plain,
% 2.53/2.70 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1777, 18152])).
% 2.53/2.70 tff(18154,plain,
% 2.53/2.70 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18153, 18136])).
% 2.53/2.70 tff(18155,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18156,plain,
% 2.53/2.70 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18157,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1)))))))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18156])).
% 2.53/2.70 tff(18158,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 2.53/2.70 inference(transitivity,[status(thm)],[18157, 18155])).
% 2.53/2.70 tff(18159,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(18160,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18159, 18158])).
% 2.53/2.70 tff(18161,plain,
% 2.53/2.70 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18160, 121, 17094, 10184, 18114])).
% 2.53/2.70 tff(18162,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18161, 18154])).
% 2.53/2.70 tff(18163,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18164,plain,
% 2.53/2.70 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18163, 1826, 107, 622, 17094, 937])).
% 2.53/2.70 tff(18165,plain,
% 2.53/2.70 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[10196, 18164, 18134])).
% 2.53/2.70 tff(18166,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18165, 18133])).
% 2.53/2.70 tff(18167,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~(z = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18168,plain,
% 2.53/2.70 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18167, 18103, 18057, 107, 622, 18055])).
% 2.53/2.70 tff(18169,plain,
% 2.53/2.70 (b(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1847, 18168, 18042])).
% 2.53/2.70 tff(18170,plain,
% 2.53/2.70 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[9946, 18169, 1536])).
% 2.53/2.70 tff(18171,plain,
% 2.53/2.70 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17066])).
% 2.53/2.70 tff(18172,plain,
% 2.53/2.70 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18171])).
% 2.53/2.70 tff(18173,plain,
% 2.53/2.70 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18172])).
% 2.53/2.70 tff(18174,plain,
% 2.53/2.70 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[1677, 18173])).
% 2.53/2.70 tff(18175,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18176,plain,
% 2.53/2.70 (((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18177,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18176])).
% 2.53/2.70 tff(18178,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[18177, 18175])).
% 2.53/2.70 tff(18179,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(18180,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18179, 18178])).
% 2.53/2.70 tff(18181,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18180, 271, 504, 17081, 6004, 18043])).
% 2.53/2.70 tff(18182,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18183,plain,
% 2.53/2.70 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18182, 18170, 504, 18039])).
% 2.53/2.70 tff(18184,plain,
% 2.53/2.70 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[9896, 18183, 107])).
% 2.53/2.70 tff(18185,plain,
% 2.53/2.70 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[4138, 18184, 18174])).
% 2.53/2.70 tff(18186,plain,
% 2.53/2.70 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18139])).
% 2.53/2.70 tff(18187,assumption,(~r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 2.53/2.70 tff(18188,plain,
% 2.53/2.70 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18187, 18186])).
% 2.53/2.70 tff(18189,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[4266, 18188])).
% 2.53/2.70 tff(18190,plain,(r(s(s(s(s(s(elem!1))))), s(elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18191,plain,
% 2.53/2.70 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18190, 18185, 107])).
% 2.53/2.70 tff(18192,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18193,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(18194,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18193, 18192])).
% 2.53/2.70 tff(18195,plain,
% 2.53/2.70 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18194, 121, 622, 18092, 18191])).
% 2.53/2.70 tff(18196,plain,
% 2.53/2.70 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[881, 21, 878, 18195])).
% 2.53/2.70 tff(18197,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18198,plain,
% 2.53/2.70 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(18199,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18198])).
% 2.53/2.70 tff(18200,plain,
% 2.53/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.70 inference(transitivity,[status(thm)],[18199, 18197])).
% 2.53/2.70 tff(18201,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(18202,plain,
% 2.53/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18201, 18200])).
% 2.53/2.70 tff(18203,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18202, 271, 504, 18196, 18170, 18039])).
% 2.53/2.70 tff(18204,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~(z = elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18205,plain,
% 2.53/2.70 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18204, 18022, 8563, 17927, 3313, 17938, 18018, 2345, 17944, 18005, 563, 18012, 17942])).
% 2.53/2.70 tff(18206,plain,
% 2.53/2.70 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[526, 18205, 211])).
% 2.53/2.70 tff(18207,plain,
% 2.53/2.70 (b(s(z), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[521, 18206, 17928])).
% 2.53/2.70 tff(18208,plain,
% 2.53/2.70 (~b(s(s(s(elem!1))), s(z))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[513, 18207, 17938, 17934])).
% 2.53/2.70 tff(18209,plain,
% 2.53/2.70 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18208, 17932])).
% 2.53/2.70 tff(18210,plain,
% 2.53/2.70 (~r(elem!1, s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[890, 18012, 17927, 2345, 17959, 8563, 17955])).
% 2.53/2.70 tff(18211,plain,
% 2.53/2.70 ((~r(elem!1, s(elem!1))) <=> (~r(z, s(elem!1)))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[5912])).
% 2.53/2.70 tff(18212,plain,
% 2.53/2.70 (~r(z, s(elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2344, 18211])).
% 2.53/2.70 tff(18213,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1441, 18212])).
% 2.53/2.70 tff(18214,plain,((~(z = elem!1)) | (~r(z, s(elem!1))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18215,plain,
% 2.53/2.70 (~r(z, s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18214, 2344, 17927])).
% 2.53/2.70 tff(18216,plain,
% 2.53/2.70 (b(z, s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1439, 18215])).
% 2.53/2.70 tff(18217,plain,
% 2.53/2.70 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[556, 2469, 4436])).
% 2.53/2.70 tff(18218,plain,
% 2.53/2.70 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[4488, 2469, 2467, 481, 4435, 675])).
% 2.53/2.70 tff(18219,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[11144, 18218, 18217, 627, 798])).
% 2.53/2.70 tff(18220,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = elem!1) | r(elem!1, s(s(elem!1))) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18221,plain,
% 2.53/2.70 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18220, 675, 481, 798, 2467, 2469, 4435])).
% 2.53/2.70 tff(18222,plain,
% 2.53/2.70 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[526, 18221, 216])).
% 2.53/2.70 tff(18223,plain,
% 2.53/2.70 (~r(s(s(elem!1)), s(z))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2125, 13705, 623, 572])).
% 2.53/2.70 tff(18224,plain,
% 2.53/2.70 (b(s(s(elem!1)), s(z))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2143, 18223])).
% 2.53/2.70 tff(18225,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2152, 18224, 18222, 1894, 1421])).
% 2.53/2.70 tff(18226,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), s(s(s(elem!1))))) | b(s(elem!1), elem!1) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18227,plain,
% 2.53/2.70 (b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18226, 18004, 18216, 211, 18012, 17941, 17937, 17942, 2467, 18011, 18210, 17959])).
% 2.53/2.70 tff(18228,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18227, 18209])).
% 2.53/2.70 tff(18229,plain,(r(elem!1, s(elem!1)) | b(s(elem!1), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(18230,plain,
% 2.53/2.70 (r(elem!1, s(elem!1))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[18229, 147, 1, 17929, 3501, 110, 3407])).
% 2.53/2.70 tff(18231,plain,
% 2.53/2.70 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17927])).
% 2.53/2.70 tff(18232,plain,
% 2.53/2.70 (r(s(z), elem!1)),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[110, 18231])).
% 2.53/2.70 tff(18233,plain,
% 2.53/2.70 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17927])).
% 2.53/2.70 tff(18234,plain,
% 2.53/2.70 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18233])).
% 2.53/2.70 tff(18235,plain,
% 2.53/2.70 (r(z, s(elem!1))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18230, 18234])).
% 2.53/2.70 tff(18236,plain,
% 2.53/2.70 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17930])).
% 2.53/2.70 tff(18237,plain,
% 2.53/2.70 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18236])).
% 2.53/2.70 tff(18238,plain,
% 2.53/2.70 (r(elem!1, s(z))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18230, 18237])).
% 2.53/2.70 tff(18239,plain,
% 2.53/2.70 (r(z, s(z)) <=> r(elem!1, s(z))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17927])).
% 2.53/2.70 tff(18240,plain,
% 2.53/2.70 (r(elem!1, s(z)) <=> r(z, s(z))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18239])).
% 2.53/2.70 tff(18241,plain,
% 2.53/2.70 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 2.53/2.70 inference(transitivity,[status(thm)],[18237, 18240])).
% 2.53/2.70 tff(18242,plain,
% 2.53/2.70 (r(z, s(z))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18230, 18241])).
% 2.53/2.70 tff(18243,plain,
% 2.53/2.70 (~r(s(s(s(z))), z)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[475, 17946, 17927])).
% 2.53/2.70 tff(18244,plain,
% 2.53/2.70 (b(s(s(s(z))), z)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1155, 18243])).
% 2.53/2.70 tff(18245,plain,
% 2.53/2.70 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17979])).
% 2.53/2.70 tff(18246,plain,
% 2.53/2.70 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18245])).
% 2.53/2.70 tff(18247,plain,
% 2.53/2.70 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18246])).
% 2.53/2.70 tff(18248,plain,
% 2.53/2.70 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18245])).
% 2.53/2.70 tff(18249,plain,
% 2.53/2.70 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18248, 18247])).
% 2.53/2.70 tff(18250,plain,
% 2.53/2.70 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18249])).
% 2.53/2.70 tff(18251,plain,
% 2.53/2.70 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17930])).
% 2.53/2.70 tff(18252,plain,
% 2.53/2.70 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.53/2.70 inference(symmetry,[status(thm)],[18251])).
% 2.53/2.70 tff(18253,plain,
% 2.53/2.70 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18252])).
% 2.53/2.70 tff(18254,plain,
% 2.53/2.70 (~b(s(s(elem!1)), z)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[13762, 543, 3407, 17972])).
% 2.53/2.70 tff(18255,plain,
% 2.53/2.70 (r(s(s(elem!1)), z)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2430, 18254])).
% 2.53/2.70 tff(18256,plain,
% 2.53/2.70 (~r(s(s(elem!1)), s(z))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2422, 18255, 110, 909])).
% 2.53/2.70 tff(18257,plain,
% 2.53/2.70 (b(s(s(elem!1)), s(z))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2143, 18256])).
% 2.53/2.70 tff(18258,plain,
% 2.53/2.70 (~b(s(z), s(s(s(elem!1))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[989, 18257, 504, 543])).
% 2.53/2.70 tff(18259,plain,
% 2.53/2.70 (r(s(z), s(s(s(elem!1))))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[760, 18258])).
% 2.53/2.70 tff(18260,plain,
% 2.53/2.70 (r(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[18259, 17939])).
% 2.53/2.70 tff(18261,plain,
% 2.53/2.70 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.53/2.70 inference(monotonicity,[status(thm)],[17927])).
% 2.53/2.70 tff(18262,plain,
% 2.53/2.70 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[18261])).
% 2.53/2.70 tff(18263,plain,
% 2.53/2.70 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[711, 18262])).
% 2.53/2.70 tff(18264,plain,
% 2.53/2.70 (~b(s(s(elem!1)), elem!1)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[13398, 271, 543, 504, 17944])).
% 2.53/2.70 tff(18265,plain,
% 2.53/2.71 (r(s(s(elem!1)), elem!1)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[862, 18264, 17955])).
% 2.53/2.71 tff(18266,plain,
% 2.53/2.71 (~b(elem!1, s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[11906, 271, 543, 504, 17944])).
% 2.53/2.71 tff(18267,plain,
% 2.53/2.71 (r(elem!1, s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[599, 18266, 17952])).
% 2.53/2.71 tff(18268,plain,
% 2.53/2.71 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18246, 17978])).
% 2.53/2.71 tff(18269,plain,
% 2.53/2.71 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18268])).
% 2.53/2.71 tff(18270,plain,
% 2.53/2.71 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[877, 18269])).
% 2.53/2.71 tff(18271,plain,
% 2.53/2.71 (r(s(elem!1), elem!1)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2243, 17929, 2207])).
% 2.53/2.71 tff(18272,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[15139, 121, 622, 627, 3456, 1624])).
% 2.53/2.71 tff(18273,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(18274,plain,
% 2.53/2.71 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18273, 18265, 3456, 18271])).
% 2.53/2.71 tff(18275,plain,
% 2.53/2.71 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[526, 18274, 211])).
% 2.53/2.71 tff(18276,plain,
% 2.53/2.71 (elem!1 = z),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[364, 17927])).
% 2.53/2.71 tff(18277,plain,
% 2.53/2.71 (~b(s(z), s(s(s(z))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[9876, 18258, 18276])).
% 2.53/2.71 tff(18278,plain,
% 2.53/2.71 (r(s(z), s(s(s(z))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[105, 18277])).
% 2.53/2.71 tff(18279,plain,
% 2.53/2.71 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.53/2.71 inference(symmetry,[status(thm)],[17945])).
% 2.53/2.71 tff(18280,plain,
% 2.53/2.71 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18279])).
% 2.53/2.71 tff(18281,plain,
% 2.53/2.71 (~b(z, s(s(elem!1)))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18266, 18280])).
% 2.53/2.71 tff(18282,plain,
% 2.53/2.71 (~b(elem!1, s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18003, 18281, 3501, 18271, 110, 18278, 3407, 504, 1])).
% 2.53/2.71 tff(18283,plain,
% 2.53/2.71 (~b(z, s(z))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[327, 18282, 17927])).
% 2.53/2.71 tff(18284,plain,
% 2.53/2.71 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[8078, 18283, 219, 3498])).
% 2.53/2.71 tff(18285,plain,
% 2.53/2.71 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[9896, 18284, 17927])).
% 2.53/2.71 tff(18286,plain,
% 2.53/2.71 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[17089, 18285, 543, 18275])).
% 2.53/2.71 tff(18287,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 2.53/2.71 tff(18288,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 2.53/2.71 tff(18289,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))), introduced(assumption)).
% 2.53/2.71 tff(18290,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[881, 21, 18289, 18288, 18287])).
% 2.53/2.71 tff(18291,plain,(r(s(s(s(s(s(elem!1))))), s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(18292,plain,
% 2.53/2.71 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18291, 18286, 18270])).
% 2.53/2.71 tff(18293,plain,
% 2.53/2.71 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[17096, 18292, 18267, 18265])).
% 2.53/2.71 tff(18294,plain,
% 2.53/2.71 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[9962, 18293, 17928])).
% 2.53/2.71 tff(18295,plain,
% 2.53/2.71 (b(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[840, 18294, 18263])).
% 2.53/2.71 tff(18296,plain,
% 2.53/2.71 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[835, 18295, 17927])).
% 2.53/2.71 tff(18297,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18298,plain,
% 2.53/2.71 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18299,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18298])).
% 2.53/2.71 tff(18300,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18299, 18297])).
% 2.53/2.71 tff(18301,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(18302,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18301, 18300])).
% 2.53/2.71 tff(18303,plain,
% 2.53/2.71 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18302, 271, 504, 18296, 17944])).
% 2.53/2.71 tff(18304,plain,
% 2.53/2.71 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18038, 18303, 17927])).
% 2.53/2.71 tff(18305,plain,
% 2.53/2.71 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1494, 18304])).
% 2.53/2.71 tff(18306,plain,
% 2.53/2.71 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[7296, 18305, 17927])).
% 2.53/2.71 tff(18307,plain,
% 2.53/2.71 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[17979])).
% 2.53/2.71 tff(18308,plain,
% 2.53/2.71 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.71 inference(symmetry,[status(thm)],[18307])).
% 2.53/2.71 tff(18309,plain,
% 2.53/2.71 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18247])).
% 2.53/2.71 tff(18310,plain,
% 2.53/2.71 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18309, 18308])).
% 2.53/2.71 tff(18311,plain,
% 2.53/2.71 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18310])).
% 2.53/2.71 tff(18312,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18313,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(18314,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18313, 18312])).
% 2.53/2.71 tff(18315,plain,
% 2.53/2.71 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18314, 271, 504, 18296, 17944])).
% 2.53/2.71 tff(18316,plain,
% 2.53/2.71 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18315, 18311])).
% 2.53/2.71 tff(18317,plain,
% 2.53/2.71 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1733, 18316])).
% 2.53/2.71 tff(18318,plain,
% 2.53/2.71 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[6039, 18317, 17927])).
% 2.53/2.71 tff(18319,plain,
% 2.53/2.71 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[7481, 18318, 18306, 18260])).
% 2.53/2.71 tff(18320,plain,
% 2.53/2.71 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18190, 18319, 17927])).
% 2.53/2.71 tff(18321,plain,
% 2.53/2.71 (~r(s(s(s(s(s(z))))), s(z))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18320, 18253])).
% 2.53/2.71 tff(18322,plain,
% 2.53/2.71 (b(s(s(s(s(s(z))))), s(z))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1682, 18321])).
% 2.53/2.71 tff(18323,plain,
% 2.53/2.71 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[17930])).
% 2.53/2.71 tff(18324,plain,
% 2.53/2.71 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(symmetry,[status(thm)],[18323])).
% 2.53/2.71 tff(18325,plain,
% 2.53/2.71 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18247])).
% 2.53/2.71 tff(18326,plain,
% 2.53/2.71 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18325, 18324])).
% 2.53/2.71 tff(18327,plain,
% 2.53/2.71 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18326])).
% 2.53/2.71 tff(18328,assumption,(r(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.53/2.71 tff(18329,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18330,plain,
% 2.53/2.71 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18331,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18330])).
% 2.53/2.71 tff(18332,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18331, 18329])).
% 2.53/2.71 tff(18333,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(18334,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18333, 18332])).
% 2.53/2.71 tff(18335,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18334, 121, 798, 7473, 6026, 18328])).
% 2.53/2.71 tff(18336,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(18337,plain,
% 2.53/2.71 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18336, 18318, 18306, 18260])).
% 2.53/2.71 tff(18338,plain,
% 2.53/2.71 (~r(s(z), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18337, 18327])).
% 2.53/2.71 tff(18339,plain,
% 2.53/2.71 (b(s(z), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1756, 18338])).
% 2.53/2.71 tff(18340,plain,
% 2.53/2.71 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[17927])).
% 2.53/2.71 tff(18341,plain,
% 2.53/2.71 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 2.53/2.71 inference(symmetry,[status(thm)],[18340])).
% 2.53/2.71 tff(18342,plain,
% 2.53/2.71 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[17979])).
% 2.53/2.71 tff(18343,plain,
% 2.53/2.71 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.53/2.71 inference(symmetry,[status(thm)],[18342])).
% 2.53/2.71 tff(18344,plain,
% 2.53/2.71 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18343, 18341])).
% 2.53/2.71 tff(18345,plain,
% 2.53/2.71 (b(z, s(s(s(z))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[17944, 18344])).
% 2.53/2.71 tff(18346,plain,
% 2.53/2.71 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18246])).
% 2.53/2.71 tff(18347,plain,
% 2.53/2.71 (b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(symmetry,[status(thm)],[18346])).
% 2.53/2.71 tff(18348,plain,
% 2.53/2.71 ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18347])).
% 2.53/2.71 tff(18349,plain,
% 2.53/2.71 (~r(s(s(elem!1)), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[14657, 18255, 3501, 1441])).
% 2.53/2.71 tff(18350,plain,
% 2.53/2.71 (b(s(s(elem!1)), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[701, 18349, 3313])).
% 2.53/2.71 tff(18351,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18352,plain,
% 2.53/2.71 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18353,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18352])).
% 2.53/2.71 tff(18354,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18353, 18351])).
% 2.53/2.71 tff(18355,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(18356,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18355, 18354])).
% 2.53/2.71 tff(18357,plain,
% 2.53/2.71 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18356, 271, 18275, 18285, 18350])).
% 2.53/2.71 tff(18358,plain,
% 2.53/2.71 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18357, 18348])).
% 2.53/2.71 tff(18359,plain,
% 2.53/2.71 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1719, 18358, 17927])).
% 2.53/2.71 tff(18360,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18361,plain,
% 2.53/2.71 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18362,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18361])).
% 2.53/2.71 tff(18363,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18362, 18360])).
% 2.53/2.71 tff(18364,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(18365,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18364, 18363])).
% 2.53/2.71 tff(18366,plain,
% 2.53/2.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18365, 121, 18292, 18359, 18306])).
% 2.53/2.71 tff(18367,plain,
% 2.53/2.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[586, 18366, 563])).
% 2.53/2.71 tff(18368,plain,
% 2.53/2.71 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1459, 18367, 543, 18275])).
% 2.53/2.71 tff(18369,plain,
% 2.53/2.71 (r(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[681, 18368, 17959])).
% 2.53/2.71 tff(18370,plain,
% 2.53/2.71 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[703, 135])).
% 2.53/2.71 tff(18371,plain,
% 2.53/2.71 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.71 inference(symmetry,[status(thm)],[18370])).
% 2.53/2.71 tff(18372,plain,
% 2.53/2.71 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18371])).
% 2.53/2.71 tff(18373,plain,
% 2.53/2.71 (r(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18101, 911, 107])).
% 2.53/2.71 tff(18374,plain,
% 2.53/2.71 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[10182, 18373, 107])).
% 2.53/2.71 tff(18375,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(18376,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(18377,plain,
% 2.53/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18376, 18375])).
% 2.53/2.71 tff(18378,plain,
% 2.53/2.71 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18377, 121, 622, 684, 18374])).
% 2.53/2.71 tff(18379,plain,
% 2.53/2.71 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18378, 18372])).
% 2.53/2.71 tff(18380,plain,
% 2.53/2.71 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[13513, 12196, 1935, 1307])).
% 2.53/2.71 tff(18381,plain,
% 2.53/2.71 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[10426, 18380])).
% 2.53/2.71 tff(18382,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18381, 18379])).
% 2.53/2.71 tff(18383,plain,((~r(s(s(s(s(z)))), s(z))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(18384,plain,
% 2.53/2.71 (~r(s(s(s(s(z)))), s(z))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18383, 18369, 18271, 17927, 1935, 18345, 909, 110])).
% 2.53/2.71 tff(18385,plain,
% 2.53/2.71 (b(s(s(s(s(z)))), s(z))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[932, 18384])).
% 2.53/2.71 tff(18386,plain,
% 2.53/2.71 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1785, 18385, 18339, 18322])).
% 2.53/2.71 tff(18387,plain,
% 2.53/2.71 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1777, 18386])).
% 2.53/2.71 tff(18388,plain,
% 2.53/2.71 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[18387, 18250])).
% 2.53/2.71 tff(18389,plain,
% 2.53/2.71 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[5833, 17959])).
% 2.53/2.71 tff(18390,plain,
% 2.53/2.71 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[18062, 18389])).
% 2.53/2.71 tff(18391,plain,
% 2.53/2.71 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[17930])).
% 2.53/2.71 tff(18392,plain,
% 2.53/2.71 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18391, 1927])).
% 2.53/2.71 tff(18393,plain,
% 2.53/2.71 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.53/2.71 inference(transitivity,[status(thm)],[18392, 10146])).
% 2.53/2.71 tff(18394,plain,
% 2.53/2.71 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[18393])).
% 2.53/2.71 tff(18395,plain,
% 2.53/2.71 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[927, 18394])).
% 2.53/2.71 tff(18396,plain,
% 2.53/2.71 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1554, 18384, 17928])).
% 2.53/2.71 tff(18397,plain,
% 2.53/2.71 (b(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1559, 18396, 18395])).
% 2.53/2.71 tff(18398,plain,
% 2.53/2.71 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1566, 18397, 17927])).
% 2.53/2.71 tff(18399,plain,
% 2.53/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18400,plain,
% 2.53/2.72 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18401,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18400])).
% 2.53/2.72 tff(18402,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18401, 18399])).
% 2.53/2.72 tff(18403,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18404,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18403, 18402])).
% 2.53/2.72 tff(18405,plain,
% 2.53/2.72 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18404, 271, 18275, 18350, 18398])).
% 2.53/2.72 tff(18406,plain,
% 2.53/2.72 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18082, 18405, 18390])).
% 2.53/2.72 tff(18407,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18408,plain,
% 2.53/2.72 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18409,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18408])).
% 2.53/2.72 tff(18410,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18409, 18407])).
% 2.53/2.72 tff(18411,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18412,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18411, 18410])).
% 2.53/2.72 tff(18413,plain,
% 2.53/2.72 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18412, 121, 18292, 18359])).
% 2.53/2.72 tff(18414,plain,
% 2.53/2.72 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18413, 18406])).
% 2.53/2.72 tff(18415,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18414, 18388])).
% 2.53/2.72 tff(18416,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | b(s(elem!1), z) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(18417,plain,
% 2.53/2.72 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18416, 18244, 18242, 110, 17938, 3498, 3407, 1, 18238, 18235])).
% 2.53/2.72 tff(18418,plain,
% 2.53/2.72 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[556, 18417, 1])).
% 2.53/2.72 tff(18419,plain,
% 2.53/2.72 (~b(s(elem!1), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[7069, 3498, 107])).
% 2.53/2.72 tff(18420,plain,
% 2.53/2.72 (r(s(elem!1), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2243, 18419, 8337])).
% 2.53/2.72 tff(18421,plain,
% 2.53/2.72 (b(s(s(s(z))), s(z))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[638, 155])).
% 2.53/2.72 tff(18422,plain,
% 2.53/2.72 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.72 tff(18423,plain,
% 2.53/2.72 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18422, 1561])).
% 2.53/2.72 tff(18424,plain,
% 2.53/2.72 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18423])).
% 2.53/2.72 tff(18425,plain,
% 2.53/2.72 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.72 tff(18426,plain,
% 2.53/2.72 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 2.53/2.72 inference(symmetry,[status(thm)],[18425])).
% 2.53/2.72 tff(18427,plain,
% 2.53/2.72 (r(elem!1, s(z))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[379, 18426])).
% 2.53/2.72 tff(18428,plain,
% 2.53/2.72 (b(elem!1, s(s(s(z))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[738, 6053])).
% 2.53/2.72 tff(18429,plain,
% 2.53/2.72 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.72 tff(18430,plain,
% 2.53/2.72 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.53/2.72 inference(symmetry,[status(thm)],[18429])).
% 2.53/2.72 tff(18431,plain,
% 2.53/2.72 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[135])).
% 2.53/2.72 tff(18432,plain,
% 2.53/2.72 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.53/2.72 inference(symmetry,[status(thm)],[18431])).
% 2.53/2.72 tff(18433,plain,
% 2.53/2.72 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18432, 18430])).
% 2.53/2.72 tff(18434,plain,
% 2.53/2.72 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(z)))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18433])).
% 2.53/2.72 tff(18435,plain,
% 2.53/2.72 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.53/2.72 inference(monotonicity,[status(thm)],[107])).
% 2.53/2.72 tff(18436,plain,
% 2.53/2.72 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18435, 2211])).
% 2.53/2.72 tff(18437,plain,
% 2.53/2.72 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18436])).
% 2.53/2.72 tff(18438,plain,
% 2.53/2.72 (~(elem!1 = s(s(elem!1)))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[59, 18437])).
% 2.53/2.72 tff(18439,plain,
% 2.53/2.72 (~r(elem!1, s(s(elem!1)))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2199, 627, 623, 379])).
% 2.53/2.72 tff(18440,plain,
% 2.53/2.72 (b(elem!1, s(s(elem!1)))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[599, 18439, 18438])).
% 2.53/2.72 tff(18441,plain,
% 2.53/2.72 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.53/2.72 inference(transitivity,[status(thm)],[18436, 2212])).
% 2.53/2.72 tff(18442,plain,
% 2.53/2.72 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18441])).
% 2.53/2.72 tff(18443,plain,
% 2.53/2.72 (~(s(s(elem!1)) = elem!1)),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[59, 18442])).
% 2.53/2.72 tff(18444,plain,
% 2.53/2.72 (~r(s(s(elem!1)), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18273, 627, 18427, 622])).
% 2.53/2.72 tff(18445,plain,
% 2.53/2.72 (b(s(s(elem!1)), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[862, 18444, 18443])).
% 2.53/2.72 tff(18446,plain,
% 2.53/2.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[594, 18445, 504, 18440])).
% 2.53/2.72 tff(18447,plain,
% 2.53/2.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[586, 18446, 6943])).
% 2.53/2.72 tff(18448,plain,
% 2.53/2.72 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[11144, 18447, 627, 623])).
% 2.53/2.72 tff(18449,plain,
% 2.53/2.72 (~r(s(z), s(s(s(z))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18448, 18434])).
% 2.53/2.72 tff(18450,plain,
% 2.53/2.72 (b(s(z), s(s(s(z))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[105, 18449])).
% 2.53/2.72 tff(18451,plain,
% 2.53/2.72 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1857, 1723, 257, 1195])).
% 2.53/2.72 tff(18452,plain,
% 2.53/2.72 (r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1847, 18451, 15994])).
% 2.53/2.72 tff(18453,plain,
% 2.53/2.72 (~r(s(s(s(s(s(z))))), s(z))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[16014, 18452, 357, 3456])).
% 2.53/2.72 tff(18454,plain,
% 2.53/2.72 (b(s(s(s(s(s(z))))), s(z))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1682, 18453])).
% 2.53/2.72 tff(18455,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18456,plain,
% 2.53/2.72 (((~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(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18457,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18456])).
% 2.53/2.72 tff(18458,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18457, 18455])).
% 2.53/2.72 tff(18459,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18460,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18459, 18458])).
% 2.53/2.72 tff(18461,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18460, 271, 3871, 222, 1723, 18454])).
% 2.53/2.72 tff(18462,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(18463,plain,
% 2.53/2.72 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18462, 18450, 257, 357, 18428, 18042, 18427, 222])).
% 2.53/2.72 tff(18464,plain,
% 2.53/2.72 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1733, 18463])).
% 2.53/2.72 tff(18465,plain,
% 2.53/2.72 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[6039, 18464, 107])).
% 2.53/2.72 tff(18466,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18467,plain,
% 2.53/2.72 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18468,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18467])).
% 2.53/2.72 tff(18469,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18468, 18466])).
% 2.53/2.72 tff(18470,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18471,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18470, 18469])).
% 2.53/2.72 tff(18472,plain,
% 2.53/2.72 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18471, 121, 623, 18447, 18465])).
% 2.53/2.72 tff(18473,plain,
% 2.53/2.72 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1716, 21, 18472])).
% 2.53/2.72 tff(18474,plain,
% 2.53/2.72 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18473, 1707])).
% 2.53/2.72 tff(18475,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18476,plain,
% 2.53/2.72 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18477,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18476])).
% 2.53/2.72 tff(18478,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18477, 18475])).
% 2.53/2.72 tff(18479,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18480,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18479, 18478])).
% 2.53/2.72 tff(18481,plain,
% 2.53/2.72 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18480, 121, 623, 18447, 18465])).
% 2.53/2.72 tff(18482,plain,
% 2.53/2.72 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18291, 18481, 878])).
% 2.53/2.72 tff(18483,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18484,plain,
% 2.53/2.72 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18485,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18484])).
% 2.53/2.72 tff(18486,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.72 inference(transitivity,[status(thm)],[18485, 18483])).
% 2.53/2.72 tff(18487,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18488,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18487, 18486])).
% 2.53/2.72 tff(18489,plain,
% 2.53/2.72 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18488, 271, 18440, 18482, 18474])).
% 2.53/2.72 tff(18490,plain,
% 2.53/2.72 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[835, 18489, 107])).
% 2.53/2.72 tff(18491,plain,
% 2.53/2.72 (r(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[840, 18490, 712])).
% 2.53/2.72 tff(18492,plain,
% 2.53/2.72 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[9962, 18491, 1536])).
% 2.53/2.72 tff(18493,plain,
% 2.53/2.72 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[703, 704])).
% 2.53/2.72 tff(18494,plain,
% 2.53/2.72 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[18135])).
% 2.53/2.72 tff(18495,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18496,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(18497,plain,
% 2.53/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[18496, 18495])).
% 2.53/2.72 tff(18498,plain,
% 2.53/2.72 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18497, 271, 504, 5606, 738])).
% 2.53/2.72 tff(18499,plain,
% 2.53/2.72 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[8221, 18498, 1591])).
% 2.53/2.72 tff(18500,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.53/2.72 tff(18501,plain,
% 2.53/2.72 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.53/2.72 inference(symmetry,[status(thm)],[18500])).
% 2.53/2.72 tff(18502,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1591, 18501])).
% 2.53/2.72 tff(18503,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(18504,plain,
% 2.53/2.72 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[18503, 1591])).
% 2.53/2.72 tff(18505,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18506,plain,
% 2.53/2.72 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(18507,plain,
% 2.53/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18506])).
% 2.53/2.73 tff(18508,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18507, 18505])).
% 2.53/2.73 tff(18509,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18510,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18509, 18508])).
% 2.53/2.73 tff(18511,plain,
% 2.53/2.73 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18510, 271, 504, 5606, 738])).
% 2.53/2.73 tff(18512,plain,
% 2.53/2.73 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[1610, 21, 18511, 18504])).
% 2.53/2.73 tff(18513,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18514,plain,
% 2.53/2.73 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18515,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18514])).
% 2.53/2.73 tff(18516,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18515, 18513])).
% 2.53/2.73 tff(18517,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18518,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18517, 18516])).
% 2.53/2.73 tff(18519,plain,
% 2.53/2.73 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18518, 121, 6026, 18512, 18499])).
% 2.53/2.73 tff(18520,plain,
% 2.53/2.73 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18519, 18494])).
% 2.53/2.73 tff(18521,plain,
% 2.53/2.73 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[1777, 18520])).
% 2.53/2.73 tff(18522,plain,
% 2.53/2.73 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18521, 18493])).
% 2.53/2.73 tff(18523,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(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(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(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(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18524,plain,
% 2.53/2.73 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), 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)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18525,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18524])).
% 2.53/2.73 tff(18526,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18525, 18523])).
% 2.53/2.73 tff(18527,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18528,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(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(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18527, 18526])).
% 2.53/2.73 tff(18529,plain,
% 2.53/2.73 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18528, 121, 623, 18512, 18499])).
% 2.53/2.73 tff(18530,plain,
% 2.53/2.73 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[5954, 21, 18058, 18529])).
% 2.53/2.73 tff(18531,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18532,plain,
% 2.53/2.73 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18533,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18532])).
% 2.53/2.73 tff(18534,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18533, 18531])).
% 2.53/2.73 tff(18535,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(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(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18536,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18535, 18534])).
% 2.53/2.73 tff(18537,plain,
% 2.53/2.73 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18536, 121, 623, 18512, 18499])).
% 2.53/2.73 tff(18538,plain,
% 2.53/2.73 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18082, 18537, 18063])).
% 2.53/2.73 tff(18539,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18540,plain,
% 2.53/2.73 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18541,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18540])).
% 2.53/2.73 tff(18542,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18541, 18539])).
% 2.53/2.73 tff(18543,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18544,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18543, 18542])).
% 2.53/2.73 tff(18545,plain,
% 2.53/2.73 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18544, 121, 623, 6026, 18512])).
% 2.53/2.73 tff(18546,plain,
% 2.53/2.73 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18291, 18545, 878])).
% 2.53/2.73 tff(18547,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18548,plain,
% 2.53/2.73 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18549,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18548])).
% 2.53/2.73 tff(18550,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18549, 18547])).
% 2.53/2.73 tff(18551,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18552,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18551, 18550])).
% 2.53/2.73 tff(18553,plain,
% 2.53/2.73 ($false),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18552, 271, 18546, 18538, 18530, 18522])).
% 2.53/2.73 tff(18554,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.73 tff(18555,plain,
% 2.53/2.73 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18554, 18465, 623, 107, 1591, 504, 738])).
% 2.53/2.73 tff(18556,plain,
% 2.53/2.73 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[10196, 18555, 18134])).
% 2.53/2.73 tff(18557,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18558,plain,
% 2.53/2.73 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(18559,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18558])).
% 2.53/2.73 tff(18560,plain,
% 2.53/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18559, 18557])).
% 2.53/2.73 tff(18561,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(18562,plain,
% 2.53/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18561, 18560])).
% 2.53/2.73 tff(18563,plain,
% 2.53/2.73 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18562, 271, 18440, 18482, 18474])).
% 2.53/2.73 tff(18564,plain,
% 2.53/2.73 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[9946, 18563, 1536])).
% 2.53/2.73 tff(18565,plain,
% 2.53/2.73 (r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[1847, 18564, 18042])).
% 2.53/2.73 tff(18566,plain,
% 2.53/2.73 (~b(s(s(s(s(z)))), s(z))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18163, 18565, 107, 622, 18556, 18492])).
% 2.53/2.73 tff(18567,plain,
% 2.53/2.73 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18566, 18424])).
% 2.53/2.73 tff(18568,plain,
% 2.53/2.73 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[1578])).
% 2.53/2.73 tff(18569,plain,
% 2.53/2.73 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18568, 1927])).
% 2.53/2.73 tff(18570,plain,
% 2.53/2.73 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.53/2.73 inference(symmetry,[status(thm)],[18569])).
% 2.53/2.73 tff(18571,plain,
% 2.53/2.73 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18570])).
% 2.53/2.73 tff(18572,plain,
% 2.53/2.73 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.73 tff(18573,plain,
% 2.53/2.73 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18572, 1927])).
% 2.53/2.73 tff(18574,plain,
% 2.53/2.73 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18573])).
% 2.53/2.73 tff(18575,plain,
% 2.53/2.73 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[927, 18574])).
% 2.53/2.73 tff(18576,plain,
% 2.53/2.73 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[18575, 18571])).
% 2.53/2.73 tff(18577,plain,
% 2.53/2.73 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[5887, 18555, 107, 622, 18576, 379])).
% 2.53/2.73 tff(18578,plain,
% 2.53/2.73 ($false),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18577, 18567])).
% 2.53/2.73 tff(18579,plain,((~r(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.73 tff(18580,plain,
% 2.53/2.73 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[18579, 18421, 18420, 623, 379, 1591, 504, 738, 257, 357, 107, 6943])).
% 2.53/2.73 tff(18581,plain,
% 2.53/2.73 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[526, 18580, 216])).
% 2.53/2.73 tff(18582,plain,
% 2.53/2.73 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[9896, 9894, 107])).
% 2.53/2.73 tff(18583,plain,
% 2.53/2.73 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[705])).
% 2.53/2.73 tff(18584,plain,
% 2.53/2.73 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.73 inference(symmetry,[status(thm)],[18583])).
% 2.53/2.73 tff(18585,plain,
% 2.53/2.73 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[135])).
% 2.53/2.73 tff(18586,plain,
% 2.53/2.73 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.73 inference(transitivity,[status(thm)],[18585, 18584])).
% 2.53/2.73 tff(18587,plain,
% 2.53/2.73 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[1578])).
% 2.53/2.73 tff(18588,plain,
% 2.53/2.73 ((~r(s(elem!1), s(s(s(s(elem!1)))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[18587])).
% 2.53/2.73 tff(18589,plain,
% 2.53/2.73 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18554, 6026, 623, 107, 1591, 504, 738])).
% 2.53/2.74 tff(18590,plain,
% 2.53/2.74 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[10196, 18589, 18134])).
% 2.53/2.74 tff(18591,plain,
% 2.53/2.74 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[11410, 121, 379, 622, 18590])).
% 2.53/2.74 tff(18592,plain,
% 2.53/2.74 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18591, 18588])).
% 2.53/2.74 tff(18593,plain,
% 2.53/2.74 (b(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1995, 18592, 18575])).
% 2.53/2.74 tff(18594,plain,
% 2.53/2.74 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[5887, 18589, 107, 622, 18576, 379])).
% 2.53/2.74 tff(18595,plain,
% 2.53/2.74 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1589, 271, 517, 638, 18594])).
% 2.53/2.74 tff(18596,plain,
% 2.53/2.74 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[8221, 18595, 1591])).
% 2.53/2.74 tff(18597,plain,
% 2.53/2.74 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1606, 271, 517, 638, 18594])).
% 2.53/2.74 tff(18598,plain,
% 2.53/2.74 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1610, 21, 18597, 18504])).
% 2.53/2.74 tff(18599,plain,
% 2.53/2.74 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18518, 121, 6026, 18598, 18596])).
% 2.53/2.74 tff(18600,plain,
% 2.53/2.74 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18599, 18494])).
% 2.53/2.74 tff(18601,plain,
% 2.53/2.74 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1777, 18600])).
% 2.53/2.74 tff(18602,plain,
% 2.53/2.74 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[705, 1578])).
% 2.53/2.74 tff(18603,plain,
% 2.53/2.74 ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[18602])).
% 2.53/2.74 tff(18604,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18605,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(18606,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18605, 18604])).
% 2.53/2.74 tff(18607,plain,
% 2.53/2.74 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18606, 121, 6026, 18598, 18596])).
% 2.53/2.74 tff(18608,plain,
% 2.53/2.74 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18607, 18603])).
% 2.53/2.74 tff(18609,plain,
% 2.53/2.74 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[9512, 18608])).
% 2.53/2.74 tff(18610,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[14690, 18609, 18601, 18593, 9894])).
% 2.53/2.74 tff(18611,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(18612,plain,
% 2.53/2.74 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18611, 517, 107, 1591, 9894, 638, 379, 622, 623, 504, 738])).
% 2.53/2.74 tff(18613,plain,
% 2.53/2.74 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[6039, 18612, 107])).
% 2.53/2.74 tff(18614,plain,
% 2.53/2.74 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1733, 18613])).
% 2.53/2.74 tff(18615,plain,
% 2.53/2.74 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18614, 18586])).
% 2.53/2.74 tff(18616,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18617,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(18618,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18617, 18616])).
% 2.53/2.74 tff(18619,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18618, 271, 517, 638, 18615, 18582])).
% 2.53/2.74 tff(18620,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(18621,plain,
% 2.53/2.74 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18620, 18581, 107, 1591, 638, 379, 18420, 623, 504, 738])).
% 2.53/2.74 tff(18622,plain,
% 2.53/2.74 (b(s(z), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[521, 18581, 1536])).
% 2.53/2.74 tff(18623,plain,
% 2.53/2.74 (~b(z, s(z))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[17276, 18622, 1935, 18421])).
% 2.53/2.74 tff(18624,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[8078, 18623, 18621, 8336, 3498])).
% 2.53/2.74 tff(18625,plain,((~b(s(s(s(elem!1))), s(elem!1))) | b(s(elem!1), z) | (~b(s(s(s(z))), z)) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(18626,plain,
% 2.53/2.74 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18625, 18244, 3498, 17927, 1577, 18230, 18418, 17938, 17944, 211, 18018, 18232, 563])).
% 2.53/2.74 tff(18627,plain,
% 2.53/2.74 (r(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[681, 18626, 17959])).
% 2.53/2.74 tff(18628,plain,
% 2.53/2.74 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[4488, 18439, 2467, 2469, 481, 675])).
% 2.53/2.74 tff(18629,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[4506, 121, 623, 684, 627, 18628])).
% 2.53/2.74 tff(18630,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | b(s(elem!1), elem!1) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), s(elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(18631,plain,
% 2.53/2.74 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18630, 18418, 18627, 17929, 18417, 17937, 18626, 18230])).
% 2.53/2.74 tff(18632,plain,
% 2.53/2.74 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[526, 18631, 211])).
% 2.53/2.74 tff(18633,plain,
% 2.53/2.74 (b(s(z), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[521, 18632, 17928])).
% 2.53/2.74 tff(18634,plain,
% 2.53/2.74 (~r(s(s(s(s(z)))), s(z))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18383, 18627, 18271, 17927, 18244, 18345, 18242, 110])).
% 2.53/2.74 tff(18635,plain,
% 2.53/2.74 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1554, 18634, 17928])).
% 2.53/2.74 tff(18636,plain,
% 2.53/2.74 (b(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1559, 18635, 18395])).
% 2.53/2.74 tff(18637,plain,
% 2.53/2.74 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1566, 18636, 17927])).
% 2.53/2.74 tff(18638,plain,
% 2.53/2.74 (b(s(s(s(s(z)))), s(z))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[932, 18634])).
% 2.53/2.74 tff(18639,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.53/2.74 tff(18640,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18641,plain,
% 2.53/2.74 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18642,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[18641])).
% 2.53/2.74 tff(18643,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(transitivity,[status(thm)],[18642, 18640])).
% 2.53/2.74 tff(18644,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(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)))))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(18645,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(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)))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18644, 18643])).
% 2.53/2.74 tff(18646,plain,
% 2.53/2.74 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18645, 121, 623, 684, 18639])).
% 2.53/2.74 tff(18647,plain,
% 2.53/2.74 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 18646])).
% 2.53/2.74 tff(18648,plain,
% 2.53/2.74 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18062, 5951])).
% 2.53/2.74 tff(18649,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18650,plain,
% 2.53/2.74 (((~r(s(s(s(elem!1))), 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(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18651,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[18650])).
% 2.53/2.74 tff(18652,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.74 inference(transitivity,[status(thm)],[18651, 18649])).
% 2.53/2.74 tff(18653,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(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)))))))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(18654,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18653, 18652])).
% 2.53/2.74 tff(18655,plain,
% 2.53/2.74 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18654, 121, 623, 684, 18639])).
% 2.53/2.74 tff(18656,plain,
% 2.53/2.74 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18082, 18655, 18648])).
% 2.53/2.74 tff(18657,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18658,plain,
% 2.53/2.74 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18659,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[18658])).
% 2.53/2.74 tff(18660,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.74 inference(transitivity,[status(thm)],[18659, 18657])).
% 2.53/2.74 tff(18661,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(18662,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18661, 18660])).
% 2.53/2.74 tff(18663,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18662, 271, 517, 1586, 18656, 18647])).
% 2.53/2.74 tff(18664,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(18665,plain,
% 2.53/2.74 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18664, 517, 1586, 18058, 623, 684])).
% 2.53/2.74 tff(18666,plain,
% 2.53/2.74 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[8221, 18665, 1591])).
% 2.53/2.74 tff(18667,plain,
% 2.53/2.74 (((~b(s(s(s(elem!1))), 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18668,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[18667])).
% 2.53/2.74 tff(18669,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(transitivity,[status(thm)],[18668, 18495])).
% 2.53/2.74 tff(18670,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(18671,plain,
% 2.53/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[18670, 18669])).
% 2.53/2.74 tff(18672,plain,
% 2.53/2.74 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18671, 271, 504, 738, 18666])).
% 2.53/2.74 tff(18673,plain,
% 2.53/2.74 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[10196, 18672, 18134])).
% 2.53/2.74 tff(18674,plain,
% 2.53/2.74 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1857, 1723, 18428, 257])).
% 2.53/2.74 tff(18675,plain,
% 2.53/2.74 (r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1847, 18674, 18042])).
% 2.53/2.74 tff(18676,plain,
% 2.53/2.74 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[18163, 18675, 107, 622, 937, 10184])).
% 2.53/2.74 tff(18677,plain,
% 2.53/2.74 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[9962, 18676, 1536])).
% 2.53/2.74 tff(18678,plain,
% 2.53/2.74 (b(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[840, 18677, 712])).
% 2.53/2.74 tff(18679,plain,
% 2.53/2.74 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[835, 18678, 107])).
% 2.53/2.74 tff(18680,plain,
% 2.53/2.74 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[1723, 18586])).
% 2.53/2.74 tff(18681,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18682,plain,
% 2.53/2.74 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(18683,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[18682])).
% 2.53/2.74 tff(18684,plain,
% 2.53/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18683, 18681])).
% 2.53/2.75 tff(18685,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(18686,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18685, 18684])).
% 2.53/2.75 tff(18687,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18686, 271, 504, 18680, 18679, 738])).
% 2.53/2.75 tff(18688,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18689,plain,
% 2.53/2.75 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18688, 18673, 738, 107, 622, 937, 504, 257])).
% 2.53/2.75 tff(18690,plain,
% 2.53/2.75 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1733, 18689])).
% 2.53/2.75 tff(18691,plain,
% 2.53/2.75 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[6039, 18690, 107])).
% 2.53/2.75 tff(18692,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18693,plain,
% 2.53/2.75 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18694,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18693])).
% 2.53/2.75 tff(18695,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18694, 18692])).
% 2.53/2.75 tff(18696,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(18697,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18696, 18695])).
% 2.53/2.75 tff(18698,plain,
% 2.53/2.75 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18697, 121, 623, 684, 18691])).
% 2.53/2.75 tff(18699,plain,
% 2.53/2.75 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1716, 21, 18698])).
% 2.53/2.75 tff(18700,plain,
% 2.53/2.75 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18699, 1707])).
% 2.53/2.75 tff(18701,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18702,plain,
% 2.53/2.75 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18703,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18702])).
% 2.53/2.75 tff(18704,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18703, 18701])).
% 2.53/2.75 tff(18705,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(18706,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18705, 18704])).
% 2.53/2.75 tff(18707,plain,
% 2.53/2.75 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18706, 121, 623, 684, 18691])).
% 2.53/2.75 tff(18708,plain,
% 2.53/2.75 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18291, 18707, 878])).
% 2.53/2.75 tff(18709,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18710,plain,
% 2.53/2.75 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18711,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18710])).
% 2.53/2.75 tff(18712,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18711, 18709])).
% 2.53/2.75 tff(18713,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(18714,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18713, 18712])).
% 2.53/2.75 tff(18715,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18714, 271, 517, 18708, 17081, 18700])).
% 2.53/2.75 tff(18716,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18717,plain,
% 2.53/2.75 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18716, 18632, 18418, 18627, 17927, 17944, 18271, 18638, 17938, 18018, 1577, 18637])).
% 2.53/2.75 tff(18718,plain,
% 2.53/2.75 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[9896, 18717, 17927])).
% 2.53/2.75 tff(18719,plain,
% 2.53/2.75 (b(z, s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[8078, 18718, 219, 3498])).
% 2.53/2.75 tff(18720,plain,
% 2.53/2.75 (b(elem!1, s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[327, 18719, 17927])).
% 2.53/2.75 tff(18721,plain,
% 2.53/2.75 (~b(s(z), s(s(s(z))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[10135, 18719, 17927, 2207, 3501, 17946])).
% 2.53/2.75 tff(18722,plain,
% 2.53/2.75 (r(s(z), s(s(s(z))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[105, 18721])).
% 2.53/2.75 tff(18723,plain,
% 2.53/2.75 (b(z, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18003, 18722, 3501, 18271, 110, 18720, 3407, 17938, 1])).
% 2.53/2.75 tff(18724,plain,
% 2.53/2.75 (~r(elem!1, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[890, 18720, 17927, 18418, 17959, 18271, 17955])).
% 2.53/2.75 tff(18725,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[4488, 18724, 17929, 18417, 17937, 18626])).
% 2.53/2.75 tff(18726,plain,
% 2.53/2.75 (~b(s(z), s(s(s(elem!1))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[15649, 18719, 3407, 17938])).
% 2.53/2.75 tff(18727,plain,
% 2.53/2.75 (r(s(z), s(s(s(elem!1))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[760, 18726])).
% 2.53/2.75 tff(18728,plain,
% 2.53/2.75 (~r(s(s(elem!1)), s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[14540, 18727, 18418, 18725])).
% 2.53/2.75 tff(18729,plain,
% 2.53/2.75 (b(s(s(elem!1)), s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2143, 18728])).
% 2.53/2.75 tff(18730,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[12176, 18729, 18723, 18719, 18633])).
% 2.53/2.75 tff(18731,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18732,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), elem!1)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18731, 13201, 26, 1, 17923])).
% 2.53/2.75 tff(18733,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), z)),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18732, 17926])).
% 2.53/2.75 tff(18734,plain,
% 2.53/2.75 (s(z) = s(elem!1)),
% 2.53/2.75 inference(monotonicity,[status(thm)],[17921])).
% 2.53/2.75 tff(18735,plain,
% 2.53/2.75 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18734])).
% 2.53/2.75 tff(18736,plain,
% 2.53/2.75 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18735, 200])).
% 2.53/2.75 tff(18737,plain,
% 2.53/2.75 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18736])).
% 2.53/2.75 tff(18738,plain,
% 2.53/2.75 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[61, 18737])).
% 2.53/2.75 tff(18739,plain,
% 2.53/2.75 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.53/2.75 inference(monotonicity,[status(thm)],[17921])).
% 2.53/2.75 tff(18740,plain,
% 2.53/2.75 ((~b(s(z), z)) <=> (~b(s(z), elem!1))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18739])).
% 2.53/2.75 tff(18741,plain,
% 2.53/2.75 (~b(s(z), elem!1)),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[2, 18740])).
% 2.53/2.75 tff(18742,plain,
% 2.53/2.75 (~b(s(elem!1), elem!1)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[7069, 17923, 17921])).
% 2.53/2.75 tff(18743,plain,
% 2.53/2.75 (r(s(elem!1), elem!1)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2243, 18742, 2207])).
% 2.53/2.75 tff(18744,plain,
% 2.53/2.75 ((s(z) = z) <=> (s(z) = elem!1)),
% 2.53/2.75 inference(monotonicity,[status(thm)],[107])).
% 2.53/2.75 tff(18745,plain,
% 2.53/2.75 ((s(z) = z) <=> (elem!1 = s(z))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18744, 1218])).
% 2.53/2.75 tff(18746,plain,
% 2.53/2.75 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18745])).
% 2.53/2.75 tff(18747,plain,
% 2.53/2.75 (~(elem!1 = s(z))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[11, 18746])).
% 2.53/2.75 tff(18748,plain,
% 2.53/2.75 (b(s(elem!1), s(z)) <=> b(s(elem!1), s(elem!1))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.75 tff(18749,plain,
% 2.53/2.75 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), s(z))),
% 2.53/2.75 inference(symmetry,[status(thm)],[18748])).
% 2.53/2.75 tff(18750,plain,
% 2.53/2.75 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), s(z)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18749])).
% 2.53/2.75 tff(18751,plain,
% 2.53/2.75 (~b(s(elem!1), s(z))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[5770, 18750])).
% 2.53/2.75 tff(18752,plain,
% 2.53/2.75 (r(s(elem!1), s(z)) <=> r(s(elem!1), s(elem!1))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.75 tff(18753,plain,
% 2.53/2.75 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), s(z))),
% 2.53/2.75 inference(symmetry,[status(thm)],[18752])).
% 2.53/2.75 tff(18754,plain,
% 2.53/2.75 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), s(z)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18753])).
% 2.53/2.75 tff(18755,plain,
% 2.53/2.75 (~r(s(elem!1), s(z))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[10005, 18754])).
% 2.53/2.75 tff(18756,plain,
% 2.53/2.75 (s(elem!1) = s(z)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[429, 18755, 18751])).
% 2.53/2.75 tff(18757,plain,
% 2.53/2.75 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[1578])).
% 2.53/2.75 tff(18758,plain,
% 2.53/2.75 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.75 inference(symmetry,[status(thm)],[18757])).
% 2.53/2.75 tff(18759,plain,
% 2.53/2.75 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[135])).
% 2.53/2.75 tff(18760,plain,
% 2.53/2.75 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18759, 934])).
% 2.53/2.75 tff(18761,plain,
% 2.53/2.75 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18760])).
% 2.53/2.75 tff(18762,plain,
% 2.53/2.75 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[1138, 18761])).
% 2.53/2.75 tff(18763,plain,
% 2.53/2.75 (b(elem!1, s(s(s(elem!1))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3407, 1179])).
% 2.53/2.75 tff(18764,plain,
% 2.53/2.75 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[156])).
% 2.53/2.75 tff(18765,plain,
% 2.53/2.75 (~b(s(s(elem!1)), z)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[5267, 638, 3407, 543])).
% 2.53/2.75 tff(18766,plain,
% 2.53/2.75 (r(s(s(elem!1)), z)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2430, 18765])).
% 2.53/2.75 tff(18767,plain,
% 2.53/2.75 (~b(elem!1, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[6906, 638, 18763, 543])).
% 2.53/2.75 tff(18768,plain,
% 2.53/2.75 (r(elem!1, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[599, 18767, 18438])).
% 2.53/2.75 tff(18769,plain,
% 2.53/2.75 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[14145, 18766, 139, 18768])).
% 2.53/2.75 tff(18770,plain,
% 2.53/2.75 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[586, 18769, 6943])).
% 2.53/2.75 tff(18771,plain,
% 2.53/2.75 (~b(s(elem!1), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1459, 543, 589, 638])).
% 2.53/2.75 tff(18772,plain,
% 2.53/2.75 (r(s(elem!1), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[526, 18771, 216])).
% 2.53/2.75 tff(18773,plain,
% 2.53/2.75 (r(s(z), s(s(elem!1)))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18772, 1547])).
% 2.53/2.75 tff(18774,plain,
% 2.53/2.75 (~b(z, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1921, 543, 110, 572, 589])).
% 2.53/2.75 tff(18775,plain,
% 2.53/2.75 (r(z, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2106, 18774])).
% 2.53/2.75 tff(18776,plain,
% 2.53/2.75 (~r(s(z), s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[11783, 18775, 110, 2417])).
% 2.53/2.75 tff(18777,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18776, 18773])).
% 2.53/2.75 tff(18778,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18779,plain,
% 2.53/2.75 (~r(s(z), s(s(s(elem!1))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18778, 18770, 110, 107, 216, 543, 638, 18766])).
% 2.53/2.75 tff(18780,plain,
% 2.53/2.75 (b(s(z), s(s(s(elem!1))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[760, 18779])).
% 2.53/2.75 tff(18781,plain,
% 2.53/2.75 (~b(s(s(s(elem!1))), s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[17333, 18780, 3407, 220])).
% 2.53/2.75 tff(18782,plain,
% 2.53/2.75 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18781, 18764])).
% 2.53/2.75 tff(18783,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[638, 18782])).
% 2.53/2.75 tff(18784,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18785,plain,
% 2.53/2.75 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18784, 18056, 3407, 107, 110, 216, 543, 6943, 139])).
% 2.53/2.75 tff(18786,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[681, 18785, 3512])).
% 2.53/2.75 tff(18787,plain,
% 2.53/2.75 (~r(elem!1, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[720, 18786, 139, 622])).
% 2.53/2.75 tff(18788,plain,
% 2.53/2.75 (b(elem!1, s(s(elem!1)))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[599, 18787, 18438])).
% 2.53/2.75 tff(18789,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.53/2.75 tff(18790,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18791,plain,
% 2.53/2.75 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18792,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18791])).
% 2.53/2.75 tff(18793,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18792, 18790])).
% 2.53/2.75 tff(18794,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(18795,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18794, 18793])).
% 2.53/2.75 tff(18796,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18795, 271, 543, 588, 738, 18789])).
% 2.53/2.75 tff(18797,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18798,plain,
% 2.53/2.75 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18797, 18788, 18763, 543])).
% 2.53/2.75 tff(18799,plain,
% 2.53/2.75 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[1578])).
% 2.53/2.75 tff(18800,plain,
% 2.53/2.75 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.75 inference(symmetry,[status(thm)],[18799])).
% 2.53/2.75 tff(18801,plain,
% 2.53/2.75 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[1066, 18800])).
% 2.53/2.75 tff(18802,assumption,(~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.53/2.75 tff(18803,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18802, 18801])).
% 2.53/2.75 tff(18804,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18805,plain,
% 2.53/2.75 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18804, 18798, 107])).
% 2.53/2.75 tff(18806,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1014, 18805, 18762])).
% 2.53/2.75 tff(18807,plain,
% 2.53/2.75 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[135])).
% 2.53/2.75 tff(18808,plain,
% 2.53/2.75 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18807])).
% 2.53/2.75 tff(18809,plain,
% 2.53/2.75 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[8810, 18808])).
% 2.53/2.75 tff(18810,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[13550, 18809])).
% 2.53/2.75 tff(18811,plain,(r(s(s(s(z))), s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18812,plain,
% 2.53/2.75 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18811, 18806, 107])).
% 2.53/2.75 tff(18813,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.53/2.75 inference(symmetry,[status(thm)],[18807])).
% 2.53/2.75 tff(18814,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[1578])).
% 2.53/2.75 tff(18815,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18814, 18813])).
% 2.53/2.75 tff(18816,plain,
% 2.53/2.75 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18815])).
% 2.53/2.75 tff(18817,plain,
% 2.53/2.75 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[6894, 18816])).
% 2.53/2.75 tff(18818,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.53/2.75 tff(18819,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18818, 18817])).
% 2.53/2.75 tff(18820,plain,(r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18821,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18820, 18812, 107])).
% 2.53/2.75 tff(18822,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[6914, 121, 622, 684, 6898, 15572])).
% 2.53/2.75 tff(18823,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(18824,plain,
% 2.53/2.75 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18823, 18786, 622, 18821])).
% 2.53/2.75 tff(18825,plain,
% 2.53/2.75 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[10182, 18824, 107])).
% 2.53/2.75 tff(18826,plain,
% 2.53/2.75 (~r(s(s(s(s(z)))), s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18101, 18825, 107])).
% 2.53/2.75 tff(18827,plain,
% 2.53/2.75 (b(s(s(s(s(z)))), s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[932, 18826])).
% 2.53/2.75 tff(18828,plain,
% 2.53/2.75 (r(s(s(s(z))), z)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[143, 139, 107])).
% 2.53/2.75 tff(18829,plain,
% 2.53/2.75 (r(s(s(s(z))), elem!1)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[475, 18828, 107])).
% 2.53/2.75 tff(18830,plain,
% 2.53/2.75 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = s(elem!1))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.75 tff(18831,plain,
% 2.53/2.75 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18830])).
% 2.53/2.75 tff(18832,plain,
% 2.53/2.75 (~(s(s(s(z))) = s(elem!1))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[97, 18831])).
% 2.53/2.75 tff(18833,plain,
% 2.53/2.75 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[154])).
% 2.53/2.75 tff(18834,plain,
% 2.53/2.75 (~b(s(s(s(z))), s(elem!1))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18785, 18833])).
% 2.53/2.75 tff(18835,plain,
% 2.53/2.75 (r(s(s(s(z))), s(elem!1))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1816, 18834, 18832])).
% 2.53/2.75 tff(18836,plain,
% 2.53/2.75 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[15194, 18835, 622, 18829])).
% 2.53/2.75 tff(18837,plain,
% 2.53/2.75 (b(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1847, 18836, 18042])).
% 2.53/2.75 tff(18838,plain,
% 2.53/2.75 (b(elem!1, s(s(s(z))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18763, 6053])).
% 2.53/2.75 tff(18839,plain,
% 2.53/2.75 (elem!1 = z),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[364, 107])).
% 2.53/2.75 tff(18840,plain,
% 2.53/2.75 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[134])).
% 2.53/2.75 tff(18841,plain,
% 2.53/2.75 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.75 tff(18842,plain,
% 2.53/2.75 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18841, 18840])).
% 2.53/2.75 tff(18843,plain,
% 2.53/2.75 ((~r(s(s(z)), s(z))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18842])).
% 2.53/2.75 tff(18844,plain,
% 2.53/2.75 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.53/2.75 inference(symmetry,[status(thm)],[156])).
% 2.53/2.75 tff(18845,plain,
% 2.53/2.75 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18844])).
% 2.53/2.75 tff(18846,plain,
% 2.53/2.75 (~b(s(s(s(elem!1))), s(z))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18785, 18845])).
% 2.53/2.75 tff(18847,plain,
% 2.53/2.75 (r(s(s(s(elem!1))), s(z))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[16580, 18846])).
% 2.53/2.75 tff(18848,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18849,plain,
% 2.53/2.75 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(18850,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[18849])).
% 2.53/2.75 tff(18851,plain,
% 2.53/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.53/2.75 inference(transitivity,[status(thm)],[18850, 18848])).
% 2.53/2.75 tff(18852,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(18853,plain,
% 2.53/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[18852, 18851])).
% 2.53/2.75 tff(18854,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[18853, 271, 543, 589, 588, 738])).
% 2.53/2.75 tff(18855,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18856,plain,
% 2.53/2.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18855, 18788, 543, 18763])).
% 2.53/2.76 tff(18857,plain,
% 2.53/2.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[586, 18856, 6943])).
% 2.53/2.76 tff(18858,plain,
% 2.53/2.76 (r(s(s(s(elem!1))), s(s(z)))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[573, 10056])).
% 2.53/2.76 tff(18859,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 2.53/2.76 tff(18860,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18859, 18858])).
% 2.53/2.76 tff(18861,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18862,plain,
% 2.53/2.76 (r(s(s(s(elem!1))), s(s(z)))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18861, 18857, 107])).
% 2.53/2.76 tff(18863,plain,
% 2.53/2.76 (~r(s(s(z)), s(z))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[4675, 18862, 110, 18847])).
% 2.53/2.76 tff(18864,plain,
% 2.53/2.76 (~r(s(s(elem!1)), s(elem!1))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18863, 18843])).
% 2.53/2.76 tff(18865,plain,
% 2.53/2.76 (b(s(s(elem!1)), s(elem!1))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[699, 21, 18864, 8423])).
% 2.53/2.76 tff(18866,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18867,plain,
% 2.53/2.76 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18868,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18867])).
% 2.53/2.76 tff(18869,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.76 inference(transitivity,[status(thm)],[18868, 18866])).
% 2.53/2.76 tff(18870,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(18871,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18870, 18869])).
% 2.53/2.76 tff(18872,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18871, 271, 307, 588, 739, 2494])).
% 2.53/2.76 tff(18873,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18874,plain,
% 2.53/2.76 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18873, 307, 18788, 18865])).
% 2.53/2.76 tff(18875,plain,
% 2.53/2.76 (~b(s(z), s(s(s(elem!1))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[754, 18874, 107])).
% 2.53/2.76 tff(18876,plain,
% 2.53/2.76 (~b(s(z), s(s(s(z))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[9876, 18875, 18839])).
% 2.53/2.76 tff(18877,plain,
% 2.53/2.76 (r(s(z), s(s(s(z))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[105, 18876])).
% 2.53/2.76 tff(18878,plain,
% 2.53/2.76 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[15217, 18877, 18835, 18057, 18837])).
% 2.53/2.76 tff(18879,plain,
% 2.53/2.76 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1733, 18878])).
% 2.53/2.76 tff(18880,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18881,plain,
% 2.53/2.76 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18882,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18881])).
% 2.53/2.76 tff(18883,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.53/2.76 inference(transitivity,[status(thm)],[18882, 18880])).
% 2.53/2.76 tff(18884,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(18885,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18884, 18883])).
% 2.53/2.76 tff(18886,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18885, 271, 1195, 1849, 1519, 1723])).
% 2.53/2.76 tff(18887,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18888,plain,
% 2.53/2.76 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18887, 18879, 18838, 18837])).
% 2.53/2.76 tff(18889,plain,
% 2.53/2.76 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1494, 18888])).
% 2.53/2.76 tff(18890,plain,
% 2.53/2.76 (r(s(z), s(s(s(elem!1))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[760, 18875])).
% 2.53/2.76 tff(18891,plain,
% 2.53/2.76 (r(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18890, 723])).
% 2.53/2.76 tff(18892,plain,
% 2.53/2.76 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(symmetry,[status(thm)],[18602])).
% 2.53/2.76 tff(18893,plain,
% 2.53/2.76 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[705, 1578])).
% 2.53/2.76 tff(18894,plain,
% 2.53/2.76 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18893])).
% 2.53/2.76 tff(18895,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.53/2.76 tff(18896,plain,
% 2.53/2.76 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18895, 18106])).
% 2.53/2.76 tff(18897,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[5606, 18896])).
% 2.53/2.76 tff(18898,plain,(b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18899,plain,
% 2.53/2.76 (b(s(s(s(s(z)))), elem!1)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18898, 5606, 107])).
% 2.53/2.76 tff(18900,plain,
% 2.53/2.76 (~b(s(z), s(s(s(s(s(z))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18131, 18899, 18057, 937])).
% 2.53/2.76 tff(18901,plain,
% 2.53/2.76 (r(s(z), s(s(s(s(s(z))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1756, 18900])).
% 2.53/2.76 tff(18902,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18903,plain,
% 2.53/2.76 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(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(z)))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18904,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18903])).
% 2.53/2.76 tff(18905,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.53/2.76 inference(transitivity,[status(thm)],[18904, 18902])).
% 2.53/2.76 tff(18906,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(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(z))))))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(18907,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18906, 18905])).
% 2.53/2.76 tff(18908,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18907, 121, 3061, 1477, 108, 1735])).
% 2.53/2.76 tff(18909,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18910,plain,
% 2.53/2.76 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18909, 18901, 108, 1477])).
% 2.53/2.76 tff(18911,plain,
% 2.53/2.76 (b(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[840, 18910, 712])).
% 2.53/2.76 tff(18912,plain,
% 2.53/2.76 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[835, 18911, 107])).
% 2.53/2.76 tff(18913,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18914,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(18915,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18914, 18913])).
% 2.53/2.76 tff(18916,plain,
% 2.53/2.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18915, 271, 307, 18912, 5606])).
% 2.53/2.76 tff(18917,plain,
% 2.53/2.76 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18916, 18894])).
% 2.53/2.76 tff(18918,plain,
% 2.53/2.76 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[9512, 18917])).
% 2.53/2.76 tff(18919,plain,
% 2.53/2.76 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18918, 18892])).
% 2.53/2.76 tff(18920,plain,
% 2.53/2.76 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[17066, 705])).
% 2.53/2.76 tff(18921,plain,
% 2.53/2.76 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(symmetry,[status(thm)],[18920])).
% 2.53/2.76 tff(18922,plain,
% 2.53/2.76 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18921])).
% 2.53/2.76 tff(18923,plain,
% 2.53/2.76 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18900, 18922])).
% 2.53/2.76 tff(18924,plain,
% 2.53/2.76 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[815, 7608])).
% 2.53/2.76 tff(18925,plain,
% 2.53/2.76 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[7634, 21])).
% 2.53/2.76 tff(18926,plain,
% 2.53/2.76 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18925, 18924, 18923])).
% 2.53/2.76 tff(18927,plain,
% 2.53/2.76 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[7296, 1477, 107])).
% 2.53/2.76 tff(18928,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18929,plain,
% 2.53/2.76 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18930,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18929])).
% 2.53/2.76 tff(18931,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(transitivity,[status(thm)],[18930, 18928])).
% 2.53/2.76 tff(18932,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(18933,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18932, 18931])).
% 2.53/2.76 tff(18934,plain,
% 2.53/2.76 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18933, 121, 798, 18927, 18926])).
% 2.53/2.76 tff(18935,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18934, 18919])).
% 2.53/2.76 tff(18936,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18937,plain,
% 2.53/2.76 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18936, 18891, 107, 307, 18877, 18889, 18827])).
% 2.53/2.76 tff(18938,plain,
% 2.53/2.76 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[10196, 18937, 18134])).
% 2.53/2.76 tff(18939,plain,
% 2.53/2.76 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(symmetry,[status(thm)],[18587])).
% 2.53/2.76 tff(18940,plain,
% 2.53/2.76 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[2002, 18939])).
% 2.53/2.76 tff(18941,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18942,plain,
% 2.53/2.76 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(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(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18943,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18942])).
% 2.53/2.76 tff(18944,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(transitivity,[status(thm)],[18943, 18941])).
% 2.53/2.76 tff(18945,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(18946,plain,
% 2.53/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18945, 18944])).
% 2.53/2.76 tff(18947,plain,
% 2.53/2.76 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18946, 121, 798, 10184, 15572])).
% 2.53/2.76 tff(18948,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18947, 18940])).
% 2.53/2.76 tff(18949,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.76 tff(18950,plain,
% 2.53/2.76 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[18949, 18891, 107, 18938, 18821])).
% 2.53/2.76 tff(18951,plain,
% 2.53/2.76 (b(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1995, 18950, 18575])).
% 2.53/2.76 tff(18952,plain,
% 2.53/2.76 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[18951, 18758])).
% 2.53/2.76 tff(18953,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18954,plain,
% 2.53/2.76 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(18955,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[18954])).
% 2.53/2.76 tff(18956,plain,
% 2.53/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(transitivity,[status(thm)],[18955, 18953])).
% 2.53/2.77 tff(18957,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(18958,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[18957, 18956])).
% 2.53/2.77 tff(18959,plain,
% 2.53/2.77 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18958, 271, 307, 18788, 18865])).
% 2.53/2.77 tff(18960,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18959, 18952])).
% 2.53/2.77 tff(18961,plain,((~b(elem!1, s(elem!1))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.77 tff(18962,plain,
% 2.53/2.77 (~b(elem!1, s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18961, 543, 622, 110, 6943, 107, 139, 3407, 216])).
% 2.53/2.77 tff(18963,plain,
% 2.53/2.77 (~b(elem!1, s(z))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[3660, 18962, 18756])).
% 2.53/2.77 tff(18964,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[4626, 121, 1258, 572, 139, 1256])).
% 2.53/2.77 tff(18965,plain,((elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.77 tff(18966,plain,
% 2.53/2.77 (~r(s(z), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18965, 18963, 1242, 18747, 139])).
% 2.53/2.77 tff(18967,plain,
% 2.53/2.77 (b(s(z), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[760, 18966])).
% 2.53/2.77 tff(18968,plain,
% 2.53/2.77 (r(elem!1, s(z))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[299, 18963, 18747])).
% 2.53/2.77 tff(18969,plain,
% 2.53/2.77 (r(s(z), elem!1)),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[110, 10049])).
% 2.53/2.77 tff(18970,plain,
% 2.53/2.77 (r(elem!1, s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[392, 18962, 8336])).
% 2.53/2.77 tff(18971,plain,
% 2.53/2.77 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[3888, 18968, 139, 622])).
% 2.53/2.77 tff(18972,plain,
% 2.53/2.77 (b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[681, 18971, 3512])).
% 2.53/2.77 tff(18973,plain,
% 2.53/2.77 (b(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[754, 18967, 107])).
% 2.53/2.77 tff(18974,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[5987, 18973, 18972, 107, 543, 18970, 622, 139, 18438, 18969, 18968, 18967])).
% 2.53/2.77 tff(18975,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | b(s(z), elem!1) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.77 tff(18976,plain,
% 2.53/2.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18975, 17921, 18743, 18732, 18741, 26, 563, 13201, 211])).
% 2.53/2.77 tff(18977,plain,
% 2.53/2.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[556, 18976, 1])).
% 2.53/2.77 tff(18978,plain,
% 2.53/2.77 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[133])).
% 2.53/2.77 tff(18979,plain,
% 2.53/2.77 (b(s(s(s(elem!1))), s(z))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[638, 18844])).
% 2.53/2.77 tff(18980,plain,
% 2.53/2.77 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.77 inference(symmetry,[status(thm)],[18585])).
% 2.53/2.77 tff(18981,plain,
% 2.53/2.77 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.77 inference(transitivity,[status(thm)],[18583, 18980])).
% 2.53/2.77 tff(18982,plain,
% 2.53/2.77 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[18981])).
% 2.53/2.77 tff(18983,plain,
% 2.53/2.77 (~b(z, s(z))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[327, 317, 107])).
% 2.53/2.77 tff(18984,plain,
% 2.53/2.77 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[8078, 18983, 8336, 3498])).
% 2.53/2.77 tff(18985,plain,
% 2.53/2.77 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[9896, 18984, 107])).
% 2.53/2.77 tff(18986,plain,
% 2.53/2.77 (~b(elem!1, s(z))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[3660, 317, 18756])).
% 2.53/2.77 tff(18987,plain,
% 2.53/2.77 (~r(s(z), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18965, 18986, 1242, 18747, 139])).
% 2.53/2.77 tff(18988,plain,
% 2.53/2.77 (b(s(z), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[760, 18987])).
% 2.53/2.77 tff(18989,plain,
% 2.53/2.77 (b(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[754, 18988, 107])).
% 2.53/2.77 tff(18990,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.53/2.77 tff(18991,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[5931, 271, 739, 638, 18990, 17081])).
% 2.53/2.77 tff(18992,plain,((~b(s(s(s(s(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(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.77 tff(18993,plain,
% 2.53/2.77 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18992, 18989, 638, 18985])).
% 2.53/2.77 tff(18994,plain,
% 2.53/2.77 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[18993, 18982])).
% 2.53/2.77 tff(18995,plain,
% 2.53/2.77 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[1733, 18994])).
% 2.53/2.77 tff(18996,plain,
% 2.53/2.77 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[6039, 18995, 107])).
% 2.53/2.77 tff(18997,plain,
% 2.53/2.77 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[6034, 18996, 139, 623])).
% 2.53/2.77 tff(18998,plain,
% 2.53/2.77 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[1716, 21, 18997])).
% 2.53/2.77 tff(18999,plain,
% 2.53/2.77 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18998, 1707])).
% 2.53/2.77 tff(19000,plain,
% 2.53/2.77 (r(elem!1, s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[392, 317, 8336])).
% 2.53/2.77 tff(19001,plain,
% 2.53/2.77 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[5933, 18989, 107, 18828, 638, 19000, 18420])).
% 2.53/2.77 tff(19002,plain,
% 2.53/2.77 (b(s(s(s(s(s(z))))), elem!1)),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[840, 19001, 712])).
% 2.53/2.77 tff(19003,plain,
% 2.53/2.77 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[835, 19002, 107])).
% 2.53/2.77 tff(19004,plain,
% 2.53/2.77 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[107])).
% 2.53/2.77 tff(19005,plain,
% 2.53/2.77 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(symmetry,[status(thm)],[19004])).
% 2.53/2.77 tff(19006,plain,
% 2.53/2.77 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[6022, 18999, 18438, 139, 19003, 623])).
% 2.53/2.77 tff(19007,plain,
% 2.53/2.77 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[9946, 19006, 1536])).
% 2.53/2.77 tff(19008,plain,
% 2.53/2.77 (r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[1847, 19007, 18042])).
% 2.53/2.77 tff(19009,plain,
% 2.53/2.77 (r(z, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19008, 19005])).
% 2.53/2.77 tff(19010,plain,
% 2.53/2.77 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[5135, 19009, 18828, 18995])).
% 2.53/2.77 tff(19011,plain,
% 2.53/2.77 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[1494, 19010])).
% 2.53/2.77 tff(19012,plain,
% 2.53/2.77 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18038, 19011, 107])).
% 2.53/2.77 tff(19013,plain,
% 2.53/2.77 (r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[1661, 19004])).
% 2.53/2.77 tff(19014,plain,
% 2.53/2.77 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[9940])).
% 2.53/2.77 tff(19015,plain,
% 2.53/2.77 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(symmetry,[status(thm)],[19014])).
% 2.53/2.77 tff(19016,plain,
% 2.53/2.77 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[1826, 19015])).
% 2.53/2.77 tff(19017,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19018,plain,
% 2.53/2.77 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19019,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19018])).
% 2.53/2.77 tff(19020,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.53/2.77 inference(transitivity,[status(thm)],[19019, 19017])).
% 2.53/2.77 tff(19021,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19022,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19021, 19020])).
% 2.53/2.77 tff(19023,plain,
% 2.53/2.77 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19022, 121, 623, 139, 1624])).
% 2.53/2.77 tff(19024,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19023, 19016])).
% 2.53/2.77 tff(19025,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~(s(z) = s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.77 tff(19026,plain,
% 2.53/2.77 (~r(s(s(elem!1)), elem!1)),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19025, 19013, 1536, 139, 623])).
% 2.53/2.77 tff(19027,plain,
% 2.53/2.77 (b(s(s(elem!1)), elem!1)),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[862, 19026, 18443])).
% 2.53/2.77 tff(19028,plain,
% 2.53/2.77 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[17916, 624, 139, 623])).
% 2.53/2.77 tff(19029,plain,
% 2.53/2.77 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[586, 19028, 6943])).
% 2.53/2.77 tff(19030,plain,
% 2.53/2.77 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[921, 18424])).
% 2.53/2.77 tff(19031,plain,
% 2.53/2.77 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[5887, 19030, 107, 622, 18576, 379])).
% 2.53/2.77 tff(19032,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19033,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19034,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19033, 19032])).
% 2.53/2.77 tff(19035,plain,
% 2.53/2.77 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19034, 271, 785, 19031, 738])).
% 2.53/2.77 tff(19036,plain,
% 2.53/2.77 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19035, 18894])).
% 2.53/2.77 tff(19037,plain,
% 2.53/2.77 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[9512, 19036])).
% 2.53/2.77 tff(19038,plain,
% 2.53/2.77 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19037, 18892])).
% 2.53/2.77 tff(19039,plain,
% 2.53/2.77 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.77 inference(symmetry,[status(thm)],[18493])).
% 2.53/2.77 tff(19040,plain,
% 2.53/2.77 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19039])).
% 2.53/2.77 tff(19041,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19042,plain,
% 2.53/2.77 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(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(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19043,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19042])).
% 2.53/2.77 tff(19044,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.53/2.77 inference(transitivity,[status(thm)],[19043, 19041])).
% 2.53/2.77 tff(19045,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19046,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19045, 19044])).
% 2.53/2.77 tff(19047,plain,
% 2.53/2.77 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19046, 271, 785, 19031, 738])).
% 2.53/2.77 tff(19048,plain,
% 2.53/2.77 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19047, 19040])).
% 2.53/2.77 tff(19049,plain,
% 2.53/2.77 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[1777, 19048])).
% 2.53/2.77 tff(19050,plain,
% 2.53/2.77 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19049, 18136])).
% 2.53/2.77 tff(19051,plain,
% 2.53/2.77 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.53/2.77 inference(commutativity,[status(thm)],[])).
% 2.53/2.77 tff(19052,plain,
% 2.53/2.77 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(symmetry,[status(thm)],[19051])).
% 2.53/2.77 tff(19053,plain,
% 2.53/2.77 ((~(s(s(s(s(elem!1)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19052])).
% 2.53/2.77 tff(19054,plain,
% 2.53/2.77 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[18134, 19053])).
% 2.53/2.77 tff(19055,plain,
% 2.53/2.77 (r(s(s(s(s(z)))), s(z))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[932, 921])).
% 2.53/2.77 tff(19056,plain,
% 2.53/2.77 (r(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18101, 19055, 107])).
% 2.53/2.77 tff(19057,plain,
% 2.53/2.77 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[10182, 19056, 107])).
% 2.53/2.77 tff(19058,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19059,plain,
% 2.53/2.77 (((~r(s(elem!1), elem!1)) | (~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(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19060,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19059])).
% 2.53/2.77 tff(19061,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.77 inference(transitivity,[status(thm)],[19060, 19058])).
% 2.53/2.77 tff(19062,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19063,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19062, 19061])).
% 2.53/2.77 tff(19064,plain,
% 2.53/2.77 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19063, 121, 379, 622, 19057])).
% 2.53/2.77 tff(19065,plain,
% 2.53/2.77 (((~![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))))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19066,plain,
% 2.53/2.77 ((~![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))))))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19067,plain,
% 2.53/2.77 ((~![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)))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19066, 19065])).
% 2.53/2.77 tff(19068,plain,
% 2.53/2.77 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19067, 21, 19064])).
% 2.53/2.77 tff(19069,plain,
% 2.53/2.77 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19068, 19054])).
% 2.53/2.77 tff(19070,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.53/2.77 tff(19071,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19072,plain,
% 2.53/2.77 (((~b(s(s(s(s(elem!1)))), 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(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19073,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19072])).
% 2.53/2.77 tff(19074,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.77 inference(transitivity,[status(thm)],[19073, 19071])).
% 2.53/2.77 tff(19075,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19076,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19075, 19074])).
% 2.53/2.77 tff(19077,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19076, 271, 5606, 542, 5021, 19070])).
% 2.53/2.77 tff(19078,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.77 tff(19079,plain,
% 2.53/2.77 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19078, 19069, 542, 19031])).
% 2.53/2.77 tff(19080,plain,
% 2.53/2.77 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[18082, 19079, 18063])).
% 2.53/2.77 tff(19081,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19082,plain,
% 2.53/2.77 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.53/2.77 inference(rewrite,[status(thm)],[])).
% 2.53/2.77 tff(19083,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.53/2.77 inference(monotonicity,[status(thm)],[19082])).
% 2.53/2.77 tff(19084,plain,
% 2.53/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.53/2.77 inference(transitivity,[status(thm)],[19083, 19081])).
% 2.53/2.77 tff(19085,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.53/2.77 inference(quant_inst,[status(thm)],[])).
% 2.53/2.77 tff(19086,plain,
% 2.53/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.53/2.77 inference(modus_ponens,[status(thm)],[19085, 19084])).
% 2.53/2.77 tff(19087,plain,
% 2.53/2.77 ($false),
% 2.53/2.77 inference(unit_resolution,[status(thm)],[19086, 121, 1661, 1477, 9502, 109])).
% 2.53/2.77 tff(19088,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19089,plain,
% 2.53/2.78 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19088, 19037, 109, 1661])).
% 2.53/2.78 tff(19090,plain,
% 2.53/2.78 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1494, 19089])).
% 2.53/2.78 tff(19091,plain,
% 2.53/2.78 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18038, 19090, 107])).
% 2.53/2.78 tff(19092,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19093,plain,
% 2.53/2.78 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19094,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19093])).
% 2.53/2.78 tff(19095,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.53/2.78 inference(transitivity,[status(thm)],[19094, 19092])).
% 2.53/2.78 tff(19096,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.53/2.78 inference(quant_inst,[status(thm)],[])).
% 2.53/2.78 tff(19097,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19096, 19095])).
% 2.53/2.78 tff(19098,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19097, 271, 589, 785, 6003, 18043])).
% 2.53/2.78 tff(19099,plain,((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19100,plain,
% 2.53/2.78 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19099, 19091, 785, 589])).
% 2.53/2.78 tff(19101,plain,
% 2.53/2.78 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19100, 7507])).
% 2.53/2.78 tff(19102,plain,
% 2.53/2.78 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1719, 19101, 107])).
% 2.53/2.78 tff(19103,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19104,plain,
% 2.53/2.78 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19105,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19104])).
% 2.53/2.78 tff(19106,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.53/2.78 inference(transitivity,[status(thm)],[19105, 19103])).
% 2.53/2.78 tff(19107,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.78 inference(quant_inst,[status(thm)],[])).
% 2.53/2.78 tff(19108,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19107, 19106])).
% 2.53/2.78 tff(19109,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19108, 121, 19102, 19080, 19050, 19038])).
% 2.53/2.78 tff(19110,plain,(b(s(s(s(s(z)))), s(z)) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19111,plain,
% 2.53/2.78 (b(s(s(s(s(z)))), s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19110, 19029, 785, 107, 18828, 1661, 19027, 738, 622, 379])).
% 2.53/2.78 tff(19112,plain,
% 2.53/2.78 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19111, 18423])).
% 2.53/2.78 tff(19113,plain,
% 2.53/2.78 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[2199, 624, 623, 379])).
% 2.53/2.78 tff(19114,plain,
% 2.53/2.78 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[526, 19113, 216])).
% 2.53/2.78 tff(19115,plain,
% 2.53/2.78 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1589, 271, 19114, 638, 19112])).
% 2.53/2.78 tff(19116,plain,
% 2.53/2.78 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[8221, 19115, 1591])).
% 2.53/2.78 tff(19117,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19118,plain,
% 2.53/2.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19119,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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)))))))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19118])).
% 2.53/2.78 tff(19120,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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))))))),
% 2.53/2.78 inference(transitivity,[status(thm)],[19119, 19117])).
% 2.53/2.78 tff(19121,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.53/2.78 inference(quant_inst,[status(thm)],[])).
% 2.53/2.78 tff(19122,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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)))))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19121, 19120])).
% 2.53/2.78 tff(19123,plain,
% 2.53/2.78 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19122, 121, 623, 139, 19116])).
% 2.53/2.78 tff(19124,plain,
% 2.53/2.78 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[5954, 21, 18058, 19123])).
% 2.53/2.78 tff(19125,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19126,plain,
% 2.53/2.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.78 inference(rewrite,[status(thm)],[])).
% 2.53/2.78 tff(19127,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19126])).
% 2.53/2.78 tff(19128,plain,
% 2.53/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.78 inference(transitivity,[status(thm)],[19127, 19125])).
% 2.53/2.78 tff(19129,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.78 inference(quant_inst,[status(thm)],[])).
% 2.53/2.78 tff(19130,plain,
% 2.53/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19129, 19128])).
% 2.53/2.78 tff(19131,plain,
% 2.53/2.78 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19130, 121, 623, 139, 19116])).
% 2.53/2.78 tff(19132,plain,
% 2.53/2.78 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18082, 19131, 18063])).
% 2.53/2.78 tff(19133,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18662, 271, 19114, 19112, 19132, 19124])).
% 2.53/2.78 tff(19134,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19135,plain,
% 2.53/2.78 (~r(elem!1, s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19134, 19009, 139, 1591, 638, 107, 19003, 623, 738, 18420, 19000, 6943, 216])).
% 2.53/2.78 tff(19136,plain,
% 2.53/2.78 (b(elem!1, s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[599, 19135, 18438])).
% 2.53/2.78 tff(19137,plain,
% 2.53/2.78 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[18289, 1706])).
% 2.53/2.78 tff(19138,plain,
% 2.53/2.78 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[6034, 6026, 139, 623])).
% 2.53/2.78 tff(19139,plain,
% 2.53/2.78 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1716, 21, 19138])).
% 2.53/2.78 tff(19140,plain,
% 2.53/2.78 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19139, 19137])).
% 2.53/2.78 tff(19141,plain,
% 2.53/2.78 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18480, 121, 623, 573, 6026])).
% 2.53/2.78 tff(19142,plain,
% 2.53/2.78 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18291, 19141, 18289])).
% 2.53/2.78 tff(19143,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18488, 271, 588, 785, 19142, 19140])).
% 2.53/2.78 tff(19144,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19145,plain,
% 2.53/2.78 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19144, 19136, 19003, 878, 623, 18996, 139])).
% 2.53/2.78 tff(19146,plain,
% 2.53/2.78 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[586, 19145, 6943])).
% 2.53/2.78 tff(19147,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19099, 19146, 19012, 19003, 18999])).
% 2.53/2.78 tff(19148,plain,(b(elem!1, s(elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(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))))) | (s(elem!1) = s(s(elem!1))) | b(s(z), elem!1) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19149,plain,
% 2.53/2.78 (b(elem!1, s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19148, 638, 107, 623, 139, 1591, 6943, 18763, 216, 1242, 3498])).
% 2.53/2.78 tff(19150,plain,
% 2.53/2.78 (b(z, s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1543, 19149, 107])).
% 2.53/2.78 tff(19151,plain,
% 2.53/2.78 (~b(s(z), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[17333, 19150, 3407, 18979])).
% 2.53/2.78 tff(19152,plain,
% 2.53/2.78 (r(s(z), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[760, 19151])).
% 2.53/2.78 tff(19153,plain,
% 2.53/2.78 (~r(s(z), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[16699, 19152, 139, 623])).
% 2.53/2.78 tff(19154,plain,
% 2.53/2.78 (b(s(z), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[2167, 19153])).
% 2.53/2.78 tff(19155,plain,
% 2.53/2.78 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[19154, 18978])).
% 2.53/2.78 tff(19156,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[651, 271, 19149, 19155, 638, 18763])).
% 2.53/2.78 tff(19157,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(elem!1) = s(s(elem!1))) | b(s(z), elem!1) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19158,plain,
% 2.53/2.78 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19157, 17921, 18732, 18977, 13201, 1577, 563, 211, 18741, 17923])).
% 2.53/2.78 tff(19159,plain,
% 2.53/2.78 (r(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[681, 19158, 18738])).
% 2.53/2.78 tff(19160,plain,
% 2.53/2.78 (~r(z, s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[6850, 19159, 18733, 17924])).
% 2.53/2.78 tff(19161,plain,
% 2.53/2.78 (b(z, s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[2106, 19160])).
% 2.53/2.78 tff(19162,plain,
% 2.53/2.78 (b(s(elem!1), s(z)) <=> b(s(elem!1), s(elem!1))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[18734])).
% 2.53/2.78 tff(19163,plain,
% 2.53/2.78 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), s(z))),
% 2.53/2.78 inference(symmetry,[status(thm)],[19162])).
% 2.53/2.78 tff(19164,plain,
% 2.53/2.78 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), s(z)))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19163])).
% 2.53/2.78 tff(19165,plain,
% 2.53/2.78 (~b(s(elem!1), s(z))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[5770, 19164])).
% 2.53/2.78 tff(19166,plain,
% 2.53/2.78 (r(s(elem!1), s(z)) <=> r(s(elem!1), s(elem!1))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[18734])).
% 2.53/2.78 tff(19167,plain,
% 2.53/2.78 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), s(z))),
% 2.53/2.78 inference(symmetry,[status(thm)],[19166])).
% 2.53/2.78 tff(19168,plain,
% 2.53/2.78 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), s(z)))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19167])).
% 2.53/2.78 tff(19169,plain,
% 2.53/2.78 (~r(s(elem!1), s(z))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[10005, 19168])).
% 2.53/2.78 tff(19170,plain,
% 2.53/2.78 (s(elem!1) = s(z)),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[429, 19169, 19165])).
% 2.53/2.78 tff(19171,plain,
% 2.53/2.78 ((s(z) = z) <=> (s(z) = elem!1)),
% 2.53/2.78 inference(monotonicity,[status(thm)],[17921])).
% 2.53/2.78 tff(19172,plain,
% 2.53/2.78 ((s(z) = z) <=> (elem!1 = s(z))),
% 2.53/2.78 inference(transitivity,[status(thm)],[19171, 1218])).
% 2.53/2.78 tff(19173,plain,
% 2.53/2.78 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19172])).
% 2.53/2.78 tff(19174,plain,
% 2.53/2.78 (~(elem!1 = s(z))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[11, 19173])).
% 2.53/2.78 tff(19175,plain,
% 2.53/2.78 (~r(elem!1, s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[3888, 19159, 18732, 18743])).
% 2.53/2.78 tff(19176,plain,
% 2.53/2.78 (b(elem!1, s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[299, 19175, 19174])).
% 2.53/2.78 tff(19177,plain,
% 2.53/2.78 (b(elem!1, s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[3660, 19176, 19170])).
% 2.53/2.78 tff(19178,plain,
% 2.53/2.78 (b(z, s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1543, 19177, 17921])).
% 2.53/2.78 tff(19179,plain,
% 2.53/2.78 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.53/2.78 inference(monotonicity,[status(thm)],[17921])).
% 2.53/2.78 tff(19180,plain,
% 2.53/2.78 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 2.53/2.78 inference(transitivity,[status(thm)],[19179, 2211])).
% 2.53/2.78 tff(19181,plain,
% 2.53/2.78 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19180])).
% 2.53/2.78 tff(19182,plain,
% 2.53/2.78 (~(elem!1 = s(s(elem!1)))),
% 2.53/2.78 inference(modus_ponens,[status(thm)],[59, 19181])).
% 2.53/2.78 tff(19183,plain,
% 2.53/2.78 (~r(elem!1, s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[720, 19159, 18732, 18743])).
% 2.53/2.78 tff(19184,plain,
% 2.53/2.78 (b(elem!1, s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[599, 19183, 19182])).
% 2.53/2.78 tff(19185,plain,
% 2.53/2.78 (~r(s(s(elem!1)), s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[692, 19159, 18743, 18977])).
% 2.53/2.78 tff(19186,plain,
% 2.53/2.78 (b(s(s(elem!1)), s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[701, 19185, 3313])).
% 2.53/2.78 tff(19187,plain,
% 2.53/2.78 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[18873, 19186, 19177, 19184])).
% 2.53/2.78 tff(19188,plain,
% 2.53/2.78 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[3190, 19187, 18738, 18977, 19158])).
% 2.53/2.78 tff(19189,plain,
% 2.53/2.78 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[526, 19188, 211])).
% 2.53/2.78 tff(19190,plain,
% 2.53/2.78 (b(s(z), s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[521, 19189, 17922])).
% 2.53/2.78 tff(19191,plain,
% 2.53/2.78 (~b(s(z), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[754, 19187, 17921])).
% 2.53/2.78 tff(19192,plain,
% 2.53/2.78 (r(s(z), s(s(s(elem!1))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[760, 19191])).
% 2.53/2.78 tff(19193,plain,
% 2.53/2.78 (~r(s(s(elem!1)), s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[2125, 19192, 18977, 19159])).
% 2.53/2.78 tff(19194,plain,
% 2.53/2.78 (b(s(s(elem!1)), s(z))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[2143, 19193])).
% 2.53/2.78 tff(19195,plain,
% 2.53/2.78 ($false),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[12176, 19194, 19190, 19178, 19161])).
% 2.53/2.78 tff(19196,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.78 tff(19197,plain,
% 2.53/2.78 (b(s(z), z)),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[19196, 1])).
% 2.53/2.78 tff(19198,plain,
% 2.53/2.78 (~(s(s(z)) = s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[960, 1257])).
% 2.53/2.78 tff(19199,plain,
% 2.53/2.78 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[953, 19198])).
% 2.53/2.78 tff(19200,plain,
% 2.53/2.78 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[946, 19199])).
% 2.53/2.78 tff(19201,plain,
% 2.53/2.78 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.53/2.78 inference(symmetry,[status(thm)],[9882])).
% 2.53/2.78 tff(19202,plain,
% 2.53/2.78 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.53/2.78 inference(monotonicity,[status(thm)],[19201])).
% 2.53/2.78 tff(19203,plain,
% 2.53/2.78 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.53/2.78 inference(symmetry,[status(thm)],[19202])).
% 2.53/2.78 tff(19204,plain,
% 2.53/2.78 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[1516, 1101])).
% 2.53/2.78 tff(19205,plain,
% 2.53/2.78 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.53/2.78 inference(unit_resolution,[status(thm)],[17419, 19204])).
% 2.53/2.78 tff(19206,plain,
% 2.53/2.78 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9879])).
% 2.53/2.79 tff(19207,plain,
% 2.53/2.79 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.53/2.79 inference(symmetry,[status(thm)],[19206])).
% 2.53/2.79 tff(19208,plain,
% 2.53/2.79 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9884])).
% 2.53/2.79 tff(19209,plain,
% 2.53/2.79 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19208, 19207])).
% 2.53/2.79 tff(19210,plain,
% 2.53/2.79 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19209])).
% 2.53/2.79 tff(19211,plain,
% 2.53/2.79 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9880, 9879])).
% 2.53/2.79 tff(19212,plain,
% 2.53/2.79 ((~b(s(s(z)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19211])).
% 2.53/2.79 tff(19213,plain,
% 2.53/2.79 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = s(elem!1))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9879])).
% 2.53/2.79 tff(19214,plain,
% 2.53/2.79 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19213])).
% 2.53/2.79 tff(19215,plain,
% 2.53/2.79 (~(s(s(s(z))) = s(elem!1))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[97, 19214])).
% 2.53/2.79 tff(19216,plain,
% 2.53/2.79 (elem!1 = z),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[364, 9878])).
% 2.53/2.79 tff(19217,plain,
% 2.53/2.79 (~b(s(z), s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[12838, 71, 9878])).
% 2.53/2.79 tff(19218,plain,
% 2.53/2.79 (r(s(z), s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[760, 19217])).
% 2.53/2.79 tff(19219,plain,
% 2.53/2.79 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9878])).
% 2.53/2.79 tff(19220,plain,
% 2.53/2.79 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 2.53/2.79 inference(symmetry,[status(thm)],[19219])).
% 2.53/2.79 tff(19221,plain,
% 2.53/2.79 (~r(s(s(s(z))), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[149, 9878, 147])).
% 2.53/2.79 tff(19222,plain,
% 2.53/2.79 (~r(s(s(s(z))), z)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[475, 19221, 9878])).
% 2.53/2.79 tff(19223,plain,
% 2.53/2.79 (b(s(s(s(elem!1))), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[490, 19222, 9878])).
% 2.53/2.79 tff(19224,plain,
% 2.53/2.79 (b(s(s(s(elem!1))), z)),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19223, 19220])).
% 2.53/2.79 tff(19225,plain,
% 2.53/2.79 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9879])).
% 2.53/2.79 tff(19226,plain,
% 2.53/2.79 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 2.53/2.79 inference(symmetry,[status(thm)],[19225])).
% 2.53/2.79 tff(19227,plain,
% 2.53/2.79 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19226])).
% 2.53/2.79 tff(19228,plain,
% 2.53/2.79 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9881])).
% 2.53/2.79 tff(19229,plain,
% 2.53/2.79 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19228])).
% 2.53/2.79 tff(19230,plain,
% 2.53/2.79 (b(s(elem!1), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[2488, 9878, 394])).
% 2.53/2.79 tff(19231,plain,
% 2.53/2.79 (~r(elem!1, s(s(s(z))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1187, 1181, 9878])).
% 2.53/2.79 tff(19232,plain,
% 2.53/2.79 (b(elem!1, s(s(s(z))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1192, 1101, 10297])).
% 2.53/2.79 tff(19233,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19234,plain,
% 2.53/2.79 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19235,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19234])).
% 2.53/2.79 tff(19236,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19235, 19233])).
% 2.53/2.79 tff(19237,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19238,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19237, 19236])).
% 2.53/2.79 tff(19239,plain,
% 2.53/2.79 ($false),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19238, 271, 2618, 19232, 3870, 908])).
% 2.53/2.79 tff(19240,plain,((s(s(s(z))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.79 tff(19241,plain,
% 2.53/2.79 (~b(s(elem!1), s(s(s(z))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19240, 19231, 907, 19230, 19221])).
% 2.53/2.79 tff(19242,plain,
% 2.53/2.79 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19241, 19229])).
% 2.53/2.79 tff(19243,plain,
% 2.53/2.79 (b(elem!1, s(s(s(z))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1192, 19231, 1101])).
% 2.53/2.79 tff(19244,plain,
% 2.53/2.79 (b(elem!1, s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1198, 19243, 9878])).
% 2.53/2.79 tff(19245,plain,
% 2.53/2.79 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[14157, 271, 19230, 19223, 19244])).
% 2.53/2.79 tff(19246,plain,
% 2.53/2.79 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9879])).
% 2.53/2.79 tff(19247,plain,
% 2.53/2.79 (r(s(elem!1), s(s(s(elem!1))))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[572, 19246])).
% 2.53/2.79 tff(19248,plain,
% 2.53/2.79 (b(s(s(s(z))), z)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1155, 19222])).
% 2.53/2.79 tff(19249,plain,
% 2.53/2.79 (b(z, s(s(s(z))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1214, 1181])).
% 2.53/2.79 tff(19250,plain,
% 2.53/2.79 (~b(s(s(s(z))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[8279, 19249, 394, 19248])).
% 2.53/2.79 tff(19251,plain,
% 2.53/2.79 (r(s(s(s(z))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1816, 19250, 19215])).
% 2.53/2.79 tff(19252,plain,
% 2.53/2.79 (r(s(s(s(elem!1))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[4527, 19251, 9878])).
% 2.53/2.79 tff(19253,plain,
% 2.53/2.79 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19254,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19253])).
% 2.53/2.79 tff(19255,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19254, 14458])).
% 2.53/2.79 tff(19256,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19257,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19256, 19255])).
% 2.53/2.79 tff(19258,plain,
% 2.53/2.79 (~r(elem!1, s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19257, 121, 379, 19252, 19247])).
% 2.53/2.79 tff(19259,plain,
% 2.53/2.79 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.53/2.79 inference(monotonicity,[status(thm)],[9878])).
% 2.53/2.79 tff(19260,plain,
% 2.53/2.79 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19259])).
% 2.53/2.79 tff(19261,plain,
% 2.53/2.79 (~(s(s(s(elem!1))) = elem!1)),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[30, 19260])).
% 2.53/2.79 tff(19262,plain,
% 2.53/2.79 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[3190, 627, 82, 675, 752])).
% 2.53/2.79 tff(19263,plain,
% 2.53/2.79 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[556, 19262, 1])).
% 2.53/2.79 tff(19264,plain,
% 2.53/2.79 (~b(s(s(elem!1)), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[13398, 271, 19263, 504, 738])).
% 2.53/2.79 tff(19265,plain,
% 2.53/2.79 (r(s(s(elem!1)), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[862, 19264, 10064])).
% 2.53/2.79 tff(19266,plain,
% 2.53/2.79 (~b(elem!1, s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[11908, 19263, 147, 481, 1043])).
% 2.53/2.79 tff(19267,plain,
% 2.53/2.79 (r(elem!1, s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[599, 19266, 10063])).
% 2.53/2.79 tff(19268,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19269,plain,
% 2.53/2.79 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19270,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19269])).
% 2.53/2.79 tff(19271,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19270, 19268])).
% 2.53/2.79 tff(19272,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19273,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19272, 19271])).
% 2.53/2.79 tff(19274,plain,
% 2.53/2.79 ($false),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19273, 121, 379, 627, 19267, 19265])).
% 2.53/2.79 tff(19275,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | r(elem!1, s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (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))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.79 tff(19276,plain,
% 2.53/2.79 (~r(s(elem!1), s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19275, 19244, 19223, 379, 147, 19261, 19258, 1, 82, 19245, 19242])).
% 2.53/2.79 tff(19277,plain,
% 2.53/2.79 (b(s(elem!1), s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[526, 19276, 211])).
% 2.53/2.79 tff(19278,plain,
% 2.53/2.79 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.79 inference(monotonicity,[status(thm)],[703, 107])).
% 2.53/2.79 tff(19279,plain,
% 2.53/2.79 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 2.53/2.79 inference(symmetry,[status(thm)],[19278])).
% 2.53/2.79 tff(19280,plain,
% 2.53/2.79 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(s(s(s(z)))), z))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19279])).
% 2.53/2.79 tff(19281,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19282,plain,
% 2.53/2.79 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19283,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19282])).
% 2.53/2.79 tff(19284,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19283, 19281])).
% 2.53/2.79 tff(19285,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19286,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19285, 19284])).
% 2.53/2.79 tff(19287,plain,
% 2.53/2.79 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19286, 121, 379, 798, 6898])).
% 2.53/2.79 tff(19288,plain,
% 2.53/2.79 (~r(s(s(s(s(z)))), z)),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19287, 19280])).
% 2.53/2.79 tff(19289,plain,
% 2.53/2.79 (b(s(s(s(s(z)))), z)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1095, 19288])).
% 2.53/2.79 tff(19290,plain,
% 2.53/2.79 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[135])).
% 2.53/2.79 tff(19291,plain,
% 2.53/2.79 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.79 inference(symmetry,[status(thm)],[19290])).
% 2.53/2.79 tff(19292,plain,
% 2.53/2.79 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[1578])).
% 2.53/2.79 tff(19293,plain,
% 2.53/2.79 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19292, 19291])).
% 2.53/2.79 tff(19294,plain,
% 2.53/2.79 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19293])).
% 2.53/2.79 tff(19295,plain,
% 2.53/2.79 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[7940, 121, 684, 798, 6898])).
% 2.53/2.79 tff(19296,plain,
% 2.53/2.79 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19295, 19294])).
% 2.53/2.79 tff(19297,plain,
% 2.53/2.79 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[10426, 19296])).
% 2.53/2.79 tff(19298,plain,
% 2.53/2.79 ($false),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[13513, 19297, 19289, 1935, 1307])).
% 2.53/2.79 tff(19299,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.79 tff(19300,plain,
% 2.53/2.79 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19299, 19249, 19248, 9878, 19252, 19247, 379])).
% 2.53/2.79 tff(19301,plain,
% 2.53/2.79 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[10182, 19300, 9878])).
% 2.53/2.79 tff(19302,plain,
% 2.53/2.79 (b(s(s(s(s(z)))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1559, 19301, 19204])).
% 2.53/2.79 tff(19303,plain,
% 2.53/2.79 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[1566, 19302, 9878])).
% 2.53/2.79 tff(19304,plain,
% 2.53/2.79 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[5833, 82])).
% 2.53/2.79 tff(19305,plain,
% 2.53/2.79 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[10142, 9878])).
% 2.53/2.79 tff(19306,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19307,plain,
% 2.53/2.79 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), 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(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19308,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(elem!1)))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19307])).
% 2.53/2.79 tff(19309,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(elem!1))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19308, 19306])).
% 2.53/2.79 tff(19310,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19311,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19310, 19309])).
% 2.53/2.79 tff(19312,plain,
% 2.53/2.79 ($false),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19311, 271, 2618, 5606, 1586, 738])).
% 2.53/2.79 tff(19313,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.79 tff(19314,plain,
% 2.53/2.79 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19313, 19303, 19230, 19244])).
% 2.53/2.79 tff(19315,plain,
% 2.53/2.79 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[10196, 19314, 19305])).
% 2.53/2.79 tff(19316,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19317,plain,
% 2.53/2.79 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19318,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.53/2.79 inference(monotonicity,[status(thm)],[19317])).
% 2.53/2.79 tff(19319,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.53/2.79 inference(transitivity,[status(thm)],[19318, 19316])).
% 2.53/2.79 tff(19320,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19321,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19320, 19319])).
% 2.53/2.79 tff(19322,plain,
% 2.53/2.79 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19321, 271, 2618, 2494, 1586])).
% 2.53/2.79 tff(19323,plain,
% 2.53/2.79 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[18082, 19322, 18648])).
% 2.53/2.79 tff(19324,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19325,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.53/2.79 inference(quant_inst,[status(thm)],[])).
% 2.53/2.79 tff(19326,plain,
% 2.53/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.53/2.79 inference(modus_ponens,[status(thm)],[19325, 19324])).
% 2.53/2.79 tff(19327,plain,
% 2.53/2.79 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[19326, 271, 2618, 2494, 1586])).
% 2.53/2.79 tff(19328,plain,
% 2.53/2.79 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.53/2.79 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 19327])).
% 2.53/2.79 tff(19329,plain,
% 2.53/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.79 inference(rewrite,[status(thm)],[])).
% 2.53/2.79 tff(19330,plain,
% 2.53/2.79 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.53/2.80 inference(rewrite,[status(thm)],[])).
% 2.53/2.80 tff(19331,plain,
% 2.53/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.53/2.80 inference(monotonicity,[status(thm)],[19330])).
% 2.53/2.80 tff(19332,plain,
% 2.53/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19331, 19329])).
% 2.63/2.80 tff(19333,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.63/2.80 inference(quant_inst,[status(thm)],[])).
% 2.63/2.80 tff(19334,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19333, 19332])).
% 2.63/2.80 tff(19335,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19334, 271, 2618, 517, 588, 2494])).
% 2.63/2.80 tff(19336,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19337,plain,
% 2.63/2.80 (~b(elem!1, s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19336, 2494, 517, 2618])).
% 2.63/2.80 tff(19338,plain,
% 2.63/2.80 (r(elem!1, s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[599, 19337, 68])).
% 2.63/2.80 tff(19339,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[8072, 121, 19338, 10184, 19328, 19323])).
% 2.63/2.80 tff(19340,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19341,plain,
% 2.63/2.80 (~b(s(s(elem!1)), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19340, 19315, 19304, 19230, 19303, 10063, 19277])).
% 2.63/2.80 tff(19342,plain,
% 2.63/2.80 (~b(s(s(elem!1)), s(z))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19341, 19227])).
% 2.63/2.80 tff(19343,plain,
% 2.63/2.80 (b(s(z), s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[521, 19277, 338])).
% 2.63/2.80 tff(19344,plain,
% 2.63/2.80 (r(s(s(elem!1)), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[701, 19341, 3313])).
% 2.63/2.80 tff(19345,plain,
% 2.63/2.80 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[3132, 19344, 19247, 19252])).
% 2.63/2.80 tff(19346,plain,
% 2.63/2.80 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[556, 19345, 1])).
% 2.63/2.80 tff(19347,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19348,plain,
% 2.63/2.80 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19349,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[19348])).
% 2.63/2.80 tff(19350,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19349, 19347])).
% 2.63/2.80 tff(19351,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 2.63/2.80 inference(quant_inst,[status(thm)],[])).
% 2.63/2.80 tff(19352,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19351, 19350])).
% 2.63/2.80 tff(19353,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19352, 271, 543, 505, 1894, 1281])).
% 2.63/2.80 tff(19354,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19355,plain,
% 2.63/2.80 (~b(z, s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19354, 19346, 19197, 19343])).
% 2.63/2.80 tff(19356,plain,
% 2.63/2.80 (r(z, s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[2106, 19355])).
% 2.63/2.80 tff(19357,plain,
% 2.63/2.80 (~r(s(s(elem!1)), s(z))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[8581, 19356, 909, 572])).
% 2.63/2.80 tff(19358,plain,
% 2.63/2.80 (b(s(s(elem!1)), s(z))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[2143, 19357])).
% 2.63/2.80 tff(19359,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19358, 19342])).
% 2.63/2.80 tff(19360,plain,(r(z, s(s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~(s(z) = s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19361,plain,
% 2.63/2.80 (r(z, s(s(s(z))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19360, 19218, 909, 1, 379, 338, 147, 82, 907, 394])).
% 2.63/2.80 tff(19362,plain,
% 2.63/2.80 (~r(s(s(s(z))), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1508, 19361, 909, 106])).
% 2.63/2.80 tff(19363,plain,
% 2.63/2.80 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1816, 19362, 19215])).
% 2.63/2.80 tff(19364,plain,
% 2.63/2.80 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[338])).
% 2.63/2.80 tff(19365,plain,
% 2.63/2.80 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.63/2.80 inference(symmetry,[status(thm)],[19364])).
% 2.63/2.80 tff(19366,plain,
% 2.63/2.80 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9937])).
% 2.63/2.80 tff(19367,plain,
% 2.63/2.80 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19366, 19365])).
% 2.63/2.80 tff(19368,plain,
% 2.63/2.80 (b(s(s(s(elem!1))), s(z))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[1422, 19367])).
% 2.63/2.80 tff(19369,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[16578, 19368])).
% 2.63/2.80 tff(19370,plain,((~b(s(s(s(z))), s(elem!1))) | b(s(s(s(elem!1))), s(z)) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19371,plain,
% 2.63/2.80 (b(s(s(s(elem!1))), s(z))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19370, 19363, 338])).
% 2.63/2.80 tff(19372,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19373,plain,
% 2.63/2.80 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19374,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[19373])).
% 2.63/2.80 tff(19375,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19374, 19372])).
% 2.63/2.80 tff(19376,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.63/2.80 inference(quant_inst,[status(thm)],[])).
% 2.63/2.80 tff(19377,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19376, 19375])).
% 2.63/2.80 tff(19378,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19377, 271, 1281, 1638, 503, 1157])).
% 2.63/2.80 tff(19379,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19380,plain,
% 2.63/2.80 (~b(z, s(s(s(s(z)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19379, 19371, 19197, 19224])).
% 2.63/2.80 tff(19381,plain,
% 2.63/2.80 (r(z, s(s(s(s(z)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1121, 19380])).
% 2.63/2.80 tff(19382,plain,
% 2.63/2.80 (~r(s(s(s(s(z)))), s(z))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[9490, 19381, 909, 19218])).
% 2.63/2.80 tff(19383,plain,
% 2.63/2.80 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1554, 19382, 338])).
% 2.63/2.80 tff(19384,plain,
% 2.63/2.80 (b(s(s(s(s(z)))), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1559, 19383, 19204])).
% 2.63/2.80 tff(19385,plain,
% 2.63/2.80 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1566, 19384, 9878])).
% 2.63/2.80 tff(19386,plain,
% 2.63/2.80 (b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19363, 9977])).
% 2.63/2.80 tff(19387,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19388,plain,
% 2.63/2.80 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19389,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[19388])).
% 2.63/2.80 tff(19390,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19389, 19387])).
% 2.63/2.80 tff(19391,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.63/2.80 inference(quant_inst,[status(thm)],[])).
% 2.63/2.80 tff(19392,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19391, 19390])).
% 2.63/2.80 tff(19393,plain,
% 2.63/2.80 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19392, 271, 19230, 19386, 19385])).
% 2.63/2.80 tff(19394,plain,
% 2.63/2.80 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[18804, 19393, 9878])).
% 2.63/2.80 tff(19395,plain,
% 2.63/2.80 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1014, 19394, 1008])).
% 2.63/2.80 tff(19396,plain,
% 2.63/2.80 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[18811, 19395, 9878])).
% 2.63/2.80 tff(19397,plain,
% 2.63/2.80 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[18820, 19396, 9878])).
% 2.63/2.80 tff(19398,plain,
% 2.63/2.80 (r(s(elem!1), s(s(s(elem!1))))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19218, 19246])).
% 2.63/2.80 tff(19399,plain,
% 2.63/2.80 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9881])).
% 2.63/2.80 tff(19400,plain,
% 2.63/2.80 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9878])).
% 2.63/2.80 tff(19401,plain,
% 2.63/2.80 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19400, 19399])).
% 2.63/2.80 tff(19402,plain,
% 2.63/2.80 (r(elem!1, s(s(s(elem!1))))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19361, 19401])).
% 2.63/2.80 tff(19403,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19404,plain,
% 2.63/2.80 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19405,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[19404])).
% 2.63/2.80 tff(19406,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19405, 19403])).
% 2.63/2.80 tff(19407,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 2.63/2.80 inference(quant_inst,[status(thm)],[])).
% 2.63/2.80 tff(19408,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19407, 19406])).
% 2.63/2.80 tff(19409,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19408, 121, 379, 19402, 19398, 19397])).
% 2.63/2.80 tff(19410,plain,(b(s(z), s(s(s(z)))) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(z) = s(elem!1))) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19411,plain,
% 2.63/2.80 (b(s(z), s(s(s(z))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19410, 338, 1008, 379, 909, 1, 147, 82, 907, 394])).
% 2.63/2.80 tff(19412,plain,
% 2.63/2.80 (b(s(z), s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[9876, 19411, 19216])).
% 2.63/2.80 tff(19413,plain,
% 2.63/2.80 (b(s(elem!1), s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[754, 19412, 9878])).
% 2.63/2.80 tff(19414,plain,
% 2.63/2.80 (b(s(s(s(z))), elem!1)),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[255, 19221, 907])).
% 2.63/2.80 tff(19415,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[4218, 271, 1281, 1307, 3871, 257])).
% 2.63/2.80 tff(19416,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19417,plain,
% 2.63/2.80 (~b(z, s(s(s(z))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19416, 19411, 19197, 19414])).
% 2.63/2.80 tff(19418,plain,
% 2.63/2.80 (~b(elem!1, s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[6057, 19417, 9878])).
% 2.63/2.80 tff(19419,plain,
% 2.63/2.80 (~b(elem!1, s(s(s(z))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1198, 19418, 9878])).
% 2.63/2.80 tff(19420,plain,
% 2.63/2.80 (r(elem!1, s(s(s(z))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[1192, 19419, 1101])).
% 2.63/2.80 tff(19421,plain,
% 2.63/2.80 (r(elem!1, s(s(s(elem!1))))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19420, 19399])).
% 2.63/2.80 tff(19422,plain,
% 2.63/2.80 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9879])).
% 2.63/2.80 tff(19423,plain,
% 2.63/2.80 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 2.63/2.80 inference(symmetry,[status(thm)],[19422])).
% 2.63/2.80 tff(19424,plain,
% 2.63/2.80 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9880])).
% 2.63/2.80 tff(19425,plain,
% 2.63/2.80 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 2.63/2.80 inference(symmetry,[status(thm)],[19424])).
% 2.63/2.80 tff(19426,plain,
% 2.63/2.80 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19425, 19423])).
% 2.63/2.80 tff(19427,plain,
% 2.63/2.80 (~r(s(elem!1), s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[14453, 684, 379, 727])).
% 2.63/2.80 tff(19428,plain,
% 2.63/2.80 (b(s(elem!1), s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[526, 19427, 211])).
% 2.63/2.80 tff(19429,plain,
% 2.63/2.80 (b(s(z), s(s(z)))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19428, 19426])).
% 2.63/2.80 tff(19430,plain,
% 2.63/2.80 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[10076, 19428, 504, 739])).
% 2.63/2.80 tff(19431,plain,
% 2.63/2.80 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[556, 19430, 1])).
% 2.63/2.80 tff(19432,plain,
% 2.63/2.80 (~r(elem!1, s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[735, 19431, 684, 727])).
% 2.63/2.80 tff(19433,plain,
% 2.63/2.80 (b(elem!1, s(s(elem!1)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[599, 19432, 68])).
% 2.63/2.80 tff(19434,plain,
% 2.63/2.80 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9878])).
% 2.63/2.80 tff(19435,plain,
% 2.63/2.80 (b(s(z), elem!1)),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19197, 19434])).
% 2.63/2.80 tff(19436,plain,
% 2.63/2.80 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9878])).
% 2.63/2.80 tff(19437,plain,
% 2.63/2.80 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[19436])).
% 2.63/2.80 tff(19438,plain,
% 2.63/2.80 (~(s(s(z)) = elem!1)),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[95, 19437])).
% 2.63/2.80 tff(19439,plain,
% 2.63/2.80 (~r(s(s(elem!1)), elem!1)),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[10103, 19431, 727, 684])).
% 2.63/2.80 tff(19440,plain,
% 2.63/2.80 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.63/2.80 inference(monotonicity,[status(thm)],[9936])).
% 2.63/2.80 tff(19441,plain,
% 2.63/2.80 (r(s(s(elem!1)), elem!1)),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[3600, 19440])).
% 2.63/2.80 tff(19442,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[860, 19441])).
% 2.63/2.80 tff(19443,plain,((~r(s(s(z)), elem!1)) | r(s(s(elem!1)), elem!1) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19444,plain,
% 2.63/2.80 (~r(s(s(z)), elem!1)),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19443, 19439, 338])).
% 2.63/2.80 tff(19445,plain,
% 2.63/2.80 (b(s(s(z)), elem!1)),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[3613, 19444, 19438])).
% 2.63/2.80 tff(19446,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 2.63/2.80 tff(19447,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19448,plain,
% 2.63/2.80 (((~b(elem!1, s(s(elem!1)))) | (~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(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.63/2.80 inference(rewrite,[status(thm)],[])).
% 2.63/2.80 tff(19449,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(z)), elem!1))))),
% 2.63/2.80 inference(monotonicity,[status(thm)],[19448])).
% 2.63/2.80 tff(19450,plain,
% 2.63/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.63/2.80 inference(transitivity,[status(thm)],[19449, 19447])).
% 2.63/2.80 tff(19451,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.63/2.80 inference(quant_inst,[status(thm)],[])).
% 2.63/2.80 tff(19452,plain,
% 2.63/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 2.63/2.80 inference(modus_ponens,[status(thm)],[19451, 19450])).
% 2.63/2.80 tff(19453,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19452, 271, 260, 588, 19446, 6763])).
% 2.63/2.80 tff(19454,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.80 tff(19455,plain,
% 2.63/2.80 (~b(s(z), s(s(z)))),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19454, 19445, 19435, 19433])).
% 2.63/2.80 tff(19456,plain,
% 2.63/2.80 ($false),
% 2.63/2.80 inference(unit_resolution,[status(thm)],[19455, 19429])).
% 2.63/2.80 tff(19457,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19458,plain,
% 2.63/2.81 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19457, 338, 10063, 19421, 1, 19223, 19413, 379])).
% 2.63/2.81 tff(19459,plain,
% 2.63/2.81 (~r(s(s(s(z))), s(elem!1))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[4527, 19458, 9878])).
% 2.63/2.81 tff(19460,plain,
% 2.63/2.81 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1816, 19459, 19215])).
% 2.63/2.81 tff(19461,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(z))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19370, 19460, 338])).
% 2.63/2.81 tff(19462,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.63/2.81 inference(symmetry,[status(thm)],[19366])).
% 2.63/2.81 tff(19463,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[503, 19364])).
% 2.63/2.81 tff(19464,plain,
% 2.63/2.81 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19463, 19462])).
% 2.63/2.81 tff(19465,plain,
% 2.63/2.81 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[338])).
% 2.63/2.81 tff(19466,plain,
% 2.63/2.81 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19465])).
% 2.63/2.81 tff(19467,plain,
% 2.63/2.81 (~b(s(s(s(z))), s(elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[2319, 19466])).
% 2.63/2.81 tff(19468,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19467, 19464])).
% 2.63/2.81 tff(19469,plain,((~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19470,plain,
% 2.63/2.81 (b(s(s(s(z))), s(z))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19469, 19461, 338])).
% 2.63/2.81 tff(19471,plain,
% 2.63/2.81 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9880])).
% 2.63/2.81 tff(19472,plain,
% 2.63/2.81 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.63/2.81 inference(symmetry,[status(thm)],[19471])).
% 2.63/2.81 tff(19473,plain,
% 2.63/2.81 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9881])).
% 2.63/2.81 tff(19474,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.81 inference(symmetry,[status(thm)],[19473])).
% 2.63/2.81 tff(19475,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19474, 19472])).
% 2.63/2.81 tff(19476,plain,
% 2.63/2.81 (r(elem!1, s(s(elem!1)))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[10472, 19458, 82, 19230, 19223])).
% 2.63/2.81 tff(19477,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[681, 19458, 82])).
% 2.63/2.81 tff(19478,plain,
% 2.63/2.81 (r(z, s(z)) <=> r(elem!1, s(z))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9878])).
% 2.63/2.81 tff(19479,plain,
% 2.63/2.81 (r(elem!1, s(z))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[909, 19478])).
% 2.63/2.81 tff(19480,plain,
% 2.63/2.81 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[5852, 19476, 19479, 19412, 19477])).
% 2.63/2.81 tff(19481,plain,
% 2.63/2.81 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[556, 19480, 1])).
% 2.63/2.81 tff(19482,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19483,plain,
% 2.63/2.81 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19484,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19483])).
% 2.63/2.81 tff(19485,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19484, 19482])).
% 2.63/2.81 tff(19486,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.63/2.81 inference(quant_inst,[status(thm)],[])).
% 2.63/2.81 tff(19487,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19486, 19485])).
% 2.63/2.81 tff(19488,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19487, 121, 623, 573, 624, 727])).
% 2.63/2.81 tff(19489,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19490,plain,
% 2.63/2.81 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19489, 19481, 19476, 19421])).
% 2.63/2.81 tff(19491,plain,
% 2.63/2.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[586, 19490, 563])).
% 2.63/2.81 tff(19492,plain,
% 2.63/2.81 (b(s(s(s(z))), s(s(z)))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19491, 19475])).
% 2.63/2.81 tff(19493,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 2.63/2.81 tff(19494,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19495,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))),
% 2.63/2.81 inference(quant_inst,[status(thm)],[])).
% 2.63/2.81 tff(19496,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19495, 19494])).
% 2.63/2.81 tff(19497,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19496, 271, 1281, 222, 1405, 19493])).
% 2.63/2.81 tff(19498,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19499,plain,
% 2.63/2.81 (~b(s(s(z)), s(z))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19498, 19492, 19197, 19470])).
% 2.63/2.81 tff(19500,plain,
% 2.63/2.81 (~b(s(s(elem!1)), s(elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19499, 19212])).
% 2.63/2.81 tff(19501,plain,
% 2.63/2.81 (r(s(s(elem!1)), s(elem!1))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[699, 21, 19500, 3313])).
% 2.63/2.81 tff(19502,plain,
% 2.63/2.81 (~r(s(elem!1), s(s(elem!1)))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[2199, 19481, 379, 19476])).
% 2.63/2.81 tff(19503,plain,
% 2.63/2.81 (b(s(elem!1), s(s(elem!1)))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[526, 19502, 211])).
% 2.63/2.81 tff(19504,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19505,plain,
% 2.63/2.81 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19506,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19505])).
% 2.63/2.81 tff(19507,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19506, 19504])).
% 2.63/2.81 tff(19508,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.63/2.81 inference(quant_inst,[status(thm)],[])).
% 2.63/2.81 tff(19509,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19508, 19507])).
% 2.63/2.81 tff(19510,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19509, 271, 517, 589, 638, 542])).
% 2.63/2.81 tff(19511,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19512,plain,
% 2.63/2.81 (~b(s(s(elem!1)), elem!1)),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19511, 19491, 19477, 19503])).
% 2.63/2.81 tff(19513,plain,
% 2.63/2.81 (r(s(s(elem!1)), elem!1)),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[862, 19512, 10064])).
% 2.63/2.81 tff(19514,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19515,plain,
% 2.63/2.81 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19516,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19515])).
% 2.63/2.81 tff(19517,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19516, 19514])).
% 2.63/2.81 tff(19518,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(quant_inst,[status(thm)],[])).
% 2.63/2.81 tff(19519,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19518, 19517])).
% 2.63/2.81 tff(19520,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19519, 121, 379, 1624, 683, 18328])).
% 2.63/2.81 tff(19521,plain,((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19522,plain,
% 2.63/2.81 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19521, 19513, 379, 19501])).
% 2.63/2.81 tff(19523,plain,
% 2.63/2.81 (~r(s(z), s(s(s(s(s(z))))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19522, 19210])).
% 2.63/2.81 tff(19524,plain,
% 2.63/2.81 (b(s(z), s(s(s(s(s(z))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1756, 19523])).
% 2.63/2.81 tff(19525,plain,
% 2.63/2.81 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[5381, 18921])).
% 2.63/2.81 tff(19526,assumption,(~b(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.63/2.81 tff(19527,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19526, 19525])).
% 2.63/2.81 tff(19528,plain,(b(s(elem!1), s(s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19529,plain,
% 2.63/2.81 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19528, 19524, 9878])).
% 2.63/2.81 tff(19530,plain,
% 2.63/2.81 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9882, 9883])).
% 2.63/2.81 tff(19531,plain,
% 2.63/2.81 (~b(z, s(s(s(s(s(z))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[4302, 19411, 19197, 19248])).
% 2.63/2.81 tff(19532,plain,
% 2.63/2.81 (r(z, s(s(s(s(s(z))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1658, 19531])).
% 2.63/2.81 tff(19533,plain,
% 2.63/2.81 (~b(z, s(s(s(s(z)))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19379, 19461, 19197, 19224])).
% 2.63/2.81 tff(19534,plain,
% 2.63/2.81 (r(z, s(s(s(s(z)))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1121, 19533])).
% 2.63/2.81 tff(19535,assumption,(b(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.63/2.81 tff(19536,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19537,plain,
% 2.63/2.81 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19538,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19537])).
% 2.63/2.81 tff(19539,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19538, 19536])).
% 2.63/2.81 tff(19540,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.63/2.81 inference(quant_inst,[status(thm)],[])).
% 2.63/2.81 tff(19541,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19540, 19539])).
% 2.63/2.81 tff(19542,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19541, 271, 589, 739, 18990, 19535])).
% 2.63/2.81 tff(19543,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19544,plain,
% 2.63/2.81 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19543, 19529, 19413, 19491])).
% 2.63/2.81 tff(19545,plain,
% 2.63/2.81 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9940])).
% 2.63/2.81 tff(19546,plain,
% 2.63/2.81 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.63/2.81 inference(symmetry,[status(thm)],[19545])).
% 2.63/2.81 tff(19547,plain,
% 2.63/2.81 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9937])).
% 2.63/2.81 tff(19548,plain,
% 2.63/2.81 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19547, 19546])).
% 2.63/2.81 tff(19549,plain,
% 2.63/2.81 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[1723, 19548])).
% 2.63/2.81 tff(19550,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.63/2.81 tff(19551,plain,
% 2.63/2.81 ($false),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19550, 19549])).
% 2.63/2.81 tff(19552,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.81 tff(19553,plain,
% 2.63/2.81 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19552, 19544, 338])).
% 2.63/2.81 tff(19554,plain,
% 2.63/2.81 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1733, 19553])).
% 2.63/2.81 tff(19555,plain,
% 2.63/2.81 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1766, 19554, 19534, 19532])).
% 2.63/2.81 tff(19556,plain,
% 2.63/2.81 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1777, 19555])).
% 2.63/2.81 tff(19557,plain,
% 2.63/2.81 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19556, 19530])).
% 2.63/2.81 tff(19558,plain,
% 2.63/2.81 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[9883, 9880])).
% 2.63/2.81 tff(19559,plain,
% 2.63/2.81 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19558])).
% 2.63/2.81 tff(19560,plain,
% 2.63/2.81 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[877, 19559])).
% 2.63/2.81 tff(19561,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19562,plain,
% 2.63/2.81 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(rewrite,[status(thm)],[])).
% 2.63/2.81 tff(19563,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.63/2.81 inference(monotonicity,[status(thm)],[19562])).
% 2.63/2.81 tff(19564,plain,
% 2.63/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.81 inference(transitivity,[status(thm)],[19563, 19561])).
% 2.63/2.81 tff(19565,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.63/2.81 inference(quant_inst,[status(thm)],[])).
% 2.63/2.81 tff(19566,plain,
% 2.63/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.63/2.81 inference(modus_ponens,[status(thm)],[19565, 19564])).
% 2.63/2.81 tff(19567,plain,
% 2.63/2.81 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19566, 121, 379, 1624, 17094])).
% 2.63/2.81 tff(19568,plain,
% 2.63/2.81 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[1716, 21, 19567])).
% 2.63/2.81 tff(19569,plain,
% 2.63/2.81 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.63/2.81 inference(unit_resolution,[status(thm)],[19568, 19137])).
% 2.63/2.81 tff(19570,plain,
% 2.63/2.81 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[17096, 17094, 624, 1624])).
% 2.63/2.82 tff(19571,plain,
% 2.63/2.82 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[18291, 19570, 18289])).
% 2.63/2.82 tff(19572,plain,
% 2.63/2.82 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19573,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19572])).
% 2.63/2.82 tff(19574,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.63/2.82 inference(transitivity,[status(thm)],[19573, 7625])).
% 2.63/2.82 tff(19575,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19576,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19575, 19574])).
% 2.63/2.82 tff(19577,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19576, 271, 517, 19571, 19569, 19535])).
% 2.63/2.82 tff(19578,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19579,plain,
% 2.63/2.82 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19578, 19529, 19503, 19560, 379, 19513, 19476])).
% 2.63/2.82 tff(19580,plain,
% 2.63/2.82 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[9962, 19579, 338])).
% 2.63/2.82 tff(19581,plain,
% 2.63/2.82 (b(s(s(s(s(s(z))))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[840, 19580, 9949])).
% 2.63/2.82 tff(19582,plain,
% 2.63/2.82 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[835, 19581, 9878])).
% 2.63/2.82 tff(19583,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19584,plain,
% 2.63/2.82 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19585,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19584])).
% 2.63/2.82 tff(19586,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(transitivity,[status(thm)],[19585, 19583])).
% 2.63/2.82 tff(19587,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19588,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19587, 19586])).
% 2.63/2.82 tff(19589,plain,
% 2.63/2.82 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19588, 271, 19582, 19557, 19529])).
% 2.63/2.82 tff(19590,plain,
% 2.63/2.82 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[338])).
% 2.63/2.82 tff(19591,plain,
% 2.63/2.82 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.63/2.82 inference(symmetry,[status(thm)],[19590])).
% 2.63/2.82 tff(19592,plain,
% 2.63/2.82 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.63/2.82 inference(symmetry,[status(thm)],[9938])).
% 2.63/2.82 tff(19593,plain,
% 2.63/2.82 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19592])).
% 2.63/2.82 tff(19594,plain,
% 2.63/2.82 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.63/2.82 inference(transitivity,[status(thm)],[19593, 19591])).
% 2.63/2.82 tff(19595,plain,
% 2.63/2.82 ((~b(s(elem!1), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19594])).
% 2.63/2.82 tff(19596,assumption,(~b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.63/2.82 tff(19597,plain,
% 2.63/2.82 (~b(s(z), s(s(s(s(z)))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19596, 19595])).
% 2.63/2.82 tff(19598,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[1067, 19597])).
% 2.63/2.82 tff(19599,plain,(b(s(elem!1), s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19600,plain,
% 2.63/2.82 (~b(s(z), s(s(s(s(z)))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19599, 19589, 338])).
% 2.63/2.82 tff(19601,plain,
% 2.63/2.82 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[133])).
% 2.63/2.82 tff(19602,plain,
% 2.63/2.82 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.63/2.82 inference(symmetry,[status(thm)],[19601])).
% 2.63/2.82 tff(19603,plain,
% 2.63/2.82 (b(s(z), s(s(s(s(z)))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[14671, 19602])).
% 2.63/2.82 tff(19604,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[9594, 19603])).
% 2.63/2.82 tff(19605,plain,((~b(s(elem!1), s(s(s(s(z)))))) | b(s(z), s(s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19606,plain,
% 2.63/2.82 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19605, 19600, 9878])).
% 2.63/2.82 tff(19607,plain,
% 2.63/2.82 (r(s(elem!1), s(s(s(s(z)))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[1995, 19606, 19205])).
% 2.63/2.82 tff(19608,plain,
% 2.63/2.82 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19607, 19203])).
% 2.63/2.82 tff(19609,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19610,plain,
% 2.63/2.82 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19611,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19610])).
% 2.63/2.82 tff(19612,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.63/2.82 inference(transitivity,[status(thm)],[19611, 19609])).
% 2.63/2.82 tff(19613,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19614,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19613, 19612])).
% 2.63/2.82 tff(19615,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19614, 121, 379, 19513, 19501, 19608])).
% 2.63/2.82 tff(19616,plain,((~(s(z) = s(elem!1))) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19617,plain,
% 2.63/2.82 (~(s(z) = s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19616, 19200, 1, 82, 379, 909, 147, 907, 394])).
% 2.63/2.82 tff(19618,plain,
% 2.63/2.82 (~(z = elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[500, 19617])).
% 2.63/2.82 tff(19619,plain,
% 2.63/2.82 (r(z, elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[355, 19618, 199])).
% 2.63/2.82 tff(19620,plain,
% 2.63/2.82 (~r(s(z), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[3673, 378, 909, 379])).
% 2.63/2.82 tff(19621,plain,
% 2.63/2.82 (b(s(z), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[236, 19620, 1257])).
% 2.63/2.82 tff(19622,plain,
% 2.63/2.82 (~r(z, s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[8454, 121, 379, 622, 378])).
% 2.63/2.82 tff(19623,plain,
% 2.63/2.82 (b(z, s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[1439, 19622])).
% 2.63/2.82 tff(19624,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19625,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19626,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19625, 19624])).
% 2.63/2.82 tff(19627,plain,
% 2.63/2.82 (~b(s(z), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19626, 271, 394, 1281, 19623])).
% 2.63/2.82 tff(19628,plain,
% 2.63/2.82 (r(s(z), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[444, 19627, 348])).
% 2.63/2.82 tff(19629,plain,
% 2.63/2.82 (~r(elem!1, s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[9007, 121, 379, 622, 19628])).
% 2.63/2.82 tff(19630,plain,
% 2.63/2.82 (b(elem!1, s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[299, 19629, 258])).
% 2.63/2.82 tff(19631,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19632,plain,
% 2.63/2.82 (((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19633,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(elem!1)))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19632])).
% 2.63/2.82 tff(19634,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 2.63/2.82 inference(transitivity,[status(thm)],[19633, 19631])).
% 2.63/2.82 tff(19635,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19636,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(elem!1)))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19635, 19634])).
% 2.63/2.82 tff(19637,plain,
% 2.63/2.82 (~b(s(elem!1), s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19636, 271, 394, 1281, 19623])).
% 2.63/2.82 tff(19638,plain,
% 2.63/2.82 (r(s(elem!1), s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[429, 19637, 2282])).
% 2.63/2.82 tff(19639,plain,
% 2.63/2.82 (~b(s(s(s(z))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[9017, 1500, 260, 622, 258, 431, 379])).
% 2.63/2.82 tff(19640,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[8987, 121, 379, 145, 1500, 411])).
% 2.63/2.82 tff(19641,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19642,plain,
% 2.63/2.82 (~r(s(s(s(z))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19641, 1500, 379, 411])).
% 2.63/2.82 tff(19643,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[255, 19642, 19639, 907])).
% 2.63/2.82 tff(19644,plain,((~r(s(s(s(z))), s(elem!1))) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19645,plain,
% 2.63/2.82 (~r(s(s(s(z))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19644, 19638, 379, 907, 19621, 622, 258, 19628])).
% 2.63/2.82 tff(19646,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19647,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19648,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19647, 19646])).
% 2.63/2.82 tff(19649,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19648, 271, 2618, 448, 638, 504])).
% 2.63/2.82 tff(19650,plain,((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19651,plain,
% 2.63/2.82 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19650, 504, 448, 2618])).
% 2.63/2.82 tff(19652,plain,
% 2.63/2.82 (r(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[681, 19651, 82])).
% 2.63/2.82 tff(19653,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19654,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19655,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19654, 19653])).
% 2.63/2.82 tff(19656,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19655, 121, 19652, 13786, 431, 411])).
% 2.63/2.82 tff(19657,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19658,plain,
% 2.63/2.82 (~b(s(elem!1), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19657, 504, 448, 431, 411, 82, 260])).
% 2.63/2.82 tff(19659,plain,
% 2.63/2.82 (r(s(elem!1), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[2243, 19658, 2564])).
% 2.63/2.82 tff(19660,plain,
% 2.63/2.82 (~r(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[9617, 19659, 431, 684])).
% 2.63/2.82 tff(19661,plain,
% 2.63/2.82 (b(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[760, 19660])).
% 2.63/2.82 tff(19662,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[12821, 271, 260, 19661, 448, 504])).
% 2.63/2.82 tff(19663,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19664,plain,
% 2.63/2.82 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19663, 504, 260, 431, 411, 2564, 82, 448])).
% 2.63/2.82 tff(19665,plain,
% 2.63/2.82 (b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[681, 19664, 82])).
% 2.63/2.82 tff(19666,plain,
% 2.63/2.82 (~b(s(s(s(elem!1))), z)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[2695, 271, 394, 1421, 19665])).
% 2.63/2.82 tff(19667,plain,
% 2.63/2.82 (r(s(s(s(elem!1))), s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[16580, 13785])).
% 2.63/2.82 tff(19668,plain,
% 2.63/2.82 (~b(s(s(s(z))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[2114, 19665, 394, 2073])).
% 2.63/2.82 tff(19669,plain,
% 2.63/2.82 (s(s(s(z))) = s(elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[1816, 19668, 1510])).
% 2.63/2.82 tff(19670,plain,
% 2.63/2.82 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19669])).
% 2.63/2.82 tff(19671,plain,
% 2.63/2.82 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19670])).
% 2.63/2.82 tff(19672,plain,
% 2.63/2.82 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19671])).
% 2.63/2.82 tff(19673,plain,
% 2.63/2.82 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.63/2.82 inference(symmetry,[status(thm)],[19672])).
% 2.63/2.82 tff(19674,plain,
% 2.63/2.82 (~b(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[12821, 271, 260, 448, 504])).
% 2.63/2.82 tff(19675,plain,
% 2.63/2.82 (r(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[760, 19674])).
% 2.63/2.82 tff(19676,plain,
% 2.63/2.82 (r(s(z), s(s(s(s(s(z))))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19675, 19673])).
% 2.63/2.82 tff(19677,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19678,plain,
% 2.63/2.82 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.63/2.82 inference(rewrite,[status(thm)],[])).
% 2.63/2.82 tff(19679,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.63/2.82 inference(monotonicity,[status(thm)],[19678])).
% 2.63/2.82 tff(19680,plain,
% 2.63/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.63/2.82 inference(transitivity,[status(thm)],[19679, 19677])).
% 2.63/2.82 tff(19681,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.63/2.82 inference(quant_inst,[status(thm)],[])).
% 2.63/2.82 tff(19682,plain,
% 2.63/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[19681, 19680])).
% 2.63/2.82 tff(19683,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19682, 121, 909, 12761, 6842, 1735])).
% 2.63/2.82 tff(19684,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19685,plain,
% 2.63/2.82 (~r(s(s(s(elem!1))), z)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19684, 19676, 909, 19667])).
% 2.63/2.82 tff(19686,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[8229, 19685, 19666])).
% 2.63/2.82 tff(19687,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | r(s(s(s(z))), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19688,plain,
% 2.63/2.82 (~b(s(s(s(elem!1))), elem!1)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19687, 19623, 394, 909, 19621, 19630, 19645, 2073, 82, 19628, 19638, 2564])).
% 2.63/2.82 tff(19689,plain,
% 2.63/2.82 (s(s(s(elem!1))) = elem!1),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[486, 19688, 147])).
% 2.63/2.82 tff(19690,plain,
% 2.63/2.82 (b(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(modus_ponens,[status(thm)],[260, 2558])).
% 2.63/2.82 tff(19691,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[9874, 19690])).
% 2.63/2.82 tff(19692,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(z), s(s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19693,plain,
% 2.63/2.82 (b(s(z), s(s(s(elem!1))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19692, 2505, 260])).
% 2.63/2.82 tff(19694,plain,
% 2.63/2.82 (~r(s(s(s(elem!1))), s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[12809, 2505, 293])).
% 2.63/2.82 tff(19695,plain,
% 2.63/2.82 (b(s(s(s(elem!1))), s(z))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[16580, 19694])).
% 2.63/2.82 tff(19696,plain,
% 2.63/2.82 ($false),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[12484, 19695, 19693, 2073, 3871])).
% 2.63/2.82 tff(19697,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.82 tff(19698,plain,
% 2.63/2.82 (~b(s(z), s(s(s(z))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[19697, 19689, 2073, 19621, 19629])).
% 2.63/2.82 tff(19699,plain,
% 2.63/2.82 (r(s(z), s(s(s(z))))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[105, 19698])).
% 2.63/2.82 tff(19700,plain,
% 2.63/2.82 (~(s(s(s(z))) = s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[2596, 19689])).
% 2.63/2.82 tff(19701,plain,
% 2.63/2.82 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[1816, 19700, 19645])).
% 2.63/2.82 tff(19702,plain,
% 2.63/2.82 (r(s(s(s(z))), z)),
% 2.63/2.82 inference(unit_resolution,[status(thm)],[1427, 19701, 19623, 394])).
% 2.63/2.83 tff(19703,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19704,plain,
% 2.63/2.83 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19705,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19704])).
% 2.63/2.83 tff(19706,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(transitivity,[status(thm)],[19705, 19703])).
% 2.63/2.83 tff(19707,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(quant_inst,[status(thm)],[])).
% 2.63/2.83 tff(19708,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[19707, 19706])).
% 2.63/2.83 tff(19709,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19708, 271, 394, 1422, 1307, 1421])).
% 2.63/2.83 tff(19710,plain,((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19711,plain,
% 2.63/2.83 (~b(z, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19710, 19701, 394, 19623])).
% 2.63/2.83 tff(19712,plain,
% 2.63/2.83 (r(z, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1214, 19711])).
% 2.63/2.83 tff(19713,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1148, 19712, 19702, 909, 19699])).
% 2.63/2.83 tff(19714,plain,((~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (s(s(s(z))) = elem!1) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19715,plain,
% 2.63/2.83 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19714, 622, 394, 909, 147, 82, 2564, 379, 907, 258, 348, 1281, 378])).
% 2.63/2.83 tff(19716,plain,
% 2.63/2.83 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1816, 2597, 1510])).
% 2.63/2.83 tff(19717,plain,
% 2.63/2.83 (r(s(s(s(z))), z)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1427, 19716, 1421, 394])).
% 2.63/2.83 tff(19718,plain,
% 2.63/2.83 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[257, 15417])).
% 2.63/2.83 tff(19719,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2066, 19718])).
% 2.63/2.83 tff(19720,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19721,plain,
% 2.63/2.83 (~b(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19720, 2505, 2066])).
% 2.63/2.83 tff(19722,plain,
% 2.63/2.83 (r(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[255, 19721, 907])).
% 2.63/2.83 tff(19723,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[10254, 121, 379, 378, 19722, 19717])).
% 2.63/2.83 tff(19724,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), s(elem!1)) | b(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19725,plain,
% 2.63/2.83 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19724, 19623, 378, 379, 394, 907, 19645, 19715])).
% 2.63/2.83 tff(19726,plain,
% 2.63/2.83 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[486, 19725, 147])).
% 2.63/2.83 tff(19727,plain,
% 2.63/2.83 (~b(s(s(s(elem!1))), s(z))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[8132, 19726, 19630, 19621])).
% 2.63/2.83 tff(19728,plain,
% 2.63/2.83 (r(s(s(s(elem!1))), s(z))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[16580, 19727])).
% 2.63/2.83 tff(19729,plain,
% 2.63/2.83 (~b(s(z), s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[12821, 271, 19621, 19630, 19726])).
% 2.63/2.83 tff(19730,plain,
% 2.63/2.83 (r(s(z), s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[760, 19729])).
% 2.63/2.83 tff(19731,plain,
% 2.63/2.83 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19663, 19726, 19621, 19628, 19638, 2564, 82, 19630])).
% 2.63/2.83 tff(19732,plain,
% 2.63/2.83 (b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[681, 19731, 82])).
% 2.63/2.83 tff(19733,plain,
% 2.63/2.83 (~b(z, s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[14106, 19732, 394, 19623])).
% 2.63/2.83 tff(19734,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.63/2.83 tff(19735,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[36, 21, 19734, 33, 32])).
% 2.63/2.83 tff(19736,plain,(b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19737,plain,
% 2.63/2.83 (r(z, s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19736, 19733])).
% 2.63/2.83 tff(19738,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19739,plain,
% 2.63/2.83 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19740,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19739])).
% 2.63/2.83 tff(19741,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.63/2.83 inference(transitivity,[status(thm)],[19740, 19738])).
% 2.63/2.83 tff(19742,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 2.63/2.83 inference(quant_inst,[status(thm)],[])).
% 2.63/2.83 tff(19743,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[19742, 19741])).
% 2.63/2.83 tff(19744,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19743, 121, 19737, 19730, 909, 19728])).
% 2.63/2.83 tff(19745,plain,((~r(s(elem!1), elem!1)) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = elem!1) | r(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(z))) = elem!1) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19746,plain,
% 2.63/2.83 (~r(s(elem!1), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19745, 19619, 394, 82, 2207, 147, 909, 379, 907, 258, 19617, 19197])).
% 2.63/2.83 tff(19747,plain,
% 2.63/2.83 (b(s(elem!1), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2243, 19746, 2207])).
% 2.63/2.83 tff(19748,plain,
% 2.63/2.83 (~(elem!1 = z)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[333, 19618])).
% 2.63/2.83 tff(19749,plain,
% 2.63/2.83 (~r(s(z), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[3673, 19619, 909, 379])).
% 2.63/2.83 tff(19750,plain,
% 2.63/2.83 (b(s(z), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[236, 19749, 1257])).
% 2.63/2.83 tff(19751,plain,
% 2.63/2.83 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2063, 19617])).
% 2.63/2.83 tff(19752,plain,
% 2.63/2.83 (~r(z, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[10262, 121, 379, 378, 17770])).
% 2.63/2.83 tff(19753,plain,
% 2.63/2.83 (b(z, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1214, 19752])).
% 2.63/2.83 tff(19754,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19755,plain,
% 2.63/2.83 (((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19756,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(z)))))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19755])).
% 2.63/2.83 tff(19757,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.63/2.83 inference(transitivity,[status(thm)],[19756, 19754])).
% 2.63/2.83 tff(19758,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.83 inference(quant_inst,[status(thm)],[])).
% 2.63/2.83 tff(19759,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(z)))))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[19758, 19757])).
% 2.63/2.83 tff(19760,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19759, 271, 394, 1281, 1307, 446])).
% 2.63/2.83 tff(19761,plain,((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19762,plain,
% 2.63/2.83 (~b(s(z), s(elem!1))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19761, 19753, 1281, 394])).
% 2.63/2.83 tff(19763,plain,
% 2.63/2.83 (r(s(z), s(elem!1))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[444, 19762, 348])).
% 2.63/2.83 tff(19764,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[10254, 121, 379, 378, 145, 109])).
% 2.63/2.83 tff(19765,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19766,plain,
% 2.63/2.83 (~r(s(s(s(z))), z)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19765, 17770, 378, 379])).
% 2.63/2.83 tff(19767,plain,
% 2.63/2.83 (b(s(s(s(z))), z)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1155, 19766])).
% 2.63/2.83 tff(19768,plain,
% 2.63/2.83 (~b(s(elem!1), s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2354, 271, 394, 19753, 19767])).
% 2.63/2.83 tff(19769,plain,
% 2.63/2.83 (r(s(elem!1), s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2044, 19768, 8606])).
% 2.63/2.83 tff(19770,plain,
% 2.63/2.83 (~b(s(z), s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[5539, 271, 1281, 19753, 19767])).
% 2.63/2.83 tff(19771,plain,
% 2.63/2.83 (r(s(z), s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[105, 19770])).
% 2.63/2.83 tff(19772,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[3445, 19771, 19769, 17770, 19763])).
% 2.63/2.83 tff(19773,plain,(b(s(s(s(z))), elem!1) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19774,plain,
% 2.63/2.83 (b(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19773, 19617, 394, 19197, 379, 19619, 19747, 907])).
% 2.63/2.83 tff(19775,plain,
% 2.63/2.83 (r(z, elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[355, 9297, 199])).
% 2.63/2.83 tff(19776,plain,
% 2.63/2.83 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2071, 9149, 906])).
% 2.63/2.83 tff(19777,plain,
% 2.63/2.83 (~r(s(elem!1), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19714, 19776, 394, 909, 147, 82, 2207, 379, 907, 258, 348, 19197, 19775])).
% 2.63/2.83 tff(19778,plain,
% 2.63/2.83 (b(s(elem!1), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2243, 19777, 2207])).
% 2.63/2.83 tff(19779,plain,
% 2.63/2.83 (~r(s(z), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[3673, 19775, 909, 379])).
% 2.63/2.83 tff(19780,plain,
% 2.63/2.83 (b(s(z), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[236, 19779, 1257])).
% 2.63/2.83 tff(19781,plain,
% 2.63/2.83 (~r(s(z), s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[3464, 3456, 909, 378])).
% 2.63/2.83 tff(19782,plain,
% 2.63/2.83 (b(s(z), s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[105, 19781])).
% 2.63/2.83 tff(19783,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19784,plain,
% 2.63/2.83 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19785,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19784])).
% 2.63/2.83 tff(19786,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 2.63/2.83 inference(transitivity,[status(thm)],[19785, 19783])).
% 2.63/2.83 tff(19787,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 2.63/2.83 inference(quant_inst,[status(thm)],[])).
% 2.63/2.83 tff(19788,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[19787, 19786])).
% 2.63/2.83 tff(19789,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19788, 121, 378, 572, 909, 3456])).
% 2.63/2.83 tff(19790,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19791,plain,
% 2.63/2.83 (~r(s(z), s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19790, 3456, 909, 378])).
% 2.63/2.83 tff(19792,plain,
% 2.63/2.83 (b(s(z), s(s(s(elem!1))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[760, 19791])).
% 2.63/2.83 tff(19793,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19794,plain,
% 2.63/2.83 (((~b(s(s(s(elem!1))), elem!1)) | (~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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19795,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19794])).
% 2.63/2.83 tff(19796,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.63/2.83 inference(transitivity,[status(thm)],[19795, 19793])).
% 2.63/2.83 tff(19797,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.63/2.83 inference(quant_inst,[status(thm)],[])).
% 2.63/2.83 tff(19798,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[19797, 19796])).
% 2.63/2.83 tff(19799,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19798, 271, 750, 2073, 3871, 504])).
% 2.63/2.83 tff(19800,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19801,plain,
% 2.63/2.83 (~b(s(s(s(elem!1))), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19800, 19792, 19776, 19782])).
% 2.63/2.83 tff(19802,plain,
% 2.63/2.83 (s(s(s(elem!1))) = elem!1),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[486, 19801, 147])).
% 2.63/2.83 tff(19803,plain,
% 2.63/2.83 (elem!1 = s(s(s(elem!1)))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[13222, 19802])).
% 2.63/2.83 tff(19804,plain,
% 2.63/2.83 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[13202])).
% 2.63/2.83 tff(19805,plain,
% 2.63/2.83 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(symmetry,[status(thm)],[19804])).
% 2.63/2.83 tff(19806,plain,
% 2.63/2.83 (b(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[2073, 19805])).
% 2.63/2.83 tff(19807,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[2346, 19806])).
% 2.63/2.83 tff(19808,plain,((~(elem!1 = s(s(s(elem!1))))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19809,plain,
% 2.63/2.83 (b(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19808, 19803, 19776])).
% 2.63/2.83 tff(19810,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19811,plain,
% 2.63/2.83 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19812,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19811])).
% 2.63/2.83 tff(19813,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.63/2.83 inference(transitivity,[status(thm)],[19812, 19810])).
% 2.63/2.83 tff(19814,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.63/2.83 inference(quant_inst,[status(thm)],[])).
% 2.63/2.83 tff(19815,plain,
% 2.63/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[19814, 19813])).
% 2.63/2.83 tff(19816,plain,
% 2.63/2.83 ($false),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19815, 271, 1281, 1307, 2073, 3871])).
% 2.63/2.83 tff(19817,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.83 tff(19818,plain,
% 2.63/2.83 (~b(z, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[19817, 19782, 19197, 19776])).
% 2.63/2.83 tff(19819,plain,
% 2.63/2.83 (r(z, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[1214, 19818])).
% 2.63/2.83 tff(19820,plain,
% 2.63/2.83 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19802])).
% 2.63/2.83 tff(19821,plain,
% 2.63/2.83 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19820])).
% 2.63/2.83 tff(19822,plain,
% 2.63/2.83 (~r(s(s(s(z))), elem!1)),
% 2.63/2.83 inference(modus_ponens,[status(thm)],[906, 19821])).
% 2.63/2.83 tff(19823,plain,
% 2.63/2.83 (r(elem!1, s(s(s(z))))),
% 2.63/2.83 inference(unit_resolution,[status(thm)],[10306, 19822, 19802, 19782, 9149, 260])).
% 2.63/2.83 tff(19824,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19825,plain,
% 2.63/2.83 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.83 inference(rewrite,[status(thm)],[])).
% 2.63/2.83 tff(19826,plain,
% 2.63/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 2.63/2.83 inference(monotonicity,[status(thm)],[19825])).
% 2.63/2.84 tff(19827,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19826, 19824])).
% 2.63/2.84 tff(19828,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19829,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19828, 19827])).
% 2.63/2.84 tff(19830,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19829, 121, 378, 1184, 2327, 1140])).
% 2.63/2.84 tff(19831,plain,((~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19832,plain,
% 2.63/2.84 (~r(s(s(s(z))), s(z))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19831, 19823, 378, 19819])).
% 2.63/2.84 tff(19833,plain,
% 2.63/2.84 (b(s(s(s(z))), s(z))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2325, 19832])).
% 2.63/2.84 tff(19834,plain,
% 2.63/2.84 (~b(elem!1, z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[276, 19833, 260, 19809])).
% 2.63/2.84 tff(19835,plain,
% 2.63/2.84 (r(elem!1, z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[284, 19834, 9298])).
% 2.63/2.84 tff(19836,plain,
% 2.63/2.84 (~r(s(z), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[12439, 19835, 909, 3456])).
% 2.63/2.84 tff(19837,plain,
% 2.63/2.84 (b(s(z), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2167, 19836])).
% 2.63/2.84 tff(19838,plain,
% 2.63/2.84 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19802])).
% 2.63/2.84 tff(19839,plain,
% 2.63/2.84 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.84 inference(symmetry,[status(thm)],[19838])).
% 2.63/2.84 tff(19840,plain,
% 2.63/2.84 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19823, 19839])).
% 2.63/2.84 tff(19841,plain,
% 2.63/2.84 (~b(s(s(s(elem!1))), z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[14970, 19833, 19776, 19792])).
% 2.63/2.84 tff(19842,plain,
% 2.63/2.84 (r(s(s(s(elem!1))), z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[8229, 19841])).
% 2.63/2.84 tff(19843,plain,
% 2.63/2.84 (~r(s(s(s(z))), z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[11676, 19842, 19840, 19819])).
% 2.63/2.84 tff(19844,plain,
% 2.63/2.84 (~b(elem!1, z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[15307, 446, 260, 2618])).
% 2.63/2.84 tff(19845,plain,
% 2.63/2.84 (r(elem!1, z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[284, 19844, 259])).
% 2.63/2.84 tff(19846,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19847,plain,
% 2.63/2.84 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19848,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19847])).
% 2.63/2.84 tff(19849,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19848, 19846])).
% 2.63/2.84 tff(19850,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19851,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19850, 19849])).
% 2.63/2.84 tff(19852,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19851, 271, 394, 1894, 1281, 446])).
% 2.63/2.84 tff(19853,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19854,plain,
% 2.63/2.84 (~b(z, s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19853, 446, 19197, 394])).
% 2.63/2.84 tff(19855,plain,
% 2.63/2.84 (r(z, s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2106, 19854])).
% 2.63/2.84 tff(19856,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19857,plain,
% 2.63/2.84 (((~b(elem!1, s(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), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19858,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19857])).
% 2.63/2.84 tff(19859,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19858, 19856])).
% 2.63/2.84 tff(19860,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19861,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19860, 19859])).
% 2.63/2.84 tff(19862,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19861, 271, 2618, 260, 588, 446])).
% 2.63/2.84 tff(19863,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19864,plain,
% 2.63/2.84 (~b(elem!1, s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19863, 446, 260, 2618])).
% 2.63/2.84 tff(19865,plain,
% 2.63/2.84 (r(elem!1, s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[599, 19864, 68])).
% 2.63/2.84 tff(19866,plain,
% 2.63/2.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2502, 19865, 378, 19855])).
% 2.63/2.84 tff(19867,plain,
% 2.63/2.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[556, 19866, 1])).
% 2.63/2.84 tff(19868,plain,
% 2.63/2.84 (~r(s(s(elem!1)), s(z))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[5075, 19865, 378, 19855])).
% 2.63/2.84 tff(19869,plain,
% 2.63/2.84 (b(s(s(elem!1)), s(z))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2143, 19868])).
% 2.63/2.84 tff(19870,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[10717, 121, 378, 1409, 145, 1140])).
% 2.63/2.84 tff(19871,plain,((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19872,plain,
% 2.63/2.84 (~r(s(s(s(z))), elem!1)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19871, 19845, 1140, 378])).
% 2.63/2.84 tff(19873,plain,
% 2.63/2.84 (b(s(s(s(z))), elem!1)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[255, 19872, 907])).
% 2.63/2.84 tff(19874,plain,
% 2.63/2.84 (~b(s(elem!1), s(s(s(z))))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[3879, 19873, 19782, 446])).
% 2.63/2.84 tff(19875,plain,
% 2.63/2.84 (~r(s(z), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[12439, 19845, 909, 3456])).
% 2.63/2.84 tff(19876,plain,
% 2.63/2.84 (b(s(z), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2167, 19875])).
% 2.63/2.84 tff(19877,plain,
% 2.63/2.84 (b(s(s(elem!1)), elem!1)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[8592, 2505, 543])).
% 2.63/2.84 tff(19878,plain,
% 2.63/2.84 (r(elem!1, s(s(s(z))))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[10306, 2505, 221, 3871, 2065, 260])).
% 2.63/2.84 tff(19879,plain,
% 2.63/2.84 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[9295, 19878, 379, 2039, 2597])).
% 2.63/2.84 tff(19880,plain,
% 2.63/2.84 (~b(s(s(s(elem!1))), z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[13843, 19693, 505, 543])).
% 2.63/2.84 tff(19881,plain,
% 2.63/2.84 (r(s(s(s(elem!1))), z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[8229, 19880])).
% 2.63/2.84 tff(19882,plain,
% 2.63/2.84 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[2505])).
% 2.63/2.84 tff(19883,plain,
% 2.63/2.84 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.84 inference(symmetry,[status(thm)],[19882])).
% 2.63/2.84 tff(19884,plain,
% 2.63/2.84 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19878, 19883])).
% 2.63/2.84 tff(19885,plain,
% 2.63/2.84 (~r(s(s(s(z))), z)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[11676, 19884, 19881, 1140])).
% 2.63/2.84 tff(19886,plain,
% 2.63/2.84 (~b(z, s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1427, 19885, 19879, 394])).
% 2.63/2.84 tff(19887,plain,
% 2.63/2.84 (r(z, s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1439, 19886])).
% 2.63/2.84 tff(19888,plain,
% 2.63/2.84 (~r(s(elem!1), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1449, 19887, 379, 378])).
% 2.63/2.84 tff(19889,plain,
% 2.63/2.84 (b(s(elem!1), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[526, 19888, 216])).
% 2.63/2.84 tff(19890,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19891,plain,
% 2.63/2.84 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19892,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19891])).
% 2.63/2.84 tff(19893,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19892, 19890])).
% 2.63/2.84 tff(19894,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19895,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19894, 19893])).
% 2.63/2.84 tff(19896,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19895, 271, 505, 19889, 446, 19877])).
% 2.63/2.84 tff(19897,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(z))))) | b(s(elem!1), s(s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19898,plain,
% 2.63/2.84 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19897, 19876, 446, 211, 379, 378, 394, 1140, 19874, 19867, 19872, 19782, 2065, 260])).
% 2.63/2.84 tff(19899,plain,
% 2.63/2.84 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[486, 19898, 147])).
% 2.63/2.84 tff(19900,plain,
% 2.63/2.84 (~b(s(z), s(s(s(elem!1))))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[989, 19899, 19869, 19867])).
% 2.63/2.84 tff(19901,plain,
% 2.63/2.84 (r(s(z), s(s(s(elem!1))))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[760, 19900])).
% 2.63/2.84 tff(19902,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19903,plain,
% 2.63/2.84 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19904,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19903])).
% 2.63/2.84 tff(19905,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19904, 19902])).
% 2.63/2.84 tff(19906,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19907,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19906, 19905])).
% 2.63/2.84 tff(19908,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19907, 121, 19901, 909, 19845, 3456])).
% 2.63/2.84 tff(19909,plain,((~b(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19910,plain,
% 2.63/2.84 (~b(s(z), s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19909, 3456, 909, 147, 379, 378, 394, 19819, 9149, 260, 1, 907, 68, 9298, 2618])).
% 2.63/2.84 tff(19911,plain,
% 2.63/2.84 (~(s(s(s(z))) = s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[4929, 19910, 19782])).
% 2.63/2.84 tff(19912,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19913,plain,
% 2.63/2.84 (((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19914,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19913])).
% 2.63/2.84 tff(19915,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19914, 19912])).
% 2.63/2.84 tff(19916,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19917,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19916, 19915])).
% 2.63/2.84 tff(19918,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19917, 121, 378, 1184, 1500, 1140])).
% 2.63/2.84 tff(19919,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19920,plain,
% 2.63/2.84 (~r(s(s(s(z))), s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19919, 19823, 378, 19819])).
% 2.63/2.84 tff(19921,plain,
% 2.63/2.84 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1816, 19920, 19911])).
% 2.63/2.84 tff(19922,plain,
% 2.63/2.84 (~b(z, s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1427, 19921, 19843, 394])).
% 2.63/2.84 tff(19923,plain,
% 2.63/2.84 (r(z, s(elem!1))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1439, 19922])).
% 2.63/2.84 tff(19924,plain,
% 2.63/2.84 (~r(s(elem!1), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[1449, 19923, 379, 378])).
% 2.63/2.84 tff(19925,plain,
% 2.63/2.84 (b(s(elem!1), s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[526, 19924, 211])).
% 2.63/2.84 tff(19926,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19927,plain,
% 2.63/2.84 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19928,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19927])).
% 2.63/2.84 tff(19929,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)))),
% 2.63/2.84 inference(transitivity,[status(thm)],[19928, 19926])).
% 2.63/2.84 tff(19930,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.63/2.84 inference(quant_inst,[status(thm)],[])).
% 2.63/2.84 tff(19931,plain,
% 2.63/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z))),
% 2.63/2.84 inference(modus_ponens,[status(thm)],[19930, 19929])).
% 2.63/2.84 tff(19932,plain,
% 2.63/2.84 ($false),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19931, 271, 394, 1894, 1281, 447])).
% 2.63/2.84 tff(19933,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.84 tff(19934,plain,
% 2.63/2.84 (~b(z, s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[19933, 447, 1281, 394])).
% 2.63/2.84 tff(19935,plain,
% 2.63/2.84 (r(z, s(s(elem!1)))),
% 2.63/2.84 inference(unit_resolution,[status(thm)],[2106, 19934])).
% 2.63/2.84 tff(19936,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19937,plain,
% 2.63/2.84 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.63/2.84 inference(rewrite,[status(thm)],[])).
% 2.63/2.84 tff(19938,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 2.63/2.84 inference(monotonicity,[status(thm)],[19937])).
% 2.63/2.84 tff(19939,plain,
% 2.63/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.63/2.85 inference(transitivity,[status(thm)],[19938, 19936])).
% 2.63/2.85 tff(19940,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(19941,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[19940, 19939])).
% 2.63/2.85 tff(19942,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19941, 121, 379, 378, 2088, 1624])).
% 2.63/2.85 tff(19943,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(19944,plain,
% 2.63/2.85 (~r(s(s(elem!1)), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19943, 19935, 378, 379])).
% 2.63/2.85 tff(19945,plain,
% 2.63/2.85 (b(s(s(elem!1)), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[862, 19944, 851])).
% 2.63/2.85 tff(19946,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[15082, 271, 505, 517, 447, 19945])).
% 2.63/2.85 tff(19947,plain,((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(19948,plain,
% 2.63/2.85 (~b(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19947, 19925, 19837, 198, 378, 379, 19197, 394])).
% 2.63/2.85 tff(19949,plain,
% 2.63/2.85 (r(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[429, 19948, 2282])).
% 2.63/2.85 tff(19950,plain,
% 2.63/2.85 (r(s(z), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[444, 19910, 348])).
% 2.63/2.85 tff(19951,plain,
% 2.63/2.85 (((~r(s(elem!1), s(z))) | (~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(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(19952,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 2.63/2.85 inference(monotonicity,[status(thm)],[19951])).
% 2.63/2.85 tff(19953,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.63/2.85 inference(transitivity,[status(thm)],[19952, 9256])).
% 2.63/2.85 tff(19954,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(19955,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[19954, 19953])).
% 2.63/2.85 tff(19956,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19955, 121, 379, 3456, 19950, 19949])).
% 2.63/2.85 tff(19957,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(19958,plain,
% 2.63/2.85 (~r(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19957, 19775, 379, 394, 909, 19780, 906, 147, 348, 1, 907, 10063, 19778])).
% 2.63/2.85 tff(19959,plain,
% 2.63/2.85 (b(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[299, 19958, 258])).
% 2.63/2.85 tff(19960,plain,
% 2.63/2.85 (~b(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[3691, 271, 19778, 19780, 19959])).
% 2.63/2.85 tff(19961,plain,
% 2.63/2.85 (r(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[429, 19960, 2282])).
% 2.63/2.85 tff(19962,plain,
% 2.63/2.85 (~b(s(z), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[3696, 271, 19778, 19780, 19959])).
% 2.63/2.85 tff(19963,plain,
% 2.63/2.85 (r(s(z), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[444, 19962, 348])).
% 2.63/2.85 tff(19964,plain,
% 2.63/2.85 (~b(s(s(s(elem!1))), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19657, 19963, 19780, 19778, 19959, 19961, 82])).
% 2.63/2.85 tff(19965,plain,
% 2.63/2.85 (s(s(s(elem!1))) = elem!1),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[486, 19964, 147])).
% 2.63/2.85 tff(19966,plain,
% 2.63/2.85 (~b(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19697, 19965, 19776, 19780, 19958])).
% 2.63/2.85 tff(19967,plain,
% 2.63/2.85 (r(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[105, 19966])).
% 2.63/2.85 tff(19968,plain,
% 2.63/2.85 (b(s(z), s(s(s(elem!1))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19692, 19965, 19780])).
% 2.63/2.85 tff(19969,plain,
% 2.63/2.85 (~r(s(s(s(elem!1))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[12809, 19965, 19958])).
% 2.63/2.85 tff(19970,plain,
% 2.63/2.85 (b(s(s(s(elem!1))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[16580, 19969])).
% 2.63/2.85 tff(19971,plain,
% 2.63/2.85 (~b(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2081, 19970, 19776, 19968])).
% 2.63/2.85 tff(19972,plain,
% 2.63/2.85 (r(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2325, 19971])).
% 2.63/2.85 tff(19973,plain,
% 2.63/2.85 (~r(z, s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2186, 19967, 909, 19961])).
% 2.63/2.85 tff(19974,plain,
% 2.63/2.85 (b(z, s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1439, 19973])).
% 2.63/2.85 tff(19975,plain,
% 2.63/2.85 (~b(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2081, 503, 2073, 750])).
% 2.63/2.85 tff(19976,plain,
% 2.63/2.85 (r(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2325, 19975])).
% 2.63/2.85 tff(19977,plain,
% 2.63/2.85 (~b(s(s(s(elem!1))), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[8132, 503, 448, 260])).
% 2.63/2.85 tff(19978,plain,
% 2.63/2.85 (s(s(s(elem!1))) = elem!1),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[486, 19977, 147])).
% 2.63/2.85 tff(19979,plain,
% 2.63/2.85 (~(s(s(s(z))) = s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2596, 19978])).
% 2.63/2.85 tff(19980,plain,
% 2.63/2.85 (r(s(s(s(z))), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1816, 19979, 3506])).
% 2.63/2.85 tff(19981,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(19982,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(19983,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[19982, 19981])).
% 2.63/2.85 tff(19984,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19983, 121, 431, 19980, 411, 19976])).
% 2.63/2.85 tff(19985,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(19986,plain,
% 2.63/2.85 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19985, 19970, 147, 19776, 19780, 19963, 19961, 19968, 19959])).
% 2.63/2.85 tff(19987,plain,
% 2.63/2.85 (~b(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19710, 19986, 394, 19974])).
% 2.63/2.85 tff(19988,plain,
% 2.63/2.85 (r(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1214, 19987])).
% 2.63/2.85 tff(19989,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2335, 19988, 19972, 909, 19967])).
% 2.63/2.85 tff(19990,plain,((s(z) = s(elem!1)) | (~r(z, s(z))) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z)) | (~r(elem!1, s(elem!1))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(19991,plain,
% 2.63/2.85 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19990, 19617, 394, 147, 82, 258, 379, 909, 1, 907, 199])).
% 2.63/2.85 tff(19992,plain,
% 2.63/2.85 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[221, 15157])).
% 2.63/2.85 tff(19993,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[5499, 19992])).
% 2.63/2.85 tff(19994,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(19995,plain,
% 2.63/2.85 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19994, 221, 5499])).
% 2.63/2.85 tff(19996,plain,
% 2.63/2.85 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[486, 19995, 147])).
% 2.63/2.85 tff(19997,plain,
% 2.63/2.85 (r(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2325, 4801])).
% 2.63/2.85 tff(19998,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(19999,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(20000,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[19999, 19998])).
% 2.63/2.85 tff(20001,plain,
% 2.63/2.85 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20000, 271, 448, 257, 542])).
% 2.63/2.85 tff(20002,plain,
% 2.63/2.85 (r(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2462, 21, 20001, 944])).
% 2.63/2.85 tff(20003,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(20004,plain,
% 2.63/2.85 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(20005,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.63/2.85 inference(monotonicity,[status(thm)],[20004])).
% 2.63/2.85 tff(20006,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.63/2.85 inference(transitivity,[status(thm)],[20005, 20003])).
% 2.63/2.85 tff(20007,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(20008,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[20007, 20006])).
% 2.63/2.85 tff(20009,plain,
% 2.63/2.85 (~b(s(z), s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20008, 271, 260, 448, 542])).
% 2.63/2.85 tff(20010,plain,
% 2.63/2.85 (r(s(z), s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2167, 20009])).
% 2.63/2.85 tff(20011,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2458, 121, 20010, 2117, 20002, 19997])).
% 2.63/2.85 tff(20012,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20013,plain,
% 2.63/2.85 (~r(s(s(elem!1)), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20012, 448, 257, 260, 944, 542])).
% 2.63/2.85 tff(20014,plain,
% 2.63/2.85 (~b(s(s(elem!1)), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[5441, 448, 260, 542])).
% 2.63/2.85 tff(20015,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2143, 20014, 20013])).
% 2.63/2.85 tff(20016,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20017,plain,
% 2.63/2.85 (~b(s(s(elem!1)), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20016, 448, 260, 257, 944])).
% 2.63/2.85 tff(20018,plain,
% 2.63/2.85 (r(s(s(elem!1)), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[862, 20017, 10064])).
% 2.63/2.85 tff(20019,plain,
% 2.63/2.85 (~r(z, s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19943, 20018, 378, 379])).
% 2.63/2.85 tff(20020,plain,
% 2.63/2.85 (b(z, s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2106, 20019])).
% 2.63/2.85 tff(20021,plain,
% 2.63/2.85 (~b(s(z), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19853, 20020, 1281, 394])).
% 2.63/2.85 tff(20022,plain,
% 2.63/2.85 (r(s(z), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[444, 20021, 348])).
% 2.63/2.85 tff(20023,plain,
% 2.63/2.85 (~b(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19933, 20020, 1281, 394])).
% 2.63/2.85 tff(20024,plain,
% 2.63/2.85 (r(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[429, 20023, 2282])).
% 2.63/2.85 tff(20025,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19657, 20024, 20022, 260, 2618, 504, 448, 82])).
% 2.63/2.85 tff(20026,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20027,plain,
% 2.63/2.85 (~b(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20026, 19996, 2618, 19780, 82, 348, 1281, 394, 19775, 379, 257, 19199])).
% 2.63/2.85 tff(20028,plain,
% 2.63/2.85 (r(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[299, 20027, 258])).
% 2.63/2.85 tff(20029,plain,
% 2.63/2.85 (~r(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[3464, 20028, 909, 19775])).
% 2.63/2.85 tff(20030,plain,
% 2.63/2.85 (b(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[105, 20029])).
% 2.63/2.85 tff(20031,plain,
% 2.63/2.85 (~b(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[4220, 20030, 1281, 221, 199])).
% 2.63/2.85 tff(20032,plain,
% 2.63/2.85 (r(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1214, 20031])).
% 2.63/2.85 tff(20033,plain,
% 2.63/2.85 (((~b(elem!1, s(s(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(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(20034,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.63/2.85 inference(monotonicity,[status(thm)],[20033])).
% 2.63/2.85 tff(20035,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.63/2.85 inference(transitivity,[status(thm)],[20034, 10299])).
% 2.63/2.85 tff(20036,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(20037,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[20036, 20035])).
% 2.63/2.85 tff(20038,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20037, 271, 260, 1195, 3871, 257])).
% 2.63/2.85 tff(20039,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20040,plain,
% 2.63/2.85 (~b(elem!1, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20039, 20030, 19780, 257])).
% 2.63/2.85 tff(20041,plain,
% 2.63/2.85 (r(elem!1, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1192, 20040, 1102])).
% 2.63/2.85 tff(20042,plain,
% 2.63/2.85 (~r(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19831, 20041, 19775, 20032])).
% 2.63/2.85 tff(20043,plain,
% 2.63/2.85 (b(s(s(s(z))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2325, 20042])).
% 2.63/2.85 tff(20044,plain,
% 2.63/2.85 (~b(elem!1, z)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[276, 20043, 19780, 257])).
% 2.63/2.85 tff(20045,plain,
% 2.63/2.85 (r(elem!1, z)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[284, 20044, 9298])).
% 2.63/2.85 tff(20046,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(20047,plain,
% 2.63/2.85 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.85 inference(rewrite,[status(thm)],[])).
% 2.63/2.85 tff(20048,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.63/2.85 inference(monotonicity,[status(thm)],[20047])).
% 2.63/2.85 tff(20049,plain,
% 2.63/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 2.63/2.85 inference(transitivity,[status(thm)],[20048, 20046])).
% 2.63/2.85 tff(20050,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 2.63/2.85 inference(quant_inst,[status(thm)],[])).
% 2.63/2.85 tff(20051,plain,
% 2.63/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z)))))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[20050, 20049])).
% 2.63/2.85 tff(20052,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20051, 121, 20041, 20045, 20032, 5499])).
% 2.63/2.85 tff(20053,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(z), z)) | b(z, elem!1) | (~r(z, s(z))) | (elem!1 = s(z)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20054,plain,
% 2.63/2.85 (r(s(s(s(z))), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20053, 19991, 19774, 1101, 19197, 199, 909, 258, 19747, 82, 19617, 394, 379, 147])).
% 2.63/2.85 tff(20055,plain,
% 2.63/2.85 (~(s(elem!1) = s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[350, 19617])).
% 2.63/2.85 tff(20056,plain,
% 2.63/2.85 (~r(s(s(s(z))), z)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19765, 145, 378, 379])).
% 2.63/2.85 tff(20057,plain,
% 2.63/2.85 (b(s(s(s(z))), z)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1155, 20056])).
% 2.63/2.85 tff(20058,plain,
% 2.63/2.85 (~r(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[10262, 121, 379, 378, 145])).
% 2.63/2.85 tff(20059,plain,
% 2.63/2.85 (b(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1214, 20058])).
% 2.63/2.85 tff(20060,plain,
% 2.63/2.85 (~b(s(s(s(z))), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[8279, 20059, 394, 20057])).
% 2.63/2.85 tff(20061,plain,
% 2.63/2.85 (r(s(s(s(z))), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1816, 20060, 2033])).
% 2.63/2.85 tff(20062,plain,
% 2.63/2.85 (~r(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19641, 20061, 379, 145])).
% 2.63/2.85 tff(20063,plain,
% 2.63/2.85 (b(s(elem!1), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[429, 20062, 422])).
% 2.63/2.85 tff(20064,plain,
% 2.63/2.85 (~b(z, s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19933, 20063, 1281, 394])).
% 2.63/2.85 tff(20065,plain,
% 2.63/2.85 (r(z, s(s(elem!1)))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2106, 20064])).
% 2.63/2.85 tff(20066,plain,
% 2.63/2.85 (~b(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19416, 20059, 1281, 257])).
% 2.63/2.85 tff(20067,plain,
% 2.63/2.85 (r(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[105, 20066])).
% 2.63/2.85 tff(20068,plain,
% 2.63/2.85 (~r(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[3464, 20067, 909, 378])).
% 2.63/2.85 tff(20069,plain,
% 2.63/2.85 (b(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[299, 20068, 258])).
% 2.63/2.85 tff(20070,plain,
% 2.63/2.85 (~b(s(s(elem!1)), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20016, 20069, 19621, 257, 19199])).
% 2.63/2.85 tff(20071,plain,
% 2.63/2.85 (r(s(s(elem!1)), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[862, 20070, 851])).
% 2.63/2.85 tff(20072,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19943, 20071, 20065, 378, 379])).
% 2.63/2.85 tff(20073,plain,((s(s(s(z))) = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20074,plain,
% 2.63/2.85 (s(s(s(z))) = s(elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20073, 19619, 379, 10064, 19774, 19197, 394, 258, 20055, 909, 20054])).
% 2.63/2.85 tff(20075,plain,
% 2.63/2.85 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[2596, 20074])).
% 2.63/2.85 tff(20076,plain,
% 2.63/2.85 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[486, 20075, 147])).
% 2.63/2.85 tff(20077,plain,
% 2.63/2.85 (~b(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20026, 20076, 19747, 19750, 82, 19617, 19197, 394, 19619, 379, 19774, 19199])).
% 2.63/2.85 tff(20078,plain,
% 2.63/2.85 (r(elem!1, s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[299, 20077, 258])).
% 2.63/2.85 tff(20079,plain,
% 2.63/2.85 (~r(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[3464, 20078, 909, 19619])).
% 2.63/2.85 tff(20080,plain,
% 2.63/2.85 (b(s(z), s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[105, 20079])).
% 2.63/2.85 tff(20081,plain,
% 2.63/2.85 (b(s(z), s(elem!1))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[4929, 20080, 20074])).
% 2.63/2.85 tff(20082,plain,
% 2.63/2.85 (~b(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19416, 20080, 19197, 19774])).
% 2.63/2.85 tff(20083,plain,
% 2.63/2.85 (r(z, s(s(s(z))))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1214, 20082])).
% 2.63/2.85 tff(20084,plain,
% 2.63/2.85 ($false),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[19909, 20083, 20081, 909, 147, 379, 19619, 394, 20078, 19751, 19750, 1, 907, 10063, 19748, 19747])).
% 2.63/2.85 tff(20085,plain,((elem!1 = s(z)) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.85 tff(20086,plain,
% 2.63/2.85 (elem!1 = s(z)),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[20085, 907, 147, 379, 394, 1, 909, 82, 199])).
% 2.63/2.85 tff(20087,plain,
% 2.63/2.85 (~r(s(s(s(s(z)))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[1234, 20086, 147])).
% 2.63/2.85 tff(20088,plain,
% 2.63/2.85 (b(s(s(s(s(z)))), s(z))),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[932, 20087])).
% 2.63/2.85 tff(20089,plain,
% 2.63/2.85 (s(z) = elem!1),
% 2.63/2.85 inference(unit_resolution,[status(thm)],[242, 20086])).
% 2.63/2.85 tff(20090,plain,
% 2.63/2.85 ((elem!1 = s(elem!1)) <=> (s(z) = s(elem!1))),
% 2.63/2.85 inference(monotonicity,[status(thm)],[20086])).
% 2.63/2.85 tff(20091,plain,
% 2.63/2.85 ((~(elem!1 = s(elem!1))) <=> (~(s(z) = s(elem!1)))),
% 2.63/2.85 inference(monotonicity,[status(thm)],[20090])).
% 2.63/2.85 tff(20092,plain,
% 2.63/2.85 (~(s(z) = s(elem!1))),
% 2.63/2.85 inference(modus_ponens,[status(thm)],[219, 20091])).
% 2.63/2.85 tff(20093,plain,
% 2.63/2.85 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(z))),
% 2.63/2.85 inference(transitivity,[status(thm)],[20090, 4396])).
% 2.63/2.85 tff(20094,plain,
% 2.63/2.85 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20093])).
% 2.63/2.86 tff(20095,plain,
% 2.63/2.86 (~(s(elem!1) = s(z))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[219, 20094])).
% 2.63/2.86 tff(20096,plain,
% 2.63/2.86 (r(z, elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1402, 20089, 894])).
% 2.63/2.86 tff(20097,plain,
% 2.63/2.86 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 2.63/2.86 inference(commutativity,[status(thm)],[])).
% 2.63/2.86 tff(20098,plain,
% 2.63/2.86 (s(elem!1) = s(s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20086])).
% 2.63/2.86 tff(20099,plain,
% 2.63/2.86 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20098])).
% 2.63/2.86 tff(20100,plain,
% 2.63/2.86 ((s(s(s(z))) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20099, 20097])).
% 2.63/2.86 tff(20101,plain,
% 2.63/2.86 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20100])).
% 2.63/2.86 tff(20102,plain,
% 2.63/2.86 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20101])).
% 2.63/2.86 tff(20103,plain,
% 2.63/2.86 (~(s(s(s(z))) = s(elem!1))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[1136, 20102])).
% 2.63/2.86 tff(20104,plain,
% 2.63/2.86 (r(s(s(elem!1)), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[14112, 17770, 223])).
% 2.63/2.86 tff(20105,plain,
% 2.63/2.86 (~r(z, s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[19943, 20104, 378, 379])).
% 2.63/2.86 tff(20106,plain,
% 2.63/2.86 (b(z, s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[2106, 20105])).
% 2.63/2.86 tff(20107,plain,
% 2.63/2.86 (~b(s(elem!1), s(z))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[19933, 20106, 1281, 394])).
% 2.63/2.86 tff(20108,plain,
% 2.63/2.86 (r(s(elem!1), s(z))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[429, 20107, 422])).
% 2.63/2.86 tff(20109,plain,
% 2.63/2.86 (~r(s(s(s(z))), s(elem!1))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[19641, 20108, 379, 17770])).
% 2.63/2.86 tff(20110,plain,
% 2.63/2.86 (b(s(s(s(z))), s(elem!1))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1816, 20109, 2033])).
% 2.63/2.86 tff(20111,plain,
% 2.63/2.86 (~b(s(elem!1), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[19773, 2346, 394, 1281, 379, 378, 348, 907])).
% 2.63/2.86 tff(20112,plain,
% 2.63/2.86 (r(s(elem!1), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[2243, 20111, 2564])).
% 2.63/2.86 tff(20113,plain,
% 2.63/2.86 (~r(s(s(elem!1)), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[8501, 20104, 379, 378])).
% 2.63/2.86 tff(20114,plain,
% 2.63/2.86 (b(s(s(elem!1)), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[2430, 20113])).
% 2.63/2.86 tff(20115,plain,
% 2.63/2.86 (b(s(z), z) <=> b(elem!1, z)),
% 2.63/2.86 inference(monotonicity,[status(thm)],[223])).
% 2.63/2.86 tff(20116,plain,
% 2.63/2.86 (b(elem!1, z) <=> b(s(z), z)),
% 2.63/2.86 inference(symmetry,[status(thm)],[20115])).
% 2.63/2.86 tff(20117,plain,
% 2.63/2.86 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20116])).
% 2.63/2.86 tff(20118,plain,
% 2.63/2.86 (~b(s(z), z)),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[279, 20117])).
% 2.63/2.86 tff(20119,plain,
% 2.63/2.86 ($false),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1281, 20118])).
% 2.63/2.86 tff(20120,plain,((~(s(z) = elem!1)) | (~b(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.86 tff(20121,plain,
% 2.63/2.86 (b(elem!1, z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20120, 223, 1281])).
% 2.63/2.86 tff(20122,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20123,plain,
% 2.63/2.86 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20124,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20123])).
% 2.63/2.86 tff(20125,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20124, 20122])).
% 2.63/2.86 tff(20126,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.63/2.86 inference(quant_inst,[status(thm)],[])).
% 2.63/2.86 tff(20127,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20126, 20125])).
% 2.63/2.86 tff(20128,plain,
% 2.63/2.86 ($false),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20127, 271, 1894, 588, 261, 2449])).
% 2.63/2.86 tff(20129,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.86 tff(20130,plain,
% 2.63/2.86 (~b(elem!1, s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20129, 20106, 20121, 20114])).
% 2.63/2.86 tff(20131,plain,
% 2.63/2.86 (r(elem!1, s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[599, 20130, 68])).
% 2.63/2.86 tff(20132,plain,
% 2.63/2.86 (~r(z, s(elem!1))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[2580, 20131, 378, 20112])).
% 2.63/2.86 tff(20133,plain,
% 2.63/2.86 (b(z, s(elem!1))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1439, 20132])).
% 2.63/2.86 tff(20134,plain,
% 2.63/2.86 ($false),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1427, 20133, 20110, 19766, 394])).
% 2.63/2.86 tff(20135,plain,(b(s(s(s(z))), elem!1) | (~b(s(elem!1), z)) | (s(s(s(z))) = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (~(s(z) = elem!1)) | (s(z) = s(elem!1)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.86 tff(20136,plain,
% 2.63/2.86 (b(s(s(s(z))), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20135, 20103, 394, 20096, 379, 10063, 20095, 19197, 2207, 20089, 20092, 907])).
% 2.63/2.86 tff(20137,plain,
% 2.63/2.86 (b(s(s(s(z))), s(z))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[8109, 20136, 20089])).
% 2.63/2.86 tff(20138,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20139,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.63/2.86 inference(quant_inst,[status(thm)],[])).
% 2.63/2.86 tff(20140,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20139, 20138])).
% 2.63/2.86 tff(20141,plain,
% 2.63/2.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20140, 271, 19197, 20137, 20088])).
% 2.63/2.86 tff(20142,plain,
% 2.63/2.86 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[10426, 20141])).
% 2.63/2.86 tff(20143,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 2.63/2.86 tff(20144,plain,
% 2.63/2.86 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20143])).
% 2.63/2.86 tff(20145,plain,
% 2.63/2.86 ($false),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1138, 20144])).
% 2.63/2.86 tff(20146,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.86 tff(20147,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20148,plain,
% 2.63/2.86 (((~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(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20149,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20148])).
% 2.63/2.86 tff(20150,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20149, 20147])).
% 2.63/2.86 tff(20151,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.63/2.86 inference(quant_inst,[status(thm)],[])).
% 2.63/2.86 tff(20152,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20151, 20150])).
% 2.63/2.86 tff(20153,plain,
% 2.63/2.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20152, 271, 19197, 20137, 20088])).
% 2.63/2.86 tff(20154,plain,
% 2.63/2.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1167, 21, 20153, 20146])).
% 2.63/2.86 tff(20155,plain,
% 2.63/2.86 (s(s(elem!1)) = s(s(s(z)))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20098])).
% 2.63/2.86 tff(20156,plain,
% 2.63/2.86 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20155])).
% 2.63/2.86 tff(20157,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20156])).
% 2.63/2.86 tff(20158,plain,
% 2.63/2.86 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20157])).
% 2.63/2.86 tff(20159,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), s(z))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20088, 20158])).
% 2.63/2.86 tff(20160,plain,
% 2.63/2.86 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20155])).
% 2.63/2.86 tff(20161,plain,
% 2.63/2.86 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20160])).
% 2.63/2.86 tff(20162,plain,
% 2.63/2.86 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20156])).
% 2.63/2.86 tff(20163,plain,
% 2.63/2.86 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20162])).
% 2.63/2.86 tff(20164,plain,
% 2.63/2.86 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20163, 20161])).
% 2.63/2.86 tff(20165,plain,
% 2.63/2.86 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20164])).
% 2.63/2.86 tff(20166,plain,
% 2.63/2.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20153, 20165])).
% 2.63/2.86 tff(20167,plain,
% 2.63/2.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[556, 20166, 1])).
% 2.63/2.86 tff(20168,plain,
% 2.63/2.86 (~r(elem!1, s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[8844, 20167, 394, 20089, 211, 379, 20096, 20137])).
% 2.63/2.86 tff(20169,plain,
% 2.63/2.86 (b(elem!1, s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[599, 20168, 10063])).
% 2.63/2.86 tff(20170,plain,
% 2.63/2.86 (b(s(z), s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[6679, 20169, 20086])).
% 2.63/2.86 tff(20171,plain,
% 2.63/2.86 (~b(z, s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[19416, 20170, 19197, 20136])).
% 2.63/2.86 tff(20172,plain,
% 2.63/2.86 (r(z, s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1214, 20171])).
% 2.63/2.86 tff(20173,plain,
% 2.63/2.86 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20162])).
% 2.63/2.86 tff(20174,plain,
% 2.63/2.86 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20142, 20173])).
% 2.63/2.86 tff(20175,plain,
% 2.63/2.86 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20086])).
% 2.63/2.86 tff(20176,plain,
% 2.63/2.86 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[3049, 20089])).
% 2.63/2.86 tff(20177,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20155])).
% 2.63/2.86 tff(20178,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20177])).
% 2.63/2.86 tff(20179,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20156])).
% 2.63/2.86 tff(20180,plain,
% 2.63/2.86 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20179])).
% 2.63/2.86 tff(20181,plain,
% 2.63/2.86 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20180, 20178])).
% 2.63/2.86 tff(20182,plain,
% 2.63/2.86 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20181])).
% 2.63/2.86 tff(20183,plain,
% 2.63/2.86 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20141, 20182])).
% 2.63/2.86 tff(20184,plain,
% 2.63/2.86 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[586, 20183, 563])).
% 2.63/2.86 tff(20185,plain,
% 2.63/2.86 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20086])).
% 2.63/2.86 tff(20186,plain,
% 2.63/2.86 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.63/2.86 inference(symmetry,[status(thm)],[20185])).
% 2.63/2.86 tff(20187,plain,
% 2.63/2.86 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20155])).
% 2.63/2.86 tff(20188,plain,
% 2.63/2.86 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20187])).
% 2.63/2.86 tff(20189,plain,
% 2.63/2.86 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.63/2.86 inference(transitivity,[status(thm)],[20188, 20186])).
% 2.63/2.86 tff(20190,plain,
% 2.63/2.86 (b(s(s(elem!1)), elem!1)),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20137, 20189])).
% 2.63/2.86 tff(20191,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20086])).
% 2.63/2.86 tff(20192,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.63/2.86 inference(symmetry,[status(thm)],[20191])).
% 2.63/2.86 tff(20193,plain,
% 2.63/2.86 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.63/2.86 inference(transitivity,[status(thm)],[20158, 20192])).
% 2.63/2.86 tff(20194,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20088, 20193])).
% 2.63/2.86 tff(20195,plain,
% 2.63/2.86 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[10405, 20169, 20089, 20194, 20190, 20184, 20167])).
% 2.63/2.86 tff(20196,plain,
% 2.63/2.86 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[8096, 20195, 20089])).
% 2.63/2.86 tff(20197,plain,
% 2.63/2.86 (r(s(s(s(s(s(z))))), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[840, 20196, 20176])).
% 2.63/2.86 tff(20198,plain,
% 2.63/2.86 (r(s(s(s(s(s(z))))), s(z))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20197, 20175])).
% 2.63/2.86 tff(20199,plain,
% 2.63/2.86 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20098])).
% 2.63/2.86 tff(20200,plain,
% 2.63/2.86 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20086])).
% 2.63/2.86 tff(20201,plain,
% 2.63/2.86 (r(s(z), s(elem!1))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[379, 20200])).
% 2.63/2.86 tff(20202,plain,
% 2.63/2.86 (r(s(z), s(s(z)))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20201, 20199])).
% 2.63/2.86 tff(20203,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20204,plain,
% 2.63/2.86 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20205,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20204])).
% 2.63/2.86 tff(20206,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20205, 20203])).
% 2.63/2.86 tff(20207,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.63/2.86 inference(quant_inst,[status(thm)],[])).
% 2.63/2.86 tff(20208,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20207, 20206])).
% 2.63/2.86 tff(20209,plain,
% 2.63/2.86 (~r(z, s(s(s(s(s(z))))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20208, 121, 909, 20202, 20198])).
% 2.63/2.86 tff(20210,plain,
% 2.63/2.86 (b(z, s(s(s(s(s(z))))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1658, 20209])).
% 2.63/2.86 tff(20211,plain,
% 2.63/2.86 (~b(s(s(s(z))), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[4302, 20210, 19197, 20170])).
% 2.63/2.86 tff(20212,plain,
% 2.63/2.86 (r(s(s(s(z))), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1155, 20211])).
% 2.63/2.86 tff(20213,plain,
% 2.63/2.86 (~r(s(s(s(elem!1))), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[11676, 20212, 20174, 20172])).
% 2.63/2.86 tff(20214,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[8229, 20213])).
% 2.63/2.86 tff(20215,plain,
% 2.63/2.86 (~b(z, s(s(s(s(z)))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[19379, 20214, 19197, 20159])).
% 2.63/2.86 tff(20216,plain,
% 2.63/2.86 (r(z, s(s(s(s(z)))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1121, 20215])).
% 2.63/2.86 tff(20217,plain,
% 2.63/2.86 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20218,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20217])).
% 2.63/2.86 tff(20219,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20218, 10432])).
% 2.63/2.86 tff(20220,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.63/2.86 inference(quant_inst,[status(thm)],[])).
% 2.63/2.86 tff(20221,plain,
% 2.63/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20220, 20219])).
% 2.63/2.86 tff(20222,plain,
% 2.63/2.86 ($false),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20221, 121, 20172, 20216, 20154, 20142])).
% 2.63/2.86 tff(20223,plain,((s(s(s(z))) = elem!1) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z)) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.86 tff(20224,plain,
% 2.63/2.86 (s(s(s(z))) = elem!1),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[20223, 394, 909, 379, 1, 894, 147, 82, 199])).
% 2.63/2.86 tff(20225,plain,
% 2.63/2.86 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20224])).
% 2.63/2.86 tff(20226,plain,
% 2.63/2.86 (~b(z, s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[4210, 20224, 199])).
% 2.63/2.86 tff(20227,plain,
% 2.63/2.86 (r(z, s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1214, 20226])).
% 2.63/2.86 tff(20228,plain,
% 2.63/2.86 (r(z, elem!1)),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[20227, 20225])).
% 2.63/2.86 tff(20229,plain,
% 2.63/2.86 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20224])).
% 2.63/2.86 tff(20230,plain,
% 2.63/2.86 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 2.63/2.86 inference(transitivity,[status(thm)],[20229, 238])).
% 2.63/2.86 tff(20231,plain,
% 2.63/2.86 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 2.63/2.86 inference(transitivity,[status(thm)],[20230, 1218])).
% 2.63/2.86 tff(20232,plain,
% 2.63/2.86 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20231])).
% 2.63/2.86 tff(20233,plain,
% 2.63/2.86 (~(elem!1 = s(z))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[97, 20232])).
% 2.63/2.86 tff(20234,plain,
% 2.63/2.86 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[2611, 20224])).
% 2.63/2.86 tff(20235,plain,
% 2.63/2.86 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[486, 20234, 147])).
% 2.63/2.86 tff(20236,plain,
% 2.63/2.86 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20230])).
% 2.63/2.86 tff(20237,plain,
% 2.63/2.86 (~(s(z) = elem!1)),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[97, 20236])).
% 2.63/2.86 tff(20238,plain,
% 2.63/2.86 (~r(s(z), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[3673, 20228, 909, 379])).
% 2.63/2.86 tff(20239,plain,
% 2.63/2.86 (b(s(z), elem!1)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[236, 20238, 20237])).
% 2.63/2.86 tff(20240,plain,
% 2.63/2.86 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.63/2.86 inference(monotonicity,[status(thm)],[20224])).
% 2.63/2.86 tff(20241,plain,
% 2.63/2.86 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.63/2.86 inference(symmetry,[status(thm)],[20240])).
% 2.63/2.86 tff(20242,plain,
% 2.63/2.86 (r(s(s(s(z))), s(elem!1))),
% 2.63/2.86 inference(modus_ponens,[status(thm)],[379, 20241])).
% 2.63/2.86 tff(20243,plain,
% 2.63/2.86 (~r(s(z), s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[1508, 20242, 909, 20227])).
% 2.63/2.86 tff(20244,plain,
% 2.63/2.86 (b(z, s(s(s(elem!1))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[36, 21, 19734, 32])).
% 2.63/2.86 tff(20245,plain,
% 2.63/2.86 (r(s(s(s(elem!1))), z)),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[8229, 8226])).
% 2.63/2.86 tff(20246,plain,
% 2.63/2.86 (b(s(z), s(s(s(z))))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[105, 100])).
% 2.63/2.86 tff(20247,plain,
% 2.63/2.86 (~(elem!1 = s(s(elem!1)))),
% 2.63/2.86 inference(unit_resolution,[status(thm)],[12308, 11211, 8226])).
% 2.63/2.86 tff(20248,plain,
% 2.63/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 2.63/2.86 inference(rewrite,[status(thm)],[])).
% 2.63/2.86 tff(20249,plain,
% 2.63/2.87 (((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20250,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(elem!1)))))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20249])).
% 2.63/2.87 tff(20251,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20250, 20248])).
% 2.63/2.87 tff(20252,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20253,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(elem!1)))))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20252, 20251])).
% 2.63/2.87 tff(20254,plain,
% 2.63/2.87 (~b(s(z), s(elem!1))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20253, 271, 394, 1281, 3407])).
% 2.63/2.87 tff(20255,plain,
% 2.63/2.87 (r(s(z), s(elem!1))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[444, 348, 20254])).
% 2.63/2.87 tff(20256,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20257,plain,
% 2.63/2.87 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20258,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20257])).
% 2.63/2.87 tff(20259,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20258, 20256])).
% 2.63/2.87 tff(20260,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20261,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20260, 20259])).
% 2.63/2.87 tff(20262,plain,
% 2.63/2.87 (~b(s(elem!1), s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20261, 271, 394, 1281, 3407])).
% 2.63/2.87 tff(20263,plain,
% 2.63/2.87 (r(s(elem!1), s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[429, 2282, 20262])).
% 2.63/2.87 tff(20264,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20265,plain,
% 2.63/2.87 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20266,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20265])).
% 2.63/2.87 tff(20267,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20266, 20264])).
% 2.63/2.87 tff(20268,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20269,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20268, 20267])).
% 2.63/2.87 tff(20270,plain,
% 2.63/2.87 (~b(s(elem!1), s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20269, 271, 394, 3407, 2449])).
% 2.63/2.87 tff(20271,plain,
% 2.63/2.87 (r(s(elem!1), s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[526, 20270, 216])).
% 2.63/2.87 tff(20272,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20273,plain,
% 2.63/2.87 (((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20274,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20273])).
% 2.63/2.87 tff(20275,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20274, 20272])).
% 2.63/2.87 tff(20276,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20277,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20276, 20275])).
% 2.63/2.87 tff(20278,plain,
% 2.63/2.87 (~b(s(s(elem!1)), s(elem!1))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20277, 271, 394, 3407, 2449])).
% 2.63/2.87 tff(20279,plain,
% 2.63/2.87 (r(s(s(elem!1)), s(elem!1))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[701, 20278, 8423])).
% 2.63/2.87 tff(20280,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20281,plain,
% 2.63/2.87 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20282,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20281])).
% 2.63/2.87 tff(20283,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20282, 20280])).
% 2.63/2.87 tff(20284,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20285,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20284, 20283])).
% 2.63/2.87 tff(20286,plain,
% 2.63/2.87 (~b(s(z), s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20285, 271, 1281, 3407, 2449])).
% 2.63/2.87 tff(20287,plain,
% 2.63/2.87 (r(s(z), s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[2167, 20286])).
% 2.63/2.87 tff(20288,plain,
% 2.63/2.87 ($false),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[3275, 20287, 20279, 431, 20271])).
% 2.63/2.87 tff(20289,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.87 tff(20290,plain,
% 2.63/2.87 (~b(s(s(elem!1)), z)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20289, 20255, 211, 1281, 3407, 394])).
% 2.63/2.87 tff(20291,plain,
% 2.63/2.87 (r(s(s(elem!1)), z)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[2430, 20290])).
% 2.63/2.87 tff(20292,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20293,plain,
% 2.63/2.87 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20294,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20293])).
% 2.63/2.87 tff(20295,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20294, 20292])).
% 2.63/2.87 tff(20296,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20297,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20296, 20295])).
% 2.63/2.87 tff(20298,plain,
% 2.63/2.87 (~r(s(z), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20297, 121, 379, 431, 411])).
% 2.63/2.87 tff(20299,plain,
% 2.63/2.87 (~r(elem!1, s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[19955, 121, 379, 431, 411])).
% 2.63/2.87 tff(20300,plain,
% 2.63/2.87 (b(s(z), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[236, 2615, 232])).
% 2.63/2.87 tff(20301,plain,
% 2.63/2.87 (b(z, elem!1)),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[3407, 5257])).
% 2.63/2.87 tff(20302,plain,
% 2.63/2.87 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 2.63/2.87 inference(transitivity,[status(thm)],[2613, 1218])).
% 2.63/2.87 tff(20303,plain,
% 2.63/2.87 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20302])).
% 2.63/2.87 tff(20304,plain,
% 2.63/2.87 (~(elem!1 = s(z))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[61, 20303])).
% 2.63/2.87 tff(20305,plain,
% 2.63/2.87 (b(elem!1, s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[299, 20304, 293])).
% 2.63/2.87 tff(20306,plain,
% 2.63/2.87 ($false),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[4760, 20305, 20301, 1281, 20300])).
% 2.63/2.87 tff(20307,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), z)) | r(elem!1, s(z)) | r(s(z), elem!1) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.87 tff(20308,plain,
% 2.63/2.87 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20307, 20299, 1281, 20298, 3407])).
% 2.63/2.87 tff(20309,plain,
% 2.63/2.87 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[486, 20308, 147])).
% 2.63/2.87 tff(20310,plain,
% 2.63/2.87 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.63/2.87 inference(monotonicity,[status(thm)],[1037])).
% 2.63/2.87 tff(20311,plain,
% 2.63/2.87 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.63/2.87 inference(symmetry,[status(thm)],[20310])).
% 2.63/2.87 tff(20312,plain,
% 2.63/2.87 (r(s(s(s(z))), z)),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[2417, 20311])).
% 2.63/2.87 tff(20313,plain,
% 2.63/2.87 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.63/2.87 inference(monotonicity,[status(thm)],[1038])).
% 2.63/2.87 tff(20314,plain,
% 2.63/2.87 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.63/2.87 inference(monotonicity,[status(thm)],[223])).
% 2.63/2.87 tff(20315,plain,
% 2.63/2.87 (~r(s(s(s(s(z)))), s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[1234, 1222, 147])).
% 2.63/2.87 tff(20316,plain,
% 2.63/2.87 (b(s(s(s(s(z)))), s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[932, 20315])).
% 2.63/2.87 tff(20317,plain,
% 2.63/2.87 (b(s(s(s(s(z)))), elem!1)),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20316, 20314])).
% 2.63/2.87 tff(20318,plain,
% 2.63/2.87 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20317, 20313])).
% 2.63/2.87 tff(20319,plain,
% 2.63/2.87 (~b(z, elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[7173, 20318, 3407, 20121])).
% 2.63/2.87 tff(20320,plain,
% 2.63/2.87 (r(s(s(s(z))), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[4220, 199, 3871, 1281, 1307])).
% 2.63/2.87 tff(20321,plain,
% 2.63/2.87 ($false),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[10254, 121, 379, 1243, 20320, 109])).
% 2.63/2.87 tff(20322,plain,(b(z, elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), z)) | (z = elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.87 tff(20323,plain,
% 2.63/2.87 (~b(z, s(s(s(z))))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20322, 20319, 331, 379, 3871, 1281, 20312])).
% 2.63/2.87 tff(20324,plain,
% 2.63/2.87 (~b(z, s(s(elem!1)))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20323, 17671])).
% 2.63/2.87 tff(20325,plain,
% 2.63/2.87 (r(z, s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[2106, 20324])).
% 2.63/2.87 tff(20326,plain,
% 2.63/2.87 (r(z, elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[355, 20319, 331])).
% 2.63/2.87 tff(20327,plain,
% 2.63/2.87 (~r(s(s(elem!1)), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[8501, 20326, 2417, 379])).
% 2.63/2.87 tff(20328,plain,
% 2.63/2.87 (b(s(s(elem!1)), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[862, 20327, 851])).
% 2.63/2.87 tff(20329,plain,
% 2.63/2.87 (b(elem!1, s(s(s(z))))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[11114, 1222, 3871])).
% 2.63/2.87 tff(20330,plain,
% 2.63/2.87 (b(elem!1, s(s(elem!1)))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20329, 7870])).
% 2.63/2.87 tff(20331,plain,
% 2.63/2.87 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[594, 20330, 20318, 20328])).
% 2.63/2.87 tff(20332,plain,
% 2.63/2.87 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[586, 20331, 6943])).
% 2.63/2.87 tff(20333,plain,
% 2.63/2.87 ($false),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[11512, 121, 623, 20332, 20325, 6842])).
% 2.63/2.87 tff(20334,plain,((~(s(z) = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(elem!1))) | (z = elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.63/2.87 tff(20335,plain,
% 2.63/2.87 (~(s(z) = elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20334, 623, 6842, 6943, 851, 2417, 379, 331, 3871, 1281, 3407, 147])).
% 2.63/2.87 tff(20336,plain,
% 2.63/2.87 (~(elem!1 = s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[242, 20335])).
% 2.63/2.87 tff(20337,plain,
% 2.63/2.87 (b(elem!1, s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[299, 20336, 293])).
% 2.63/2.87 tff(20338,plain,
% 2.63/2.87 (b(s(z), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[236, 20335, 232])).
% 2.63/2.87 tff(20339,plain,
% 2.63/2.87 (~b(z, elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[4760, 20337, 1281, 20338])).
% 2.63/2.87 tff(20340,plain,
% 2.63/2.87 (r(z, elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[355, 20339, 331])).
% 2.63/2.87 tff(20341,plain,
% 2.63/2.87 (~r(s(s(elem!1)), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[8501, 20340, 2417, 379])).
% 2.63/2.87 tff(20342,plain,
% 2.63/2.87 (b(s(s(elem!1)), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[862, 20341, 851])).
% 2.63/2.87 tff(20343,plain,
% 2.63/2.87 (~b(s(s(elem!1)), s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[5441, 20342, 20338, 20337])).
% 2.63/2.87 tff(20344,plain,
% 2.63/2.87 (r(s(s(elem!1)), s(z))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[2143, 20343])).
% 2.63/2.87 tff(20345,plain,
% 2.63/2.87 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[2511, 20341, 623])).
% 2.63/2.87 tff(20346,plain,
% 2.63/2.87 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[486, 20345, 147])).
% 2.63/2.87 tff(20347,plain,
% 2.63/2.87 (~b(s(z), s(s(s(elem!1))))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[12821, 271, 20338, 20337, 20346])).
% 2.63/2.87 tff(20348,plain,
% 2.63/2.87 (r(s(z), s(s(s(elem!1))))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[760, 20347])).
% 2.63/2.87 tff(20349,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20350,plain,
% 2.63/2.87 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.63/2.87 inference(rewrite,[status(thm)],[])).
% 2.63/2.87 tff(20351,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 2.63/2.87 inference(monotonicity,[status(thm)],[20350])).
% 2.63/2.87 tff(20352,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.63/2.87 inference(transitivity,[status(thm)],[20351, 20349])).
% 2.63/2.87 tff(20353,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.63/2.87 inference(quant_inst,[status(thm)],[])).
% 2.63/2.87 tff(20354,plain,
% 2.63/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 2.63/2.87 inference(modus_ponens,[status(thm)],[20353, 20352])).
% 2.63/2.87 tff(20355,plain,
% 2.63/2.87 ($false),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20354, 121, 623, 20348, 20344, 6842])).
% 2.63/2.87 tff(20356,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(elem!1))) | (z = elem!1) | (~b(s(z), z)) | r(elem!1, s(z)) | r(s(z), elem!1) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.87 tff(20357,plain,
% 2.63/2.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[20356, 379, 147, 198, 2417, 6842, 331, 1281, 20299, 20298, 563, 3871, 3407])).
% 2.63/2.87 tff(20358,plain,
% 2.63/2.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[556, 20357, 1])).
% 2.63/2.87 tff(20359,plain,
% 2.63/2.87 (~b(z, s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[15601, 271, 20358, 3407, 20309])).
% 2.63/2.87 tff(20360,plain,
% 2.63/2.87 (r(z, s(s(elem!1)))),
% 2.63/2.87 inference(unit_resolution,[status(thm)],[2106, 20359])).
% 2.63/2.87 tff(20361,plain,
% 2.63/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20362,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.63/2.88 inference(quant_inst,[status(thm)],[])).
% 2.63/2.88 tff(20363,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20362, 20361])).
% 2.63/2.88 tff(20364,plain,
% 2.63/2.88 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20363, 121, 20360, 6842, 2417])).
% 2.63/2.88 tff(20365,plain,
% 2.63/2.88 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[586, 20364, 563])).
% 2.63/2.88 tff(20366,plain,
% 2.63/2.88 (~r(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[14498, 20309, 3407, 331, 20360, 2417])).
% 2.63/2.88 tff(20367,plain,
% 2.63/2.88 (b(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[599, 20366, 68])).
% 2.63/2.88 tff(20368,plain,
% 2.63/2.88 (~b(s(s(elem!1)), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[594, 20367, 20309, 20365])).
% 2.63/2.88 tff(20369,plain,
% 2.63/2.88 (r(s(s(elem!1)), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[862, 20368, 198])).
% 2.63/2.88 tff(20370,plain,
% 2.63/2.88 (~b(z, elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[15594, 20367, 3407, 20309])).
% 2.63/2.88 tff(20371,plain,
% 2.63/2.88 (r(z, elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[355, 20370, 331])).
% 2.63/2.88 tff(20372,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[8501, 20371, 20369, 2417, 379])).
% 2.63/2.88 tff(20373,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)) | (z = elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20374,plain,
% 2.63/2.88 (~r(elem!1, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20373, 20291, 9297, 3407, 68, 6842, 147, 1281, 1, 3871, 20255, 20263])).
% 2.63/2.88 tff(20375,plain,
% 2.63/2.88 (b(elem!1, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[392, 20374, 219])).
% 2.63/2.88 tff(20376,plain,
% 2.63/2.88 (~b(elem!1, z)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[3415, 20375, 3407, 394])).
% 2.63/2.88 tff(20377,plain,
% 2.63/2.88 (r(elem!1, z)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[284, 20376, 9298])).
% 2.63/2.88 tff(20378,plain,
% 2.63/2.88 (~b(s(elem!1), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[4598, 20301, 394, 2345])).
% 2.63/2.88 tff(20379,plain,
% 2.63/2.88 (r(s(elem!1), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[2243, 20378, 2207])).
% 2.63/2.88 tff(20380,plain,
% 2.63/2.88 (~(s(z) = elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[1276, 2345, 20254])).
% 2.63/2.88 tff(20381,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[4084, 271, 307, 1326, 260, 1281])).
% 2.63/2.88 tff(20382,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20383,plain,
% 2.63/2.88 (~b(s(z), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20382, 20301, 2345, 1281])).
% 2.63/2.88 tff(20384,plain,
% 2.63/2.88 (r(s(z), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[236, 20383, 20380])).
% 2.63/2.88 tff(20385,plain,
% 2.63/2.88 (~r(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[9643, 20384, 20379, 431])).
% 2.63/2.88 tff(20386,plain,
% 2.63/2.88 (b(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[599, 20385, 68])).
% 2.63/2.88 tff(20387,plain,
% 2.63/2.88 (~b(s(s(elem!1)), s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[3324, 20386, 394, 2345])).
% 2.63/2.88 tff(20388,plain,
% 2.63/2.88 (r(s(s(elem!1)), s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[701, 20387, 3313])).
% 2.63/2.88 tff(20389,plain,
% 2.63/2.88 (~(elem!1 = s(z))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[242, 20380])).
% 2.63/2.88 tff(20390,plain,
% 2.63/2.88 (~r(elem!1, s(z))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[6525, 20384, 431, 20379])).
% 2.63/2.88 tff(20391,plain,
% 2.63/2.88 (b(elem!1, s(z))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[299, 20390, 20389])).
% 2.63/2.88 tff(20392,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20393,plain,
% 2.63/2.88 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20394,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20393])).
% 2.63/2.88 tff(20395,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20394, 20392])).
% 2.63/2.88 tff(20396,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.63/2.88 inference(quant_inst,[status(thm)],[])).
% 2.63/2.88 tff(20397,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20396, 20395])).
% 2.63/2.88 tff(20398,plain,
% 2.63/2.88 ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20397, 271])).
% 2.63/2.88 tff(20399,plain,
% 2.63/2.88 (~b(z, s(z))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20398, 20391, 1281, 20301])).
% 2.63/2.88 tff(20400,plain,
% 2.63/2.88 (r(z, s(z))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[904, 20399])).
% 2.63/2.88 tff(20401,plain,
% 2.63/2.88 (~r(z, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[10675, 20400, 411, 20384])).
% 2.63/2.88 tff(20402,plain,
% 2.63/2.88 (b(z, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[1439, 20401])).
% 2.63/2.88 tff(20403,plain,
% 2.63/2.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[3359, 20402, 394, 259, 2345, 20379, 20388, 10730])).
% 2.63/2.88 tff(20404,plain,
% 2.63/2.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[556, 20403, 1])).
% 2.63/2.88 tff(20405,plain,
% 2.63/2.88 (~b(s(elem!1), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[9687, 20404, 2345, 20386])).
% 2.63/2.88 tff(20406,plain,
% 2.63/2.88 (r(s(elem!1), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[526, 20405, 211])).
% 2.63/2.88 tff(20407,plain,
% 2.63/2.88 (~b(s(z), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[4433, 20404, 20391, 20386])).
% 2.63/2.88 tff(20408,plain,
% 2.63/2.88 (r(s(z), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[2167, 20407])).
% 2.63/2.88 tff(20409,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[3275, 20408, 20406, 431, 20388])).
% 2.63/2.88 tff(20410,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (elem!1 = z) | (~r(s(elem!1), s(z))) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20411,plain,
% 2.63/2.88 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20410, 20255, 1, 394, 9298, 20263, 1281, 68, 3407, 20374])).
% 2.63/2.88 tff(20412,plain,
% 2.63/2.88 (b(s(s(s(elem!1))), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[486, 20411, 147])).
% 2.63/2.88 tff(20413,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20414,plain,
% 2.63/2.88 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20415,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20414])).
% 2.63/2.88 tff(20416,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20415, 20413])).
% 2.63/2.88 tff(20417,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.63/2.88 inference(quant_inst,[status(thm)],[])).
% 2.63/2.88 tff(20418,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20417, 20416])).
% 2.63/2.88 tff(20419,plain,
% 2.63/2.88 (~r(s(s(elem!1)), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20418, 121, 378, 1409, 2417])).
% 2.63/2.88 tff(20420,plain,
% 2.63/2.88 (b(s(s(elem!1)), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[862, 20419, 851])).
% 2.63/2.88 tff(20421,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20422,plain,
% 2.63/2.88 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20423,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20422])).
% 2.63/2.88 tff(20424,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20423, 20421])).
% 2.63/2.88 tff(20425,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.63/2.88 inference(quant_inst,[status(thm)],[])).
% 2.63/2.88 tff(20426,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20425, 20424])).
% 2.63/2.88 tff(20427,plain,
% 2.63/2.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20426, 121, 378, 6842, 2417])).
% 2.63/2.88 tff(20428,plain,
% 2.63/2.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[556, 20427, 1])).
% 2.63/2.88 tff(20429,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[551, 20428, 20420, 307, 504])).
% 2.63/2.88 tff(20430,plain,((~r(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20431,plain,
% 2.63/2.88 (~r(z, elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20430, 20375, 20412, 1, 198, 6842, 20291, 20377])).
% 2.63/2.88 tff(20432,plain,
% 2.63/2.88 (b(z, elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[355, 20431, 9297])).
% 2.63/2.88 tff(20433,plain,
% 2.63/2.88 (~b(s(elem!1), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[4598, 20432, 394, 20375])).
% 2.63/2.88 tff(20434,plain,
% 2.63/2.88 (r(s(elem!1), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[2243, 20433, 2207])).
% 2.63/2.88 tff(20435,plain,
% 2.63/2.88 (~(s(z) = elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[1276, 20375, 20254])).
% 2.63/2.88 tff(20436,plain,
% 2.63/2.88 (~b(s(z), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20382, 20432, 20375, 1281])).
% 2.63/2.88 tff(20437,plain,
% 2.63/2.88 (r(s(z), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[236, 20436, 20435])).
% 2.63/2.88 tff(20438,plain,
% 2.63/2.88 (~b(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[15594, 20432, 3407, 20412])).
% 2.63/2.88 tff(20439,plain,
% 2.63/2.88 (r(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[599, 20438, 68])).
% 2.63/2.88 tff(20440,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[9643, 20439, 20437, 20434, 20255])).
% 2.63/2.88 tff(20441,plain,((s(z) = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20442,plain,
% 2.63/2.88 (s(z) = s(elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20441, 147, 3407, 1281, 394, 1, 6842, 68, 3871])).
% 2.63/2.88 tff(20443,plain,
% 2.63/2.88 (z = elem!1),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[343, 20442])).
% 2.63/2.88 tff(20444,plain,
% 2.63/2.88 (~r(s(s(s(z))), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[149, 20443, 147])).
% 2.63/2.88 tff(20445,plain,
% 2.63/2.88 (b(s(elem!1), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[2488, 20443, 394])).
% 2.63/2.88 tff(20446,plain,
% 2.63/2.88 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[10027])).
% 2.63/2.88 tff(20447,plain,
% 2.63/2.88 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20446])).
% 2.63/2.88 tff(20448,plain,
% 2.63/2.88 (b(elem!1, s(s(s(z))))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[18763, 20447])).
% 2.63/2.88 tff(20449,plain,
% 2.63/2.88 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[10027])).
% 2.63/2.88 tff(20450,plain,
% 2.63/2.88 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[1536])).
% 2.63/2.88 tff(20451,plain,
% 2.63/2.88 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20450, 20449])).
% 2.63/2.88 tff(20452,plain,
% 2.63/2.88 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20451])).
% 2.63/2.88 tff(20453,plain,
% 2.63/2.88 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20447, 6052])).
% 2.63/2.88 tff(20454,plain,
% 2.63/2.88 (b(z, s(s(s(z))))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[18763, 20453])).
% 2.63/2.88 tff(20455,plain,
% 2.63/2.88 (~b(s(s(s(z))), s(z))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[2029, 10030, 394, 20454])).
% 2.63/2.88 tff(20456,plain,
% 2.63/2.88 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20455, 20452])).
% 2.63/2.88 tff(20457,plain,
% 2.63/2.88 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[1536])).
% 2.63/2.88 tff(20458,plain,
% 2.63/2.88 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20457, 200])).
% 2.63/2.88 tff(20459,plain,
% 2.63/2.88 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20458])).
% 2.63/2.88 tff(20460,plain,
% 2.63/2.88 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[61, 20459])).
% 2.63/2.88 tff(20461,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[679, 21, 20460, 20456])).
% 2.63/2.88 tff(20462,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.63/2.88 inference(monotonicity,[status(thm)],[107])).
% 2.63/2.88 tff(20463,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), elem!1)),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[6842, 20462])).
% 2.63/2.88 tff(20464,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20465,plain,
% 2.63/2.88 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20466,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20465])).
% 2.63/2.88 tff(20467,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20466, 20464])).
% 2.63/2.88 tff(20468,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.63/2.88 inference(quant_inst,[status(thm)],[])).
% 2.63/2.88 tff(20469,plain,
% 2.63/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20468, 20467])).
% 2.63/2.88 tff(20470,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20469, 271, 1281, 1307, 3871, 2448])).
% 2.63/2.88 tff(20471,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20472,plain,
% 2.63/2.88 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20471, 20454, 1281, 3871])).
% 2.63/2.88 tff(20473,plain,
% 2.63/2.88 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[9937])).
% 2.63/2.88 tff(20474,plain,
% 2.63/2.88 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20473])).
% 2.63/2.88 tff(20475,plain,
% 2.63/2.88 (b(s(s(s(z))), s(s(elem!1)))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[589, 20474])).
% 2.63/2.88 tff(20476,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.63/2.88 tff(20477,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20476, 20475])).
% 2.63/2.88 tff(20478,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(z))), s(s(elem!1))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20479,plain,
% 2.63/2.88 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20478, 20472, 1536])).
% 2.63/2.88 tff(20480,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[586, 20479, 563])).
% 2.63/2.88 tff(20481,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[10026])).
% 2.63/2.88 tff(20482,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20481])).
% 2.63/2.88 tff(20483,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), s(s(z)))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[573, 20482])).
% 2.63/2.88 tff(20484,plain,
% 2.63/2.88 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.63/2.88 inference(monotonicity,[status(thm)],[9936])).
% 2.63/2.88 tff(20485,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 2.63/2.88 tff(20486,plain,
% 2.63/2.88 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[9936])).
% 2.63/2.88 tff(20487,plain,
% 2.63/2.88 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20486])).
% 2.63/2.88 tff(20488,plain,
% 2.63/2.88 (~b(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[14419, 517, 543, 2618])).
% 2.63/2.88 tff(20489,plain,
% 2.63/2.88 (r(elem!1, s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[599, 20488, 68])).
% 2.63/2.88 tff(20490,plain,
% 2.63/2.88 (r(elem!1, s(s(z)))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20489, 20487])).
% 2.63/2.88 tff(20491,plain,
% 2.63/2.88 (~r(s(s(z)), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[14387, 20490, 1463, 139])).
% 2.63/2.88 tff(20492,plain,
% 2.63/2.88 (b(s(s(z)), elem!1)),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[3613, 20491, 20485])).
% 2.63/2.88 tff(20493,plain,
% 2.63/2.88 (b(s(s(elem!1)), elem!1)),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[20492, 20484])).
% 2.63/2.88 tff(20494,plain,
% 2.63/2.88 ($false),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[14396, 271, 2618, 517, 20493, 738])).
% 2.63/2.88 tff(20495,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (s(s(z)) = elem!1) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.88 tff(20496,plain,
% 2.63/2.88 (~b(s(elem!1), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20495, 543, 738, 1536, 10121, 20483, 139, 18438, 2618])).
% 2.63/2.88 tff(20497,plain,
% 2.63/2.88 (r(s(elem!1), s(s(elem!1)))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[526, 20496, 216])).
% 2.63/2.88 tff(20498,plain,
% 2.63/2.88 (~r(elem!1, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[11463, 20497, 139, 684])).
% 2.63/2.88 tff(20499,plain,
% 2.63/2.88 (b(elem!1, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[392, 20498, 8336])).
% 2.63/2.88 tff(20500,plain,
% 2.63/2.88 (~r(z, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[18214, 20498, 107])).
% 2.63/2.88 tff(20501,plain,
% 2.63/2.88 (b(z, s(elem!1))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[1439, 20500])).
% 2.63/2.88 tff(20502,plain,
% 2.63/2.88 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[18797, 543, 588, 738])).
% 2.63/2.88 tff(20503,plain,
% 2.63/2.88 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[1610, 21, 20502])).
% 2.63/2.88 tff(20504,plain,
% 2.63/2.88 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.63/2.88 inference(unit_resolution,[status(thm)],[20503, 1600])).
% 2.63/2.88 tff(20505,plain,
% 2.63/2.88 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[10027])).
% 2.63/2.88 tff(20506,plain,
% 2.63/2.88 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20505])).
% 2.63/2.88 tff(20507,plain,
% 2.63/2.88 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20506])).
% 2.63/2.88 tff(20508,plain,
% 2.63/2.88 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20507])).
% 2.63/2.88 tff(20509,plain,
% 2.63/2.88 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[1536])).
% 2.63/2.88 tff(20510,plain,
% 2.63/2.88 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20509, 1927])).
% 2.63/2.88 tff(20511,plain,
% 2.63/2.88 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.63/2.88 inference(transitivity,[status(thm)],[20510, 10146])).
% 2.63/2.88 tff(20512,plain,
% 2.63/2.88 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20511])).
% 2.63/2.88 tff(20513,plain,
% 2.63/2.88 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[927, 20512])).
% 2.63/2.88 tff(20514,plain,
% 2.63/2.88 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20506])).
% 2.63/2.88 tff(20515,plain,
% 2.63/2.88 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20514])).
% 2.63/2.88 tff(20516,plain,
% 2.63/2.88 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.63/2.88 inference(commutativity,[status(thm)],[])).
% 2.63/2.88 tff(20517,plain,
% 2.63/2.88 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[804])).
% 2.63/2.88 tff(20518,plain,
% 2.63/2.88 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.63/2.88 inference(transitivity,[status(thm)],[20517, 20516])).
% 2.63/2.88 tff(20519,plain,
% 2.63/2.88 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.63/2.88 inference(symmetry,[status(thm)],[20518])).
% 2.63/2.88 tff(20520,plain,
% 2.63/2.88 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20519])).
% 2.63/2.88 tff(20521,plain,
% 2.63/2.88 (~(elem!1 = s(s(s(s(z)))))),
% 2.63/2.88 inference(modus_ponens,[status(thm)],[1090, 20520])).
% 2.63/2.88 tff(20522,plain,
% 2.63/2.88 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20506])).
% 2.63/2.88 tff(20523,plain,
% 2.63/2.88 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20522])).
% 2.63/2.88 tff(20524,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20525,plain,
% 2.63/2.88 (((~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))))),
% 2.63/2.88 inference(rewrite,[status(thm)],[])).
% 2.63/2.88 tff(20526,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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)))))),
% 2.63/2.88 inference(monotonicity,[status(thm)],[20525])).
% 2.63/2.88 tff(20527,plain,
% 2.63/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 2.63/2.89 inference(transitivity,[status(thm)],[20526, 20524])).
% 2.63/2.89 tff(20528,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20529,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20528, 20527])).
% 2.63/2.89 tff(20530,plain,
% 2.63/2.89 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20529, 271, 307, 2618, 1586])).
% 2.63/2.89 tff(20531,plain,
% 2.63/2.89 (~b(elem!1, s(s(s(s(z)))))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20530, 20523])).
% 2.63/2.89 tff(20532,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 2.63/2.89 tff(20533,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.63/2.89 tff(20534,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.63/2.89 tff(20535,plain,
% 2.63/2.89 (((~![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))))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20536,plain,
% 2.63/2.89 ((~![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))))))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20537,plain,
% 2.63/2.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20536, 20535])).
% 2.63/2.89 tff(20538,plain,
% 2.63/2.89 ($false),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20537, 21, 20534, 20533, 20532])).
% 2.63/2.89 tff(20539,plain,(b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.89 tff(20540,plain,
% 2.63/2.89 (r(elem!1, s(s(s(s(z)))))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20539, 20531, 20521])).
% 2.63/2.89 tff(20541,plain,
% 2.63/2.89 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20540, 20515])).
% 2.63/2.89 tff(20542,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20543,plain,
% 2.63/2.89 (((~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))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20544,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20543])).
% 2.63/2.89 tff(20545,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 2.63/2.89 inference(transitivity,[status(thm)],[20544, 20542])).
% 2.63/2.89 tff(20546,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20547,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20546, 20545])).
% 2.63/2.89 tff(20548,plain,
% 2.63/2.89 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20547, 271, 307, 2618, 1586])).
% 2.63/2.89 tff(20549,plain,
% 2.63/2.89 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[5877, 21, 20548])).
% 2.63/2.89 tff(20550,plain,
% 2.63/2.89 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20549, 5874])).
% 2.63/2.89 tff(20551,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20552,plain,
% 2.63/2.89 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20553,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20552])).
% 2.63/2.89 tff(20554,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.63/2.89 inference(transitivity,[status(thm)],[20553, 20551])).
% 2.63/2.89 tff(20555,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20556,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20555, 20554])).
% 2.63/2.89 tff(20557,plain,
% 2.63/2.89 ($false),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20556, 121, 139, 20550, 15572, 20541])).
% 2.63/2.89 tff(20558,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.89 tff(20559,plain,
% 2.63/2.89 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20558, 20504, 139, 107, 307, 2618])).
% 2.63/2.89 tff(20560,plain,
% 2.63/2.89 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[1566, 20559, 107])).
% 2.63/2.89 tff(20561,plain,
% 2.63/2.89 (r(s(s(s(s(z)))), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[1559, 20560, 20513])).
% 2.63/2.89 tff(20562,plain,
% 2.63/2.89 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20561, 20508])).
% 2.63/2.89 tff(20563,plain,
% 2.63/2.89 (b(z, s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[7550, 588, 107])).
% 2.63/2.89 tff(20564,plain,
% 2.63/2.89 (~b(s(elem!1), s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[8781, 543, 20563, 1421])).
% 2.63/2.89 tff(20565,plain,
% 2.63/2.89 (r(s(elem!1), s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[526, 20564, 216])).
% 2.63/2.89 tff(20566,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20567,plain,
% 2.63/2.89 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20568,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20567])).
% 2.63/2.89 tff(20569,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.63/2.89 inference(transitivity,[status(thm)],[20568, 20566])).
% 2.63/2.89 tff(20570,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20571,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20570, 20569])).
% 2.63/2.89 tff(20572,plain,
% 2.63/2.89 ($false),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20571, 121, 684, 20565, 20562, 20504])).
% 2.63/2.89 tff(20573,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.89 tff(20574,plain,
% 2.63/2.89 (~b(elem!1, s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20573, 20501, 107, 139, 543, 2618, 1591, 684, 738, 216, 20499])).
% 2.63/2.89 tff(20575,plain,
% 2.63/2.89 (r(elem!1, s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[599, 20574, 18438])).
% 2.63/2.89 tff(20576,plain,
% 2.63/2.89 (r(z, s(s(elem!1)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20575, 10061])).
% 2.63/2.89 tff(20577,plain,
% 2.63/2.89 (b(z, s(z))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[1543, 20499, 107])).
% 2.63/2.89 tff(20578,plain,
% 2.63/2.89 (~r(s(s(elem!1)), z)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[14145, 20575, 573, 139])).
% 2.63/2.89 tff(20579,plain,
% 2.63/2.89 (b(s(s(elem!1)), z)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[2430, 20578])).
% 2.63/2.89 tff(20580,plain,
% 2.63/2.89 (z = elem!1),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[17205, 2088, 68, 258, 543, 2449, 220])).
% 2.63/2.89 tff(20581,plain,
% 2.63/2.89 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20580])).
% 2.63/2.89 tff(20582,plain,
% 2.63/2.89 (b(s(s(elem!1)), elem!1)),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[2449, 20581])).
% 2.63/2.89 tff(20583,plain,
% 2.63/2.89 (s(z) = s(elem!1)),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20580])).
% 2.63/2.89 tff(20584,plain,
% 2.63/2.89 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20583])).
% 2.63/2.89 tff(20585,plain,
% 2.63/2.89 (b(elem!1, s(z))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[324, 20580, 220])).
% 2.63/2.89 tff(20586,plain,
% 2.63/2.89 (b(elem!1, s(elem!1))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20585, 20584])).
% 2.63/2.89 tff(20587,plain,
% 2.63/2.89 (~b(s(elem!1), s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[14623, 271, 20586, 17118, 20582])).
% 2.63/2.89 tff(20588,plain,
% 2.63/2.89 (r(s(elem!1), s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[526, 20587, 2209])).
% 2.63/2.89 tff(20589,plain,
% 2.63/2.89 (~b(s(s(elem!1)), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[4717, 271, 20586, 17118, 20582])).
% 2.63/2.89 tff(20590,plain,
% 2.63/2.89 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[699, 21, 20589])).
% 2.63/2.89 tff(20591,plain,
% 2.63/2.89 (r(s(s(elem!1)), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20590, 16703])).
% 2.63/2.89 tff(20592,plain,
% 2.63/2.89 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20580])).
% 2.63/2.89 tff(20593,plain,
% 2.63/2.89 (r(elem!1, s(s(elem!1)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[2088, 20592])).
% 2.63/2.89 tff(20594,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20595,plain,
% 2.63/2.89 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20596,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20595])).
% 2.63/2.89 tff(20597,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.63/2.89 inference(transitivity,[status(thm)],[20596, 20594])).
% 2.63/2.89 tff(20598,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20599,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20598, 20597])).
% 2.63/2.89 tff(20600,plain,
% 2.63/2.89 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20599, 121, 627, 17093, 683])).
% 2.63/2.89 tff(20601,plain,
% 2.63/2.89 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[818, 21, 815, 20600])).
% 2.63/2.89 tff(20602,plain,
% 2.63/2.89 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[706])).
% 2.63/2.89 tff(20603,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20604,plain,
% 2.63/2.89 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20605,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20604])).
% 2.63/2.89 tff(20606,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.63/2.89 inference(transitivity,[status(thm)],[20605, 20603])).
% 2.63/2.89 tff(20607,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20608,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20607, 20606])).
% 2.63/2.89 tff(20609,plain,
% 2.63/2.89 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20608, 121, 624, 17093, 683])).
% 2.63/2.89 tff(20610,plain,
% 2.63/2.89 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20609, 20602])).
% 2.63/2.89 tff(20611,plain,
% 2.63/2.89 (b(s(s(s(s(s(z))))), elem!1)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[840, 20610, 712])).
% 2.63/2.89 tff(20612,plain,
% 2.63/2.89 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20611, 830])).
% 2.63/2.89 tff(20613,plain,
% 2.63/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.63/2.89 inference(rewrite,[status(thm)],[])).
% 2.63/2.89 tff(20614,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.63/2.89 inference(quant_inst,[status(thm)],[])).
% 2.63/2.89 tff(20615,plain,
% 2.63/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[20614, 20613])).
% 2.63/2.89 tff(20616,plain,
% 2.63/2.89 ($false),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20615, 271, 307, 2618, 20612, 20601])).
% 2.63/2.89 tff(20617,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.89 tff(20618,plain,
% 2.63/2.89 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[20617, 20586, 17118, 20580, 20593, 20591, 20588])).
% 2.63/2.89 tff(20619,plain,
% 2.63/2.89 (s(s(z)) = s(s(elem!1))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20583])).
% 2.63/2.89 tff(20620,plain,
% 2.63/2.89 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20619])).
% 2.63/2.89 tff(20621,plain,
% 2.63/2.89 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20620])).
% 2.63/2.89 tff(20622,plain,
% 2.63/2.89 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20621])).
% 2.63/2.89 tff(20623,plain,
% 2.63/2.89 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20622, 20619])).
% 2.63/2.89 tff(20624,plain,
% 2.63/2.89 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20623])).
% 2.63/2.89 tff(20625,plain,
% 2.63/2.89 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[877, 20624])).
% 2.63/2.89 tff(20626,plain,
% 2.63/2.89 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[881, 21, 20625, 20618])).
% 2.63/2.89 tff(20627,plain,
% 2.63/2.89 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20622])).
% 2.63/2.89 tff(20628,plain,
% 2.63/2.89 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20580])).
% 2.63/2.89 tff(20629,plain,
% 2.63/2.89 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.63/2.89 inference(monotonicity,[status(thm)],[20628])).
% 2.63/2.89 tff(20630,plain,
% 2.63/2.89 (~(s(s(s(elem!1))) = elem!1)),
% 2.63/2.89 inference(modus_ponens,[status(thm)],[30, 20629])).
% 2.63/2.89 tff(20631,plain,
% 2.63/2.89 (~b(s(s(s(elem!1))), elem!1)),
% 2.63/2.89 inference(unit_resolution,[status(thm)],[551, 20582, 543, 20586])).
% 2.63/2.90 tff(20632,plain,
% 2.63/2.90 (r(s(s(s(elem!1))), elem!1)),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[486, 20631, 20630])).
% 2.63/2.90 tff(20633,plain,
% 2.63/2.90 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[562, 615])).
% 2.63/2.90 tff(20634,plain,
% 2.63/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.63/2.90 inference(rewrite,[status(thm)],[])).
% 2.63/2.90 tff(20635,plain,
% 2.63/2.90 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.63/2.90 inference(rewrite,[status(thm)],[])).
% 2.63/2.90 tff(20636,plain,
% 2.63/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.63/2.90 inference(monotonicity,[status(thm)],[20635])).
% 2.63/2.90 tff(20637,plain,
% 2.63/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.63/2.90 inference(transitivity,[status(thm)],[20636, 20634])).
% 2.63/2.90 tff(20638,plain,
% 2.63/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.63/2.90 inference(quant_inst,[status(thm)],[])).
% 2.63/2.90 tff(20639,plain,
% 2.63/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.63/2.90 inference(modus_ponens,[status(thm)],[20638, 20637])).
% 2.63/2.90 tff(20640,plain,
% 2.63/2.90 ($false),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[20639, 271, 543, 638, 18990, 17080])).
% 2.63/2.90 tff(20641,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.63/2.90 tff(20642,plain,
% 2.63/2.90 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[20641, 18990, 543, 17080])).
% 2.63/2.90 tff(20643,plain,
% 2.63/2.90 (r(s(s(s(elem!1))), s(elem!1))),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[681, 20642, 82])).
% 2.63/2.90 tff(20644,plain,
% 2.63/2.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[14922, 121, 20643, 627, 683])).
% 2.63/2.90 tff(20645,plain,
% 2.63/2.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.63/2.90 inference(unit_resolution,[status(thm)],[586, 20644, 20633])).
% 2.63/2.90 tff(20646,plain,
% 2.63/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20647,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.73/2.90 inference(quant_inst,[status(thm)],[])).
% 2.73/2.90 tff(20648,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20647, 20646])).
% 2.73/2.90 tff(20649,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20648, 271, 543, 20645, 18990, 17080])).
% 2.73/2.90 tff(20650,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20651,plain,
% 2.73/2.90 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20650, 20626, 543, 20588, 20591, 79])).
% 2.73/2.90 tff(20652,plain,
% 2.73/2.90 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[19550, 7494])).
% 2.73/2.90 tff(20653,plain,
% 2.73/2.90 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[1733, 20652])).
% 2.73/2.90 tff(20654,plain,
% 2.73/2.90 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20653, 781])).
% 2.73/2.90 tff(20655,assumption,(~b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.73/2.90 tff(20656,plain,
% 2.73/2.90 (r(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[840, 20655, 712])).
% 2.73/2.90 tff(20657,plain,
% 2.73/2.90 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20656, 707])).
% 2.73/2.90 tff(20658,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20659,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.73/2.90 inference(quant_inst,[status(thm)],[])).
% 2.73/2.90 tff(20660,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20659, 20658])).
% 2.73/2.90 tff(20661,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20660, 121, 624, 139, 20657, 20654])).
% 2.73/2.90 tff(20662,plain,(b(s(s(s(s(s(z))))), elem!1) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20663,plain,
% 2.73/2.90 (b(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20662, 20651, 20632, 20580, 20593])).
% 2.73/2.90 tff(20664,plain,
% 2.73/2.90 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20663, 20627])).
% 2.73/2.90 tff(20665,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20666,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.73/2.90 inference(quant_inst,[status(thm)],[])).
% 2.73/2.90 tff(20667,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20666, 20665])).
% 2.73/2.90 tff(20668,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20667, 271, 20586, 20664, 20626, 20582])).
% 2.73/2.90 tff(20669,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20670,plain,
% 2.73/2.90 (~r(z, s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20669, 20579, 20577, 543, 18438, 258])).
% 2.73/2.90 tff(20671,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20670, 20576])).
% 2.73/2.90 tff(20672,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (elem!1 = s(z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20673,plain,
% 2.73/2.90 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20672, 107, 258, 20480, 20463, 10032, 1577, 20461, 18763, 211])).
% 2.73/2.90 tff(20674,plain,
% 2.73/2.90 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[556, 20673, 1])).
% 2.73/2.90 tff(20675,plain,
% 2.73/2.90 (~r(elem!1, s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[17916, 20674, 20480, 20463])).
% 2.73/2.90 tff(20676,plain,
% 2.73/2.90 (b(elem!1, s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[599, 20675, 18438])).
% 2.73/2.90 tff(20677,plain,
% 2.73/2.90 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.73/2.90 inference(monotonicity,[status(thm)],[107])).
% 2.73/2.90 tff(20678,plain,
% 2.73/2.90 (b(s(z), elem!1)),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[1281, 20677])).
% 2.73/2.90 tff(20679,plain,
% 2.73/2.90 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[338])).
% 2.73/2.90 tff(20680,plain,
% 2.73/2.90 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 2.73/2.90 inference(symmetry,[status(thm)],[20679])).
% 2.73/2.90 tff(20681,plain,
% 2.73/2.90 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[9936])).
% 2.73/2.90 tff(20682,plain,
% 2.73/2.90 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 2.73/2.90 inference(symmetry,[status(thm)],[20681])).
% 2.73/2.90 tff(20683,plain,
% 2.73/2.90 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.73/2.90 inference(transitivity,[status(thm)],[20682, 20680])).
% 2.73/2.90 tff(20684,plain,
% 2.73/2.90 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[11463, 379, 139, 684])).
% 2.73/2.90 tff(20685,plain,
% 2.73/2.90 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[526, 20684, 216])).
% 2.73/2.90 tff(20686,plain,
% 2.73/2.90 (b(s(z), s(s(z)))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20685, 20683])).
% 2.73/2.90 tff(20687,plain,
% 2.73/2.90 (~b(s(s(z)), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[19454, 20686, 260, 588])).
% 2.73/2.90 tff(20688,plain,
% 2.73/2.90 (r(s(s(z)), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[3613, 20687, 20485])).
% 2.73/2.90 tff(20689,plain,
% 2.73/2.90 (r(s(s(elem!1)), elem!1)),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20688, 19440])).
% 2.73/2.90 tff(20690,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[13178, 121, 379, 623, 139, 20689])).
% 2.73/2.90 tff(20691,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1))) | (s(s(z)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20692,plain,
% 2.73/2.90 (~r(elem!1, s(elem!1))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20691, 20674, 20463, 1536, 10121, 20678, 20676, 211, 20461])).
% 2.73/2.90 tff(20693,plain,
% 2.73/2.90 (b(elem!1, s(elem!1))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[392, 20692, 219])).
% 2.73/2.90 tff(20694,plain,
% 2.73/2.90 (b(z, s(z))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[1543, 20693, 107])).
% 2.73/2.90 tff(20695,plain,
% 2.73/2.90 (b(elem!1, s(z))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[324, 20694, 107])).
% 2.73/2.90 tff(20696,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20697,plain,
% 2.73/2.90 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20698,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20697])).
% 2.73/2.90 tff(20699,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.73/2.90 inference(transitivity,[status(thm)],[20698, 20696])).
% 2.73/2.90 tff(20700,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.73/2.90 inference(quant_inst,[status(thm)],[])).
% 2.73/2.90 tff(20701,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20700, 20699])).
% 2.73/2.90 tff(20702,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20701, 271, 448, 1195, 3871, 1519])).
% 2.73/2.90 tff(20703,plain,((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20704,plain,
% 2.73/2.90 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20703, 20695, 3871, 20448])).
% 2.73/2.90 tff(20705,plain,
% 2.73/2.90 (~r(z, s(elem!1))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[18214, 20692, 107])).
% 2.73/2.90 tff(20706,plain,
% 2.73/2.90 (b(z, s(elem!1))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[1439, 20705])).
% 2.73/2.90 tff(20707,plain,
% 2.73/2.90 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20505])).
% 2.73/2.90 tff(20708,plain,
% 2.73/2.90 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.73/2.90 inference(symmetry,[status(thm)],[20707])).
% 2.73/2.90 tff(20709,plain,
% 2.73/2.90 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20506, 20708])).
% 2.73/2.90 tff(20710,plain,
% 2.73/2.90 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(symmetry,[status(thm)],[20709])).
% 2.73/2.90 tff(20711,plain,
% 2.73/2.90 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20505, 20707])).
% 2.73/2.90 tff(20712,plain,
% 2.73/2.90 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.90 inference(symmetry,[status(thm)],[20711])).
% 2.73/2.90 tff(20713,plain,
% 2.73/2.90 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20712])).
% 2.73/2.90 tff(20714,plain,
% 2.73/2.90 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.73/2.90 inference(symmetry,[status(thm)],[20522])).
% 2.73/2.90 tff(20715,plain,
% 2.73/2.90 ((~r(elem!1, s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20514])).
% 2.73/2.90 tff(20716,plain,
% 2.73/2.90 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.73/2.90 inference(monotonicity,[status(thm)],[10026])).
% 2.73/2.90 tff(20717,plain,
% 2.73/2.90 (~b(s(s(elem!1)), s(elem!1))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[3324, 588, 394, 307])).
% 2.73/2.90 tff(20718,plain,
% 2.73/2.90 (r(s(s(elem!1)), s(elem!1))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[701, 20717, 3313])).
% 2.73/2.90 tff(20719,plain,
% 2.73/2.90 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20573, 588, 107, 139, 307, 10032, 1577, 684, 738, 211, 1421])).
% 2.73/2.90 tff(20720,plain,
% 2.73/2.90 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[556, 20719, 1])).
% 2.73/2.90 tff(20721,plain,
% 2.73/2.90 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[3201, 20720, 20718, 684])).
% 2.73/2.90 tff(20722,plain,
% 2.73/2.90 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[526, 20721, 211])).
% 2.73/2.90 tff(20723,plain,
% 2.73/2.90 (b(s(s(elem!1)), elem!1)),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[19446, 17061])).
% 2.73/2.90 tff(20724,plain,
% 2.73/2.90 (~b(s(s(elem!1)), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[14623, 271, 307, 2618, 517])).
% 2.73/2.90 tff(20725,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20724, 20723])).
% 2.73/2.90 tff(20726,plain,((~b(s(s(z)), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20727,plain,
% 2.73/2.90 (~b(s(s(z)), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20726, 20722, 107, 10032, 307])).
% 2.73/2.90 tff(20728,plain,
% 2.73/2.90 (r(s(s(z)), elem!1)),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[3613, 20727, 10121])).
% 2.73/2.90 tff(20729,plain,
% 2.73/2.90 (r(s(s(elem!1)), elem!1)),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20728, 20716])).
% 2.73/2.90 tff(20730,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20731,plain,
% 2.73/2.90 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20732,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20731])).
% 2.73/2.90 tff(20733,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.90 inference(transitivity,[status(thm)],[20732, 20730])).
% 2.73/2.90 tff(20734,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.73/2.90 inference(quant_inst,[status(thm)],[])).
% 2.73/2.90 tff(20735,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20734, 20733])).
% 2.73/2.90 tff(20736,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20735, 121, 623, 139, 1624, 1596])).
% 2.73/2.90 tff(20737,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20738,plain,
% 2.73/2.90 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20737, 20720, 139, 20729])).
% 2.73/2.90 tff(20739,plain,
% 2.73/2.90 (~r(elem!1, s(s(s(s(z)))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20738, 20715])).
% 2.73/2.90 tff(20740,plain,
% 2.73/2.90 (b(elem!1, s(s(s(s(z)))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20539, 20739, 20521])).
% 2.73/2.90 tff(20741,plain,
% 2.73/2.90 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20740, 20714])).
% 2.73/2.90 tff(20742,plain,
% 2.73/2.90 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[19025, 20720, 1536, 139, 20729])).
% 2.73/2.90 tff(20743,plain,
% 2.73/2.90 (b(elem!1, s(s(s(s(s(z))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[1847, 20742, 18042])).
% 2.73/2.90 tff(20744,plain,
% 2.73/2.90 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[9946, 20743, 1536])).
% 2.73/2.90 tff(20745,plain,
% 2.73/2.90 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20707, 10027])).
% 2.73/2.90 tff(20746,plain,
% 2.73/2.90 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20707, 10026])).
% 2.73/2.90 tff(20747,plain,
% 2.73/2.90 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20746])).
% 2.73/2.90 tff(20748,plain,
% 2.73/2.90 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[877, 20747])).
% 2.73/2.90 tff(20749,plain,
% 2.73/2.90 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[6034, 6026, 623, 139])).
% 2.73/2.90 tff(20750,plain,
% 2.73/2.90 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[1716, 21, 20749])).
% 2.73/2.90 tff(20751,plain,
% 2.73/2.90 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20750, 19137])).
% 2.73/2.90 tff(20752,plain,
% 2.73/2.90 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[18706, 121, 623, 684, 6026])).
% 2.73/2.90 tff(20753,plain,
% 2.73/2.90 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[881, 21, 18289, 20752])).
% 2.73/2.90 tff(20754,plain,
% 2.73/2.90 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20755,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.73/2.90 inference(monotonicity,[status(thm)],[20754])).
% 2.73/2.90 tff(20756,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.73/2.90 inference(transitivity,[status(thm)],[20755, 18557])).
% 2.73/2.90 tff(20757,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.73/2.90 inference(quant_inst,[status(thm)],[])).
% 2.73/2.90 tff(20758,plain,
% 2.73/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20757, 20756])).
% 2.73/2.90 tff(20759,plain,
% 2.73/2.90 ($false),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20758, 271, 588, 20753, 20751, 6004])).
% 2.73/2.90 tff(20760,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.90 tff(20761,plain,
% 2.73/2.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[20760, 20744, 588, 20748, 20720, 684, 139])).
% 2.73/2.90 tff(20762,plain,
% 2.73/2.90 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[6039, 20761, 107])).
% 2.73/2.90 tff(20763,plain,
% 2.73/2.90 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.73/2.90 inference(unit_resolution,[status(thm)],[1733, 20762])).
% 2.73/2.90 tff(20764,plain,
% 2.73/2.90 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.73/2.90 inference(modus_ponens,[status(thm)],[20763, 20745])).
% 2.73/2.90 tff(20765,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20766,plain,
% 2.73/2.90 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.90 inference(rewrite,[status(thm)],[])).
% 2.73/2.90 tff(20767,plain,
% 2.73/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20766])).
% 2.73/2.91 tff(20768,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(transitivity,[status(thm)],[20767, 20765])).
% 2.73/2.91 tff(20769,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(quant_inst,[status(thm)],[])).
% 2.73/2.91 tff(20770,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20769, 20768])).
% 2.73/2.91 tff(20771,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20770, 271, 18990, 6004, 7564, 19070])).
% 2.73/2.91 tff(20772,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20773,plain,
% 2.73/2.91 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20772, 20764, 20744, 20741])).
% 2.73/2.91 tff(20774,plain,
% 2.73/2.91 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20773, 20713])).
% 2.73/2.91 tff(20775,plain,
% 2.73/2.91 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1777, 20774])).
% 2.73/2.91 tff(20776,plain,
% 2.73/2.91 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20775, 20710])).
% 2.73/2.91 tff(20777,plain,
% 2.73/2.91 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[5833, 20460])).
% 2.73/2.91 tff(20778,plain,
% 2.73/2.91 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1610, 21, 6894])).
% 2.73/2.91 tff(20779,plain,
% 2.73/2.91 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20778, 1600])).
% 2.73/2.91 tff(20780,plain,
% 2.73/2.91 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1594, 21, 1591, 8218])).
% 2.73/2.91 tff(20781,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20782,plain,
% 2.73/2.91 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20783,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20782])).
% 2.73/2.91 tff(20784,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(transitivity,[status(thm)],[20783, 20781])).
% 2.73/2.91 tff(20785,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(quant_inst,[status(thm)],[])).
% 2.73/2.91 tff(20786,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20785, 20784])).
% 2.73/2.91 tff(20787,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20786, 271, 738, 20780, 20779, 19070])).
% 2.73/2.91 tff(20788,plain,(r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20789,plain,
% 2.73/2.91 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20788, 6894, 19070, 738, 1591])).
% 2.73/2.91 tff(20790,plain,
% 2.73/2.91 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[18645, 121, 623, 684, 20789])).
% 2.73/2.91 tff(20791,plain,
% 2.73/2.91 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 20790])).
% 2.73/2.91 tff(20792,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20793,plain,
% 2.73/2.91 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20794,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20793])).
% 2.73/2.91 tff(20795,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.73/2.91 inference(transitivity,[status(thm)],[20794, 20792])).
% 2.73/2.91 tff(20796,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.73/2.91 inference(quant_inst,[status(thm)],[])).
% 2.73/2.91 tff(20797,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20796, 20795])).
% 2.73/2.91 tff(20798,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20797, 271, 738, 20791, 20779, 19070])).
% 2.73/2.91 tff(20799,plain,(r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (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(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20800,plain,
% 2.73/2.91 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20799, 20741, 738, 20777, 1577, 20720, 684])).
% 2.73/2.91 tff(20801,plain,
% 2.73/2.91 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[19592, 9940])).
% 2.73/2.91 tff(20802,plain,
% 2.73/2.91 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(symmetry,[status(thm)],[20801])).
% 2.73/2.91 tff(20803,plain,
% 2.73/2.91 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[1758, 20802])).
% 2.73/2.91 tff(20804,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20805,plain,
% 2.73/2.91 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20806,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20805])).
% 2.73/2.91 tff(20807,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(transitivity,[status(thm)],[20806, 20804])).
% 2.73/2.91 tff(20808,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(quant_inst,[status(thm)],[])).
% 2.73/2.91 tff(20809,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20808, 20807])).
% 2.73/2.91 tff(20810,plain,
% 2.73/2.91 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20809, 121, 17094, 7473, 15572])).
% 2.73/2.91 tff(20811,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20810, 20803])).
% 2.73/2.91 tff(20812,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20813,plain,
% 2.73/2.91 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20812, 20775, 1536, 7473, 20800])).
% 2.73/2.91 tff(20814,plain,
% 2.73/2.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[9962, 20813, 1536])).
% 2.73/2.91 tff(20815,plain,
% 2.73/2.91 (b(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[840, 20814, 712])).
% 2.73/2.91 tff(20816,plain,
% 2.73/2.91 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[835, 20815, 107])).
% 2.73/2.91 tff(20817,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20818,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.73/2.91 inference(quant_inst,[status(thm)],[])).
% 2.73/2.91 tff(20819,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20818, 20817])).
% 2.73/2.91 tff(20820,plain,
% 2.73/2.91 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20819, 271, 307, 10032, 20816])).
% 2.73/2.91 tff(20821,plain,
% 2.73/2.91 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[818, 21, 815, 20820])).
% 2.73/2.91 tff(20822,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20823,plain,
% 2.73/2.91 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(rewrite,[status(thm)],[])).
% 2.73/2.91 tff(20824,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20823])).
% 2.73/2.91 tff(20825,plain,
% 2.73/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.73/2.91 inference(transitivity,[status(thm)],[20824, 20822])).
% 2.73/2.91 tff(20826,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(quant_inst,[status(thm)],[])).
% 2.73/2.91 tff(20827,plain,
% 2.73/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.73/2.91 inference(modus_ponens,[status(thm)],[20826, 20825])).
% 2.73/2.91 tff(20828,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20827, 121, 7473, 20800, 20821, 20776])).
% 2.73/2.91 tff(20829,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20830,plain,
% 2.73/2.91 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20829, 20706, 20676, 107, 20461, 20463, 18763, 1, 20693, 394])).
% 2.73/2.91 tff(20831,plain,
% 2.73/2.91 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[7296, 20830, 107])).
% 2.73/2.91 tff(20832,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1494, 20831, 20704])).
% 2.73/2.91 tff(20833,plain,((~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (elem!1 = s(z)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20834,plain,
% 2.73/2.91 (elem!1 = s(z)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20833, 20443, 1, 394, 3871, 1281, 6842, 3407])).
% 2.73/2.91 tff(20835,plain,
% 2.73/2.91 (b(elem!1, s(s(s(z))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[11114, 20834, 3871])).
% 2.73/2.91 tff(20836,plain,
% 2.73/2.91 (~b(z, elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[9291, 20835, 394, 20445])).
% 2.73/2.91 tff(20837,plain,
% 2.73/2.91 (b(elem!1, s(s(s(elem!1))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1198, 20835, 20443])).
% 2.73/2.91 tff(20838,plain,
% 2.73/2.91 (b(z, s(s(s(z))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[6057, 20837, 20443])).
% 2.73/2.91 tff(20839,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[4220, 20838, 20836, 3871, 1281, 20444])).
% 2.73/2.91 tff(20840,plain,(r(s(s(s(elem!1))), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20841,plain,
% 2.73/2.91 (r(s(s(s(elem!1))), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20840, 11211, 1281, 3871, 1, 20245, 3407, 20247])).
% 2.73/2.91 tff(20842,plain,
% 2.73/2.91 (~r(elem!1, s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[8972, 378, 139, 6842])).
% 2.73/2.91 tff(20843,plain,
% 2.73/2.91 (b(elem!1, s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[392, 20842, 219])).
% 2.73/2.91 tff(20844,plain,
% 2.73/2.91 (~b(elem!1, z)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[3415, 20843, 3407, 394])).
% 2.73/2.91 tff(20845,plain,
% 2.73/2.91 (~(s(z) = elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1276, 20843, 20254])).
% 2.73/2.91 tff(20846,plain,
% 2.73/2.91 (~(elem!1 = s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[242, 20845])).
% 2.73/2.91 tff(20847,plain,
% 2.73/2.91 (~(z = elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20833, 20846, 1, 394, 3871, 1281, 6842, 3407])).
% 2.73/2.91 tff(20848,plain,
% 2.73/2.91 (~(elem!1 = z)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[333, 20847])).
% 2.73/2.91 tff(20849,plain,
% 2.73/2.91 (r(elem!1, z)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[284, 20848, 20844])).
% 2.73/2.91 tff(20850,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[8913, 121, 378, 20849, 139, 6842])).
% 2.73/2.91 tff(20851,plain,((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20852,plain,
% 2.73/2.91 (~r(z, elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20851, 20841, 20245, 1, 11211, 3871, 1281, 3407])).
% 2.73/2.91 tff(20853,plain,
% 2.73/2.91 (elem!1 = s(z)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20833, 8716, 1, 394, 3871, 1281, 6842, 3407])).
% 2.73/2.91 tff(20854,plain,
% 2.73/2.91 (s(z) = elem!1),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[242, 20853])).
% 2.73/2.91 tff(20855,plain,
% 2.73/2.91 (~b(elem!1, s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1276, 20854, 20254])).
% 2.73/2.91 tff(20856,plain,
% 2.73/2.91 (b(z, s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1402, 20854, 1391])).
% 2.73/2.91 tff(20857,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[327, 20856, 20855, 8716])).
% 2.73/2.91 tff(20858,plain,(r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20859,plain,
% 2.73/2.91 (b(z, elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20858, 20852, 11211, 3871, 1281, 20245, 3407, 1])).
% 2.73/2.91 tff(20860,plain,
% 2.73/2.91 (~b(s(z), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20253, 271, 11211, 1281, 3407])).
% 2.73/2.91 tff(20861,plain,
% 2.73/2.91 (r(s(z), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[444, 344, 20860])).
% 2.73/2.91 tff(20862,plain,
% 2.73/2.91 (~b(s(elem!1), s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20261, 271, 11211, 1281, 3407])).
% 2.73/2.91 tff(20863,plain,
% 2.73/2.91 (r(s(elem!1), s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[429, 351, 20862])).
% 2.73/2.91 tff(20864,plain,
% 2.73/2.91 (~b(s(elem!1), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[4598, 2345, 394, 1326])).
% 2.73/2.91 tff(20865,plain,
% 2.73/2.91 (r(s(elem!1), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[2243, 20864, 2207])).
% 2.73/2.91 tff(20866,plain,
% 2.73/2.91 (~b(s(z), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20382, 2345, 1326, 1281])).
% 2.73/2.91 tff(20867,plain,
% 2.73/2.91 (r(s(z), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[236, 20866, 20380])).
% 2.73/2.91 tff(20868,plain,
% 2.73/2.91 (~r(elem!1, s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[9643, 20867, 20865, 431])).
% 2.73/2.91 tff(20869,plain,
% 2.73/2.91 (b(elem!1, s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[599, 20868, 68])).
% 2.73/2.91 tff(20870,plain,
% 2.73/2.91 (~b(s(s(elem!1)), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[3324, 20869, 394, 2345])).
% 2.73/2.91 tff(20871,plain,
% 2.73/2.91 (r(s(s(elem!1)), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[701, 20870, 3313])).
% 2.73/2.91 tff(20872,plain,
% 2.73/2.91 (~r(elem!1, s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[6525, 20867, 431, 20865])).
% 2.73/2.91 tff(20873,plain,
% 2.73/2.91 (b(elem!1, s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[299, 20872, 20389])).
% 2.73/2.91 tff(20874,plain,
% 2.73/2.91 (~b(z, s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20398, 20873, 1281, 1326])).
% 2.73/2.91 tff(20875,plain,
% 2.73/2.91 (r(z, s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[904, 20874])).
% 2.73/2.91 tff(20876,plain,
% 2.73/2.91 (~r(z, s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[10675, 20875, 411, 20867])).
% 2.73/2.91 tff(20877,plain,
% 2.73/2.91 (b(z, s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[1439, 20876])).
% 2.73/2.91 tff(20878,plain,
% 2.73/2.91 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[3351, 20877, 394, 139, 259, 2345])).
% 2.73/2.91 tff(20879,plain,
% 2.73/2.91 (r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[681, 20878, 79])).
% 2.73/2.91 tff(20880,plain,
% 2.73/2.91 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[15594, 20869, 3407, 1326])).
% 2.73/2.91 tff(20881,plain,
% 2.73/2.91 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[692, 20879, 20871, 20865])).
% 2.73/2.91 tff(20882,plain,
% 2.73/2.91 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[556, 20881, 1])).
% 2.73/2.91 tff(20883,plain,
% 2.73/2.91 (~b(s(elem!1), s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[16735, 20882, 2344, 20880, 68, 20865, 20879])).
% 2.73/2.91 tff(20884,plain,
% 2.73/2.91 (r(s(elem!1), s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[526, 20883, 211])).
% 2.73/2.91 tff(20885,plain,
% 2.73/2.91 (~b(s(z), s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[4433, 20882, 20873, 20869])).
% 2.73/2.91 tff(20886,plain,
% 2.73/2.91 (r(s(z), s(s(elem!1)))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[2167, 20885])).
% 2.73/2.91 tff(20887,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[3275, 20886, 20884, 431, 20871])).
% 2.73/2.91 tff(20888,plain,(r(elem!1, s(elem!1)) | (~r(s(z), s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (~r(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20889,plain,
% 2.73/2.91 (r(elem!1, s(elem!1))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20888, 20861, 68, 1, 11211, 139, 358, 20863, 3407, 1326, 1281])).
% 2.73/2.91 tff(20890,plain,
% 2.73/2.91 (~r(elem!1, s(z))),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[9263, 20889, 1281, 1326, 344, 20861])).
% 2.73/2.91 tff(20891,plain,
% 2.73/2.91 (~r(s(z), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20297, 121, 20889, 20861, 20863])).
% 2.73/2.91 tff(20892,plain,
% 2.73/2.91 (b(s(z), elem!1)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[236, 1257, 232])).
% 2.73/2.91 tff(20893,plain,
% 2.73/2.91 ($false),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[4760, 20892, 3655, 1281, 1326])).
% 2.73/2.91 tff(20894,plain,((elem!1 = s(z)) | (~b(s(z), z)) | (~b(z, elem!1)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.91 tff(20895,plain,
% 2.73/2.91 (elem!1 = s(z)),
% 2.73/2.91 inference(unit_resolution,[status(thm)],[20894, 20891, 1326, 1281, 20890])).
% 2.73/2.91 tff(20896,plain,
% 2.73/2.91 (s(elem!1) = s(s(z))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20895])).
% 2.73/2.91 tff(20897,plain,
% 2.73/2.91 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.91 inference(monotonicity,[status(thm)],[20896])).
% 2.73/2.91 tff(20898,plain,
% 2.73/2.91 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.91 inference(symmetry,[status(thm)],[20897])).
% 2.73/2.92 tff(20899,plain,
% 2.73/2.92 (s(s(elem!1)) = s(s(s(z)))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20896])).
% 2.73/2.92 tff(20900,plain,
% 2.73/2.92 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20899])).
% 2.73/2.92 tff(20901,plain,
% 2.73/2.92 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20900])).
% 2.73/2.92 tff(20902,plain,
% 2.73/2.92 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20901])).
% 2.73/2.92 tff(20903,plain,
% 2.73/2.92 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.92 inference(transitivity,[status(thm)],[20902, 20898])).
% 2.73/2.92 tff(20904,plain,
% 2.73/2.92 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20903])).
% 2.73/2.92 tff(20905,plain,
% 2.73/2.92 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20900])).
% 2.73/2.92 tff(20906,plain,
% 2.73/2.92 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20905])).
% 2.73/2.92 tff(20907,plain,
% 2.73/2.92 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20906])).
% 2.73/2.92 tff(20908,plain,
% 2.73/2.92 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20895])).
% 2.73/2.92 tff(20909,plain,
% 2.73/2.92 (r(s(s(s(elem!1))), s(z))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[139, 20908])).
% 2.73/2.92 tff(20910,plain,
% 2.73/2.92 (r(s(s(s(s(z)))), s(z))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20909, 20907])).
% 2.73/2.92 tff(20911,plain,
% 2.73/2.92 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20896])).
% 2.73/2.92 tff(20912,plain,
% 2.73/2.92 (r(s(s(z)), s(z))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20863, 20911])).
% 2.73/2.92 tff(20913,plain,
% 2.73/2.92 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20896])).
% 2.73/2.92 tff(20914,plain,
% 2.73/2.92 (r(s(z), s(s(z)))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20861, 20913])).
% 2.73/2.92 tff(20915,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(20916,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(20917,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20916, 20915])).
% 2.73/2.92 tff(20918,plain,
% 2.73/2.92 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20917, 121, 20914, 20912, 20910])).
% 2.73/2.92 tff(20919,plain,
% 2.73/2.92 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20918, 20904])).
% 2.73/2.92 tff(20920,plain,
% 2.73/2.92 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[681, 20919, 79])).
% 2.73/2.92 tff(20921,plain,
% 2.73/2.92 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20899])).
% 2.73/2.92 tff(20922,plain,
% 2.73/2.92 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20921])).
% 2.73/2.92 tff(20923,plain,
% 2.73/2.92 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20922])).
% 2.73/2.92 tff(20924,plain,
% 2.73/2.92 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20895])).
% 2.73/2.92 tff(20925,plain,
% 2.73/2.92 (b(z, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1397, 20895, 1326])).
% 2.73/2.92 tff(20926,plain,
% 2.73/2.92 (r(s(s(s(z))), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[11593, 20925, 3871, 2207, 10994, 1391])).
% 2.73/2.92 tff(20927,plain,
% 2.73/2.92 (r(s(s(s(z))), s(z))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20926, 20924])).
% 2.73/2.92 tff(20928,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(20929,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(20930,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20929, 20928])).
% 2.73/2.92 tff(20931,plain,
% 2.73/2.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20930, 121, 20914, 20910, 20927])).
% 2.73/2.92 tff(20932,plain,
% 2.73/2.92 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[8812, 20931, 20895])).
% 2.73/2.92 tff(20933,plain,
% 2.73/2.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20932, 20923])).
% 2.73/2.92 tff(20934,plain,
% 2.73/2.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[556, 20933, 1])).
% 2.73/2.92 tff(20935,plain,
% 2.73/2.92 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20896])).
% 2.73/2.92 tff(20936,plain,
% 2.73/2.92 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20935])).
% 2.73/2.92 tff(20937,plain,
% 2.73/2.92 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20900])).
% 2.73/2.92 tff(20938,plain,
% 2.73/2.92 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20937])).
% 2.73/2.92 tff(20939,plain,
% 2.73/2.92 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20896])).
% 2.73/2.92 tff(20940,plain,
% 2.73/2.92 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.92 inference(transitivity,[status(thm)],[20939, 20938, 20936])).
% 2.73/2.92 tff(20941,plain,
% 2.73/2.92 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20896, 20905])).
% 2.73/2.92 tff(20942,plain,
% 2.73/2.92 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.73/2.92 inference(transitivity,[status(thm)],[20941, 10493])).
% 2.73/2.92 tff(20943,plain,
% 2.73/2.92 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20942])).
% 2.73/2.92 tff(20944,plain,
% 2.73/2.92 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20943])).
% 2.73/2.92 tff(20945,plain,
% 2.73/2.92 (s(s(z)) = s(elem!1)),
% 2.73/2.92 inference(symmetry,[status(thm)],[20896])).
% 2.73/2.92 tff(20946,plain,
% 2.73/2.92 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20945])).
% 2.73/2.92 tff(20947,plain,
% 2.73/2.92 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20946])).
% 2.73/2.92 tff(20948,plain,
% 2.73/2.92 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20947])).
% 2.73/2.92 tff(20949,plain,
% 2.73/2.92 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[79, 20948])).
% 2.73/2.92 tff(20950,plain,
% 2.73/2.92 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20949, 20944])).
% 2.73/2.92 tff(20951,plain,
% 2.73/2.92 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20900])).
% 2.73/2.92 tff(20952,plain,
% 2.73/2.92 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20951])).
% 2.73/2.92 tff(20953,plain,
% 2.73/2.92 (b(elem!1, s(s(s(z))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[11114, 20895, 3871])).
% 2.73/2.92 tff(20954,plain,
% 2.73/2.92 (~b(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[9291, 20953, 11211, 1326])).
% 2.73/2.92 tff(20955,plain,
% 2.73/2.92 (r(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[2243, 20954, 2207])).
% 2.73/2.92 tff(20956,plain,
% 2.73/2.92 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[9184, 20955, 139, 20889])).
% 2.73/2.92 tff(20957,plain,
% 2.73/2.92 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20956, 20952])).
% 2.73/2.92 tff(20958,plain,
% 2.73/2.92 (b(s(elem!1), s(s(s(s(z)))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1995, 20957, 20950])).
% 2.73/2.92 tff(20959,plain,
% 2.73/2.92 (b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20958, 20940])).
% 2.73/2.92 tff(20960,plain,
% 2.73/2.92 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[20899, 20896])).
% 2.73/2.92 tff(20961,plain,
% 2.73/2.92 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.73/2.92 inference(symmetry,[status(thm)],[20960])).
% 2.73/2.92 tff(20962,plain,
% 2.73/2.92 (~(s(s(s(z))) = s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[4929, 20860, 3871])).
% 2.73/2.92 tff(20963,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(20964,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(20965,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20964, 20963])).
% 2.73/2.92 tff(20966,plain,
% 2.73/2.92 (~r(s(s(s(z))), s(s(z)))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20965, 121, 20914, 20912, 20927])).
% 2.73/2.92 tff(20967,plain,
% 2.73/2.92 (~r(s(s(s(z))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[10458, 20966, 20895])).
% 2.73/2.92 tff(20968,plain,
% 2.73/2.92 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1816, 20967, 20962])).
% 2.73/2.92 tff(20969,plain,
% 2.73/2.92 (b(s(s(s(z))), s(s(z)))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[14223, 20968, 20895])).
% 2.73/2.92 tff(20970,plain,
% 2.73/2.92 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[20969, 20961])).
% 2.73/2.92 tff(20971,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[5254, 20970, 20959, 20934, 20920])).
% 2.73/2.92 tff(20972,plain,((z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(z))))) | r(s(elem!1), z) | r(z, elem!1) | (~b(z, elem!1)) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(20973,plain,
% 2.73/2.92 (z = elem!1),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20972, 20841, 1, 3871, 10994, 20852, 20859, 1281, 20247, 3407])).
% 2.73/2.92 tff(20974,plain,
% 2.73/2.92 (elem!1 = s(z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20833, 20973, 1, 11211, 3871, 1281, 20245, 3407])).
% 2.73/2.92 tff(20975,plain,
% 2.73/2.92 (b(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[2488, 20973, 11211])).
% 2.73/2.92 tff(20976,plain,
% 2.73/2.92 (~b(elem!1, s(s(s(z))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[9291, 20975, 11211, 20859])).
% 2.73/2.92 tff(20977,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[11114, 20976, 20974, 3871])).
% 2.73/2.92 tff(20978,plain,(r(s(elem!1), z) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(20979,plain,
% 2.73/2.92 (r(s(elem!1), z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20978, 8226, 1, 1281, 20244, 20246])).
% 2.73/2.92 tff(20980,plain,
% 2.73/2.92 (~b(s(elem!1), z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20858, 1391, 199, 3871, 1281, 6842, 3407, 1])).
% 2.73/2.92 tff(20981,plain,
% 2.73/2.92 (b(s(elem!1), z) <=> b(s(z), z)),
% 2.73/2.92 inference(monotonicity,[status(thm)],[9868])).
% 2.73/2.92 tff(20982,plain,
% 2.73/2.92 (b(s(z), z) <=> b(s(elem!1), z)),
% 2.73/2.92 inference(symmetry,[status(thm)],[20981])).
% 2.73/2.92 tff(20983,plain,
% 2.73/2.92 (b(s(elem!1), z)),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[1281, 20982])).
% 2.73/2.92 tff(20984,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[3498, 20983])).
% 2.73/2.92 tff(20985,plain,((~(elem!1 = z)) | b(s(elem!1), z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(20986,plain,
% 2.73/2.92 (~(elem!1 = z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20985, 20980, 1281])).
% 2.73/2.92 tff(20987,plain,
% 2.73/2.92 (~r(s(s(s(z))), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[149, 8716, 147])).
% 2.73/2.92 tff(20988,plain,
% 2.73/2.92 (~b(z, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[10135, 20987, 3871, 2207, 412, 8716])).
% 2.73/2.92 tff(20989,plain,
% 2.73/2.92 (r(z, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[904, 20988])).
% 2.73/2.92 tff(20990,plain,
% 2.73/2.92 (~(s(z) = elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1402, 20988, 1391])).
% 2.73/2.92 tff(20991,plain,
% 2.73/2.92 ((~(elem!1 = z)) <=> (~(z = elem!1))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[360])).
% 2.73/2.92 tff(20992,plain,
% 2.73/2.92 (~(z = elem!1)),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[259, 20991])).
% 2.73/2.92 tff(20993,plain,
% 2.73/2.92 (r(z, elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[355, 199, 20992])).
% 2.73/2.92 tff(20994,plain,
% 2.73/2.92 (~(s(z) = s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[343, 20992])).
% 2.73/2.92 tff(20995,plain,
% 2.73/2.92 (r(elem!1, z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[284, 279, 259])).
% 2.73/2.92 tff(20996,plain,
% 2.73/2.92 (~r(elem!1, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1417, 20995, 909, 412])).
% 2.73/2.92 tff(20997,plain,
% 2.73/2.92 (b(elem!1, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[392, 20996, 377])).
% 2.73/2.92 tff(20998,plain,
% 2.73/2.92 (~(s(z) = elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20120, 279, 1281])).
% 2.73/2.92 tff(20999,plain,
% 2.73/2.92 (~(s(elem!1) = s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[350, 20994])).
% 2.73/2.92 tff(21000,plain,
% 2.73/2.92 (~(elem!1 = s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[242, 20998])).
% 2.73/2.92 tff(21001,plain,
% 2.73/2.92 (~r(s(elem!1), s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1254, 357, 412, 909])).
% 2.73/2.92 tff(21002,plain,
% 2.73/2.92 (b(s(elem!1), s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[429, 21001, 422])).
% 2.73/2.92 tff(21003,plain,
% 2.73/2.92 (~b(elem!1, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1290, 21002, 1281, 307])).
% 2.73/2.92 tff(21004,plain,
% 2.73/2.92 (r(elem!1, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[299, 21003, 258])).
% 2.73/2.92 tff(21005,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[4690, 121, 357, 909, 1409, 21004])).
% 2.73/2.92 tff(21006,plain,((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (elem!1 = s(z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(21007,plain,
% 2.73/2.92 (~r(s(z), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21006, 20995, 909, 21000, 1281, 20997, 20999, 412])).
% 2.73/2.92 tff(21008,plain,
% 2.73/2.92 (b(s(z), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[236, 21007, 20998])).
% 2.73/2.92 tff(21009,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21010,plain,
% 2.73/2.92 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21011,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[21010])).
% 2.73/2.92 tff(21012,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 2.73/2.92 inference(transitivity,[status(thm)],[21011, 21009])).
% 2.73/2.92 tff(21013,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(21014,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[21013, 21012])).
% 2.73/2.92 tff(21015,plain,
% 2.73/2.92 (~r(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21014, 121, 909, 20995, 412])).
% 2.73/2.92 tff(21016,plain,
% 2.73/2.92 (b(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[2243, 21015, 3500])).
% 2.73/2.92 tff(21017,plain,
% 2.73/2.92 (~b(s(z), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[3435, 21008, 20997, 21016])).
% 2.73/2.92 tff(21018,plain,
% 2.73/2.92 (~b(z, elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[5323, 21008, 412, 20997, 909, 20994])).
% 2.73/2.92 tff(21019,plain,
% 2.73/2.92 (r(z, elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[355, 21018, 20992])).
% 2.73/2.92 tff(21020,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[5347, 21019, 21017, 412, 21008, 20997, 3500, 909, 20994])).
% 2.73/2.92 tff(21021,plain,(b(elem!1, z) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(21022,plain,
% 2.73/2.92 (b(elem!1, z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21021, 909, 412, 1281, 377, 259])).
% 2.73/2.92 tff(21023,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21024,plain,
% 2.73/2.92 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21025,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[21024])).
% 2.73/2.92 tff(21026,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 2.73/2.92 inference(transitivity,[status(thm)],[21025, 21023])).
% 2.73/2.92 tff(21027,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(21028,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[21027, 21026])).
% 2.73/2.92 tff(21029,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21028, 271, 260, 1281, 261, 3407])).
% 2.73/2.92 tff(21030,plain,((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(21031,plain,
% 2.73/2.92 (~b(s(z), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21030, 21022, 1281, 3407])).
% 2.73/2.92 tff(21032,plain,
% 2.73/2.92 (r(s(z), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[236, 21031, 231])).
% 2.73/2.92 tff(21033,plain,
% 2.73/2.92 (~b(elem!1, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1305, 21031, 412, 20992, 199, 231, 909])).
% 2.73/2.92 tff(21034,plain,
% 2.73/2.92 (r(elem!1, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[392, 21033, 377])).
% 2.73/2.92 tff(21035,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[3673, 21034, 21032, 20993, 909])).
% 2.73/2.92 tff(21036,plain,((~r(z, s(z))) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (~r(s(elem!1), z)) | b(z, elem!1) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(21037,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21036, 20990, 20989, 412, 199, 219, 1281, 3407, 20986])).
% 2.73/2.92 tff(21038,plain,(r(z, elem!1) | (~r(s(elem!1), z)) | b(z, elem!1) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(21039,plain,
% 2.73/2.92 (r(z, elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21038, 199, 412, 1281, 3407, 20246, 147, 6842, 1])).
% 2.73/2.92 tff(21040,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21041,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(21042,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[21041, 21040])).
% 2.73/2.92 tff(21043,plain,
% 2.73/2.92 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21042, 121, 21039, 412, 6842])).
% 2.73/2.92 tff(21044,plain,
% 2.73/2.92 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[6858, 121, 21039, 412, 6842])).
% 2.73/2.92 tff(21045,plain,
% 2.73/2.92 (b(s(s(s(elem!1))), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[486, 13588, 147])).
% 2.73/2.92 tff(21046,plain,
% 2.73/2.92 (r(z, elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21038, 199, 412, 1281, 3407, 3871, 147, 6842, 1])).
% 2.73/2.92 tff(21047,plain,
% 2.73/2.92 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21042, 121, 21046, 412, 6842])).
% 2.73/2.92 tff(21048,plain,
% 2.73/2.92 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[6858, 121, 21046, 412, 6842])).
% 2.73/2.92 tff(21049,plain,
% 2.73/2.92 (~r(z, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21036, 358, 412, 199, 377, 1281, 3407, 1257])).
% 2.73/2.92 tff(21050,plain,
% 2.73/2.92 (b(z, s(z))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[904, 21049])).
% 2.73/2.92 tff(21051,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21052,plain,
% 2.73/2.92 (((~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(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.92 tff(21053,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.73/2.92 inference(monotonicity,[status(thm)],[21052])).
% 2.73/2.92 tff(21054,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.73/2.92 inference(transitivity,[status(thm)],[21053, 21051])).
% 2.73/2.92 tff(21055,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.73/2.92 inference(quant_inst,[status(thm)],[])).
% 2.73/2.92 tff(21056,plain,
% 2.73/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.73/2.92 inference(modus_ponens,[status(thm)],[21055, 21054])).
% 2.73/2.92 tff(21057,plain,
% 2.73/2.92 ($false),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21056, 271, 1281, 220, 3871, 1935])).
% 2.73/2.92 tff(21058,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.92 tff(21059,plain,
% 2.73/2.92 (~b(s(s(s(z))), z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[21058, 21050, 1281, 3871])).
% 2.73/2.92 tff(21060,plain,
% 2.73/2.92 (r(s(s(s(z))), z)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1155, 21059])).
% 2.73/2.92 tff(21061,plain,
% 2.73/2.92 (~r(s(s(s(z))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[3650, 21060, 412, 378])).
% 2.73/2.92 tff(21062,plain,
% 2.73/2.92 (~b(elem!1, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[13943, 21061, 3407, 378, 344, 504, 11148, 676])).
% 2.73/2.92 tff(21063,plain,
% 2.73/2.92 (r(elem!1, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[392, 21062, 377])).
% 2.73/2.92 tff(21064,plain,
% 2.73/2.92 (~b(z, s(s(s(z))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[20322, 21063, 199, 331, 3871, 1281, 21060])).
% 2.73/2.92 tff(21065,plain,
% 2.73/2.92 (~r(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[3683, 21063, 412, 378])).
% 2.73/2.92 tff(21066,plain,
% 2.73/2.92 (b(s(elem!1), elem!1)),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[2243, 21065, 3500])).
% 2.73/2.92 tff(21067,plain,
% 2.73/2.92 (~r(s(s(s(z))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[3650, 109, 412, 378])).
% 2.73/2.92 tff(21068,plain,
% 2.73/2.92 (~r(z, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[12090, 379, 378, 412])).
% 2.73/2.92 tff(21069,plain,
% 2.73/2.92 (b(z, s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1439, 21068])).
% 2.73/2.92 tff(21070,plain,
% 2.73/2.92 (~(s(s(s(z))) = s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[16218, 21069, 1209])).
% 2.73/2.92 tff(21071,plain,
% 2.73/2.92 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[1816, 21070, 21067])).
% 2.73/2.92 tff(21072,plain,
% 2.73/2.92 (~(s(elem!1) = s(s(s(z))))),
% 2.73/2.92 inference(unit_resolution,[status(thm)],[2035, 21070])).
% 2.73/2.92 tff(21073,plain,
% 2.73/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 2.73/2.92 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21074,plain,
% 2.73/2.93 (((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21075,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21074])).
% 2.73/2.93 tff(21076,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 2.73/2.93 inference(transitivity,[status(thm)],[21075, 21073])).
% 2.73/2.93 tff(21077,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.73/2.93 inference(quant_inst,[status(thm)],[])).
% 2.73/2.93 tff(21078,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21077, 21076])).
% 2.73/2.93 tff(21079,plain,
% 2.73/2.93 (~r(s(elem!1), s(s(s(z))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21078, 121, 378, 412, 109])).
% 2.73/2.93 tff(21080,plain,
% 2.73/2.93 (b(s(elem!1), s(s(s(z))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2044, 21079, 21072])).
% 2.73/2.93 tff(21081,plain,
% 2.73/2.93 (~b(s(z), s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[3879, 21080, 3871, 257])).
% 2.73/2.93 tff(21082,plain,
% 2.73/2.93 (r(s(z), s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[444, 21081, 348])).
% 2.73/2.93 tff(21083,plain,
% 2.73/2.93 (~r(elem!1, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[3709, 21082, 412, 379])).
% 2.73/2.93 tff(21084,plain,
% 2.73/2.93 (b(elem!1, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[299, 21083, 258])).
% 2.73/2.93 tff(21085,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21086,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))),
% 2.73/2.93 inference(quant_inst,[status(thm)],[])).
% 2.73/2.93 tff(21087,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21086, 21085])).
% 2.73/2.93 tff(21088,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21087, 271, 2618, 21084, 21071, 257])).
% 2.73/2.93 tff(21089,plain,((~r(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21090,plain,
% 2.73/2.93 (~b(s(s(s(z))), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21089, 21066, 412, 258, 21063, 344, 3871, 378, 21060, 21064])).
% 2.73/2.93 tff(21091,plain,
% 2.73/2.93 (~r(z, s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[12090, 21063, 412, 378])).
% 2.73/2.93 tff(21092,plain,
% 2.73/2.93 (b(z, s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[1439, 21091])).
% 2.73/2.93 tff(21093,plain,
% 2.73/2.93 (~(s(s(s(z))) = s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[16218, 21092, 21064])).
% 2.73/2.93 tff(21094,plain,
% 2.73/2.93 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[1816, 21093, 21061])).
% 2.73/2.93 tff(21095,plain,
% 2.73/2.93 (~(s(s(s(z))) = elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[6165, 21094, 21062])).
% 2.73/2.93 tff(21096,plain,
% 2.73/2.93 (r(s(s(s(z))), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[255, 21095, 21090])).
% 2.73/2.93 tff(21097,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[10254, 121, 21063, 378, 21096, 21060])).
% 2.73/2.93 tff(21098,plain,((z = elem!1) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(z))))) | b(z, elem!1) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21099,plain,
% 2.73/2.93 (z = elem!1),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21098, 258, 412, 21046, 3871, 199, 1281, 219, 3407, 21045, 21048, 21047])).
% 2.73/2.93 tff(21100,plain,
% 2.73/2.93 (~b(s(elem!1), z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[20833, 21099, 1, 258, 3871, 1281, 6842, 3407])).
% 2.73/2.93 tff(21101,plain,
% 2.73/2.93 (~(elem!1 = z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[20985, 21100, 1281])).
% 2.73/2.93 tff(21102,plain,
% 2.73/2.93 (~r(s(s(s(z))), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[149, 21099, 147])).
% 2.73/2.93 tff(21103,plain,
% 2.73/2.93 (~b(z, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[10135, 21102, 3871, 2207, 412, 21099])).
% 2.73/2.93 tff(21104,plain,
% 2.73/2.93 (r(z, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[904, 21103])).
% 2.73/2.93 tff(21105,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21036, 21104, 21101, 412, 199, 219, 1281, 3407, 1257])).
% 2.73/2.93 tff(21106,plain,((elem!1 = s(z)) | (~r(s(elem!1), z)) | b(z, elem!1) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21107,plain,
% 2.73/2.93 (elem!1 = s(z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21106, 199, 412, 1281, 3407, 20246, 1, 6842, 147])).
% 2.73/2.93 tff(21108,plain,
% 2.73/2.93 (s(z) = elem!1),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[242, 21107])).
% 2.73/2.93 tff(21109,plain,
% 2.73/2.93 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21108])).
% 2.73/2.93 tff(21110,plain,
% 2.73/2.93 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21109])).
% 2.73/2.93 tff(21111,plain,
% 2.73/2.93 (~(elem!1 = s(s(elem!1)))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[2137, 21110])).
% 2.73/2.93 tff(21112,plain,
% 2.73/2.93 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[78, 21111])).
% 2.73/2.93 tff(21113,plain,
% 2.73/2.93 (~b(elem!1, s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[11152, 21112, 21045, 21044, 21043])).
% 2.73/2.93 tff(21114,plain,
% 2.73/2.93 (r(elem!1, s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[392, 21113, 219])).
% 2.73/2.93 tff(21115,plain,
% 2.73/2.93 (s(s(z)) = s(elem!1)),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21108])).
% 2.73/2.93 tff(21116,plain,
% 2.73/2.93 (s(s(s(z))) = s(s(elem!1))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21115])).
% 2.73/2.93 tff(21117,plain,
% 2.73/2.93 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21116])).
% 2.73/2.93 tff(21118,plain,
% 2.73/2.93 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21117])).
% 2.73/2.93 tff(21119,plain,
% 2.73/2.93 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21108])).
% 2.73/2.93 tff(21120,plain,
% 2.73/2.93 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21119])).
% 2.73/2.93 tff(21121,plain,
% 2.73/2.93 (~r(elem!1, s(s(s(z))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[100, 21120])).
% 2.73/2.93 tff(21122,plain,
% 2.73/2.93 (~r(elem!1, s(s(elem!1)))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21121, 21118])).
% 2.73/2.93 tff(21123,plain,
% 2.73/2.93 (~b(s(elem!1), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[10472, 21112, 21043, 21045, 21122])).
% 2.73/2.93 tff(21124,plain,
% 2.73/2.93 (r(s(elem!1), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2243, 21123, 2207])).
% 2.73/2.93 tff(21125,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[3683, 21124, 21114, 412, 21039])).
% 2.73/2.93 tff(21126,plain,(b(z, elem!1) | (~r(s(elem!1), z)) | r(s(z), s(s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21127,plain,
% 2.73/2.93 (b(z, elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21126, 147, 100, 1281, 20244, 1, 20245, 20979])).
% 2.73/2.93 tff(21128,plain,
% 2.73/2.93 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.73/2.93 inference(monotonicity,[status(thm)],[2505])).
% 2.73/2.93 tff(21129,plain,
% 2.73/2.93 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.73/2.93 inference(transitivity,[status(thm)],[21128, 360])).
% 2.73/2.93 tff(21130,plain,
% 2.73/2.93 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.73/2.93 inference(transitivity,[status(thm)],[21129, 361])).
% 2.73/2.93 tff(21131,plain,
% 2.73/2.93 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21130])).
% 2.73/2.93 tff(21132,plain,
% 2.73/2.93 (~(elem!1 = z)),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[30, 21131])).
% 2.73/2.93 tff(21133,plain,
% 2.73/2.93 (r(s(elem!1), z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[20978, 8226, 1, 1281, 3407, 20246])).
% 2.73/2.93 tff(21134,plain,
% 2.73/2.93 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[15292])).
% 2.73/2.93 tff(21135,plain,
% 2.73/2.93 (~b(elem!1, z)),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[8226, 21134])).
% 2.73/2.93 tff(21136,plain,
% 2.73/2.93 (~r(z, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21021, 21135, 21133, 1281, 219, 21132])).
% 2.73/2.93 tff(21137,plain,
% 2.73/2.93 (b(z, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[904, 21136])).
% 2.73/2.93 tff(21138,plain,
% 2.73/2.93 (~b(s(s(s(z))), z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21058, 21137, 1281, 20246])).
% 2.73/2.93 tff(21139,plain,
% 2.73/2.93 (r(s(s(s(z))), z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[1155, 21138])).
% 2.73/2.93 tff(21140,plain,
% 2.73/2.93 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[15278])).
% 2.73/2.93 tff(21141,plain,
% 2.73/2.93 (~(elem!1 = s(s(elem!1)))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[1, 21140])).
% 2.73/2.93 tff(21142,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21143,plain,
% 2.73/2.93 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21144,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21143])).
% 2.73/2.93 tff(21145,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.73/2.93 inference(transitivity,[status(thm)],[21144, 21142])).
% 2.73/2.93 tff(21146,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.73/2.93 inference(quant_inst,[status(thm)],[])).
% 2.73/2.93 tff(21147,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21146, 21145])).
% 2.73/2.93 tff(21148,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21147, 271, 1281, 1307, 3871, 222])).
% 2.73/2.93 tff(21149,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21150,plain,
% 2.73/2.93 (~b(s(s(s(z))), s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21149, 1307, 1281, 20246])).
% 2.73/2.93 tff(21151,plain,
% 2.73/2.93 (r(s(s(s(z))), s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2325, 21150])).
% 2.73/2.93 tff(21152,plain,
% 2.73/2.93 (~b(s(s(s(z))), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[19416, 1307, 1281, 3871])).
% 2.73/2.93 tff(21153,plain,
% 2.73/2.93 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[19817, 1307, 1281, 3871])).
% 2.73/2.93 tff(21154,plain,
% 2.73/2.93 (b(z, elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[4220, 221, 3871, 1281, 1307])).
% 2.73/2.93 tff(21155,plain,
% 2.73/2.93 (s(s(s(z))) = elem!1),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[255, 221, 21152])).
% 2.73/2.93 tff(21156,plain,
% 2.73/2.93 (b(s(z), elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[10599, 21155, 3871])).
% 2.73/2.93 tff(21157,plain,
% 2.73/2.93 (~b(elem!1, z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[3964, 21156, 21154, 1281])).
% 2.73/2.93 tff(21158,plain,
% 2.73/2.93 (~r(z, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21021, 21157, 412, 1281, 219, 259])).
% 2.73/2.93 tff(21159,plain,
% 2.73/2.93 (b(z, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[904, 21158])).
% 2.73/2.93 tff(21160,plain,
% 2.73/2.93 (r(elem!1, z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[284, 21157, 259])).
% 2.73/2.93 tff(21161,plain,
% 2.73/2.93 (~b(s(s(s(z))), s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21149, 1307, 1281, 3871])).
% 2.73/2.93 tff(21162,plain,
% 2.73/2.93 (r(s(s(s(z))), s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2325, 21161])).
% 2.73/2.93 tff(21163,plain,
% 2.73/2.93 (~b(elem!1, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[4760, 21156, 1281, 21154])).
% 2.73/2.93 tff(21164,plain,
% 2.73/2.93 (~(s(z) = elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[20120, 21157, 1281])).
% 2.73/2.93 tff(21165,plain,
% 2.73/2.93 (~(elem!1 = s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[242, 21164])).
% 2.73/2.93 tff(21166,plain,
% 2.73/2.93 (r(elem!1, s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[299, 21165, 21163])).
% 2.73/2.93 tff(21167,plain,
% 2.73/2.93 (s(s(s(z))) = elem!1),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[255, 221, 2346])).
% 2.73/2.93 tff(21168,plain,
% 2.73/2.93 (s(elem!1) = s(s(s(s(z))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2605, 21167])).
% 2.73/2.93 tff(21169,plain,
% 2.73/2.93 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21168])).
% 2.73/2.93 tff(21170,plain,
% 2.73/2.93 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21169])).
% 2.73/2.93 tff(21171,plain,
% 2.73/2.93 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.73/2.93 inference(symmetry,[status(thm)],[21170])).
% 2.73/2.93 tff(21172,plain,
% 2.73/2.93 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21167])).
% 2.73/2.93 tff(21173,plain,
% 2.73/2.93 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.73/2.93 inference(transitivity,[status(thm)],[21172, 1836])).
% 2.73/2.93 tff(21174,plain,
% 2.73/2.93 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21173])).
% 2.73/2.93 tff(21175,plain,
% 2.73/2.93 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[1489, 21174])).
% 2.73/2.93 tff(21176,plain,
% 2.73/2.93 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21167])).
% 2.73/2.93 tff(21177,plain,
% 2.73/2.93 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.93 inference(symmetry,[status(thm)],[21176])).
% 2.73/2.93 tff(21178,plain,
% 2.73/2.93 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21169])).
% 2.73/2.93 tff(21179,plain,
% 2.73/2.93 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.93 inference(transitivity,[status(thm)],[21178, 21177])).
% 2.73/2.93 tff(21180,plain,
% 2.73/2.93 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[624, 21179])).
% 2.73/2.93 tff(21181,plain,
% 2.73/2.93 (~b(elem!1, s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[9079, 260, 1326, 220])).
% 2.73/2.93 tff(21182,plain,
% 2.73/2.93 (r(elem!1, s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[392, 21181, 219])).
% 2.73/2.93 tff(21183,plain,
% 2.73/2.93 (~r(z, s(s(elem!1)))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[17642, 21182, 1409, 412])).
% 2.73/2.93 tff(21184,plain,
% 2.73/2.93 (b(z, s(s(elem!1)))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2106, 21183])).
% 2.73/2.93 tff(21185,plain,
% 2.73/2.93 (~(s(s(s(elem!1))) = elem!1)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2611, 21167])).
% 2.73/2.93 tff(21186,plain,
% 2.73/2.93 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21167])).
% 2.73/2.93 tff(21187,plain,
% 2.73/2.93 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21186])).
% 2.73/2.93 tff(21188,plain,
% 2.73/2.93 (~b(elem!1, s(s(s(elem!1))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[2066, 21187])).
% 2.73/2.93 tff(21189,plain,
% 2.73/2.93 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21167])).
% 2.73/2.93 tff(21190,plain,
% 2.73/2.93 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21189])).
% 2.73/2.93 tff(21191,plain,
% 2.73/2.93 (s(s(s(s(z)))) = s(elem!1)),
% 2.73/2.93 inference(symmetry,[status(thm)],[21168])).
% 2.73/2.93 tff(21192,plain,
% 2.73/2.93 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21191])).
% 2.73/2.93 tff(21193,plain,
% 2.73/2.93 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.73/2.93 inference(symmetry,[status(thm)],[21192])).
% 2.73/2.93 tff(21194,plain,
% 2.73/2.93 (r(elem!1, s(s(s(s(z)))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21182, 21193])).
% 2.73/2.93 tff(21195,plain,
% 2.73/2.93 (~r(s(z), s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[3709, 21182, 412, 3456])).
% 2.73/2.93 tff(21196,plain,
% 2.73/2.93 (b(s(z), s(elem!1))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[444, 21195, 348])).
% 2.73/2.93 tff(21197,plain,
% 2.73/2.93 (b(s(z), s(s(s(s(z)))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[9597, 21168, 21196])).
% 2.73/2.93 tff(21198,plain,
% 2.73/2.93 (elem!1 = s(s(s(z)))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21167, 159])).
% 2.73/2.93 tff(21199,plain,
% 2.73/2.93 (~b(s(s(s(z))), z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21058, 220, 1281, 3871])).
% 2.73/2.93 tff(21200,plain,
% 2.73/2.93 (r(s(s(s(z))), z)),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[1155, 21199])).
% 2.73/2.93 tff(21201,plain,
% 2.73/2.93 (s(s(s(z))) = elem!1),
% 2.73/2.93 inference(symmetry,[status(thm)],[1097])).
% 2.73/2.93 tff(21202,plain,
% 2.73/2.93 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21201])).
% 2.73/2.93 tff(21203,plain,
% 2.73/2.93 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.93 inference(symmetry,[status(thm)],[21202])).
% 2.73/2.93 tff(21204,plain,
% 2.73/2.93 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[16461, 21203])).
% 2.73/2.93 tff(21205,plain,
% 2.73/2.93 (s(s(s(z))) = elem!1),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[1100, 1097])).
% 2.73/2.93 tff(21206,plain,
% 2.73/2.93 (s(elem!1) = s(s(s(s(z))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2605, 21205])).
% 2.73/2.93 tff(21207,plain,
% 2.73/2.93 (s(s(s(s(z)))) = s(elem!1)),
% 2.73/2.93 inference(symmetry,[status(thm)],[21206])).
% 2.73/2.93 tff(21208,plain,
% 2.73/2.93 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21207])).
% 2.73/2.93 tff(21209,plain,
% 2.73/2.93 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 2.73/2.93 inference(symmetry,[status(thm)],[21208])).
% 2.73/2.93 tff(21210,plain,
% 2.73/2.93 (r(s(s(s(s(z)))), z)),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[412, 21209])).
% 2.73/2.93 tff(21211,plain,
% 2.73/2.93 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[11616, 121, 109, 1518])).
% 2.73/2.93 tff(21212,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21211, 21210, 21204])).
% 2.73/2.93 tff(21213,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21214,plain,
% 2.73/2.93 (~r(z, s(s(s(s(z)))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21213, 21194, 412, 21200, 21198])).
% 2.73/2.93 tff(21215,plain,
% 2.73/2.93 (b(z, s(s(s(s(z)))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[1121, 21214])).
% 2.73/2.93 tff(21216,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21217,plain,
% 2.73/2.93 (((~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(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21218,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z))))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21217])).
% 2.73/2.93 tff(21219,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))))),
% 2.73/2.93 inference(transitivity,[status(thm)],[21218, 21216])).
% 2.73/2.93 tff(21220,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.73/2.93 inference(quant_inst,[status(thm)],[])).
% 2.73/2.93 tff(21221,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21220, 21219])).
% 2.73/2.93 tff(21222,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21221, 271, 1281, 1067, 1157, 937])).
% 2.73/2.93 tff(21223,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21224,plain,
% 2.73/2.93 (~b(s(s(s(s(z)))), s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21223, 21215, 1281, 21197])).
% 2.73/2.93 tff(21225,plain,
% 2.73/2.93 (r(s(s(s(s(z)))), s(z))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[932, 21224])).
% 2.73/2.93 tff(21226,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21227,plain,
% 2.73/2.93 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21228,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21227])).
% 2.73/2.93 tff(21229,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.73/2.93 inference(transitivity,[status(thm)],[21228, 21226])).
% 2.73/2.93 tff(21230,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.73/2.93 inference(quant_inst,[status(thm)],[])).
% 2.73/2.93 tff(21231,plain,
% 2.73/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21230, 21229])).
% 2.73/2.93 tff(21232,plain,
% 2.73/2.93 ($false),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21231, 121, 572, 3456, 911, 16461])).
% 2.73/2.93 tff(21233,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.93 tff(21234,plain,
% 2.73/2.93 (~r(s(z), s(s(s(elem!1))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[21233, 21225, 3456, 21194])).
% 2.73/2.93 tff(21235,plain,
% 2.73/2.93 (b(s(z), s(s(s(elem!1))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[760, 21234])).
% 2.73/2.93 tff(21236,plain,
% 2.73/2.93 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[16071, 21235, 220, 3407])).
% 2.73/2.93 tff(21237,plain,
% 2.73/2.93 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.93 inference(modus_ponens,[status(thm)],[21236, 21190])).
% 2.73/2.93 tff(21238,plain,
% 2.73/2.93 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[671, 21237, 624, 21188, 21185])).
% 2.73/2.93 tff(21239,plain,
% 2.73/2.93 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[556, 21238, 1])).
% 2.73/2.93 tff(21240,plain,
% 2.73/2.93 (~b(s(z), s(s(elem!1)))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[19354, 21239, 1281, 21184])).
% 2.73/2.93 tff(21241,plain,
% 2.73/2.93 (r(s(z), s(s(elem!1)))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[2167, 21240])).
% 2.73/2.93 tff(21242,plain,
% 2.73/2.93 (r(s(z), s(s(s(s(s(z))))))),
% 2.73/2.93 inference(unit_resolution,[status(thm)],[9700, 21241, 21168])).
% 2.73/2.93 tff(21243,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21244,plain,
% 2.73/2.93 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.73/2.93 inference(rewrite,[status(thm)],[])).
% 2.73/2.93 tff(21245,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.73/2.93 inference(monotonicity,[status(thm)],[21244])).
% 2.73/2.93 tff(21246,plain,
% 2.73/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21245, 21243])).
% 2.73/2.94 tff(21247,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(21248,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21247, 21246])).
% 2.73/2.94 tff(21249,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21248, 121, 3061, 1477, 2327, 1735])).
% 2.73/2.94 tff(21250,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21251,plain,
% 2.73/2.94 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21250, 21242, 2327, 21180])).
% 2.73/2.94 tff(21252,plain,
% 2.73/2.94 (b(s(s(s(s(s(z))))), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[840, 21251, 21175])).
% 2.73/2.94 tff(21253,plain,
% 2.73/2.94 (b(s(s(elem!1)), elem!1)),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21252, 21171])).
% 2.73/2.94 tff(21254,plain,
% 2.73/2.94 (b(elem!1, s(s(s(z)))) <=> b(elem!1, elem!1)),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21167])).
% 2.73/2.94 tff(21255,plain,
% 2.73/2.94 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(z))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21254])).
% 2.73/2.94 tff(21256,plain,
% 2.73/2.94 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(z)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21255])).
% 2.73/2.94 tff(21257,plain,
% 2.73/2.94 (~b(elem!1, s(s(s(z))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[192, 21256])).
% 2.73/2.94 tff(21258,plain,
% 2.73/2.94 (r(elem!1, s(s(s(z)))) <=> r(elem!1, elem!1)),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21167])).
% 2.73/2.94 tff(21259,plain,
% 2.73/2.94 (r(elem!1, elem!1) <=> r(elem!1, s(s(s(z))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21258])).
% 2.73/2.94 tff(21260,plain,
% 2.73/2.94 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(s(s(z)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21259])).
% 2.73/2.94 tff(21261,plain,
% 2.73/2.94 (~r(elem!1, s(s(s(z))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[9971, 21260])).
% 2.73/2.94 tff(21262,plain,
% 2.73/2.94 (r(s(s(s(elem!1))), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[484, 21, 21185, 21237])).
% 2.73/2.94 tff(21263,plain,
% 2.73/2.94 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[671, 624, 657, 479, 481])).
% 2.73/2.94 tff(21264,plain,
% 2.73/2.94 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[5852, 624, 3456, 750, 638])).
% 2.73/2.94 tff(21265,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[556, 21264, 21263, 1])).
% 2.73/2.94 tff(21266,plain,((~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21267,plain,
% 2.73/2.94 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21266, 21237, 3456, 1, 624, 21188, 21235, 21185])).
% 2.73/2.94 tff(21268,plain,
% 2.73/2.94 (r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[681, 21267, 82])).
% 2.73/2.94 tff(21269,plain,
% 2.73/2.94 (~r(s(elem!1), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[3888, 21268, 3456, 21262])).
% 2.73/2.94 tff(21270,plain,
% 2.73/2.94 (b(s(elem!1), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2243, 21269, 2207])).
% 2.73/2.94 tff(21271,plain,
% 2.73/2.94 (elem!1 = s(s(s(z)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1192, 10297, 11112])).
% 2.73/2.94 tff(21272,plain,
% 2.73/2.94 (s(s(s(z))) = elem!1),
% 2.73/2.94 inference(symmetry,[status(thm)],[21271])).
% 2.73/2.94 tff(21273,plain,
% 2.73/2.94 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21272])).
% 2.73/2.94 tff(21274,plain,
% 2.73/2.94 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21273])).
% 2.73/2.94 tff(21275,plain,
% 2.73/2.94 (s(s(s(z))) = elem!1),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1100, 21271])).
% 2.73/2.94 tff(21276,plain,
% 2.73/2.94 (s(elem!1) = s(s(s(s(z))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2605, 21275])).
% 2.73/2.94 tff(21277,plain,
% 2.73/2.94 (s(s(s(s(z)))) = s(elem!1)),
% 2.73/2.94 inference(symmetry,[status(thm)],[21276])).
% 2.73/2.94 tff(21278,plain,
% 2.73/2.94 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(elem!1))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21271, 21277])).
% 2.73/2.94 tff(21279,plain,
% 2.73/2.94 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21278])).
% 2.73/2.94 tff(21280,plain,
% 2.73/2.94 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21271])).
% 2.73/2.94 tff(21281,plain,
% 2.73/2.94 (r(s(s(s(z))), s(elem!1))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[379, 21280])).
% 2.73/2.94 tff(21282,plain,
% 2.73/2.94 (r(elem!1, s(s(s(s(z)))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21281, 21279])).
% 2.73/2.94 tff(21283,plain,
% 2.73/2.94 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21282, 21274])).
% 2.73/2.94 tff(21284,plain,
% 2.73/2.94 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21271])).
% 2.73/2.94 tff(21285,plain,
% 2.73/2.94 (r(s(s(s(z))), s(z))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[3456, 21284])).
% 2.73/2.94 tff(21286,plain,
% 2.73/2.94 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21276])).
% 2.73/2.94 tff(21287,plain,
% 2.73/2.94 (~r(s(z), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[3709, 3456, 412, 379])).
% 2.73/2.94 tff(21288,plain,
% 2.73/2.94 (b(s(z), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[444, 21287, 348])).
% 2.73/2.94 tff(21289,plain,
% 2.73/2.94 (b(s(z), s(s(s(s(z)))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21288, 21286])).
% 2.73/2.94 tff(21290,plain,
% 2.73/2.94 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21271])).
% 2.73/2.94 tff(21291,plain,
% 2.73/2.94 (r(s(s(s(z))), z)),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[1409, 21290])).
% 2.73/2.94 tff(21292,plain,
% 2.73/2.94 (~r(z, s(s(s(s(z)))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21213, 21291, 412, 21282, 21271])).
% 2.73/2.94 tff(21293,plain,
% 2.73/2.94 (b(z, s(s(s(s(z)))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1119, 21, 21292, 1114])).
% 2.73/2.94 tff(21294,plain,
% 2.73/2.94 (~b(s(s(s(s(z)))), s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21223, 21293, 1281, 21289])).
% 2.73/2.94 tff(21295,plain,
% 2.73/2.94 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21277])).
% 2.73/2.94 tff(21296,plain,
% 2.73/2.94 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21295, 345])).
% 2.73/2.94 tff(21297,plain,
% 2.73/2.94 ((s(z) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21296])).
% 2.73/2.94 tff(21298,plain,
% 2.73/2.94 ((~(s(z) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21297])).
% 2.73/2.94 tff(21299,plain,
% 2.73/2.94 (~(s(s(s(s(z)))) = s(z))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[348, 21298])).
% 2.73/2.94 tff(21300,plain,
% 2.73/2.94 (r(s(s(s(s(z)))), s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[930, 21, 21299, 21294])).
% 2.73/2.94 tff(21301,plain,
% 2.73/2.94 (~(elem!1 = s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[3790, 479, 2618])).
% 2.73/2.94 tff(21302,plain,
% 2.73/2.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[78, 21301])).
% 2.73/2.94 tff(21303,plain,
% 2.73/2.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[614, 21302])).
% 2.73/2.94 tff(21304,plain,
% 2.73/2.94 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21271])).
% 2.73/2.94 tff(21305,plain,
% 2.73/2.94 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21304])).
% 2.73/2.94 tff(21306,plain,
% 2.73/2.94 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21305])).
% 2.73/2.94 tff(21307,plain,
% 2.73/2.94 (b(z, s(s(s(z))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[6548, 21275, 1326])).
% 2.73/2.94 tff(21308,plain,
% 2.73/2.94 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[19817, 21307, 1281, 3871])).
% 2.73/2.94 tff(21309,plain,
% 2.73/2.94 (~b(elem!1, s(s(s(elem!1))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21308, 21306])).
% 2.73/2.94 tff(21310,plain,
% 2.73/2.94 (~(s(s(s(elem!1))) = elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[10306, 10297, 221, 3871, 9149, 260])).
% 2.73/2.94 tff(21311,plain,
% 2.73/2.94 (~(s(elem!1) = s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[210, 21303])).
% 2.73/2.94 tff(21312,plain,
% 2.73/2.94 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21276])).
% 2.73/2.94 tff(21313,plain,
% 2.73/2.94 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21271])).
% 2.73/2.94 tff(21314,plain,
% 2.73/2.94 (b(s(elem!1), s(s(s(z))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[2618, 21313])).
% 2.73/2.94 tff(21315,plain,
% 2.73/2.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21314, 21312])).
% 2.73/2.94 tff(21316,plain,
% 2.73/2.94 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21206])).
% 2.73/2.94 tff(21317,plain,
% 2.73/2.94 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21316])).
% 2.73/2.94 tff(21318,plain,
% 2.73/2.94 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[1097])).
% 2.73/2.94 tff(21319,plain,
% 2.73/2.94 (b(s(s(elem!1)), s(s(s(z))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[542, 21318])).
% 2.73/2.94 tff(21320,plain,
% 2.73/2.94 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21319, 21317])).
% 2.73/2.94 tff(21321,plain,
% 2.73/2.94 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21316])).
% 2.73/2.94 tff(21322,plain,
% 2.73/2.94 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[1097])).
% 2.73/2.94 tff(21323,plain,
% 2.73/2.94 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21322, 21321])).
% 2.73/2.94 tff(21324,plain,
% 2.73/2.94 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[588, 21323])).
% 2.73/2.94 tff(21325,plain,
% 2.73/2.94 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21316])).
% 2.73/2.94 tff(21326,plain,
% 2.73/2.94 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21325])).
% 2.73/2.94 tff(21327,plain,
% 2.73/2.94 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21326])).
% 2.73/2.94 tff(21328,plain,
% 2.73/2.94 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21206])).
% 2.73/2.94 tff(21329,plain,
% 2.73/2.94 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21328, 21327])).
% 2.73/2.94 tff(21330,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21331,plain,
% 2.73/2.94 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21332,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21331])).
% 2.73/2.94 tff(21333,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21332, 21330])).
% 2.73/2.94 tff(21334,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(21335,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21334, 21333])).
% 2.73/2.94 tff(21336,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21335, 271, 260, 588, 542, 981])).
% 2.73/2.94 tff(21337,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21338,plain,
% 2.73/2.94 (~b(s(s(elem!1)), s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21337, 588, 260, 542])).
% 2.73/2.94 tff(21339,plain,
% 2.73/2.94 (r(s(s(elem!1)), s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2143, 21338])).
% 2.73/2.94 tff(21340,plain,
% 2.73/2.94 (~b(z, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2222, 588, 1326, 542])).
% 2.73/2.94 tff(21341,plain,
% 2.73/2.94 (r(z, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2106, 21340])).
% 2.73/2.94 tff(21342,plain,
% 2.73/2.94 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[5431, 21341, 412, 21339])).
% 2.73/2.94 tff(21343,plain,
% 2.73/2.94 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[526, 21342, 216])).
% 2.73/2.94 tff(21344,plain,
% 2.73/2.94 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21343, 21329])).
% 2.73/2.94 tff(21345,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21346,plain,
% 2.73/2.94 (((~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(s(s(z)))), s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21347,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21346])).
% 2.73/2.94 tff(21348,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21347, 21345])).
% 2.73/2.94 tff(21349,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(21350,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21349, 21348])).
% 2.73/2.94 tff(21351,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21350, 271, 21344, 21324, 21320, 13508])).
% 2.73/2.94 tff(21352,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21353,plain,
% 2.73/2.94 (~b(elem!1, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21352, 21315, 21271, 21311, 412, 260, 542, 1326])).
% 2.73/2.94 tff(21354,plain,
% 2.73/2.94 (r(elem!1, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[599, 21353, 21301])).
% 2.73/2.94 tff(21355,plain,
% 2.73/2.94 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[671, 21354, 479, 21310, 21309])).
% 2.73/2.94 tff(21356,plain,
% 2.73/2.94 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[556, 21355, 21303])).
% 2.73/2.94 tff(21357,plain,
% 2.73/2.94 (r(s(s(s(elem!1))), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[486, 21310, 479])).
% 2.73/2.94 tff(21358,plain,
% 2.73/2.94 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21276])).
% 2.73/2.94 tff(21359,plain,
% 2.73/2.94 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 2.73/2.94 inference(symmetry,[status(thm)],[21358])).
% 2.73/2.94 tff(21360,plain,
% 2.73/2.94 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(elem!1)))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21359])).
% 2.73/2.94 tff(21361,plain,
% 2.73/2.94 (~r(z, s(elem!1))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21292, 21360])).
% 2.73/2.94 tff(21362,plain,
% 2.73/2.94 (b(z, s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1439, 21361])).
% 2.73/2.94 tff(21363,plain,
% 2.73/2.94 (~b(s(elem!1), s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2905, 21362, 21288, 1281])).
% 2.73/2.94 tff(21364,plain,
% 2.73/2.94 (r(s(elem!1), s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[526, 21363, 21311])).
% 2.73/2.94 tff(21365,plain,
% 2.73/2.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[11463, 21364, 379, 21357])).
% 2.73/2.94 tff(21366,plain,
% 2.73/2.94 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[681, 21365, 21302])).
% 2.73/2.94 tff(21367,plain,
% 2.73/2.94 (~b(s(z), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[5852, 21366, 3456, 21354, 21356])).
% 2.73/2.94 tff(21368,plain,
% 2.73/2.94 (r(s(z), s(s(s(elem!1))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[760, 21367])).
% 2.73/2.94 tff(21369,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~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)))))))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21370,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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)))))))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(21371,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21370, 21369])).
% 2.73/2.94 tff(21372,plain,
% 2.73/2.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21371, 121, 21368, 21300, 21285])).
% 2.73/2.94 tff(21373,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21372, 21283])).
% 2.73/2.94 tff(21374,plain,(r(elem!1, s(s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(z), z)) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | r(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21375,plain,
% 2.73/2.94 (~b(s(s(elem!1)), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21374, 21270, 1281, 21182, 412, 3456, 260, 21261, 1326, 3871, 348, 1409, 21237, 221, 21257])).
% 2.73/2.94 tff(21376,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21375, 21253])).
% 2.73/2.94 tff(21377,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21378,plain,
% 2.73/2.94 (~r(elem!1, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21377, 21166, 1281, 412, 21162, 221, 21154, 3871, 20994, 21156, 79, 1, 21160, 21159, 3407, 21153, 21152])).
% 2.73/2.94 tff(21379,plain,
% 2.73/2.94 (b(elem!1, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[599, 21378, 68])).
% 2.73/2.94 tff(21380,plain,
% 2.73/2.94 (~b(elem!1, s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[9079, 21159, 21154, 21156])).
% 2.73/2.94 tff(21381,plain,
% 2.73/2.94 (r(elem!1, s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[392, 21380, 219])).
% 2.73/2.94 tff(21382,plain,
% 2.73/2.94 (~r(z, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[17642, 21381, 21160, 412])).
% 2.73/2.94 tff(21383,plain,
% 2.73/2.94 (b(z, s(s(elem!1)))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2106, 21382])).
% 2.73/2.94 tff(21384,plain,
% 2.73/2.94 (~r(s(z), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[3709, 21381, 412, 21166])).
% 2.73/2.94 tff(21385,plain,
% 2.73/2.94 (b(s(z), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[444, 21384, 20994])).
% 2.73/2.94 tff(21386,plain,
% 2.73/2.94 (~b(s(elem!1), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[19863, 588, 260, 446])).
% 2.73/2.94 tff(21387,plain,
% 2.73/2.94 (~r(s(elem!1), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2238, 588, 1326, 379, 1894, 68])).
% 2.73/2.94 tff(21388,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[2243, 21387, 21386, 2564])).
% 2.73/2.94 tff(21389,plain,((~b(elem!1, s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21390,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21389, 21385, 21383, 2207, 21154, 21381, 68, 21156, 21379])).
% 2.73/2.94 tff(21391,plain,(r(s(s(s(z))), elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21392,plain,
% 2.73/2.94 (r(s(s(s(z))), elem!1)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21391, 1307, 412, 1281, 20246, 1, 3407, 259, 68])).
% 2.73/2.94 tff(21393,plain,
% 2.73/2.94 (~r(z, s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21021, 279, 412, 1281, 377, 259])).
% 2.73/2.94 tff(21394,plain,
% 2.73/2.94 (b(z, s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[904, 21393])).
% 2.73/2.94 tff(21395,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[10709, 121, 1243, 1409, 20320, 109])).
% 2.73/2.94 tff(21396,plain,(b(z, elem!1) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (z = elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21397,plain,
% 2.73/2.94 (~r(s(s(s(z))), z)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21396, 20995, 199, 20992, 3871, 1281, 1307])).
% 2.73/2.94 tff(21398,plain,
% 2.73/2.94 (b(s(s(s(z))), z)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1155, 21397])).
% 2.73/2.94 tff(21399,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21058, 21398, 21394, 1281, 3871])).
% 2.73/2.94 tff(21400,plain,(b(elem!1, z) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | b(z, elem!1) | (~b(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.94 tff(21401,plain,
% 2.73/2.94 (b(elem!1, z)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21400, 199, 3871, 1281, 1307, 412, 377, 259])).
% 2.73/2.94 tff(21402,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21403,plain,
% 2.73/2.94 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 2.73/2.94 inference(rewrite,[status(thm)],[])).
% 2.73/2.94 tff(21404,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21403])).
% 2.73/2.94 tff(21405,plain,
% 2.73/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 2.73/2.94 inference(transitivity,[status(thm)],[21404, 21402])).
% 2.73/2.94 tff(21406,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.73/2.94 inference(quant_inst,[status(thm)],[])).
% 2.73/2.94 tff(21407,plain,
% 2.73/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21406, 21405])).
% 2.73/2.94 tff(21408,plain,
% 2.73/2.94 (~b(elem!1, s(z))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[21407, 271, 1281, 261, 3407])).
% 2.73/2.94 tff(21409,plain,
% 2.73/2.94 (elem!1 = s(z)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[299, 21408, 293])).
% 2.73/2.94 tff(21410,plain,
% 2.73/2.94 (b(z, elem!1) <=> b(z, s(z))),
% 2.73/2.94 inference(monotonicity,[status(thm)],[21409])).
% 2.73/2.94 tff(21411,plain,
% 2.73/2.94 (b(z, s(z)) <=> b(z, elem!1)),
% 2.73/2.94 inference(symmetry,[status(thm)],[21410])).
% 2.73/2.94 tff(21412,plain,
% 2.73/2.94 (s(z) = elem!1),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[242, 21409])).
% 2.73/2.94 tff(21413,plain,
% 2.73/2.94 (b(z, s(s(elem!1)))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[1307, 8834])).
% 2.73/2.94 tff(21414,plain,
% 2.73/2.94 (~b(s(s(elem!1)), z)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[20129, 21413, 20330, 261])).
% 2.73/2.94 tff(21415,plain,
% 2.73/2.94 (~b(s(s(s(z))), z)),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21414, 11344])).
% 2.73/2.94 tff(21416,plain,
% 2.73/2.94 (r(s(s(s(z))), z)),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1155, 21415])).
% 2.73/2.94 tff(21417,plain,
% 2.73/2.94 (~r(s(s(s(z))), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[5155, 21416, 412, 909])).
% 2.73/2.94 tff(21418,plain,
% 2.73/2.94 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[1816, 21417, 7853])).
% 2.73/2.94 tff(21419,plain,
% 2.73/2.94 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.94 inference(modus_ponens,[status(thm)],[21418, 7849])).
% 2.73/2.94 tff(21420,plain,
% 2.73/2.94 ($false),
% 2.73/2.94 inference(unit_resolution,[status(thm)],[6924, 271, 21413, 20330, 261, 21419])).
% 2.73/2.95 tff(21421,plain,((~(s(z) = elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21422,plain,
% 2.73/2.95 (~r(z, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21421, 21412, 412, 261, 1307, 3871])).
% 2.73/2.95 tff(21423,plain,
% 2.73/2.95 (b(z, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[904, 21422])).
% 2.73/2.95 tff(21424,plain,
% 2.73/2.95 (b(z, elem!1)),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21423, 21411])).
% 2.73/2.95 tff(21425,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[199, 21424])).
% 2.73/2.95 tff(21426,plain,((~b(elem!1, z)) | b(z, elem!1) | (~r(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21427,plain,
% 2.73/2.95 (r(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21426, 21401, 412, 1307, 3871, 199, 1281, 3407])).
% 2.73/2.95 tff(21428,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21429,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(21430,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21429, 21428])).
% 2.73/2.95 tff(21431,plain,
% 2.73/2.95 (~r(s(s(s(z))), z)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21430, 121, 20993, 21427, 145])).
% 2.73/2.95 tff(21432,plain,
% 2.73/2.95 (b(s(s(s(z))), z)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1155, 21431])).
% 2.73/2.95 tff(21433,plain,
% 2.73/2.95 (~b(z, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21058, 21432, 1281, 3871])).
% 2.73/2.95 tff(21434,plain,
% 2.73/2.95 (r(z, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[904, 21433])).
% 2.73/2.95 tff(21435,plain,
% 2.73/2.95 (~b(s(z), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21028, 271, 1281, 21401, 3407])).
% 2.73/2.95 tff(21436,plain,
% 2.73/2.95 (~b(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21407, 271, 1281, 21401, 3407])).
% 2.73/2.95 tff(21437,plain,
% 2.73/2.95 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[3732, 1398, 2564, 412, 905, 294, 379, 331, 317])).
% 2.73/2.95 tff(21438,plain,
% 2.73/2.95 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21437, 7849])).
% 2.73/2.95 tff(21439,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[6924, 271, 21413, 20330, 261, 21438])).
% 2.73/2.95 tff(21440,plain,((~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | b(elem!1, s(z)) | (~r(elem!1, s(elem!1))) | (z = elem!1) | b(elem!1, s(elem!1)) | (~b(s(z), s(s(s(z))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21441,plain,
% 2.73/2.95 (~(s(z) = elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21440, 3502, 1307, 3500, 412, 294, 261, 331, 317, 3871, 894])).
% 2.73/2.95 tff(21442,plain,
% 2.73/2.95 (~(elem!1 = s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[242, 21441])).
% 2.73/2.95 tff(21443,plain,
% 2.73/2.95 (~r(z, elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1266, 21442, 294, 1242, 905])).
% 2.73/2.95 tff(21444,plain,
% 2.73/2.95 (r(s(z), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[236, 21441, 1242])).
% 2.73/2.95 tff(21445,plain,
% 2.73/2.95 (~(s(s(z)) = s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[960, 21441])).
% 2.73/2.95 tff(21446,plain,
% 2.73/2.95 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[953, 21445])).
% 2.73/2.95 tff(21447,plain,
% 2.73/2.95 (b(z, elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[355, 21443, 331])).
% 2.73/2.95 tff(21448,plain,
% 2.73/2.95 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[7173, 21447, 3407, 261])).
% 2.73/2.95 tff(21449,plain,
% 2.73/2.95 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[3994, 21448, 412, 894, 3502, 3500, 317, 294])).
% 2.73/2.95 tff(21450,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[5759, 21449, 21448, 331, 905, 3502, 412, 21446, 21444, 21443, 21442])).
% 2.73/2.95 tff(21451,plain,(b(elem!1, s(elem!1)) | (z = elem!1) | (~r(s(elem!1), z)) | b(z, s(z)) | b(elem!1, s(z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | b(s(z), elem!1) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21452,plain,
% 2.73/2.95 (b(elem!1, s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21451, 21433, 412, 20992, 21436, 3407, 21401, 21435, 1307, 3871, 377])).
% 2.73/2.95 tff(21453,plain,
% 2.73/2.95 (s(z) = elem!1),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1305, 21434, 412, 20992, 21435, 199, 21452])).
% 2.73/2.95 tff(21454,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21421, 21453, 21434, 412, 21401, 1307, 3871])).
% 2.73/2.95 tff(21455,plain,(b(z, elem!1) | (~r(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21456,plain,
% 2.73/2.95 (b(z, elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21455, 1307, 412, 20246, 3407, 219, 1281, 21392, 259])).
% 2.73/2.95 tff(21457,plain,
% 2.73/2.95 (~(elem!1 = s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1397, 894, 1326])).
% 2.73/2.95 tff(21458,plain,
% 2.73/2.95 (b(elem!1, z)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21021, 905, 412, 1281, 377, 259])).
% 2.73/2.95 tff(21459,plain,
% 2.73/2.95 (~b(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[4775, 21458, 1326, 1281])).
% 2.73/2.95 tff(21460,plain,
% 2.73/2.95 (r(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[299, 21459, 21457])).
% 2.73/2.95 tff(21461,plain,
% 2.73/2.95 (~b(s(z), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[3964, 21458, 1326, 1281])).
% 2.73/2.95 tff(21462,plain,
% 2.73/2.95 (~(s(z) = elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21421, 905, 412, 21458, 1307, 3871])).
% 2.73/2.95 tff(21463,plain,
% 2.73/2.95 (r(s(z), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[236, 21462, 21461])).
% 2.73/2.95 tff(21464,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[4174, 121, 21463, 21460, 145, 21162])).
% 2.73/2.95 tff(21465,plain,(b(z, s(z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~r(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21466,plain,
% 2.73/2.95 (b(z, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21465, 21392, 21456, 1281, 412, 1307, 20246, 219, 259])).
% 2.73/2.95 tff(21467,plain,
% 2.73/2.95 (~b(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[20398, 21466, 1281, 21456])).
% 2.73/2.95 tff(21468,plain,
% 2.73/2.95 (~b(s(s(s(z))), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[19416, 1307, 1281, 20246])).
% 2.73/2.95 tff(21469,plain,
% 2.73/2.95 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[20471, 1307, 1281, 20246])).
% 2.73/2.95 tff(21470,plain,
% 2.73/2.95 (~(s(s(z)) = s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[960, 20998])).
% 2.73/2.95 tff(21471,plain,
% 2.73/2.95 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[953, 21470])).
% 2.73/2.95 tff(21472,plain,
% 2.73/2.95 ((s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2462, 21, 20476])).
% 2.73/2.95 tff(21473,plain,
% 2.73/2.95 (r(s(s(s(z))), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21472, 21471])).
% 2.73/2.95 tff(21474,plain,
% 2.73/2.95 (b(s(z), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[12711, 20998, 2327, 2346, 20995, 3871])).
% 2.73/2.95 tff(21475,plain,
% 2.73/2.95 (~b(elem!1, s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[9079, 21474, 1326, 220])).
% 2.73/2.95 tff(21476,plain,
% 2.73/2.95 (r(elem!1, s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[392, 21475, 219])).
% 2.73/2.95 tff(21477,plain,
% 2.73/2.95 (~r(z, s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[17642, 21476, 20995, 412])).
% 2.73/2.95 tff(21478,plain,
% 2.73/2.95 (b(z, s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2106, 21477])).
% 2.73/2.95 tff(21479,plain,
% 2.73/2.95 (~b(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[20398, 220, 1281, 1326])).
% 2.73/2.95 tff(21480,plain,
% 2.73/2.95 (r(elem!1, s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[299, 21000, 21479])).
% 2.73/2.95 tff(21481,plain,
% 2.73/2.95 (~r(s(z), s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[3709, 21476, 412, 21480])).
% 2.73/2.95 tff(21482,plain,
% 2.73/2.95 (b(s(z), s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[444, 21481, 20994])).
% 2.73/2.95 tff(21483,plain,
% 2.73/2.95 (~b(elem!1, s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21389, 21482, 2207, 1326, 21476, 68, 21474, 21478])).
% 2.73/2.95 tff(21484,plain,
% 2.73/2.95 (r(elem!1, s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[599, 21483, 68])).
% 2.73/2.95 tff(21485,plain,
% 2.73/2.95 (~r(s(z), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[12518, 21480, 2327, 145])).
% 2.73/2.95 tff(21486,plain,
% 2.73/2.95 (b(s(z), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2167, 21485])).
% 2.73/2.95 tff(21487,plain,
% 2.73/2.95 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[19354, 21478, 1281, 21486])).
% 2.73/2.95 tff(21488,plain,
% 2.73/2.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[556, 21487, 1])).
% 2.73/2.95 tff(21489,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21490,plain,
% 2.73/2.95 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21491,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21490])).
% 2.73/2.95 tff(21492,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21491, 21489])).
% 2.73/2.95 tff(21493,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(21494,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21493, 21492])).
% 2.73/2.95 tff(21495,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21494, 121, 21488, 21484, 145, 21473])).
% 2.73/2.95 tff(21496,plain,(b(elem!1, z) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~r(s(elem!1), z)) | b(s(s(s(z))), s(s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | b(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21497,plain,
% 2.73/2.95 (b(elem!1, z)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21496, 21392, 68, 1, 21456, 1281, 412, 21469, 21151, 21466, 21468, 20246, 259])).
% 2.73/2.95 tff(21498,plain,
% 2.73/2.95 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[7173, 21497, 3407, 21456])).
% 2.73/2.95 tff(21499,plain,
% 2.73/2.95 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[19817, 1307, 1281, 20246])).
% 2.73/2.95 tff(21500,plain,
% 2.73/2.95 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2063, 20994])).
% 2.73/2.95 tff(21501,plain,
% 2.73/2.95 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2069, 21, 21499, 21500])).
% 2.73/2.95 tff(21502,plain,
% 2.73/2.95 (~b(s(s(s(z))), z)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21058, 21466, 1281, 20246])).
% 2.73/2.95 tff(21503,plain,
% 2.73/2.95 (r(s(s(s(z))), z)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1155, 21502])).
% 2.73/2.95 tff(21504,plain,
% 2.73/2.95 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[8812, 239, 5499])).
% 2.73/2.95 tff(21505,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1225])).
% 2.73/2.95 tff(21506,plain,
% 2.73/2.95 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21505])).
% 2.73/2.95 tff(21507,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[239])).
% 2.73/2.95 tff(21508,plain,
% 2.73/2.95 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21507])).
% 2.73/2.95 tff(21509,plain,
% 2.73/2.95 (~b(s(s(s(elem!1))), s(z))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[479, 21508])).
% 2.73/2.95 tff(21510,plain,
% 2.73/2.95 (~b(s(s(s(s(z)))), s(z))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21509, 21506])).
% 2.73/2.95 tff(21511,plain,
% 2.73/2.95 (r(s(s(s(s(z)))), s(z))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[932, 21510])).
% 2.73/2.95 tff(21512,plain,
% 2.73/2.95 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1223])).
% 2.73/2.95 tff(21513,plain,
% 2.73/2.95 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[239])).
% 2.73/2.95 tff(21514,plain,
% 2.73/2.95 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21513, 21512])).
% 2.73/2.95 tff(21515,plain,
% 2.73/2.95 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[239])).
% 2.73/2.95 tff(21516,plain,
% 2.73/2.95 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21515])).
% 2.73/2.95 tff(21517,plain,
% 2.73/2.95 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1224])).
% 2.73/2.95 tff(21518,plain,
% 2.73/2.95 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21517])).
% 2.73/2.95 tff(21519,plain,
% 2.73/2.95 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21518, 21516])).
% 2.73/2.95 tff(21520,plain,
% 2.73/2.95 ((~r(s(z), s(s(s(z))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21519])).
% 2.73/2.95 tff(21521,plain,
% 2.73/2.95 (~r(elem!1, s(s(elem!1)))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[100, 21520])).
% 2.73/2.95 tff(21522,plain,
% 2.73/2.95 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(symmetry,[status(thm)],[6662])).
% 2.73/2.95 tff(21523,plain,
% 2.73/2.95 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21522])).
% 2.73/2.95 tff(21524,plain,
% 2.73/2.95 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[2066, 21523])).
% 2.73/2.95 tff(21525,plain,
% 2.73/2.95 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1224])).
% 2.73/2.95 tff(21526,plain,
% 2.73/2.95 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21525])).
% 2.73/2.95 tff(21527,plain,
% 2.73/2.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[5499, 21526])).
% 2.73/2.95 tff(21528,plain,
% 2.73/2.95 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1225])).
% 2.73/2.95 tff(21529,plain,
% 2.73/2.95 (b(z, s(s(s(s(z)))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[3407, 21528])).
% 2.73/2.95 tff(21530,plain,
% 2.73/2.95 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1225])).
% 2.73/2.95 tff(21531,plain,
% 2.73/2.95 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21530])).
% 2.73/2.95 tff(21532,plain,
% 2.73/2.95 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21531])).
% 2.73/2.95 tff(21533,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(z), s(s(s(s(z)))))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21534,plain,
% 2.73/2.95 (((~r(s(s(s(s(z)))), s(z))) | (~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)))) <=> ((~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(z), s(s(s(s(z)))))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21535,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21534])).
% 2.73/2.95 tff(21536,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21535, 21533])).
% 2.73/2.95 tff(21537,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(21538,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21537, 21536])).
% 2.73/2.95 tff(21539,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21538, 121, 911, 2327, 1026, 18818])).
% 2.73/2.95 tff(21540,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21541,plain,
% 2.73/2.95 (~r(s(z), s(s(s(s(z)))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21540, 21511, 2327, 21504])).
% 2.73/2.95 tff(21542,plain,
% 2.73/2.95 (~r(s(z), s(s(s(elem!1))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21541, 21532])).
% 2.73/2.95 tff(21543,plain,
% 2.73/2.95 (b(s(z), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[760, 21542])).
% 2.73/2.95 tff(21544,plain,
% 2.73/2.95 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1226, 1223])).
% 2.73/2.95 tff(21545,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21544])).
% 2.73/2.95 tff(21546,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1223])).
% 2.73/2.95 tff(21547,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21546, 21545])).
% 2.73/2.95 tff(21548,plain,
% 2.73/2.95 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1223])).
% 2.73/2.95 tff(21549,plain,
% 2.73/2.95 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.73/2.95 inference(transitivity,[status(thm)],[3572, 21548])).
% 2.73/2.95 tff(21550,plain,
% 2.73/2.95 (b(s(z), s(s(z)))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[15089, 21549])).
% 2.73/2.95 tff(21551,plain,
% 2.73/2.95 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[2376])).
% 2.73/2.95 tff(21552,plain,
% 2.73/2.95 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21551])).
% 2.73/2.95 tff(21553,plain,
% 2.73/2.95 (~b(z, s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[15101, 15091, 1326, 8336, 2344])).
% 2.73/2.95 tff(21554,plain,
% 2.73/2.95 (r(z, s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1439, 21553])).
% 2.73/2.95 tff(21555,plain,
% 2.73/2.95 (r(z, s(s(z)))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21554, 21552])).
% 2.73/2.95 tff(21556,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 2.73/2.95 tff(21557,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21558,plain,
% 2.73/2.95 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.73/2.95 inference(rewrite,[status(thm)],[])).
% 2.73/2.95 tff(21559,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21558])).
% 2.73/2.95 tff(21560,plain,
% 2.73/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21559, 21557])).
% 2.73/2.95 tff(21561,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.73/2.95 inference(quant_inst,[status(thm)],[])).
% 2.73/2.95 tff(21562,plain,
% 2.73/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21561, 21560])).
% 2.73/2.95 tff(21563,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21562, 121, 3599, 109, 1348, 21556])).
% 2.73/2.95 tff(21564,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21565,plain,
% 2.73/2.95 (~r(s(s(s(z))), s(s(z)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21564, 21555, 109, 3599])).
% 2.73/2.95 tff(21566,plain,
% 2.73/2.95 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[239])).
% 2.73/2.95 tff(21567,plain,
% 2.73/2.95 ((s(s(s(elem!1))) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 2.73/2.95 inference(transitivity,[status(thm)],[21566, 2858])).
% 2.73/2.95 tff(21568,plain,
% 2.73/2.95 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.73/2.95 inference(symmetry,[status(thm)],[21567])).
% 2.73/2.95 tff(21569,plain,
% 2.73/2.95 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21568])).
% 2.73/2.95 tff(21570,plain,
% 2.73/2.95 (~(s(s(s(elem!1))) = elem!1)),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[61, 21569])).
% 2.73/2.95 tff(21571,plain,
% 2.73/2.95 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[239])).
% 2.73/2.95 tff(21572,plain,
% 2.73/2.95 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21571])).
% 2.73/2.95 tff(21573,plain,
% 2.73/2.95 (b(elem!1, s(s(s(elem!1))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[750, 21572])).
% 2.73/2.95 tff(21574,plain,
% 2.73/2.95 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[12887, 15092, 15089, 21573])).
% 2.73/2.95 tff(21575,plain,
% 2.73/2.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[556, 2469, 615])).
% 2.73/2.95 tff(21576,plain,
% 2.73/2.95 (b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[3190, 627, 21575, 82, 675])).
% 2.73/2.95 tff(21577,plain,
% 2.73/2.95 (r(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[13705, 14231])).
% 2.73/2.95 tff(21578,plain,
% 2.73/2.95 (r(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21577, 14230])).
% 2.73/2.95 tff(21579,plain,
% 2.73/2.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2395, 627, 239, 145, 21578])).
% 2.73/2.95 tff(21580,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[586, 21579, 20633])).
% 2.73/2.95 tff(21581,plain,
% 2.73/2.95 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21580, 11160])).
% 2.73/2.95 tff(21582,plain,
% 2.73/2.95 (b(s(elem!1), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[4488, 21579, 481, 675, 4435, 2469])).
% 2.73/2.95 tff(21583,plain,
% 2.73/2.95 (b(s(elem!1), s(z))),
% 2.73/2.95 inference(modus_ponens,[status(thm)],[21582, 14244])).
% 2.73/2.95 tff(21584,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[6230, 21583, 21581, 21576, 750])).
% 2.73/2.95 tff(21585,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), s(elem!1)) | r(elem!1, s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21586,plain,
% 2.73/2.95 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21585, 21574, 239, 2469, 21570, 145, 750, 4435, 82])).
% 2.73/2.95 tff(21587,plain,
% 2.73/2.95 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[526, 21586, 216])).
% 2.73/2.95 tff(21588,plain,
% 2.73/2.95 (b(s(elem!1), s(s(s(z))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2369, 21587, 239])).
% 2.73/2.95 tff(21589,plain,
% 2.73/2.95 (~b(s(s(s(z))), s(s(z)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[6772, 21588, 3871, 239, 21550])).
% 2.73/2.95 tff(21590,plain,
% 2.73/2.95 ($false),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[1366, 21, 21589, 1362, 21565])).
% 2.73/2.95 tff(21591,plain,(r(s(elem!1), elem!1) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.95 tff(21592,plain,
% 2.73/2.95 (r(s(elem!1), elem!1)),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21591, 750, 3599, 239, 3871, 216, 2469, 145, 109, 4435, 82, 1326, 2344])).
% 2.73/2.95 tff(21593,plain,
% 2.73/2.95 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[1224, 1223])).
% 2.73/2.95 tff(21594,plain,
% 2.73/2.95 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.73/2.95 inference(symmetry,[status(thm)],[21593])).
% 2.73/2.95 tff(21595,plain,
% 2.73/2.95 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 2.73/2.95 inference(monotonicity,[status(thm)],[21594])).
% 2.73/2.95 tff(21596,plain,
% 2.73/2.95 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[21585, 675, 239, 2469, 21570, 145, 750, 4435, 82])).
% 2.73/2.95 tff(21597,plain,
% 2.73/2.95 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[526, 21596, 216])).
% 2.73/2.95 tff(21598,plain,
% 2.73/2.95 (b(s(elem!1), s(s(s(z))))),
% 2.73/2.95 inference(unit_resolution,[status(thm)],[2369, 21597, 239])).
% 2.73/2.95 tff(21599,plain,
% 2.73/2.95 (~b(s(s(s(z))), s(s(z)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6772, 21598, 3871, 239, 6763])).
% 2.73/2.96 tff(21600,plain,
% 2.73/2.96 (~b(s(s(elem!1)), s(elem!1))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21599, 21595])).
% 2.73/2.96 tff(21601,plain,
% 2.73/2.96 (~r(s(s(elem!1)), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[692, 13705, 623, 622])).
% 2.73/2.96 tff(21602,plain,
% 2.73/2.96 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[701, 21601, 8423])).
% 2.73/2.96 tff(21603,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21602, 21600])).
% 2.73/2.96 tff(21604,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21605,plain,
% 2.73/2.96 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21604, 21592, 3871, 21550, 216, 623, 239, 2469, 145, 750, 4435, 82])).
% 2.73/2.96 tff(21606,plain,
% 2.73/2.96 (b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21605, 21547])).
% 2.73/2.96 tff(21607,plain,
% 2.73/2.96 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[1225])).
% 2.73/2.96 tff(21608,plain,
% 2.73/2.96 (b(s(z), s(s(s(s(z)))))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[750, 21607])).
% 2.73/2.96 tff(21609,plain,
% 2.73/2.96 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[2376])).
% 2.73/2.96 tff(21610,plain,
% 2.73/2.96 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.96 inference(symmetry,[status(thm)],[21609])).
% 2.73/2.96 tff(21611,plain,
% 2.73/2.96 (b(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[1562, 21610])).
% 2.73/2.96 tff(21612,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21613,plain,
% 2.73/2.96 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21614,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21613])).
% 2.73/2.96 tff(21615,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21614, 21612])).
% 2.73/2.96 tff(21616,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 2.73/2.96 inference(quant_inst,[status(thm)],[])).
% 2.73/2.96 tff(21617,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21616, 21615])).
% 2.73/2.96 tff(21618,plain,
% 2.73/2.96 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21617, 271, 220, 1067, 1157])).
% 2.73/2.96 tff(21619,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21618, 21611])).
% 2.73/2.96 tff(21620,plain,((~b(s(s(s(s(z)))), s(elem!1))) | (~(elem!1 = s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21621,plain,
% 2.73/2.96 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21620, 21608, 220, 239, 1157])).
% 2.73/2.96 tff(21622,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21621, 21606])).
% 2.73/2.96 tff(21623,plain,((~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21624,plain,
% 2.73/2.96 (r(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21623, 21543, 220, 21529, 20246, 216, 21527, 21524, 145, 21521, 82, 4276, 109, 1326, 239])).
% 2.73/2.96 tff(21625,plain,
% 2.73/2.96 (r(s(z), s(s(z)))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21624, 21514])).
% 2.73/2.96 tff(21626,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20930, 121, 21625, 21511, 2327, 21504])).
% 2.73/2.96 tff(21627,plain,((~(elem!1 = s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | r(s(z), s(s(s(z)))) | b(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21628,plain,
% 2.73/2.96 (~(elem!1 = s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21627, 21151, 21466, 211, 21392, 79, 21503, 21456, 21501, 3407, 100, 21499, 412, 21498])).
% 2.73/2.96 tff(21629,plain,
% 2.73/2.96 (r(elem!1, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[299, 21628, 21467])).
% 2.73/2.96 tff(21630,plain,
% 2.73/2.96 (~b(s(z), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[3964, 21497, 21456, 1281])).
% 2.73/2.96 tff(21631,plain,
% 2.73/2.96 (~(s(z) = elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1221, 21628])).
% 2.73/2.96 tff(21632,plain,
% 2.73/2.96 (r(s(z), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[236, 21631, 21630])).
% 2.73/2.96 tff(21633,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[4174, 121, 21632, 21629, 21392, 21151])).
% 2.73/2.96 tff(21634,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | r(s(z), s(s(s(z)))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21635,plain,
% 2.73/2.96 (~b(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21634, 21141, 100, 3407, 1281, 21133, 1, 21132])).
% 2.73/2.96 tff(21636,plain,
% 2.73/2.96 (r(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1214, 21635])).
% 2.73/2.96 tff(21637,plain,
% 2.73/2.96 (r(elem!1, z)),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[20245, 15940])).
% 2.73/2.96 tff(21638,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21639,plain,
% 2.73/2.96 (((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21640,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21639])).
% 2.73/2.96 tff(21641,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21640, 21638])).
% 2.73/2.96 tff(21642,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.73/2.96 inference(quant_inst,[status(thm)],[])).
% 2.73/2.96 tff(21643,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21642, 21641])).
% 2.73/2.96 tff(21644,plain,
% 2.73/2.96 (~r(s(elem!1), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21643, 121, 21637, 21133, 21636])).
% 2.73/2.96 tff(21645,plain,
% 2.73/2.96 (b(s(elem!1), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[2243, 21644, 2207])).
% 2.73/2.96 tff(21646,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21647,plain,
% 2.73/2.96 (((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21648,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21647])).
% 2.73/2.96 tff(21649,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21648, 21646])).
% 2.73/2.96 tff(21650,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 2.73/2.96 inference(quant_inst,[status(thm)],[])).
% 2.73/2.96 tff(21651,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21650, 21649])).
% 2.73/2.96 tff(21652,plain,
% 2.73/2.96 (~r(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21651, 121, 21637, 21133, 21636])).
% 2.73/2.96 tff(21653,plain,
% 2.73/2.96 (b(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[392, 21652, 219])).
% 2.73/2.96 tff(21654,plain,
% 2.73/2.96 (~b(s(s(s(z))), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[13140, 21636, 21133, 2597, 21653, 21645])).
% 2.73/2.96 tff(21655,plain,
% 2.73/2.96 (r(s(s(s(z))), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[255, 21654, 2612])).
% 2.73/2.96 tff(21656,plain,
% 2.73/2.96 (~b(z, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[15101, 21652, 1326, 219, 21644])).
% 2.73/2.96 tff(21657,plain,
% 2.73/2.96 (r(z, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1439, 21656])).
% 2.73/2.96 tff(21658,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21659,plain,
% 2.73/2.96 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21660,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21659])).
% 2.73/2.96 tff(21661,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21660, 21658])).
% 2.73/2.96 tff(21662,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 2.73/2.96 inference(quant_inst,[status(thm)],[])).
% 2.73/2.96 tff(21663,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21662, 21661])).
% 2.73/2.96 tff(21664,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21663, 121, 21657, 21637, 21655, 21139])).
% 2.73/2.96 tff(21665,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | r(s(z), s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21666,plain,
% 2.73/2.96 (~(s(s(s(elem!1))) = elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21665, 21127, 1281, 100, 20244, 1, 8226])).
% 2.73/2.96 tff(21667,plain,
% 2.73/2.96 (b(s(s(s(elem!1))), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[486, 21666, 147])).
% 2.73/2.96 tff(21668,plain,
% 2.73/2.96 (~b(elem!1, z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[7173, 21667, 20244, 21127])).
% 2.73/2.96 tff(21669,plain,
% 2.73/2.96 (~b(s(elem!1), z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20840, 68, 1281, 20246, 1, 6842, 3407, 147])).
% 2.73/2.96 tff(21670,plain,
% 2.73/2.96 (~(elem!1 = z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20985, 21669, 1281])).
% 2.73/2.96 tff(21671,plain,
% 2.73/2.96 (~b(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21634, 21670, 100, 3407, 1281, 412, 1, 68])).
% 2.73/2.96 tff(21672,plain,
% 2.73/2.96 (r(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1214, 21671])).
% 2.73/2.96 tff(21673,plain,
% 2.73/2.96 (r(elem!1, z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[284, 21670, 279])).
% 2.73/2.96 tff(21674,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21651, 121, 379, 21673, 412, 21672])).
% 2.73/2.96 tff(21675,plain,((elem!1 = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | r(s(z), s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(elem!1, z) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21676,plain,
% 2.73/2.96 (elem!1 = s(s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21675, 379, 20979, 100, 20244, 1281, 1, 21668, 20245, 147])).
% 2.73/2.96 tff(21677,plain,
% 2.73/2.96 (s(elem!1) = s(s(s(elem!1)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21676])).
% 2.73/2.96 tff(21678,plain,
% 2.73/2.96 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21677])).
% 2.73/2.96 tff(21679,plain,
% 2.73/2.96 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 2.73/2.96 inference(symmetry,[status(thm)],[21678])).
% 2.73/2.96 tff(21680,plain,
% 2.73/2.96 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(elem!1)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21679])).
% 2.73/2.96 tff(21681,plain,
% 2.73/2.96 (~r(z, s(elem!1))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[19734, 21680])).
% 2.73/2.96 tff(21682,plain,
% 2.73/2.96 (~(elem!1 = s(s(elem!1)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[12364, 2467, 147, 1])).
% 2.73/2.96 tff(21683,plain,
% 2.73/2.96 (~b(s(elem!1), z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20840, 21682, 1281, 20246, 1, 6842, 3407, 147])).
% 2.73/2.96 tff(21684,plain,
% 2.73/2.96 (~(elem!1 = z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20985, 21683, 1281])).
% 2.73/2.96 tff(21685,plain,
% 2.73/2.96 (~b(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21634, 21684, 100, 3407, 1281, 412, 1, 21682])).
% 2.73/2.96 tff(21686,plain,
% 2.73/2.96 (r(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1214, 21685])).
% 2.73/2.96 tff(21687,plain,
% 2.73/2.96 (r(elem!1, z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[284, 21684, 279])).
% 2.73/2.96 tff(21688,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21643, 121, 8563, 21687, 412, 21686])).
% 2.73/2.96 tff(21689,plain,(b(s(elem!1), elem!1) | (~r(s(elem!1), z)) | r(s(z), s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(elem!1, z) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21690,plain,
% 2.73/2.96 (b(s(elem!1), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21689, 21668, 100, 20244, 1281, 1, 20979, 20245, 147])).
% 2.73/2.96 tff(21691,plain,
% 2.73/2.96 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[3787, 21676, 21690])).
% 2.73/2.96 tff(21692,plain,
% 2.73/2.96 (~b(s(elem!1), z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[12308, 21676, 8226])).
% 2.73/2.96 tff(21693,plain,
% 2.73/2.96 (~(z = elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[7069, 21692, 21690])).
% 2.73/2.96 tff(21694,plain,
% 2.73/2.96 (~(s(z) = s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[343, 21693])).
% 2.73/2.96 tff(21695,plain,
% 2.73/2.96 (~(s(z) = elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20120, 21668, 1281])).
% 2.73/2.96 tff(21696,plain,
% 2.73/2.96 (~(elem!1 = s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[242, 21695])).
% 2.73/2.96 tff(21697,plain,
% 2.73/2.96 (~(elem!1 = z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20985, 21692, 1281])).
% 2.73/2.96 tff(21698,plain,
% 2.73/2.96 (~r(z, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21021, 21697, 20979, 1281, 219, 21668])).
% 2.73/2.96 tff(21699,plain,
% 2.73/2.96 (b(z, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[904, 21698])).
% 2.73/2.96 tff(21700,plain,
% 2.73/2.96 (~b(elem!1, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[11002, 21699, 21127, 20246])).
% 2.73/2.96 tff(21701,plain,
% 2.73/2.96 (r(elem!1, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[299, 21700, 21696])).
% 2.73/2.96 tff(21702,plain,
% 2.73/2.96 (~r(s(z), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[3709, 21701, 20979, 379])).
% 2.73/2.96 tff(21703,plain,
% 2.73/2.96 (b(s(z), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[444, 21702, 21694])).
% 2.73/2.96 tff(21704,plain,
% 2.73/2.96 (~b(z, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[2905, 21703, 1281, 21691])).
% 2.73/2.96 tff(21705,plain,
% 2.73/2.96 (r(z, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1439, 21704])).
% 2.73/2.96 tff(21706,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21705, 21681])).
% 2.73/2.96 tff(21707,plain,((~r(elem!1, s(elem!1))) | r(z, s(s(s(elem!1)))) | (~b(s(z), z)) | b(s(s(s(elem!1))), z) | r(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21708,plain,
% 2.73/2.96 (~r(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21707, 147, 1281, 8226, 100, 1, 19734])).
% 2.73/2.96 tff(21709,plain,
% 2.73/2.96 (b(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[392, 21708, 219])).
% 2.73/2.96 tff(21710,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[7685, 271, 21709, 21127, 20244, 21667])).
% 2.73/2.96 tff(21711,plain,(r(s(s(s(elem!1))), elem!1) | (~b(s(z), z)) | b(s(s(s(elem!1))), z) | r(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21712,plain,
% 2.73/2.96 (r(s(s(s(elem!1))), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21711, 8226, 1281, 100, 1, 19734])).
% 2.73/2.96 tff(21713,plain,
% 2.73/2.96 (elem!1 = z),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[8716, 361])).
% 2.73/2.96 tff(21714,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20986, 21713])).
% 2.73/2.96 tff(21715,plain,(r(z, elem!1) | (~b(s(z), z)) | b(z, elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21716,plain,
% 2.73/2.96 (r(z, elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21715, 199, 1281, 3871, 6842, 3407, 1])).
% 2.73/2.96 tff(21717,plain,
% 2.73/2.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21042, 121, 21716, 412, 6842])).
% 2.73/2.96 tff(21718,plain,
% 2.73/2.96 (~b(s(elem!1), z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20851, 21716, 6842, 1, 139, 3871, 1281, 3407])).
% 2.73/2.96 tff(21719,plain,
% 2.73/2.96 (~(elem!1 = z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[20985, 21718, 1281])).
% 2.73/2.96 tff(21720,plain,
% 2.73/2.96 (~r(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[8972, 21716, 139, 6842])).
% 2.73/2.96 tff(21721,plain,
% 2.73/2.96 (b(elem!1, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[392, 21720, 219])).
% 2.73/2.96 tff(21722,plain,
% 2.73/2.96 (~r(elem!1, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[5343, 622, 412, 378])).
% 2.73/2.96 tff(21723,plain,
% 2.73/2.96 (~r(elem!1, z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[5358, 622, 412, 378])).
% 2.73/2.96 tff(21724,plain,
% 2.73/2.96 (b(elem!1, z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[284, 21723, 259])).
% 2.73/2.96 tff(21725,plain,
% 2.73/2.96 (~b(elem!1, s(z))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21407, 271, 1281, 21724, 3407])).
% 2.73/2.96 tff(21726,plain,
% 2.73/2.96 (elem!1 = s(z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[299, 21725, 21722])).
% 2.73/2.96 tff(21727,plain,
% 2.73/2.96 (s(z) = elem!1),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[242, 21726])).
% 2.73/2.96 tff(21728,plain,
% 2.73/2.96 (s(s(z)) = s(elem!1)),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21727])).
% 2.73/2.96 tff(21729,plain,
% 2.73/2.96 (s(s(s(z))) = s(s(elem!1))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21728])).
% 2.73/2.96 tff(21730,plain,
% 2.73/2.96 (s(s(elem!1)) = s(s(s(z)))),
% 2.73/2.96 inference(symmetry,[status(thm)],[21729])).
% 2.73/2.96 tff(21731,plain,
% 2.73/2.96 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21730])).
% 2.73/2.96 tff(21732,plain,
% 2.73/2.96 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.73/2.96 inference(symmetry,[status(thm)],[21731])).
% 2.73/2.96 tff(21733,plain,
% 2.73/2.96 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21728])).
% 2.73/2.96 tff(21734,plain,
% 2.73/2.96 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21733, 3535])).
% 2.73/2.96 tff(21735,plain,
% 2.73/2.96 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21734])).
% 2.73/2.96 tff(21736,plain,
% 2.73/2.96 (~(s(s(s(z))) = s(elem!1))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[1136, 21735])).
% 2.73/2.96 tff(21737,plain,
% 2.73/2.96 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21727])).
% 2.73/2.96 tff(21738,plain,
% 2.73/2.96 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.73/2.96 inference(symmetry,[status(thm)],[21737])).
% 2.73/2.96 tff(21739,plain,
% 2.73/2.96 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21728])).
% 2.73/2.96 tff(21740,plain,
% 2.73/2.96 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.73/2.96 inference(symmetry,[status(thm)],[21739])).
% 2.73/2.96 tff(21741,plain,
% 2.73/2.96 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21740, 21738])).
% 2.73/2.96 tff(21742,plain,
% 2.73/2.96 (b(s(z), s(s(z)))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[307, 21741])).
% 2.73/2.96 tff(21743,plain,
% 2.73/2.96 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21729])).
% 2.73/2.96 tff(21744,plain,
% 2.73/2.96 (~b(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21426, 21722, 412, 199, 3871, 21724, 1281, 3407])).
% 2.73/2.96 tff(21745,plain,
% 2.73/2.96 (r(z, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1214, 21744])).
% 2.73/2.96 tff(21746,plain,
% 2.73/2.96 (r(z, s(s(elem!1)))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21745, 21743])).
% 2.73/2.96 tff(21747,plain,
% 2.73/2.96 (~r(elem!1, s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6817, 622, 412, 378])).
% 2.73/2.96 tff(21748,plain,
% 2.73/2.96 (b(elem!1, s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[660, 21, 21747, 13208])).
% 2.73/2.96 tff(21749,plain,
% 2.73/2.96 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21727])).
% 2.73/2.96 tff(21750,plain,
% 2.73/2.96 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21749])).
% 2.73/2.96 tff(21751,plain,
% 2.73/2.96 (~(elem!1 = s(s(elem!1)))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[2137, 21750])).
% 2.73/2.96 tff(21752,plain,
% 2.73/2.96 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[78, 21751])).
% 2.73/2.96 tff(21753,plain,
% 2.73/2.96 (~b(z, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6868, 21752, 412, 21748, 378, 21746, 307, 21724])).
% 2.73/2.96 tff(21754,plain,
% 2.73/2.96 (r(z, s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1439, 21753])).
% 2.73/2.96 tff(21755,plain,
% 2.73/2.96 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21729])).
% 2.73/2.96 tff(21756,plain,
% 2.73/2.96 (b(elem!1, s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[11114, 21726, 3871])).
% 2.73/2.96 tff(21757,plain,
% 2.73/2.96 (b(elem!1, s(s(elem!1)))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21756, 21755])).
% 2.73/2.96 tff(21758,plain,
% 2.73/2.96 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[681, 21752, 676])).
% 2.73/2.96 tff(21759,plain,
% 2.73/2.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6906, 21758, 21748, 21757])).
% 2.73/2.96 tff(21760,plain,
% 2.73/2.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[556, 21759, 1])).
% 2.73/2.96 tff(21761,plain,
% 2.73/2.96 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6878, 21760, 21754, 21746])).
% 2.73/2.96 tff(21762,plain,
% 2.73/2.96 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[526, 21761, 211])).
% 2.73/2.96 tff(21763,plain,
% 2.73/2.96 (b(s(elem!1), s(s(s(z))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[2369, 21762, 21726])).
% 2.73/2.96 tff(21764,plain,
% 2.73/2.96 (~b(s(s(s(z))), s(s(z)))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6772, 21763, 3871, 21726, 21742])).
% 2.73/2.96 tff(21765,plain,
% 2.73/2.96 (~b(s(s(s(z))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[14223, 21764, 21726])).
% 2.73/2.96 tff(21766,plain,
% 2.73/2.96 (r(s(s(s(z))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1816, 21765, 21736])).
% 2.73/2.96 tff(21767,plain,
% 2.73/2.96 (r(s(s(elem!1)), s(elem!1))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21766, 21732])).
% 2.73/2.96 tff(21768,plain,
% 2.73/2.96 (~r(s(z), s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[1045, 21747, 223])).
% 2.73/2.96 tff(21769,plain,
% 2.73/2.96 (b(s(z), s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[760, 21768])).
% 2.73/2.96 tff(21770,plain,
% 2.73/2.96 (b(elem!1, s(s(s(elem!1))))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21769, 6792])).
% 2.73/2.96 tff(21771,plain,
% 2.73/2.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[692, 622, 623, 683])).
% 2.73/2.96 tff(21772,plain,
% 2.73/2.96 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[681, 21771, 82])).
% 2.73/2.96 tff(21773,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21774,plain,
% 2.73/2.96 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.73/2.96 inference(rewrite,[status(thm)],[])).
% 2.73/2.96 tff(21775,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.73/2.96 inference(monotonicity,[status(thm)],[21774])).
% 2.73/2.96 tff(21776,plain,
% 2.73/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.73/2.96 inference(transitivity,[status(thm)],[21775, 21773])).
% 2.73/2.96 tff(21777,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 2.73/2.96 inference(quant_inst,[status(thm)],[])).
% 2.73/2.96 tff(21778,plain,
% 2.73/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.73/2.96 inference(modus_ponens,[status(thm)],[21777, 21776])).
% 2.73/2.96 tff(21779,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21778, 271, 261, 3407, 21772, 21770])).
% 2.73/2.96 tff(21780,plain,((~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21781,plain,
% 2.73/2.96 (~r(s(s(elem!1)), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21780, 21760, 3407, 412, 21727, 21752, 21724, 378, 622])).
% 2.73/2.96 tff(21782,plain,
% 2.73/2.96 ($false),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21781, 21767])).
% 2.73/2.96 tff(21783,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | r(s(s(s(elem!1))), s(elem!1)) | (~b(s(z), z)) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.96 tff(21784,plain,
% 2.73/2.96 (~r(s(elem!1), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21783, 21716, 3407, 412, 3871, 1, 21721, 21717, 1281, 199, 21719])).
% 2.73/2.96 tff(21785,plain,
% 2.73/2.96 (b(s(elem!1), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[2243, 21784, 2207])).
% 2.73/2.96 tff(21786,plain,
% 2.73/2.96 (~r(elem!1, s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[13723, 21716, 139, 6842])).
% 2.73/2.96 tff(21787,plain,
% 2.73/2.96 (b(elem!1, s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[660, 21, 21786, 13208])).
% 2.73/2.96 tff(21788,plain,
% 2.73/2.96 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[12887, 21787, 21721, 21785])).
% 2.73/2.96 tff(21789,plain,
% 2.73/2.96 (s(s(s(elem!1))) = s(elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[681, 21788, 21717])).
% 2.73/2.96 tff(21790,plain,
% 2.73/2.96 (elem!1 = s(s(elem!1))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[78, 21789])).
% 2.73/2.96 tff(21791,plain,
% 2.73/2.96 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[6858, 121, 21716, 412, 6842])).
% 2.73/2.96 tff(21792,plain,
% 2.73/2.96 (~(z = elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[7069, 21785, 21718])).
% 2.73/2.96 tff(21793,plain,
% 2.73/2.96 (b(s(s(s(elem!1))), elem!1)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[3790, 21790, 21785])).
% 2.73/2.96 tff(21794,plain,
% 2.73/2.96 (elem!1 = s(z)),
% 2.73/2.96 inference(unit_resolution,[status(thm)],[21098, 21793, 412, 199, 3871, 21716, 1281, 219, 3407, 21792, 21791, 21717])).
% 2.73/2.97 tff(21795,plain,
% 2.73/2.97 (s(z) = elem!1),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[242, 21794])).
% 2.73/2.97 tff(21796,plain,
% 2.73/2.97 (s(z) = s(s(elem!1))),
% 2.73/2.97 inference(transitivity,[status(thm)],[21795, 21790])).
% 2.73/2.97 tff(21797,plain,
% 2.73/2.97 ($false),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[2137, 21796])).
% 2.73/2.97 tff(21798,plain,(b(z, elem!1) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.97 tff(21799,plain,
% 2.73/2.97 (b(z, elem!1)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21798, 20979, 20246, 1281, 20244, 21712, 20245, 1])).
% 2.73/2.97 tff(21800,plain,
% 2.73/2.97 (z = elem!1),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[333, 329])).
% 2.73/2.97 tff(21801,plain,
% 2.73/2.97 (b(s(elem!1), z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[20985, 329, 1281])).
% 2.73/2.97 tff(21802,plain,
% 2.73/2.97 (elem!1 = s(z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[20833, 21801, 1, 21800, 3871, 1281, 6842, 3407])).
% 2.73/2.97 tff(21803,plain,
% 2.73/2.97 (b(s(elem!1), elem!1)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[2488, 21801, 21800])).
% 2.73/2.97 tff(21804,plain,
% 2.73/2.97 (~b(elem!1, s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[9291, 21803, 1326, 21801])).
% 2.73/2.97 tff(21805,plain,
% 2.73/2.97 ($false),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[11114, 21804, 21802, 3871])).
% 2.73/2.97 tff(21806,plain,((~(elem!1 = z)) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.97 tff(21807,plain,
% 2.73/2.97 (~(elem!1 = z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21806, 21799, 20246, 1, 1281, 20245, 20244])).
% 2.73/2.97 tff(21808,plain,
% 2.73/2.97 (b(z, elem!1)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21798, 412, 20246, 1281, 3407, 139, 6842, 1])).
% 2.73/2.97 tff(21809,plain,
% 2.73/2.97 (~b(elem!1, z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[4775, 448, 1326, 1281])).
% 2.73/2.97 tff(21810,plain,
% 2.73/2.97 (~b(z, s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[20398, 448, 1281, 1326])).
% 2.73/2.97 tff(21811,plain,
% 2.73/2.97 (r(z, s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[904, 21810])).
% 2.73/2.97 tff(21812,plain,
% 2.73/2.97 ($false),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21021, 21811, 21809, 412, 1281, 377, 259])).
% 2.73/2.97 tff(21813,plain,((~b(elem!1, s(z))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (elem!1 = z) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.97 tff(21814,plain,
% 2.73/2.97 (~b(elem!1, s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21813, 259, 1281, 219, 412, 21808])).
% 2.73/2.97 tff(21815,plain,
% 2.73/2.97 (~b(z, s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21634, 68, 100, 3407, 1281, 412, 1, 259])).
% 2.73/2.97 tff(21816,plain,
% 2.73/2.97 (r(z, s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[1214, 21815])).
% 2.73/2.97 tff(21817,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21818,plain,
% 2.73/2.97 (((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21819,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21818])).
% 2.73/2.97 tff(21820,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.97 inference(transitivity,[status(thm)],[21819, 21817])).
% 2.73/2.97 tff(21821,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.73/2.97 inference(quant_inst,[status(thm)],[])).
% 2.73/2.97 tff(21822,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21821, 21820])).
% 2.73/2.97 tff(21823,plain,
% 2.73/2.97 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21822, 121, 412, 6842, 21816])).
% 2.73/2.97 tff(21824,plain,
% 2.73/2.97 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[681, 21823, 79])).
% 2.73/2.97 tff(21825,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21826,plain,
% 2.73/2.97 (((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21827,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21826])).
% 2.73/2.97 tff(21828,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))))),
% 2.73/2.97 inference(transitivity,[status(thm)],[21827, 21825])).
% 2.73/2.97 tff(21829,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.73/2.97 inference(quant_inst,[status(thm)],[])).
% 2.73/2.97 tff(21830,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21829, 21828])).
% 2.73/2.97 tff(21831,plain,
% 2.73/2.97 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21830, 121, 412, 6842, 21816])).
% 2.73/2.97 tff(21832,plain,
% 2.73/2.97 (b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[2293, 21, 21831, 85])).
% 2.73/2.97 tff(21833,plain,
% 2.73/2.97 (~b(z, s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[14647, 271, 3407, 21832, 21824])).
% 2.73/2.97 tff(21834,plain,
% 2.73/2.97 (r(z, s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[1439, 21833])).
% 2.73/2.97 tff(21835,plain,
% 2.73/2.97 (~r(elem!1, z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[12939, 121, 9983, 21834, 412])).
% 2.73/2.97 tff(21836,plain,
% 2.73/2.97 (b(elem!1, z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[284, 21835, 259])).
% 2.73/2.97 tff(21837,plain,
% 2.73/2.97 (~b(elem!1, s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[4775, 21836, 21808, 1281])).
% 2.73/2.97 tff(21838,plain,
% 2.73/2.97 (~b(s(z), elem!1)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21030, 21836, 1281, 3407])).
% 2.73/2.97 tff(21839,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21840,plain,
% 2.73/2.97 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21841,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21840])).
% 2.73/2.97 tff(21842,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.73/2.97 inference(transitivity,[status(thm)],[21841, 21839])).
% 2.73/2.97 tff(21843,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.73/2.97 inference(quant_inst,[status(thm)],[])).
% 2.73/2.97 tff(21844,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21843, 21842])).
% 2.73/2.97 tff(21845,plain,
% 2.73/2.97 ($false),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21844, 271, 750, 1281, 3407, 638])).
% 2.73/2.97 tff(21846,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.97 tff(21847,plain,
% 2.73/2.97 (~b(s(z), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21846, 21824, 3407, 1281])).
% 2.73/2.97 tff(21848,plain,
% 2.73/2.97 (r(s(z), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[760, 21847])).
% 2.73/2.97 tff(21849,plain,
% 2.73/2.97 (elem!1 = s(z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[18965, 21848, 139, 21838, 21837])).
% 2.73/2.97 tff(21850,plain,
% 2.73/2.97 (s(elem!1) = s(s(z))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21849])).
% 2.73/2.97 tff(21851,plain,
% 2.73/2.97 (s(s(z)) = s(elem!1)),
% 2.73/2.97 inference(symmetry,[status(thm)],[21850])).
% 2.73/2.97 tff(21852,plain,
% 2.73/2.97 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21851])).
% 2.73/2.97 tff(21853,plain,
% 2.73/2.97 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.97 inference(symmetry,[status(thm)],[21852])).
% 2.73/2.97 tff(21854,plain,
% 2.73/2.97 (s(s(elem!1)) = s(s(s(z)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21850])).
% 2.73/2.97 tff(21855,plain,
% 2.73/2.97 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21854])).
% 2.73/2.97 tff(21856,plain,
% 2.73/2.97 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.73/2.97 inference(symmetry,[status(thm)],[21855])).
% 2.73/2.97 tff(21857,plain,
% 2.73/2.97 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21856, 21850])).
% 2.73/2.97 tff(21858,plain,
% 2.73/2.97 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.97 inference(symmetry,[status(thm)],[21857])).
% 2.73/2.97 tff(21859,plain,
% 2.73/2.97 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21850])).
% 2.73/2.97 tff(21860,plain,
% 2.73/2.97 (b(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21824, 21859])).
% 2.73/2.97 tff(21861,plain,
% 2.73/2.97 (b(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21860, 21858])).
% 2.73/2.97 tff(21862,plain,
% 2.73/2.97 (b(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21861, 21853])).
% 2.73/2.97 tff(21863,plain,
% 2.73/2.97 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21850, 21854])).
% 2.73/2.97 tff(21864,plain,
% 2.73/2.97 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21854])).
% 2.73/2.97 tff(21865,plain,
% 2.73/2.97 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.73/2.97 inference(symmetry,[status(thm)],[21864])).
% 2.73/2.97 tff(21866,plain,
% 2.73/2.97 (r(z, s(s(elem!1)))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21816, 21865])).
% 2.73/2.97 tff(21867,plain,
% 2.73/2.97 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21854])).
% 2.73/2.97 tff(21868,plain,
% 2.73/2.97 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.73/2.97 inference(symmetry,[status(thm)],[21867])).
% 2.73/2.97 tff(21869,plain,
% 2.73/2.97 (b(z, s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[1397, 21849, 21808])).
% 2.73/2.97 tff(21870,plain,
% 2.73/2.97 (~b(s(s(s(z))), z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21058, 21869, 1281, 20246])).
% 2.73/2.97 tff(21871,plain,
% 2.73/2.97 (r(s(s(s(z))), z)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[1155, 21870])).
% 2.73/2.97 tff(21872,plain,
% 2.73/2.97 (r(s(s(elem!1)), z)),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21871, 21868])).
% 2.73/2.97 tff(21873,plain,
% 2.73/2.97 (~r(s(s(elem!1)), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[14657, 21872, 412, 21834])).
% 2.73/2.97 tff(21874,plain,
% 2.73/2.97 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[701, 21873, 3313])).
% 2.73/2.97 tff(21875,plain,
% 2.73/2.97 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[5254, 21874, 21832, 21824])).
% 2.73/2.97 tff(21876,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[556, 21875, 1])).
% 2.73/2.97 tff(21877,plain,
% 2.73/2.97 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[6878, 21876, 21834, 21866])).
% 2.73/2.97 tff(21878,plain,
% 2.73/2.97 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[526, 21877, 211])).
% 2.73/2.97 tff(21879,plain,
% 2.73/2.97 (b(s(s(z)), s(s(s(z))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21878, 21863])).
% 2.73/2.97 tff(21880,plain,
% 2.73/2.97 (~b(s(z), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[3576, 21849, 317])).
% 2.73/2.97 tff(21881,plain,
% 2.73/2.97 (~(s(s(s(z))) = s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[4929, 21880, 20246])).
% 2.73/2.97 tff(21882,plain,
% 2.73/2.97 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21850])).
% 2.73/2.97 tff(21883,plain,
% 2.73/2.97 (r(z, s(s(z)))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21834, 21882])).
% 2.73/2.97 tff(21884,plain,
% 2.73/2.97 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21850])).
% 2.73/2.97 tff(21885,plain,
% 2.73/2.97 (r(s(s(z)), z)),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[412, 21884])).
% 2.73/2.97 tff(21886,plain,
% 2.73/2.97 (~r(s(s(s(z))), s(s(z)))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21564, 21885, 21871, 21883])).
% 2.73/2.97 tff(21887,plain,
% 2.73/2.97 (~r(s(s(s(z))), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[10458, 21886, 21849])).
% 2.73/2.97 tff(21888,plain,
% 2.73/2.97 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[1816, 21887, 21881])).
% 2.73/2.97 tff(21889,plain,
% 2.73/2.97 (b(s(s(s(z))), s(s(z)))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[14223, 21888, 21849])).
% 2.73/2.97 tff(21890,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21891,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/2.97 inference(quant_inst,[status(thm)],[])).
% 2.73/2.97 tff(21892,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21891, 21890])).
% 2.73/2.97 tff(21893,plain,
% 2.73/2.97 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21892, 271, 21889, 21879])).
% 2.73/2.97 tff(21894,plain,
% 2.73/2.97 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21893, 21862])).
% 2.73/2.97 tff(21895,plain,
% 2.73/2.97 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[10424, 21, 21894, 1138])).
% 2.73/2.97 tff(21896,plain,
% 2.73/2.97 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21856])).
% 2.73/2.97 tff(21897,plain,
% 2.73/2.97 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.97 inference(symmetry,[status(thm)],[21896])).
% 2.73/2.97 tff(21898,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21854])).
% 2.73/2.97 tff(21899,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.97 inference(transitivity,[status(thm)],[21898, 21897])).
% 2.73/2.97 tff(21900,plain,
% 2.73/2.97 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21876, 21899])).
% 2.73/2.97 tff(21901,plain,
% 2.73/2.97 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21855])).
% 2.73/2.97 tff(21902,plain,
% 2.73/2.97 (r(s(s(s(s(z)))), z)),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[6842, 21901])).
% 2.73/2.97 tff(21903,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21904,plain,
% 2.73/2.97 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.73/2.97 inference(rewrite,[status(thm)],[])).
% 2.73/2.97 tff(21905,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21904])).
% 2.73/2.97 tff(21906,plain,
% 2.73/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.73/2.97 inference(transitivity,[status(thm)],[21905, 21903])).
% 2.73/2.97 tff(21907,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.73/2.97 inference(quant_inst,[status(thm)],[])).
% 2.73/2.97 tff(21908,plain,
% 2.73/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21907, 21906])).
% 2.73/2.97 tff(21909,plain,
% 2.73/2.97 ($false),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21908, 121, 21816, 21902, 21900, 21895])).
% 2.73/2.97 tff(21910,plain,((elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | b(elem!1, s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.97 tff(21911,plain,
% 2.73/2.97 (elem!1 = s(s(elem!1))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21910, 317, 412, 6842, 1281, 1, 139, 3407, 259, 100])).
% 2.73/2.97 tff(21912,plain,
% 2.73/2.97 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21911])).
% 2.73/2.97 tff(21913,plain,
% 2.73/2.97 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 2.73/2.97 inference(symmetry,[status(thm)],[21912])).
% 2.73/2.97 tff(21914,plain,
% 2.73/2.97 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21913])).
% 2.73/2.97 tff(21915,plain,
% 2.73/2.97 (~(s(z) = elem!1)),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[2137, 21914])).
% 2.73/2.97 tff(21916,plain,
% 2.73/2.97 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21911])).
% 2.73/2.97 tff(21917,plain,
% 2.73/2.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[139, 21916])).
% 2.73/2.97 tff(21918,plain,
% 2.73/2.97 (s(elem!1) = s(s(s(elem!1)))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21911])).
% 2.73/2.97 tff(21919,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21918])).
% 2.73/2.97 tff(21920,plain,
% 2.73/2.97 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.73/2.97 inference(monotonicity,[status(thm)],[21911])).
% 2.73/2.97 tff(21921,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(elem!1))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[9983, 21920])).
% 2.73/2.97 tff(21922,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21921, 21919])).
% 2.73/2.97 tff(21923,plain,
% 2.73/2.97 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[12230, 6199])).
% 2.73/2.97 tff(21924,plain,
% 2.73/2.97 (~b(elem!1, s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[11002, 220, 1326, 3871])).
% 2.73/2.97 tff(21925,plain,
% 2.73/2.97 (~b(s(s(elem!1)), s(z))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21924, 12397])).
% 2.73/2.97 tff(21926,plain,
% 2.73/2.97 (r(s(s(elem!1)), s(z))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 21925])).
% 2.73/2.97 tff(21927,plain,
% 2.73/2.97 (~r(s(z), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[14540, 21926, 573, 623])).
% 2.73/2.97 tff(21928,plain,
% 2.73/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[760, 21927])).
% 2.73/2.97 tff(21929,plain,
% 2.73/2.97 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[16071, 21928, 220, 3407])).
% 2.73/2.97 tff(21930,plain,
% 2.73/2.97 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[6237, 21, 21929])).
% 2.73/2.97 tff(21931,plain,
% 2.73/2.97 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[21930, 21923])).
% 2.73/2.97 tff(21932,plain,
% 2.73/2.97 (~r(z, s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[11676, 21200, 6842, 21931])).
% 2.73/2.97 tff(21933,plain,
% 2.73/2.97 (b(z, s(s(s(z))))),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[1214, 21932])).
% 2.73/2.97 tff(21934,plain,
% 2.73/2.97 (~b(s(s(s(z))), elem!1)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[19416, 21933, 1281, 3871])).
% 2.73/2.97 tff(21935,plain,
% 2.73/2.97 (r(s(s(s(z))), elem!1)),
% 2.73/2.97 inference(unit_resolution,[status(thm)],[255, 21934, 3907])).
% 2.73/2.97 tff(21936,plain,
% 2.73/2.97 (r(s(s(s(z))), s(s(elem!1)))),
% 2.73/2.97 inference(modus_ponens,[status(thm)],[21935, 3908])).
% 2.73/2.97 tff(21937,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.73/2.98 inference(rewrite,[status(thm)],[])).
% 2.73/2.98 tff(21938,plain,
% 2.73/2.98 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.73/2.98 inference(rewrite,[status(thm)],[])).
% 2.73/2.98 tff(21939,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21938])).
% 2.73/2.98 tff(21940,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.73/2.98 inference(transitivity,[status(thm)],[21939, 21937])).
% 2.73/2.98 tff(21941,plain,
% 2.73/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.73/2.98 inference(quant_inst,[status(thm)],[])).
% 2.73/2.98 tff(21942,plain,
% 2.73/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21941, 21940])).
% 2.73/2.98 tff(21943,plain,
% 2.73/2.98 ($false),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21942, 121, 623, 573, 21936, 21931])).
% 2.73/2.98 tff(21944,plain,((~b(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.98 tff(21945,plain,
% 2.73/2.98 (~b(z, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21944, 21922, 21917, 21911, 1281, 20246, 6842, 3407, 21808])).
% 2.73/2.98 tff(21946,plain,
% 2.73/2.98 (r(z, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[904, 21945])).
% 2.73/2.98 tff(21947,plain,
% 2.73/2.98 (b(elem!1, z)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21021, 21946, 412, 1281, 219, 259])).
% 2.73/2.98 tff(21948,plain,
% 2.73/2.98 (~b(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21030, 21947, 1281, 3407])).
% 2.73/2.98 tff(21949,plain,
% 2.73/2.98 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 2.73/2.98 inference(transitivity,[status(thm)],[21913, 1218])).
% 2.73/2.98 tff(21950,plain,
% 2.73/2.98 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21949])).
% 2.73/2.98 tff(21951,plain,
% 2.73/2.98 (~(elem!1 = s(z))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[2137, 21950])).
% 2.73/2.98 tff(21952,plain,
% 2.73/2.98 (s(s(elem!1)) = elem!1),
% 2.73/2.98 inference(symmetry,[status(thm)],[21911])).
% 2.73/2.98 tff(21953,plain,
% 2.73/2.98 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21952])).
% 2.73/2.98 tff(21954,plain,
% 2.73/2.98 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.73/2.98 inference(transitivity,[status(thm)],[21953, 159])).
% 2.73/2.98 tff(21955,plain,
% 2.73/2.98 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.73/2.98 inference(symmetry,[status(thm)],[21954])).
% 2.73/2.98 tff(21956,plain,
% 2.73/2.98 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21955])).
% 2.73/2.98 tff(21957,plain,
% 2.73/2.98 (~(s(s(s(z))) = elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[3906, 21911])).
% 2.73/2.98 tff(21958,plain,
% 2.73/2.98 (~(elem!1 = s(s(s(z))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[1100, 21957])).
% 2.73/2.98 tff(21959,plain,
% 2.73/2.98 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21958, 21956])).
% 2.73/2.98 tff(21960,plain,
% 2.73/2.98 (s(s(s(elem!1))) = s(elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[7490, 21911])).
% 2.73/2.98 tff(21961,plain,
% 2.73/2.98 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21918])).
% 2.73/2.98 tff(21962,plain,
% 2.73/2.98 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.73/2.98 inference(symmetry,[status(thm)],[21961])).
% 2.73/2.98 tff(21963,plain,
% 2.73/2.98 (b(z, s(elem!1))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[3407, 21962])).
% 2.73/2.98 tff(21964,plain,
% 2.73/2.98 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21918])).
% 2.73/2.98 tff(21965,plain,
% 2.73/2.98 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(elem!1))),
% 2.73/2.98 inference(symmetry,[status(thm)],[21964])).
% 2.73/2.98 tff(21966,plain,
% 2.73/2.98 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21965])).
% 2.73/2.98 tff(21967,plain,
% 2.73/2.98 (~(s(z) = s(elem!1))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[61, 21966])).
% 2.73/2.98 tff(21968,plain,
% 2.73/2.98 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21911])).
% 2.73/2.98 tff(21969,plain,
% 2.73/2.98 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 2.73/2.98 inference(symmetry,[status(thm)],[21968])).
% 2.73/2.98 tff(21970,plain,
% 2.73/2.98 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21918])).
% 2.73/2.98 tff(21971,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(symmetry,[status(thm)],[21970])).
% 2.73/2.98 tff(21972,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 2.73/2.98 inference(transitivity,[status(thm)],[21971, 21969])).
% 2.73/2.98 tff(21973,plain,
% 2.73/2.98 (r(s(elem!1), elem!1)),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21917, 21972])).
% 2.73/2.98 tff(21974,plain,
% 2.73/2.98 (~r(elem!1, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[9263, 431, 379, 1326, 348, 1281])).
% 2.73/2.98 tff(21975,plain,
% 2.73/2.98 (b(elem!1, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[297, 21, 21974, 258])).
% 2.73/2.98 tff(21976,plain,
% 2.73/2.98 (~b(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[4760, 21975, 1326, 1281])).
% 2.73/2.98 tff(21977,plain,
% 2.73/2.98 (r(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[236, 21976, 1257])).
% 2.73/2.98 tff(21978,plain,
% 2.73/2.98 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 2.73/2.98 inference(rewrite,[status(thm)],[])).
% 2.73/2.98 tff(21979,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21978])).
% 2.73/2.98 tff(21980,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 2.73/2.98 inference(transitivity,[status(thm)],[21979, 9620])).
% 2.73/2.98 tff(21981,plain,
% 2.73/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 2.73/2.98 inference(quant_inst,[status(thm)],[])).
% 2.73/2.98 tff(21982,plain,
% 2.73/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21981, 21980])).
% 2.73/2.98 tff(21983,plain,
% 2.73/2.98 ($false),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21982, 121, 379, 622, 21977, 431])).
% 2.73/2.98 tff(21984,plain,((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (elem!1 = s(z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.98 tff(21985,plain,
% 2.73/2.98 (~r(s(z), s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21984, 21973, 1281, 21808, 21951, 9983, 21967])).
% 2.73/2.98 tff(21986,plain,
% 2.73/2.98 (b(s(z), s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[444, 21985, 21967])).
% 2.73/2.98 tff(21987,plain,
% 2.73/2.98 (~b(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[2905, 21986, 1281, 21963])).
% 2.73/2.98 tff(21988,plain,
% 2.73/2.98 (~b(s(elem!1), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[3787, 21987, 21911])).
% 2.73/2.98 tff(21989,plain,
% 2.73/2.98 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[7281, 21988, 21960])).
% 2.73/2.98 tff(21990,plain,
% 2.73/2.98 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[3952, 21946, 9983, 412, 21911, 21959, 21988, 20992, 21986, 21808, 211])).
% 2.73/2.98 tff(21991,plain,
% 2.73/2.98 (~r(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[5759, 21990, 9983, 20992, 21989, 412, 21959, 21946, 1391, 21951])).
% 2.73/2.98 tff(21992,plain,
% 2.73/2.98 ($false),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[236, 21991, 21948, 21915])).
% 2.73/2.98 tff(21993,plain,(b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | r(z, elem!1) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.98 tff(21994,plain,
% 2.73/2.98 (b(elem!1, s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21993, 259, 1391, 1281, 3407, 412, 6842, 139, 1, 100])).
% 2.73/2.98 tff(21995,plain,
% 2.73/2.98 (~b(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[20382, 21994, 21808, 1281])).
% 2.73/2.98 tff(21996,plain,
% 2.73/2.98 (~b(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[20382, 307, 21808, 1281])).
% 2.73/2.98 tff(21997,plain,
% 2.73/2.98 (elem!1 = s(z)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[18965, 21848, 139, 21996, 21814])).
% 2.73/2.98 tff(21998,plain,
% 2.73/2.98 (s(elem!1) = s(s(z))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21997])).
% 2.73/2.98 tff(21999,plain,
% 2.73/2.98 (s(s(elem!1)) = s(s(s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21998])).
% 2.73/2.98 tff(22000,plain,
% 2.73/2.98 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21999])).
% 2.73/2.98 tff(22001,plain,
% 2.73/2.98 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21999])).
% 2.73/2.98 tff(22002,plain,
% 2.73/2.98 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22001])).
% 2.73/2.98 tff(22003,plain,
% 2.73/2.98 (r(z, s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21816, 22002])).
% 2.73/2.98 tff(22004,plain,
% 2.73/2.98 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21999])).
% 2.73/2.98 tff(22005,plain,
% 2.73/2.98 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.73/2.98 inference(symmetry,[status(thm)],[22004])).
% 2.73/2.98 tff(22006,plain,
% 2.73/2.98 (b(z, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[1397, 21997, 21808])).
% 2.73/2.98 tff(22007,plain,
% 2.73/2.98 (~b(s(s(s(z))), z)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21058, 22006, 1281, 20246])).
% 2.73/2.98 tff(22008,plain,
% 2.73/2.98 (r(s(s(s(z))), z)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[1155, 22007])).
% 2.73/2.98 tff(22009,plain,
% 2.73/2.98 (r(s(s(elem!1)), z)),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22008, 22005])).
% 2.73/2.98 tff(22010,plain,
% 2.73/2.98 (~r(s(s(elem!1)), s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[4880, 22009, 412, 22003])).
% 2.73/2.98 tff(22011,plain,
% 2.73/2.98 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[701, 22010, 3313])).
% 2.73/2.98 tff(22012,plain,
% 2.73/2.98 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21998])).
% 2.73/2.98 tff(22013,plain,
% 2.73/2.98 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22012])).
% 2.73/2.98 tff(22014,plain,
% 2.73/2.98 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21999])).
% 2.73/2.98 tff(22015,plain,
% 2.73/2.98 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22014])).
% 2.73/2.98 tff(22016,plain,
% 2.73/2.98 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22015])).
% 2.73/2.98 tff(22017,plain,
% 2.73/2.98 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21998])).
% 2.73/2.98 tff(22018,plain,
% 2.73/2.98 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.98 inference(transitivity,[status(thm)],[22017, 22016, 22013])).
% 2.73/2.98 tff(22019,plain,
% 2.73/2.98 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22014])).
% 2.73/2.98 tff(22020,plain,
% 2.73/2.98 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22019])).
% 2.73/2.98 tff(22021,plain,
% 2.73/2.98 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21831, 22020])).
% 2.73/2.98 tff(22022,plain,
% 2.73/2.98 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22014])).
% 2.73/2.98 tff(22023,plain,
% 2.73/2.98 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21998, 22022])).
% 2.73/2.98 tff(22024,plain,
% 2.73/2.98 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.73/2.98 inference(transitivity,[status(thm)],[22023, 10493])).
% 2.73/2.98 tff(22025,plain,
% 2.73/2.98 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22024])).
% 2.73/2.98 tff(22026,plain,
% 2.73/2.98 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22025])).
% 2.73/2.98 tff(22027,plain,
% 2.73/2.98 (s(s(z)) = s(elem!1)),
% 2.73/2.98 inference(symmetry,[status(thm)],[21998])).
% 2.73/2.98 tff(22028,plain,
% 2.73/2.98 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22027])).
% 2.73/2.98 tff(22029,plain,
% 2.73/2.98 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22028])).
% 2.73/2.98 tff(22030,plain,
% 2.73/2.98 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22029])).
% 2.73/2.98 tff(22031,plain,
% 2.73/2.98 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[79, 22030])).
% 2.73/2.98 tff(22032,plain,
% 2.73/2.98 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22031, 22026])).
% 2.73/2.98 tff(22033,plain,
% 2.73/2.98 (b(s(elem!1), s(s(s(s(z)))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[1995, 22032, 22021])).
% 2.73/2.98 tff(22034,plain,
% 2.73/2.98 (b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22033, 22018])).
% 2.73/2.98 tff(22035,plain,
% 2.73/2.98 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[5254, 22034, 22011, 21824])).
% 2.73/2.98 tff(22036,plain,
% 2.73/2.98 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[556, 22035, 1])).
% 2.73/2.98 tff(22037,plain,
% 2.73/2.98 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22036, 22000])).
% 2.73/2.98 tff(22038,plain,
% 2.73/2.98 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22022])).
% 2.73/2.98 tff(22039,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22038])).
% 2.73/2.98 tff(22040,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21997])).
% 2.73/2.98 tff(22041,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(z))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[139, 22040])).
% 2.73/2.98 tff(22042,plain,
% 2.73/2.98 (r(s(s(s(s(z)))), s(z))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22041, 22039])).
% 2.73/2.98 tff(22043,plain,
% 2.73/2.98 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22014])).
% 2.73/2.98 tff(22044,plain,
% 2.73/2.98 (r(s(z), s(s(s(s(z)))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21848, 22043])).
% 2.73/2.98 tff(22045,plain,
% 2.73/2.98 (b(elem!1, s(s(s(z))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[11114, 21997, 20246])).
% 2.73/2.98 tff(22046,plain,
% 2.73/2.98 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22014])).
% 2.73/2.98 tff(22047,plain,
% 2.73/2.98 (b(z, s(s(s(s(z)))))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[3407, 22046])).
% 2.73/2.98 tff(22048,plain,
% 2.73/2.98 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21998])).
% 2.73/2.98 tff(22049,plain,
% 2.73/2.98 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22048])).
% 2.73/2.98 tff(22050,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22014])).
% 2.73/2.98 tff(22051,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.98 inference(transitivity,[status(thm)],[22050, 22049])).
% 2.73/2.98 tff(22052,plain,
% 2.73/2.98 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22051])).
% 2.73/2.98 tff(22053,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[21998])).
% 2.73/2.98 tff(22054,plain,
% 2.73/2.98 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(s(z))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22053])).
% 2.73/2.98 tff(22055,plain,
% 2.73/2.98 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21823, 22054])).
% 2.73/2.98 tff(22056,plain,
% 2.73/2.98 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22055, 22052])).
% 2.73/2.98 tff(22057,plain,
% 2.73/2.98 (~b(z, s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[14020, 22021, 22056, 22032, 22047])).
% 2.73/2.98 tff(22058,plain,
% 2.73/2.98 (r(z, s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[1439, 22057])).
% 2.73/2.98 tff(22059,plain,
% 2.73/2.98 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[6878, 22036, 22058, 22003])).
% 2.73/2.98 tff(22060,plain,
% 2.73/2.98 (b(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[526, 22059, 211])).
% 2.73/2.98 tff(22061,plain,
% 2.73/2.98 (b(s(elem!1), s(s(s(z))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[2369, 22060, 21997])).
% 2.73/2.98 tff(22062,plain,
% 2.73/2.98 (~b(s(s(s(z))), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[10690, 22061, 307, 22045])).
% 2.73/2.98 tff(22063,plain,
% 2.73/2.98 (r(s(s(s(z))), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[2325, 22062])).
% 2.73/2.98 tff(22064,plain,
% 2.73/2.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21540, 22063, 22044, 22042])).
% 2.73/2.98 tff(22065,plain,
% 2.73/2.98 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[8812, 22064, 21997])).
% 2.73/2.98 tff(22066,plain,
% 2.73/2.98 ($false),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[22065, 22037])).
% 2.73/2.98 tff(22067,plain,((elem!1 = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | r(s(z), s(s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.98 tff(22068,plain,
% 2.73/2.98 (elem!1 = s(s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[22067, 21994, 1, 412, 3407, 139, 1281, 6842, 100, 259])).
% 2.73/2.98 tff(22069,plain,
% 2.73/2.98 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22068])).
% 2.73/2.98 tff(22070,plain,
% 2.73/2.98 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 2.73/2.98 inference(symmetry,[status(thm)],[22069])).
% 2.73/2.98 tff(22071,plain,
% 2.73/2.98 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 2.73/2.98 inference(transitivity,[status(thm)],[22070, 1218])).
% 2.73/2.98 tff(22072,plain,
% 2.73/2.98 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22071])).
% 2.73/2.98 tff(22073,plain,
% 2.73/2.98 (~(elem!1 = s(z))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[2137, 22072])).
% 2.73/2.98 tff(22074,plain,
% 2.73/2.98 (~r(s(z), s(s(s(elem!1))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[18965, 22073, 139, 21995, 21814])).
% 2.73/2.98 tff(22075,plain,
% 2.73/2.98 (b(s(z), s(s(s(elem!1))))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[760, 22074])).
% 2.73/2.98 tff(22076,plain,
% 2.73/2.98 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22070])).
% 2.73/2.98 tff(22077,plain,
% 2.73/2.98 (~(s(z) = elem!1)),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[2137, 22076])).
% 2.73/2.98 tff(22078,plain,
% 2.73/2.98 (r(s(z), elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[236, 22077, 21995])).
% 2.73/2.98 tff(22079,plain,
% 2.73/2.98 (s(elem!1) = s(s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22068])).
% 2.73/2.98 tff(22080,plain,
% 2.73/2.98 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22079])).
% 2.73/2.98 tff(22081,plain,
% 2.73/2.98 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22080])).
% 2.73/2.98 tff(22082,plain,
% 2.73/2.98 (b(z, s(elem!1))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[3407, 22081])).
% 2.73/2.98 tff(22083,plain,
% 2.73/2.98 (~b(s(elem!1), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[4122, 22082, 21808, 21994])).
% 2.73/2.98 tff(22084,plain,
% 2.73/2.98 (r(s(elem!1), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[429, 22083, 20999])).
% 2.73/2.98 tff(22085,plain,
% 2.73/2.98 (~r(z, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[1254, 22084, 412, 22078])).
% 2.73/2.98 tff(22086,plain,
% 2.73/2.98 (b(z, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[904, 22085])).
% 2.73/2.98 tff(22087,plain,
% 2.73/2.98 (~b(s(s(s(elem!1))), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[17333, 22086, 22075, 3407])).
% 2.73/2.98 tff(22088,plain,
% 2.73/2.98 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22068])).
% 2.73/2.98 tff(22089,plain,
% 2.73/2.98 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22088])).
% 2.73/2.98 tff(22090,plain,
% 2.73/2.98 (~b(s(s(elem!1)), s(z))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21814, 22089])).
% 2.73/2.98 tff(22091,plain,
% 2.73/2.98 (r(s(s(elem!1)), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 22090])).
% 2.73/2.98 tff(22092,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22068])).
% 2.73/2.98 tff(22093,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[139, 22092])).
% 2.73/2.98 tff(22094,plain,
% 2.73/2.98 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22068])).
% 2.73/2.98 tff(22095,plain,
% 2.73/2.98 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(elem!1))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22094])).
% 2.73/2.98 tff(22096,plain,
% 2.73/2.98 (~b(s(z), s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21995, 22095])).
% 2.73/2.98 tff(22097,plain,
% 2.73/2.98 (r(s(z), s(s(elem!1)))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[2167, 22096])).
% 2.73/2.98 tff(22098,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.73/2.98 inference(rewrite,[status(thm)],[])).
% 2.73/2.98 tff(22099,plain,
% 2.73/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.73/2.98 inference(quant_inst,[status(thm)],[])).
% 2.73/2.98 tff(22100,plain,
% 2.73/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22099, 22098])).
% 2.73/2.98 tff(22101,plain,
% 2.73/2.98 (~r(s(s(s(elem!1))), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[22100, 121, 22097, 22093, 22091])).
% 2.73/2.98 tff(22102,plain,
% 2.73/2.98 ($false),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[66, 21, 22101, 22087, 63])).
% 2.73/2.98 tff(22103,plain,((elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | r(s(z), s(s(s(z)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.98 tff(22104,plain,
% 2.73/2.98 (r(z, elem!1)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[22103, 21807, 20979, 21712, 1, 1281, 20245, 100, 20244])).
% 2.73/2.98 tff(22105,plain,
% 2.73/2.98 (~r(elem!1, s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[8972, 22104, 21712, 20245])).
% 2.73/2.98 tff(22106,plain,
% 2.73/2.98 (b(elem!1, s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[392, 22105, 219])).
% 2.73/2.98 tff(22107,plain,
% 2.73/2.98 (elem!1 = s(s(elem!1))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[22067, 22106, 1, 20979, 20244, 21712, 1281, 20245, 100, 21807])).
% 2.73/2.98 tff(22108,plain,
% 2.73/2.98 (s(elem!1) = s(s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22107])).
% 2.73/2.98 tff(22109,plain,
% 2.73/2.98 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22108])).
% 2.73/2.98 tff(22110,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(symmetry,[status(thm)],[22109])).
% 2.73/2.98 tff(22111,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22107])).
% 2.73/2.98 tff(22112,plain,
% 2.73/2.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[21712, 22111])).
% 2.73/2.98 tff(22113,plain,
% 2.73/2.98 (r(s(elem!1), s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22112, 22110])).
% 2.73/2.98 tff(22114,plain,
% 2.73/2.98 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22107])).
% 2.73/2.98 tff(22115,plain,
% 2.73/2.98 (r(z, s(s(elem!1)))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22104, 22114])).
% 2.73/2.98 tff(22116,plain,
% 2.73/2.98 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22107])).
% 2.73/2.98 tff(22117,plain,
% 2.73/2.98 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22116])).
% 2.73/2.98 tff(22118,plain,
% 2.73/2.98 (~b(elem!1, s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[21813, 21807, 1281, 219, 20979, 21799])).
% 2.73/2.98 tff(22119,plain,
% 2.73/2.98 (~b(s(s(elem!1)), s(z))),
% 2.73/2.98 inference(modus_ponens,[status(thm)],[22118, 22117])).
% 2.73/2.98 tff(22120,plain,
% 2.73/2.98 (r(s(s(elem!1)), s(z))),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 22119])).
% 2.73/2.98 tff(22121,plain,
% 2.73/2.98 ($false),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[5431, 22120, 22115, 20979, 22113])).
% 2.73/2.98 tff(22122,plain,(b(s(s(s(elem!1))), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | r(s(z), s(s(s(z)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.98 tff(22123,plain,
% 2.73/2.98 (b(s(s(s(elem!1))), z)),
% 2.73/2.98 inference(unit_resolution,[status(thm)],[22122, 1, 1281, 100, 19734])).
% 2.73/2.98 tff(22124,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.73/2.98 inference(rewrite,[status(thm)],[])).
% 2.73/2.98 tff(22125,plain,
% 2.73/2.98 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.73/2.98 inference(rewrite,[status(thm)],[])).
% 2.73/2.98 tff(22126,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.73/2.98 inference(monotonicity,[status(thm)],[22125])).
% 2.73/2.98 tff(22127,plain,
% 2.73/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.73/2.99 inference(transitivity,[status(thm)],[22126, 22124])).
% 2.73/2.99 tff(22128,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22129,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22128, 22127])).
% 2.73/2.99 tff(22130,plain,
% 2.73/2.99 (~b(s(z), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22129, 271, 1281, 3407, 1638])).
% 2.73/2.99 tff(22131,plain,
% 2.73/2.99 (~(elem!1 = z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[9876, 22130, 20246])).
% 2.73/2.99 tff(22132,plain,
% 2.73/2.99 (~(s(z) = s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[343, 365])).
% 2.73/2.99 tff(22133,plain,
% 2.73/2.99 (~(s(elem!1) = s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[350, 22132])).
% 2.73/2.99 tff(22134,plain,
% 2.73/2.99 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13282, 271, 394, 3407, 1638])).
% 2.73/2.99 tff(22135,plain,
% 2.73/2.99 (r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2293, 21, 22134, 6201])).
% 2.73/2.99 tff(22136,plain,
% 2.73/2.99 (r(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[429, 20262, 422])).
% 2.73/2.99 tff(22137,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22138,plain,
% 2.73/2.99 (((~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22139,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.73/2.99 inference(monotonicity,[status(thm)],[22138])).
% 2.73/2.99 tff(22140,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.73/2.99 inference(transitivity,[status(thm)],[22139, 22137])).
% 2.73/2.99 tff(22141,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22142,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22141, 22140])).
% 2.73/2.99 tff(22143,plain,
% 2.73/2.99 (~b(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22142, 271, 1281, 3407, 1638])).
% 2.73/2.99 tff(22144,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[66, 21, 22143, 63])).
% 2.73/2.99 tff(22145,plain,
% 2.73/2.99 (r(s(z), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[760, 22130])).
% 2.73/2.99 tff(22146,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13276, 121, 22145, 22144, 22136, 22135])).
% 2.73/2.99 tff(22147,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22148,plain,
% 2.73/2.99 (~b(s(elem!1), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22147, 22133, 85, 3407, 1638, 1281])).
% 2.73/2.99 tff(22149,plain,
% 2.73/2.99 (r(s(elem!1), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[409, 22148])).
% 2.73/2.99 tff(22150,plain,
% 2.73/2.99 (~b(z, s(s(s(z))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[21634, 22149, 100, 3407, 1281, 68, 1, 259])).
% 2.73/2.99 tff(22151,plain,
% 2.73/2.99 (b(s(s(s(elem!1))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[486, 147, 13588])).
% 2.73/2.99 tff(22152,plain,
% 2.73/2.99 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[4393, 379, 3407, 412, 331, 4358, 13223])).
% 2.73/2.99 tff(22153,plain,
% 2.73/2.99 (~r(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[3683, 379, 412, 378])).
% 2.73/2.99 tff(22154,plain,
% 2.73/2.99 (b(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2243, 22153, 2207])).
% 2.73/2.99 tff(22155,plain,
% 2.73/2.99 (r(elem!1, s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[10472, 22154, 82, 504, 22152])).
% 2.73/2.99 tff(22156,plain,
% 2.73/2.99 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[681, 22152, 82])).
% 2.73/2.99 tff(22157,plain,
% 2.73/2.99 (~b(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[19650, 504, 638, 2618])).
% 2.73/2.99 tff(22158,plain,
% 2.73/2.99 (r(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[297, 21, 22157, 258])).
% 2.73/2.99 tff(22159,plain,
% 2.73/2.99 (~(s(s(s(elem!1))) = s(z))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[11298, 2860])).
% 2.73/2.99 tff(22160,plain,
% 2.73/2.99 (~r(s(z), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[3709, 22158, 379, 412])).
% 2.73/2.99 tff(22161,plain,
% 2.73/2.99 (b(s(z), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[442, 21, 348, 22160])).
% 2.73/2.99 tff(22162,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22163,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22164,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22163, 22162])).
% 2.73/2.99 tff(22165,plain,
% 2.73/2.99 (~b(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22164, 271, 2618, 22161, 638])).
% 2.73/2.99 tff(22166,plain,
% 2.73/2.99 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[66, 21, 22165])).
% 2.73/2.99 tff(22167,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22166, 22159])).
% 2.73/2.99 tff(22168,plain,
% 2.73/2.99 (~b(s(z), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[5852, 22158, 624, 543, 638])).
% 2.73/2.99 tff(22169,plain,
% 2.73/2.99 (r(s(z), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[759, 22168, 11298])).
% 2.73/2.99 tff(22170,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22171,plain,
% 2.73/2.99 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22172,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 2.73/2.99 inference(monotonicity,[status(thm)],[22171])).
% 2.73/2.99 tff(22173,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.73/2.99 inference(transitivity,[status(thm)],[22172, 22170])).
% 2.73/2.99 tff(22174,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22175,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22174, 22173])).
% 2.73/2.99 tff(22176,plain,
% 2.73/2.99 (~r(elem!1, s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22175, 121, 22169, 22167, 22158])).
% 2.73/2.99 tff(22177,plain,
% 2.73/2.99 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[660, 21, 22176])).
% 2.73/2.99 tff(22178,plain,
% 2.73/2.99 (b(elem!1, s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22177, 656])).
% 2.73/2.99 tff(22179,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[14157, 271, 2618, 638, 504, 22178])).
% 2.73/2.99 tff(22180,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (s(z) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22181,plain,
% 2.73/2.99 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (s(z) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22180, 61])).
% 2.73/2.99 tff(22182,plain,
% 2.73/2.99 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22181, 22155, 13223, 22154, 22156, 344, 504, 379, 412, 258])).
% 2.73/2.99 tff(22183,plain,
% 2.73/2.99 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[556, 22182, 1])).
% 2.73/2.99 tff(22184,plain,
% 2.73/2.99 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2199, 22183, 22155, 379])).
% 2.73/2.99 tff(22185,plain,
% 2.73/2.99 (~r(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[12090, 379, 412, 378])).
% 2.73/2.99 tff(22186,plain,
% 2.73/2.99 (b(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1439, 22185])).
% 2.73/2.99 tff(22187,plain,
% 2.73/2.99 (~b(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[19650, 22156, 504, 22154])).
% 2.73/2.99 tff(22188,plain,
% 2.73/2.99 (r(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[299, 22187, 258])).
% 2.73/2.99 tff(22189,plain,
% 2.73/2.99 (~r(s(z), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[3709, 22188, 412, 379])).
% 2.73/2.99 tff(22190,plain,
% 2.73/2.99 (b(s(z), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[444, 22189, 344])).
% 2.73/2.99 tff(22191,plain,
% 2.73/2.99 (~b(s(elem!1), s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2905, 22190, 1281, 22186])).
% 2.73/2.99 tff(22192,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[526, 22191, 22184, 211])).
% 2.73/2.99 tff(22193,plain,((~r(elem!1, s(elem!1))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22194,plain,
% 2.73/2.99 (~r(elem!1, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22193, 258, 1, 412, 22151, 1281, 79, 366, 3407, 365, 13208])).
% 2.73/2.99 tff(22195,plain,
% 2.73/2.99 (b(elem!1, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[392, 22194, 219])).
% 2.73/2.99 tff(22196,plain,
% 2.73/2.99 (~r(z, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[21036, 1257, 199, 412, 219, 1281, 3407, 259])).
% 2.73/2.99 tff(22197,plain,
% 2.73/2.99 (b(z, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[904, 22196])).
% 2.73/2.99 tff(22198,plain,
% 2.73/2.99 (~r(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[5343, 3456, 412, 378])).
% 2.73/2.99 tff(22199,plain,
% 2.73/2.99 (b(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2243, 22198, 2207])).
% 2.73/2.99 tff(22200,plain,
% 2.73/2.99 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2930, 271, 307, 22199, 11843])).
% 2.73/2.99 tff(22201,plain,
% 2.73/2.99 (r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2293, 21, 22200, 85])).
% 2.73/2.99 tff(22202,plain,
% 2.73/2.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[3177, 271, 307, 22199, 11843])).
% 2.73/2.99 tff(22203,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[681, 22202, 79])).
% 2.73/2.99 tff(22204,plain,
% 2.73/2.99 (~r(s(z), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13742, 121, 22203, 572, 22201])).
% 2.73/2.99 tff(22205,plain,
% 2.73/2.99 (b(s(z), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[444, 22204, 348])).
% 2.73/2.99 tff(22206,plain,
% 2.73/2.99 (~r(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13411, 121, 22203, 572, 22201])).
% 2.73/2.99 tff(22207,plain,
% 2.73/2.99 (b(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[429, 22206, 2282])).
% 2.73/2.99 tff(22208,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22209,plain,
% 2.73/2.99 (((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22210,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 2.73/2.99 inference(monotonicity,[status(thm)],[22209])).
% 2.73/2.99 tff(22211,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.73/2.99 inference(transitivity,[status(thm)],[22210, 22208])).
% 2.73/2.99 tff(22212,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22213,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22212, 22211])).
% 2.73/2.99 tff(22214,plain,
% 2.73/2.99 (~b(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22213, 271, 1281, 220, 22207])).
% 2.73/2.99 tff(22215,plain,
% 2.73/2.99 (r(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1439, 22214])).
% 2.73/2.99 tff(22216,plain,
% 2.73/2.99 (~b(s(s(elem!1)), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[16949, 981, 1281, 220])).
% 2.73/2.99 tff(22217,plain,
% 2.73/2.99 (r(s(s(elem!1)), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2430, 22216])).
% 2.73/2.99 tff(22218,plain,
% 2.73/2.99 (~r(s(s(elem!1)), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[14657, 22217, 412, 1441])).
% 2.73/2.99 tff(22219,plain,
% 2.73/2.99 (b(s(s(elem!1)), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[701, 22218, 694])).
% 2.73/2.99 tff(22220,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22221,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22222,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22221, 22220])).
% 2.73/2.99 tff(22223,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22222, 271, 2618, 446, 981, 22219])).
% 2.73/2.99 tff(22224,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22225,plain,
% 2.73/2.99 (~b(s(s(elem!1)), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22224, 22215, 22199, 3313, 412, 22205, 1281, 220])).
% 2.73/2.99 tff(22226,plain,
% 2.73/2.99 (r(s(s(elem!1)), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2143, 22225])).
% 2.73/2.99 tff(22227,plain,
% 2.73/2.99 (~r(elem!1, s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22175, 121, 572, 12761, 3456])).
% 2.73/2.99 tff(22228,plain,
% 2.73/2.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2125, 22226, 572, 22203])).
% 2.73/2.99 tff(22229,plain,
% 2.73/2.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[556, 22228, 1])).
% 2.73/2.99 tff(22230,plain,
% 2.73/2.99 (~b(elem!1, s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[11908, 22229, 147, 481, 22227])).
% 2.73/2.99 tff(22231,plain,
% 2.73/2.99 (r(elem!1, s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[599, 22230, 68])).
% 2.73/2.99 tff(22232,plain,
% 2.73/2.99 (~r(z, s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[5075, 22231, 378, 22226])).
% 2.73/2.99 tff(22233,plain,
% 2.73/2.99 (b(z, s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2106, 22232])).
% 2.73/2.99 tff(22234,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[15601, 271, 22229, 22233, 3407, 11843])).
% 2.73/2.99 tff(22235,plain,((~r(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22236,plain,
% 2.73/2.99 (~r(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22235, 22197, 366, 68, 147, 13588, 1, 572, 412, 1281, 3407, 22132, 12761, 22195])).
% 2.73/2.99 tff(22237,plain,
% 2.73/2.99 (b(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[299, 22236, 258])).
% 2.73/2.99 tff(22238,plain,
% 2.73/2.99 (~b(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1290, 22237, 1281, 22195])).
% 2.73/2.99 tff(22239,plain,
% 2.73/2.99 (r(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[429, 22238, 22133])).
% 2.73/2.99 tff(22240,plain,
% 2.73/2.99 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13276, 121, 572, 12761, 22239])).
% 2.73/2.99 tff(22241,plain,
% 2.73/2.99 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13251, 121, 572, 12761, 22239])).
% 2.73/2.99 tff(22242,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[11152, 22241, 22240, 79, 22151, 22195])).
% 2.73/2.99 tff(22243,plain,((elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22244,plain,
% 2.73/2.99 (elem!1 = s(z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22243, 147, 12761, 1281, 68, 572, 1, 412, 3407, 199, 259])).
% 2.73/2.99 tff(22245,plain,
% 2.73/2.99 (s(z) = elem!1),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[242, 22244])).
% 2.73/2.99 tff(22246,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.73/2.99 inference(monotonicity,[status(thm)],[22245])).
% 2.73/2.99 tff(22247,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(symmetry,[status(thm)],[22246])).
% 2.73/2.99 tff(22248,plain,
% 2.73/2.99 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), s(z)))),
% 2.73/2.99 inference(monotonicity,[status(thm)],[22247])).
% 2.73/2.99 tff(22249,plain,
% 2.73/2.99 (~r(s(s(s(elem!1))), s(z))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[147, 22248])).
% 2.73/2.99 tff(22250,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[12761, 22249])).
% 2.73/2.99 tff(22251,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22252,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22251, 22149, 1281, 68, 22145, 1, 22144, 3407, 199, 259])).
% 2.73/2.99 tff(22253,plain,
% 2.73/2.99 (~b(s(s(s(z))), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[21058, 22197, 1281, 3871])).
% 2.73/2.99 tff(22254,plain,
% 2.73/2.99 (r(s(s(s(z))), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1155, 22253])).
% 2.73/2.99 tff(22255,plain,
% 2.73/2.99 (~r(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[3683, 3502, 412, 378])).
% 2.73/2.99 tff(22256,plain,
% 2.73/2.99 (b(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2243, 22255, 3500])).
% 2.73/2.99 tff(22257,plain,
% 2.73/2.99 (~b(s(s(s(z))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[21089, 22256, 412, 378, 258, 3502, 3871, 348, 109, 1209])).
% 2.73/2.99 tff(22258,plain,
% 2.73/2.99 (~r(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[12090, 3502, 412, 378])).
% 2.73/2.99 tff(22259,plain,
% 2.73/2.99 (b(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1439, 22258])).
% 2.73/2.99 tff(22260,plain,
% 2.73/2.99 (~(s(s(s(z))) = s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[16218, 22259, 1209])).
% 2.73/2.99 tff(22261,plain,
% 2.73/2.99 (b(s(s(s(z))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1816, 22260, 21067])).
% 2.73/2.99 tff(22262,plain,
% 2.73/2.99 (~(s(s(s(z))) = elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[6165, 22261, 317])).
% 2.73/2.99 tff(22263,plain,
% 2.73/2.99 (r(s(s(s(z))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[255, 22262, 22257])).
% 2.73/2.99 tff(22264,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[10254, 121, 3502, 378, 22263, 109])).
% 2.73/2.99 tff(22265,plain,(b(elem!1, s(elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~r(s(elem!1), z)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22266,plain,
% 2.73/2.99 (b(elem!1, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22265, 22254, 366, 1209, 412, 258, 3871, 22132, 219])).
% 2.73/2.99 tff(22267,plain,
% 2.73/2.99 ($false),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[3992, 121, 572, 139, 12761, 3456])).
% 2.73/2.99 tff(22268,plain,((~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.99 tff(22269,plain,
% 2.73/2.99 (~r(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22268, 139, 572, 12761])).
% 2.73/2.99 tff(22270,plain,
% 2.73/2.99 (b(elem!1, s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[299, 258, 22269])).
% 2.73/2.99 tff(22271,plain,
% 2.73/2.99 (~b(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1290, 22266, 1281, 22270])).
% 2.73/2.99 tff(22272,plain,
% 2.73/2.99 (r(s(elem!1), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[429, 22271, 22133])).
% 2.73/2.99 tff(22273,plain,
% 2.73/2.99 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13251, 121, 572, 12761, 22272])).
% 2.73/2.99 tff(22274,plain,
% 2.73/2.99 (~r(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[21783, 22273, 3407, 412, 3871, 1, 366, 22266, 1281, 199, 259])).
% 2.73/2.99 tff(22275,plain,
% 2.73/2.99 (b(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2243, 22274, 2207])).
% 2.73/2.99 tff(22276,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22277,plain,
% 2.73/2.99 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 2.73/2.99 inference(rewrite,[status(thm)],[])).
% 2.73/2.99 tff(22278,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 2.73/2.99 inference(monotonicity,[status(thm)],[22277])).
% 2.73/2.99 tff(22279,plain,
% 2.73/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 2.73/2.99 inference(transitivity,[status(thm)],[22278, 22276])).
% 2.73/2.99 tff(22280,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.73/2.99 inference(quant_inst,[status(thm)],[])).
% 2.73/2.99 tff(22281,plain,
% 2.73/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 2.73/2.99 inference(modus_ponens,[status(thm)],[22280, 22279])).
% 2.73/2.99 tff(22282,plain,
% 2.73/2.99 (~b(elem!1, z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[22281, 271, 1281, 22270, 22197])).
% 2.73/2.99 tff(22283,plain,
% 2.73/2.99 (r(elem!1, z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[284, 22282, 259])).
% 2.73/2.99 tff(22284,plain,
% 2.73/2.99 (~r(s(s(elem!1)), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[6958, 22283, 139, 1, 563, 366])).
% 2.73/2.99 tff(22285,plain,
% 2.73/2.99 (b(s(s(elem!1)), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[862, 22284, 851])).
% 2.73/2.99 tff(22286,plain,
% 2.73/2.99 (~b(s(s(elem!1)), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[6807, 22285, 22266, 22275])).
% 2.73/2.99 tff(22287,plain,
% 2.73/2.99 (r(s(s(elem!1)), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[701, 22286, 3313])).
% 2.73/2.99 tff(22288,plain,
% 2.73/2.99 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[681, 22273, 82])).
% 2.73/2.99 tff(22289,plain,
% 2.73/2.99 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[13276, 121, 572, 12761, 22272])).
% 2.73/2.99 tff(22290,plain,
% 2.73/2.99 (b(s(elem!1), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2293, 21, 22289, 2280])).
% 2.73/2.99 tff(22291,plain,
% 2.73/2.99 (~b(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[14647, 271, 3407, 22290, 22288])).
% 2.73/2.99 tff(22292,plain,
% 2.73/2.99 (r(z, s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[1439, 22291])).
% 2.73/2.99 tff(22293,plain,
% 2.73/2.99 (~r(s(s(elem!1)), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[14657, 22292, 412, 22287])).
% 2.73/2.99 tff(22294,plain,
% 2.73/2.99 (b(s(s(elem!1)), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2430, 22293])).
% 2.73/2.99 tff(22295,plain,
% 2.73/2.99 (~b(s(s(elem!1)), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[16949, 22294, 1281, 22197])).
% 2.73/2.99 tff(22296,plain,
% 2.73/2.99 (r(s(s(elem!1)), s(z))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2143, 22295])).
% 2.73/2.99 tff(22297,plain,
% 2.73/2.99 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[5267, 22294, 22288, 3407])).
% 2.73/2.99 tff(22298,plain,
% 2.73/2.99 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[556, 22297, 1])).
% 2.73/2.99 tff(22299,plain,
% 2.73/2.99 (~b(elem!1, s(s(s(elem!1))))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[12887, 22288, 22266, 22275])).
% 2.73/2.99 tff(22300,plain,
% 2.73/2.99 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[11152, 22289, 82, 22273, 22266])).
% 2.73/2.99 tff(22301,plain,
% 2.73/2.99 (~r(elem!1, s(s(elem!1)))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[671, 22298, 22300, 22299, 13588])).
% 2.73/2.99 tff(22302,plain,
% 2.73/2.99 (~r(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[5358, 1409, 412, 378])).
% 2.73/2.99 tff(22303,plain,
% 2.73/2.99 (b(s(elem!1), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2243, 22302, 2207])).
% 2.73/2.99 tff(22304,plain,
% 2.73/2.99 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2125, 572, 2117, 623])).
% 2.73/2.99 tff(22305,plain,
% 2.73/2.99 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[10472, 22304, 22303, 82, 4435])).
% 2.73/2.99 tff(22306,plain,
% 2.73/2.99 (r(s(s(s(elem!1))), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[486, 22305, 481])).
% 2.73/2.99 tff(22307,plain,
% 2.73/2.99 (~r(s(s(elem!1)), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[6958, 22306, 378, 1, 563, 1409])).
% 2.73/2.99 tff(22308,plain,
% 2.73/2.99 (b(s(s(elem!1)), elem!1)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[862, 22307, 851])).
% 2.73/2.99 tff(22309,plain,
% 2.73/2.99 (~b(s(s(elem!1)), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[6807, 22308, 307, 22303])).
% 2.73/2.99 tff(22310,plain,
% 2.73/2.99 (r(s(s(elem!1)), s(elem!1))),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[701, 22309, 3313])).
% 2.73/2.99 tff(22311,plain,
% 2.73/2.99 (~r(s(s(elem!1)), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[14657, 22310, 412, 1441])).
% 2.73/2.99 tff(22312,plain,
% 2.73/2.99 (b(s(s(elem!1)), z)),
% 2.73/2.99 inference(unit_resolution,[status(thm)],[2430, 22311])).
% 2.73/2.99 tff(22313,plain,
% 2.73/2.99 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[681, 22304, 82])).
% 2.73/3.00 tff(22314,plain,
% 2.73/3.00 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[14540, 572, 2117, 623])).
% 2.73/3.00 tff(22315,plain,
% 2.73/3.00 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[586, 22314, 563])).
% 2.73/3.00 tff(22316,plain,
% 2.73/3.00 (~b(z, s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[14530, 22315, 3407, 22312])).
% 2.73/3.00 tff(22317,plain,
% 2.73/3.00 (r(z, s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2106, 22316])).
% 2.73/3.00 tff(22318,plain,
% 2.73/3.00 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[6878, 22317, 623, 1441])).
% 2.73/3.00 tff(22319,plain,
% 2.73/3.00 (b(s(elem!1), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[526, 22318, 211])).
% 2.73/3.00 tff(22320,plain,
% 2.73/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.73/3.00 inference(rewrite,[status(thm)],[])).
% 2.73/3.00 tff(22321,plain,
% 2.73/3.00 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.73/3.00 inference(rewrite,[status(thm)],[])).
% 2.73/3.00 tff(22322,plain,
% 2.73/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22321])).
% 2.73/3.00 tff(22323,plain,
% 2.73/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22322, 22320])).
% 2.73/3.00 tff(22324,plain,
% 2.73/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.73/3.00 inference(quant_inst,[status(thm)],[])).
% 2.73/3.00 tff(22325,plain,
% 2.73/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22324, 22323])).
% 2.73/3.00 tff(22326,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22325, 271, 22319, 22315, 22313, 22312])).
% 2.73/3.00 tff(22327,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22328,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22327, 22301, 22298, 572, 3407, 366, 412, 851, 22266, 1, 22283, 13588, 82, 22292, 22296])).
% 2.73/3.00 tff(22329,plain,((elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (~b(s(z), s(s(s(z))))) | b(z, elem!1) | (~r(s(s(s(elem!1))), s(z))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22330,plain,
% 2.73/3.00 (elem!1 = s(z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22329, 22149, 3407, 22145, 198, 1, 79, 1281, 22252, 259, 20246, 199, 22144, 22150])).
% 2.73/3.00 tff(22331,plain,
% 2.73/3.00 (s(elem!1) = s(s(z))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22330])).
% 2.73/3.00 tff(22332,plain,
% 2.73/3.00 (s(s(elem!1)) = s(s(s(z)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22331])).
% 2.73/3.00 tff(22333,plain,
% 2.73/3.00 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22332])).
% 2.73/3.00 tff(22334,plain,
% 2.73/3.00 (b(z, elem!1) <=> b(z, s(z))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22330])).
% 2.73/3.00 tff(22335,plain,
% 2.73/3.00 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22334])).
% 2.73/3.00 tff(22336,plain,
% 2.73/3.00 (~b(z, s(z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[199, 22335])).
% 2.73/3.00 tff(22337,plain,
% 2.73/3.00 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22330])).
% 2.73/3.00 tff(22338,plain,
% 2.73/3.00 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.73/3.00 inference(symmetry,[status(thm)],[22337])).
% 2.73/3.00 tff(22339,plain,
% 2.73/3.00 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22338])).
% 2.73/3.00 tff(22340,plain,
% 2.73/3.00 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22143, 22339])).
% 2.73/3.00 tff(22341,plain,
% 2.73/3.00 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22331])).
% 2.73/3.00 tff(22342,plain,
% 2.73/3.00 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22330])).
% 2.73/3.00 tff(22343,plain,
% 2.73/3.00 (s(z) = elem!1),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[242, 22330])).
% 2.73/3.00 tff(22344,plain,
% 2.73/3.00 (r(elem!1, s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1045, 22343, 22145])).
% 2.73/3.00 tff(22345,plain,
% 2.73/3.00 (~r(s(elem!1), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[6817, 22344, 22149, 366])).
% 2.73/3.00 tff(22346,plain,
% 2.73/3.00 (b(s(elem!1), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2243, 22345, 2207])).
% 2.73/3.00 tff(22347,plain,
% 2.73/3.00 (b(s(elem!1), s(z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22346, 22342])).
% 2.73/3.00 tff(22348,plain,
% 2.73/3.00 (b(s(s(z)), s(z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22347, 22341])).
% 2.73/3.00 tff(22349,plain,
% 2.73/3.00 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22332])).
% 2.73/3.00 tff(22350,plain,
% 2.73/3.00 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22349])).
% 2.73/3.00 tff(22351,plain,
% 2.73/3.00 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22350])).
% 2.73/3.00 tff(22352,plain,
% 2.73/3.00 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22351])).
% 2.73/3.00 tff(22353,plain,
% 2.73/3.00 (r(s(s(s(s(z)))), s(z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22144, 22352])).
% 2.73/3.00 tff(22354,plain,
% 2.73/3.00 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22349])).
% 2.73/3.00 tff(22355,plain,
% 2.73/3.00 (r(s(z), s(s(s(s(z)))))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22145, 22354])).
% 2.73/3.00 tff(22356,plain,
% 2.73/3.00 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[4393, 9983, 3407, 412, 331, 4358, 13223])).
% 2.73/3.00 tff(22357,plain,
% 2.73/3.00 (b(s(s(s(elem!1))), s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[681, 22356, 82])).
% 2.73/3.00 tff(22358,plain,
% 2.73/3.00 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[10364])).
% 2.73/3.00 tff(22359,plain,
% 2.73/3.00 (b(s(s(s(z))), s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[3994, 317, 412, 3534, 479, 2207, 9983, 894])).
% 2.73/3.00 tff(22360,plain,
% 2.73/3.00 (b(s(s(s(z))), s(s(z)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[14223, 22359, 239])).
% 2.73/3.00 tff(22361,plain,
% 2.73/3.00 (~b(s(s(s(z))), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[19498, 22360, 1281, 19493])).
% 2.73/3.00 tff(22362,plain,
% 2.73/3.00 (~b(s(s(elem!1)), elem!1)),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22361, 22358])).
% 2.73/3.00 tff(22363,plain,
% 2.73/3.00 (r(s(s(elem!1)), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[862, 22362, 851])).
% 2.73/3.00 tff(22364,plain,
% 2.73/3.00 (~r(s(s(elem!1)), z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[8501, 22363, 378, 9983])).
% 2.73/3.00 tff(22365,plain,
% 2.73/3.00 (b(s(s(elem!1)), z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2430, 22364])).
% 2.73/3.00 tff(22366,plain,
% 2.73/3.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[5267, 22365, 22357, 3407])).
% 2.73/3.00 tff(22367,plain,
% 2.73/3.00 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[556, 22366, 1])).
% 2.73/3.00 tff(22368,plain,
% 2.73/3.00 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22367, 21525])).
% 2.73/3.00 tff(22369,plain,
% 2.73/3.00 (r(s(s(s(z))), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2325, 22361])).
% 2.73/3.00 tff(22370,plain,
% 2.73/3.00 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[21540, 22369, 1026, 911])).
% 2.73/3.00 tff(22371,plain,
% 2.73/3.00 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[8812, 22370, 239])).
% 2.73/3.00 tff(22372,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22371, 22368])).
% 2.73/3.00 tff(22373,plain,(b(elem!1, s(elem!1)) | (~(elem!1 = s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z)) | (z = elem!1) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22374,plain,
% 2.73/3.00 (b(elem!1, s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22373, 22330, 1, 3407, 366, 198, 22355, 22353, 1281, 22348, 79, 22149, 365, 13208, 22340, 22336])).
% 2.73/3.00 tff(22375,plain,
% 2.73/3.00 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22330])).
% 2.73/3.00 tff(22376,plain,
% 2.73/3.00 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22375])).
% 2.73/3.00 tff(22377,plain,
% 2.73/3.00 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22332])).
% 2.73/3.00 tff(22378,plain,
% 2.73/3.00 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22377])).
% 2.73/3.00 tff(22379,plain,
% 2.73/3.00 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22378, 22376])).
% 2.73/3.00 tff(22380,plain,
% 2.73/3.00 (b(elem!1, s(s(elem!1)))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[20246, 22379])).
% 2.73/3.00 tff(22381,plain,
% 2.73/3.00 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22332])).
% 2.73/3.00 tff(22382,plain,
% 2.73/3.00 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22381])).
% 2.73/3.00 tff(22383,plain,
% 2.73/3.00 (r(z, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1214, 22150])).
% 2.73/3.00 tff(22384,plain,
% 2.73/3.00 (r(z, s(s(elem!1)))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22383, 22382])).
% 2.73/3.00 tff(22385,plain,
% 2.73/3.00 (b(elem!1, z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[20120, 22343, 1281])).
% 2.73/3.00 tff(22386,plain,
% 2.73/3.00 (~b(s(z), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[21030, 22385, 1281, 3407])).
% 2.73/3.00 tff(22387,plain,
% 2.73/3.00 (~(s(s(s(z))) = elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[10599, 22386, 20246])).
% 2.73/3.00 tff(22388,plain,
% 2.73/3.00 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22331])).
% 2.73/3.00 tff(22389,plain,
% 2.73/3.00 ((s(s(s(z))) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22388, 20097])).
% 2.73/3.00 tff(22390,plain,
% 2.73/3.00 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22389])).
% 2.73/3.00 tff(22391,plain,
% 2.73/3.00 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22390])).
% 2.73/3.00 tff(22392,plain,
% 2.73/3.00 (~(s(s(s(z))) = s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[1136, 22391])).
% 2.73/3.00 tff(22393,plain,
% 2.73/3.00 (~b(s(s(s(z))), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[13140, 22374, 22149, 22383, 22392, 22346])).
% 2.73/3.00 tff(22394,plain,
% 2.73/3.00 (r(s(s(s(z))), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[255, 22393, 22387])).
% 2.73/3.00 tff(22395,plain,
% 2.73/3.00 (r(s(s(elem!1)), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[6824, 22394, 22343])).
% 2.73/3.00 tff(22396,plain,
% 2.73/3.00 (~r(s(elem!1), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[5431, 22395, 22149, 22384])).
% 2.73/3.00 tff(22397,plain,
% 2.73/3.00 (b(s(elem!1), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[526, 22396, 211])).
% 2.73/3.00 tff(22398,plain,
% 2.73/3.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[9687, 22397, 22380, 22374])).
% 2.73/3.00 tff(22399,plain,
% 2.73/3.00 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[556, 22398, 1])).
% 2.73/3.00 tff(22400,plain,
% 2.73/3.00 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22399, 22333])).
% 2.73/3.00 tff(22401,plain,
% 2.73/3.00 (b(elem!1, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[11114, 22330, 20246])).
% 2.73/3.00 tff(22402,plain,
% 2.73/3.00 (b(s(elem!1), s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2369, 22397, 22330])).
% 2.73/3.00 tff(22403,plain,
% 2.73/3.00 (~b(s(s(s(z))), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[10690, 22402, 22374, 22401])).
% 2.73/3.00 tff(22404,plain,
% 2.73/3.00 (r(s(s(s(z))), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2325, 22403])).
% 2.73/3.00 tff(22405,plain,
% 2.73/3.00 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[21540, 22404, 22355, 22353])).
% 2.73/3.00 tff(22406,plain,
% 2.73/3.00 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[8812, 22405, 22330])).
% 2.73/3.00 tff(22407,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22406, 22400])).
% 2.73/3.00 tff(22408,plain,((elem!1 = z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | b(z, elem!1) | (elem!1 = s(s(elem!1))) | r(s(z), s(s(s(z)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22409,plain,
% 2.73/3.00 (b(z, elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22408, 68, 3407, 1281, 22131, 1, 100, 1638])).
% 2.73/3.00 tff(22410,plain,
% 2.73/3.00 (~(elem!1 = z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[9876, 22130, 3871])).
% 2.73/3.00 tff(22411,plain,
% 2.73/3.00 (~(z = elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[364, 22410])).
% 2.73/3.00 tff(22412,plain,
% 2.73/3.00 (~(s(z) = s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[343, 22411])).
% 2.73/3.00 tff(22413,plain,
% 2.73/3.00 (~(s(elem!1) = s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[350, 22412])).
% 2.73/3.00 tff(22414,plain,
% 2.73/3.00 (s(elem!1) = s(s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22147, 394, 22413, 3407, 1638, 1281])).
% 2.73/3.00 tff(22415,plain,
% 2.73/3.00 (s(s(s(elem!1))) = s(elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[84, 22414])).
% 2.73/3.00 tff(22416,plain,
% 2.73/3.00 (elem!1 = s(s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[78, 22415])).
% 2.73/3.00 tff(22417,plain,
% 2.73/3.00 (s(elem!1) = s(s(s(elem!1)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22416])).
% 2.73/3.00 tff(22418,plain,
% 2.73/3.00 (s(s(s(elem!1))) = s(elem!1)),
% 2.73/3.00 inference(symmetry,[status(thm)],[22417])).
% 2.73/3.00 tff(22419,plain,
% 2.73/3.00 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22418])).
% 2.73/3.00 tff(22420,plain,
% 2.73/3.00 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22419])).
% 2.73/3.00 tff(22421,plain,
% 2.73/3.00 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22418])).
% 2.73/3.00 tff(22422,plain,
% 2.73/3.00 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22421, 10146])).
% 2.73/3.00 tff(22423,plain,
% 2.73/3.00 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22422])).
% 2.73/3.00 tff(22424,plain,
% 2.73/3.00 (s(s(elem!1)) = elem!1),
% 2.73/3.00 inference(symmetry,[status(thm)],[22416])).
% 2.73/3.00 tff(22425,plain,
% 2.73/3.00 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22424])).
% 2.73/3.00 tff(22426,plain,
% 2.73/3.00 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22425, 159])).
% 2.73/3.00 tff(22427,plain,
% 2.73/3.00 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22426])).
% 2.73/3.00 tff(22428,plain,
% 2.73/3.00 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22427])).
% 2.73/3.00 tff(22429,plain,
% 2.73/3.00 (~(s(s(s(z))) = elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[3906, 22416])).
% 2.73/3.00 tff(22430,plain,
% 2.73/3.00 (~(elem!1 = s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1100, 22429])).
% 2.73/3.00 tff(22431,plain,
% 2.73/3.00 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22430, 22428])).
% 2.73/3.00 tff(22432,plain,
% 2.73/3.00 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[946, 22431])).
% 2.73/3.00 tff(22433,plain,
% 2.73/3.00 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22432, 22423])).
% 2.73/3.00 tff(22434,plain,
% 2.73/3.00 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22418])).
% 2.73/3.00 tff(22435,plain,
% 2.73/3.00 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22434])).
% 2.73/3.00 tff(22436,plain,
% 2.73/3.00 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22416])).
% 2.73/3.00 tff(22437,plain,
% 2.73/3.00 (r(s(z), s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22145, 13839])).
% 2.73/3.00 tff(22438,plain,
% 2.73/3.00 (b(z, s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[3407, 6487])).
% 2.73/3.00 tff(22439,plain,
% 2.73/3.00 (~r(elem!1, s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[9263, 379, 1281, 431, 1326, 348])).
% 2.73/3.00 tff(22440,plain,
% 2.73/3.00 (~r(s(s(elem!1)), s(z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22439, 12126])).
% 2.73/3.00 tff(22441,plain,
% 2.73/3.00 (~r(s(elem!1), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[21984, 379, 1281, 431, 12075, 1326, 348])).
% 2.73/3.00 tff(22442,plain,
% 2.73/3.00 (b(s(elem!1), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2243, 22441, 2564])).
% 2.73/3.00 tff(22443,plain,
% 2.73/3.00 (b(s(elem!1), s(s(elem!1)))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[3787, 22442, 2470])).
% 2.73/3.00 tff(22444,plain,
% 2.73/3.00 (~b(s(s(elem!1)), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2152, 22443, 1421, 3936])).
% 2.73/3.00 tff(22445,plain,
% 2.73/3.00 (r(s(s(elem!1)), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2143, 22444])).
% 2.73/3.00 tff(22446,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22445, 22440])).
% 2.73/3.00 tff(22447,plain,((~r(elem!1, s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (~b(z, s(elem!1))) | (s(elem!1) = elem!1) | (~b(s(z), z)) | (~r(s(z), s(elem!1))) | (~b(z, elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22448,plain,
% 2.73/3.00 (~r(elem!1, s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22447, 1326, 22438, 3500, 1281, 22437, 2470, 348])).
% 2.73/3.00 tff(22449,plain,
% 2.73/3.00 (b(elem!1, s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[392, 22448, 377])).
% 2.73/3.00 tff(22450,plain,
% 2.73/3.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2479, 22449, 2470])).
% 2.73/3.00 tff(22451,plain,
% 2.73/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.73/3.00 inference(rewrite,[status(thm)],[])).
% 2.73/3.00 tff(22452,plain,
% 2.73/3.00 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.73/3.00 inference(rewrite,[status(thm)],[])).
% 2.73/3.00 tff(22453,plain,
% 2.73/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22452])).
% 2.73/3.00 tff(22454,plain,
% 2.73/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22453, 22451])).
% 2.73/3.00 tff(22455,plain,
% 2.73/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.73/3.00 inference(quant_inst,[status(thm)],[])).
% 2.73/3.00 tff(22456,plain,
% 2.73/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22455, 22454])).
% 2.73/3.00 tff(22457,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22456, 271, 22450, 3936, 3407, 1638])).
% 2.73/3.00 tff(22458,plain,((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~(elem!1 = s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22459,plain,
% 2.73/3.00 (~b(z, elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22458, 22416, 1638, 3407, 219, 1281, 22412])).
% 2.73/3.00 tff(22460,plain,
% 2.73/3.00 (r(z, elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[355, 22459, 22411])).
% 2.73/3.00 tff(22461,plain,
% 2.73/3.00 (r(z, s(s(elem!1)))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22460, 22436])).
% 2.73/3.00 tff(22462,plain,
% 2.73/3.00 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2063, 22412])).
% 2.73/3.00 tff(22463,plain,
% 2.73/3.00 (~(s(s(s(z))) = s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[3917, 22416, 22412])).
% 2.73/3.00 tff(22464,plain,
% 2.73/3.00 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22416])).
% 2.73/3.00 tff(22465,plain,
% 2.73/3.00 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22464])).
% 2.73/3.00 tff(22466,plain,
% 2.73/3.00 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22417])).
% 2.73/3.00 tff(22467,plain,
% 2.73/3.00 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22466])).
% 2.73/3.00 tff(22468,plain,
% 2.73/3.00 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.73/3.00 inference(transitivity,[status(thm)],[22467, 22465])).
% 2.73/3.00 tff(22469,plain,
% 2.73/3.00 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22417])).
% 2.73/3.00 tff(22470,plain,
% 2.73/3.00 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22469])).
% 2.73/3.00 tff(22471,plain,
% 2.73/3.00 (b(z, s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[3407, 22470])).
% 2.73/3.00 tff(22472,plain,
% 2.73/3.00 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 2.73/3.00 inference(monotonicity,[status(thm)],[22417])).
% 2.73/3.00 tff(22473,plain,
% 2.73/3.00 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 2.73/3.00 inference(symmetry,[status(thm)],[22472])).
% 2.73/3.00 tff(22474,plain,
% 2.73/3.00 (r(s(z), s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22145, 22473])).
% 2.73/3.00 tff(22475,plain,
% 2.73/3.00 (~b(s(s(elem!1)), z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[20289, 22474, 211, 1281, 3407, 394])).
% 2.73/3.00 tff(22476,plain,
% 2.73/3.00 (r(s(s(elem!1)), z)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2430, 22475])).
% 2.73/3.00 tff(22477,plain,
% 2.73/3.00 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[13674, 22461, 22416, 3871, 22476, 394, 22471, 22463, 22462, 22145, 22144])).
% 2.73/3.00 tff(22478,plain,
% 2.73/3.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[556, 22477, 1])).
% 2.73/3.00 tff(22479,plain,
% 2.73/3.00 (b(elem!1, s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[22478, 22468])).
% 2.73/3.00 tff(22480,plain,
% 2.73/3.00 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2069, 21, 2065, 906])).
% 2.73/3.00 tff(22481,plain,
% 2.73/3.00 (~b(z, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[19817, 22480, 1281, 3871])).
% 2.73/3.00 tff(22482,plain,
% 2.73/3.00 (r(z, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1214, 22481])).
% 2.73/3.00 tff(22483,plain,
% 2.73/3.00 (~r(s(s(s(z))), s(elem!1))),
% 2.73/3.00 inference(modus_ponens,[status(thm)],[906, 13651])).
% 2.73/3.00 tff(22484,plain,
% 2.73/3.00 (b(s(s(s(z))), s(elem!1))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1816, 22483, 2033])).
% 2.73/3.00 tff(22485,plain,
% 2.73/3.00 (~b(elem!1, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1811, 22484, 394, 307])).
% 2.73/3.00 tff(22486,plain,
% 2.73/3.00 (r(elem!1, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[1192, 22485, 12183])).
% 2.73/3.00 tff(22487,plain,
% 2.73/3.00 (~b(s(s(s(z))), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[3288, 22484, 394, 307])).
% 2.73/3.00 tff(22488,plain,
% 2.73/3.00 (r(s(s(s(z))), elem!1)),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[255, 22487, 3907])).
% 2.73/3.00 tff(22489,plain,
% 2.73/3.00 ($false),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[6723, 22488, 22486, 378, 22482])).
% 2.73/3.00 tff(22490,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.00 tff(22491,plain,
% 2.73/3.00 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[22490, 22460, 394, 22479, 1281, 3871, 22463, 22462, 22416])).
% 2.73/3.00 tff(22492,plain,
% 2.73/3.00 (~r(s(s(s(z))), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[13310, 121, 22145, 22144, 22491])).
% 2.73/3.00 tff(22493,plain,
% 2.73/3.00 (b(s(s(s(z))), s(z))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[2325, 22492])).
% 2.73/3.00 tff(22494,plain,
% 2.73/3.00 (~b(z, s(s(s(z))))),
% 2.73/3.00 inference(unit_resolution,[status(thm)],[21149, 222, 1281, 3871])).
% 2.73/3.01 tff(22495,plain,
% 2.73/3.01 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 2.73/3.01 inference(symmetry,[status(thm)],[12492])).
% 2.73/3.01 tff(22496,plain,
% 2.73/3.01 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22495])).
% 2.73/3.01 tff(22497,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22498,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22499,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22498, 22497])).
% 2.73/3.01 tff(22500,plain,
% 2.73/3.01 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22499, 271, 1281, 222, 981])).
% 2.73/3.01 tff(22501,plain,
% 2.73/3.01 (~b(s(s(s(z))), elem!1)),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22500, 22496])).
% 2.73/3.01 tff(22502,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22503,plain,
% 2.73/3.01 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22504,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22503])).
% 2.73/3.01 tff(22505,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(transitivity,[status(thm)],[22504, 22502])).
% 2.73/3.01 tff(22506,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22507,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22506, 22505])).
% 2.73/3.01 tff(22508,plain,
% 2.73/3.01 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22507, 271, 1281, 222, 981])).
% 2.73/3.01 tff(22509,plain,
% 2.73/3.01 (~b(elem!1, s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[5482, 22508, 2470])).
% 2.73/3.01 tff(22510,plain,
% 2.73/3.01 (r(elem!1, s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[1192, 22509, 12183])).
% 2.73/3.01 tff(22511,plain,
% 2.73/3.01 (~r(s(s(s(z))), elem!1)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[6723, 22510, 378, 1140])).
% 2.73/3.01 tff(22512,plain,
% 2.73/3.01 (b(s(s(s(z))), elem!1)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[255, 22511, 3907])).
% 2.73/3.01 tff(22513,plain,
% 2.73/3.01 ($false),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22512, 22501])).
% 2.73/3.01 tff(22514,plain,((~b(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.01 tff(22515,plain,
% 2.73/3.01 (~r(z, s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22514, 222, 2470, 378, 1281, 981])).
% 2.73/3.01 tff(22516,plain,
% 2.73/3.01 ($false),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[1214, 22515, 22494])).
% 2.73/3.01 tff(22517,plain,((~b(s(s(s(z))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.01 tff(22518,plain,
% 2.73/3.01 (~b(s(s(elem!1)), s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22517, 22493, 22460, 1281, 22416, 3871])).
% 2.73/3.01 tff(22519,plain,
% 2.73/3.01 (r(s(s(elem!1)), s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[2143, 22518])).
% 2.73/3.01 tff(22520,plain,
% 2.73/3.01 (~r(z, s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[8581, 22519, 22145, 22461])).
% 2.73/3.01 tff(22521,plain,
% 2.73/3.01 (b(z, s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[904, 22520])).
% 2.73/3.01 tff(22522,plain,
% 2.73/3.01 (~b(s(s(s(z))), z)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[21058, 22521, 1281, 3871])).
% 2.73/3.01 tff(22523,plain,
% 2.73/3.01 (r(s(s(s(z))), z)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[1155, 22522])).
% 2.73/3.01 tff(22524,plain,
% 2.73/3.01 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[12235, 22416, 22462])).
% 2.73/3.01 tff(22525,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22526,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22527,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22526, 22525])).
% 2.73/3.01 tff(22528,plain,
% 2.73/3.01 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22527, 121, 22461, 22476, 22523])).
% 2.73/3.01 tff(22529,plain,
% 2.73/3.01 (b(s(s(s(z))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[2462, 21, 22528, 22431])).
% 2.73/3.01 tff(22530,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22531,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22532,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22531, 22530])).
% 2.73/3.01 tff(22533,plain,
% 2.73/3.01 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22532, 121, 2088, 109, 910])).
% 2.73/3.01 tff(22534,plain,
% 2.73/3.01 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[10424, 21, 1138, 22533])).
% 2.73/3.01 tff(22535,plain,
% 2.73/3.01 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[13526, 121, 2088, 2417, 910])).
% 2.73/3.01 tff(22536,plain,
% 2.73/3.01 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[12253, 21, 13528, 22535])).
% 2.73/3.01 tff(22537,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22538,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22539,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22538, 22537])).
% 2.73/3.01 tff(22540,plain,
% 2.73/3.01 ($false),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22539, 271, 543, 2448, 22536, 22534])).
% 2.73/3.01 tff(22541,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.01 tff(22542,plain,
% 2.73/3.01 (~r(s(s(s(s(z)))), z)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22541, 22529, 22478, 22524, 22461, 22523, 22476])).
% 2.73/3.01 tff(22543,plain,
% 2.73/3.01 (b(s(s(s(s(z)))), z)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[1095, 22542])).
% 2.73/3.01 tff(22544,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22545,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22546,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22545, 22544])).
% 2.73/3.01 tff(22547,plain,
% 2.73/3.01 ($false),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22546, 271, 1281, 220, 937, 1103])).
% 2.73/3.01 tff(22548,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.01 tff(22549,plain,
% 2.73/3.01 (~b(s(s(s(s(z)))), s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22548, 22543, 22521, 1281])).
% 2.73/3.01 tff(22550,plain,
% 2.73/3.01 (r(s(s(s(s(z)))), s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[932, 22549])).
% 2.73/3.01 tff(22551,plain,
% 2.73/3.01 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[13661, 121, 22461, 22476, 22523])).
% 2.73/3.01 tff(22552,plain,
% 2.73/3.01 (~r(elem!1, s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[12242, 22551, 22416])).
% 2.73/3.01 tff(22553,plain,
% 2.73/3.01 (b(elem!1, s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[1192, 22552, 22430])).
% 2.73/3.01 tff(22554,plain,
% 2.73/3.01 (b(s(s(elem!1)), s(s(s(z))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[5482, 22553, 22416])).
% 2.73/3.01 tff(22555,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22556,plain,
% 2.73/3.01 (((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22557,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22556])).
% 2.73/3.01 tff(22558,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.73/3.01 inference(transitivity,[status(thm)],[22557, 22555])).
% 2.73/3.01 tff(22559,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22560,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22559, 22558])).
% 2.73/3.01 tff(22561,plain,
% 2.73/3.01 (~b(s(z), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22560, 271, 3871, 22493, 22554])).
% 2.73/3.01 tff(22562,plain,
% 2.73/3.01 (r(s(z), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[2167, 22561])).
% 2.73/3.01 tff(22563,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22564,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22565,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22564, 22563])).
% 2.73/3.01 tff(22566,plain,
% 2.73/3.01 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22565, 121, 22562, 22144, 22550])).
% 2.73/3.01 tff(22567,plain,
% 2.73/3.01 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22566, 22435])).
% 2.73/3.01 tff(22568,plain,
% 2.73/3.01 (b(s(s(s(s(z)))), s(elem!1))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[1559, 22567, 22433])).
% 2.73/3.01 tff(22569,plain,
% 2.73/3.01 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22568, 22420])).
% 2.73/3.01 tff(22570,plain,
% 2.73/3.01 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22417])).
% 2.73/3.01 tff(22571,plain,
% 2.73/3.01 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22416])).
% 2.73/3.01 tff(22572,plain,
% 2.73/3.01 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/3.01 inference(transitivity,[status(thm)],[22571, 22570])).
% 2.73/3.01 tff(22573,plain,
% 2.73/3.01 (r(elem!1, s(z))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[12129, 22519, 22416])).
% 2.73/3.01 tff(22574,plain,
% 2.73/3.01 (~r(s(s(s(elem!1))), elem!1)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22268, 22573, 22145, 22144])).
% 2.73/3.01 tff(22575,plain,
% 2.73/3.01 (b(s(elem!1), elem!1)),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[12364, 22574, 22416, 1])).
% 2.73/3.01 tff(22576,plain,
% 2.73/3.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22575, 22572])).
% 2.73/3.01 tff(22577,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22578,plain,
% 2.73/3.01 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22579,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22578])).
% 2.73/3.01 tff(22580,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(transitivity,[status(thm)],[22579, 22577])).
% 2.73/3.01 tff(22581,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22582,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22581, 22580])).
% 2.73/3.01 tff(22583,plain,
% 2.73/3.01 ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22582, 271, 543, 589])).
% 2.73/3.01 tff(22584,plain,
% 2.73/3.01 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22583, 12562])).
% 2.73/3.01 tff(22585,plain,
% 2.73/3.01 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[12253, 21, 22584, 13528])).
% 2.73/3.01 tff(22586,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22587,plain,
% 2.73/3.01 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(elem!1))), s(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))))))),
% 2.73/3.01 inference(rewrite,[status(thm)],[])).
% 2.73/3.01 tff(22588,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.73/3.01 inference(monotonicity,[status(thm)],[22587])).
% 2.73/3.01 tff(22589,plain,
% 2.73/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.73/3.01 inference(transitivity,[status(thm)],[22588, 22586])).
% 2.73/3.01 tff(22590,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 2.73/3.01 inference(quant_inst,[status(thm)],[])).
% 2.73/3.01 tff(22591,plain,
% 2.73/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.73/3.01 inference(modus_ponens,[status(thm)],[22590, 22589])).
% 2.73/3.01 tff(22592,plain,
% 2.73/3.01 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.73/3.01 inference(unit_resolution,[status(thm)],[22591, 271, 589, 3407])).
% 2.73/3.01 tff(22593,plain,
% 2.73/3.01 (~b(s(s(s(s(z)))), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22592, 12562])).
% 2.73/3.02 tff(22594,plain,
% 2.73/3.02 (r(s(s(s(s(z)))), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[1093, 21, 1090, 22593])).
% 2.73/3.02 tff(22595,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22596,plain,
% 2.73/3.02 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22597,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22596])).
% 2.73/3.02 tff(22598,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.73/3.02 inference(transitivity,[status(thm)],[22597, 22595])).
% 2.73/3.02 tff(22599,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 2.73/3.02 inference(quant_inst,[status(thm)],[])).
% 2.73/3.02 tff(22600,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22599, 22598])).
% 2.73/3.02 tff(22601,plain,
% 2.73/3.02 ($false),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22600, 121, 2088, 2117, 22594, 22585])).
% 2.73/3.02 tff(22602,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.02 tff(22603,plain,
% 2.73/3.02 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22602, 22576, 22519, 22524, 22461, 3407, 22478])).
% 2.73/3.02 tff(22604,plain,
% 2.73/3.02 ($false),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22603, 22569])).
% 2.73/3.02 tff(22605,plain,((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.02 tff(22606,plain,
% 2.73/3.02 (~b(s(elem!1), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22605, 1, 20246, 3407, 1281, 1638])).
% 2.73/3.02 tff(22607,plain,
% 2.73/3.02 (r(s(elem!1), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[409, 22606])).
% 2.73/3.02 tff(22608,plain,
% 2.73/3.02 (~b(z, s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[21634, 68, 100, 3407, 1281, 22607, 1, 22131])).
% 2.73/3.02 tff(22609,plain,
% 2.73/3.02 (~b(s(elem!1), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22605, 1, 3871, 3407, 1281, 1638])).
% 2.73/3.02 tff(22610,plain,
% 2.73/3.02 (r(s(elem!1), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[409, 22609])).
% 2.73/3.02 tff(22611,plain,
% 2.73/3.02 (~b(elem!1, s(z))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[21813, 1326, 1281, 219, 22410, 22610])).
% 2.73/3.02 tff(22612,plain,
% 2.73/3.02 (~(s(s(s(z))) = elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[6548, 1326, 1209])).
% 2.73/3.02 tff(22613,plain,
% 2.73/3.02 (~b(elem!1, s(z))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[21813, 1326, 1281, 377, 259, 412])).
% 2.73/3.02 tff(22614,plain,
% 2.73/3.02 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[7173, 21458, 3407, 1326])).
% 2.73/3.02 tff(22615,plain,
% 2.73/3.02 (b(s(s(s(z))), s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[3994, 22614, 412, 22613, 317, 3500, 3502, 894])).
% 2.73/3.02 tff(22616,plain,
% 2.73/3.02 (~(s(z) = elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[1402, 894, 1391])).
% 2.73/3.02 tff(22617,plain,
% 2.73/3.02 (~(s(s(z)) = s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[960, 22616])).
% 2.73/3.02 tff(22618,plain,
% 2.73/3.02 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[953, 22617])).
% 2.73/3.02 tff(22619,plain,
% 2.73/3.02 (~b(s(z), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[21030, 21458, 1281, 3407])).
% 2.73/3.02 tff(22620,plain,
% 2.73/3.02 (r(s(z), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[236, 22619, 22616])).
% 2.73/3.02 tff(22621,plain,
% 2.73/3.02 ($false),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[5759, 22620, 22614, 3502, 365, 905, 412, 22618, 22615, 1391, 21457])).
% 2.73/3.02 tff(22622,plain,(b(z, s(z)) | (~r(s(elem!1), z)) | r(z, elem!1) | b(elem!1, s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.73/3.02 tff(22623,plain,
% 2.73/3.02 (b(z, s(z))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22622, 317, 1391, 22610, 3407, 1326, 1281, 219, 22410])).
% 2.73/3.02 tff(22624,plain,
% 2.73/3.02 (~b(s(s(s(z))), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[21058, 22623, 1281, 3871])).
% 2.73/3.02 tff(22625,plain,
% 2.73/3.02 (r(s(s(s(z))), z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[1155, 22624])).
% 2.73/3.02 tff(22626,plain,
% 2.73/3.02 (~r(s(s(s(elem!1))), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22268, 1256, 572, 12761])).
% 2.73/3.02 tff(22627,plain,
% 2.73/3.02 (~r(s(z), s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[3709, 1256, 412, 379])).
% 2.73/3.02 tff(22628,plain,
% 2.73/3.02 (b(s(z), s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[444, 22627, 22132])).
% 2.73/3.02 tff(22629,plain,
% 2.73/3.02 (~r(s(elem!1), s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[15486, 121, 412, 109, 1140])).
% 2.73/3.02 tff(22630,plain,
% 2.73/3.02 (~b(z, s(s(elem!1)))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22456, 271, 543, 3407, 1638])).
% 2.73/3.02 tff(22631,plain,
% 2.73/3.02 (r(z, s(s(elem!1)))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2106, 22630])).
% 2.73/3.02 tff(22632,plain,
% 2.73/3.02 (~r(elem!1, z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[17642, 22631, 412, 379])).
% 2.73/3.02 tff(22633,plain,
% 2.73/3.02 (b(elem!1, z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[284, 22632, 259])).
% 2.73/3.02 tff(22634,plain,
% 2.73/3.02 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[7173, 22633, 3407, 1326])).
% 2.73/3.02 tff(22635,plain,
% 2.73/3.02 (s(s(s(elem!1))) = elem!1),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[486, 22634, 147])).
% 2.73/3.02 tff(22636,plain,
% 2.73/3.02 (~(s(s(s(z))) = s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2596, 22635])).
% 2.73/3.02 tff(22637,plain,
% 2.73/3.02 (~(s(elem!1) = s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2035, 22636])).
% 2.73/3.02 tff(22638,plain,
% 2.73/3.02 (b(s(elem!1), s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2044, 22637, 22629])).
% 2.73/3.02 tff(22639,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22640,plain,
% 2.73/3.02 (((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22641,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22640])).
% 2.73/3.02 tff(22642,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))))),
% 2.73/3.02 inference(transitivity,[status(thm)],[22641, 22639])).
% 2.73/3.02 tff(22643,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.73/3.02 inference(quant_inst,[status(thm)],[])).
% 2.73/3.02 tff(22644,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22643, 22642])).
% 2.73/3.02 tff(22645,plain,
% 2.73/3.02 (~r(s(s(s(z))), s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22644, 121, 412, 109, 1140])).
% 2.73/3.02 tff(22646,plain,
% 2.73/3.02 (b(s(s(s(z))), s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[1816, 22636, 22645])).
% 2.73/3.02 tff(22647,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22648,plain,
% 2.73/3.02 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22649,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22648])).
% 2.73/3.02 tff(22650,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.73/3.02 inference(transitivity,[status(thm)],[22649, 22647])).
% 2.73/3.02 tff(22651,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))))),
% 2.73/3.02 inference(quant_inst,[status(thm)],[])).
% 2.73/3.02 tff(22652,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22651, 22650])).
% 2.73/3.02 tff(22653,plain,
% 2.73/3.02 ($false),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22652, 271, 22646, 3871, 22638, 446])).
% 2.73/3.02 tff(22654,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = z) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.02 tff(22655,plain,
% 2.73/3.02 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22654, 22628, 3871, 22626, 3407, 1326, 259, 412, 379, 1638, 109, 1140])).
% 2.73/3.02 tff(22656,plain,
% 2.73/3.02 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[556, 22655, 1])).
% 2.73/3.02 tff(22657,plain,
% 2.73/3.02 (~b(z, s(s(elem!1)))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[12176, 13320, 220, 981])).
% 2.73/3.02 tff(22658,plain,
% 2.73/3.02 (r(z, s(s(elem!1)))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2106, 22657])).
% 2.73/3.02 tff(22659,plain,
% 2.73/3.02 (~r(elem!1, z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[17642, 22658, 412, 379])).
% 2.73/3.02 tff(22660,plain,
% 2.73/3.02 (b(elem!1, z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[284, 22659, 259])).
% 2.73/3.02 tff(22661,plain,
% 2.73/3.02 (~b(s(s(s(elem!1))), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[7173, 22660, 3407, 1326])).
% 2.73/3.02 tff(22662,plain,
% 2.73/3.02 (s(s(s(elem!1))) = elem!1),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[486, 22661, 147])).
% 2.73/3.02 tff(22663,plain,
% 2.73/3.02 (~(s(s(s(z))) = s(elem!1))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2596, 22662])).
% 2.73/3.02 tff(22664,plain,
% 2.73/3.02 (~(s(elem!1) = s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2035, 22663])).
% 2.73/3.02 tff(22665,plain,
% 2.73/3.02 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22662])).
% 2.73/3.02 tff(22666,plain,
% 2.73/3.02 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22665])).
% 2.73/3.02 tff(22667,plain,
% 2.73/3.02 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[13328, 623, 572, 12761, 944])).
% 2.73/3.02 tff(22668,plain,
% 2.73/3.02 (~r(s(s(s(z))), elem!1)),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22667, 22666])).
% 2.73/3.02 tff(22669,plain,
% 2.73/3.02 (b(s(s(s(z))), elem!1)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[255, 22668, 907])).
% 2.73/3.02 tff(22670,plain,
% 2.73/3.02 (~b(s(elem!1), s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[3879, 22669, 3871, 446])).
% 2.73/3.02 tff(22671,plain,
% 2.73/3.02 (r(s(elem!1), s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2044, 22670, 22664])).
% 2.73/3.02 tff(22672,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22673,plain,
% 2.73/3.02 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22674,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22673])).
% 2.73/3.02 tff(22675,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.73/3.02 inference(transitivity,[status(thm)],[22674, 22672])).
% 2.73/3.02 tff(22676,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.73/3.02 inference(quant_inst,[status(thm)],[])).
% 2.73/3.02 tff(22677,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22676, 22675])).
% 2.73/3.02 tff(22678,plain,
% 2.73/3.02 ($false),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22677, 121, 22658, 412, 109, 22671])).
% 2.73/3.02 tff(22679,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (s(s(s(z))) = elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.02 tff(22680,plain,
% 2.73/3.02 (~b(s(s(elem!1)), s(z))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22679, 22656, 109, 3871, 22628, 907, 22626, 3407, 1326, 259, 379, 220, 412, 572, 12761, 19199])).
% 2.73/3.02 tff(22681,plain,
% 2.73/3.02 (r(s(s(elem!1)), s(z))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[2143, 22680])).
% 2.73/3.02 tff(22682,plain,
% 2.73/3.02 ($false),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[13294, 121, 22656, 572, 22681, 12761])).
% 2.73/3.02 tff(22683,plain,((elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.73/3.02 tff(22684,plain,
% 2.73/3.02 (elem!1 = s(z)),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22683, 22625, 22144, 22145, 3871, 907, 3407, 1326, 22410, 9983, 22623, 22610, 1, 1638, 1140, 22611])).
% 2.73/3.02 tff(22685,plain,
% 2.73/3.02 (s(elem!1) = s(s(z))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22684])).
% 2.73/3.02 tff(22686,plain,
% 2.73/3.02 (s(s(elem!1)) = s(s(s(z)))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22685])).
% 2.73/3.02 tff(22687,plain,
% 2.73/3.02 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22686])).
% 2.73/3.02 tff(22688,plain,
% 2.73/3.02 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.73/3.02 inference(symmetry,[status(thm)],[22687])).
% 2.73/3.02 tff(22689,plain,
% 2.73/3.02 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22685, 22688])).
% 2.73/3.02 tff(22690,plain,
% 2.73/3.02 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.73/3.02 inference(transitivity,[status(thm)],[22689, 10493])).
% 2.73/3.02 tff(22691,plain,
% 2.73/3.02 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.73/3.02 inference(symmetry,[status(thm)],[22690])).
% 2.73/3.02 tff(22692,plain,
% 2.73/3.02 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22691])).
% 2.73/3.02 tff(22693,plain,
% 2.73/3.02 (s(s(z)) = s(elem!1)),
% 2.73/3.02 inference(symmetry,[status(thm)],[22685])).
% 2.73/3.02 tff(22694,plain,
% 2.73/3.02 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22693])).
% 2.73/3.02 tff(22695,plain,
% 2.73/3.02 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.73/3.02 inference(symmetry,[status(thm)],[22694])).
% 2.73/3.02 tff(22696,plain,
% 2.73/3.02 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22695])).
% 2.73/3.02 tff(22697,plain,
% 2.73/3.02 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[82, 22696])).
% 2.73/3.02 tff(22698,plain,
% 2.73/3.02 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22697, 22692])).
% 2.73/3.02 tff(22699,plain,
% 2.73/3.02 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22693])).
% 2.73/3.02 tff(22700,plain,
% 2.73/3.02 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22699])).
% 2.73/3.02 tff(22701,plain,
% 2.73/3.02 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22688])).
% 2.73/3.02 tff(22702,plain,
% 2.73/3.02 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.73/3.02 inference(symmetry,[status(thm)],[22701])).
% 2.73/3.02 tff(22703,plain,
% 2.73/3.02 (r(s(s(s(s(z)))), s(z))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22144, 22702])).
% 2.73/3.02 tff(22704,plain,
% 2.73/3.02 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22685])).
% 2.73/3.02 tff(22705,plain,
% 2.73/3.02 (r(s(s(z)), z)),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22610, 22704])).
% 2.73/3.02 tff(22706,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22707,plain,
% 2.73/3.02 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.73/3.02 inference(rewrite,[status(thm)],[])).
% 2.73/3.02 tff(22708,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.73/3.02 inference(monotonicity,[status(thm)],[22707])).
% 2.73/3.02 tff(22709,plain,
% 2.73/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.73/3.02 inference(transitivity,[status(thm)],[22708, 22706])).
% 2.73/3.02 tff(22710,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.73/3.02 inference(quant_inst,[status(thm)],[])).
% 2.73/3.02 tff(22711,plain,
% 2.73/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.73/3.02 inference(modus_ponens,[status(thm)],[22710, 22709])).
% 2.73/3.02 tff(22712,plain,
% 2.73/3.02 (~r(s(s(z)), s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[22711, 121, 22705, 22625, 1140])).
% 2.73/3.02 tff(22713,plain,
% 2.73/3.02 (b(s(s(z)), s(s(s(z))))),
% 2.73/3.02 inference(unit_resolution,[status(thm)],[10571, 21, 1136, 22712])).
% 2.85/3.02 tff(22714,plain,
% 2.85/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.85/3.02 inference(rewrite,[status(thm)],[])).
% 2.85/3.02 tff(22715,plain,
% 2.85/3.02 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.85/3.02 inference(rewrite,[status(thm)],[])).
% 2.85/3.02 tff(22716,plain,
% 2.85/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22715])).
% 2.85/3.03 tff(22717,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22716, 22714])).
% 2.85/3.03 tff(22718,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.85/3.03 inference(quant_inst,[status(thm)],[])).
% 2.85/3.03 tff(22719,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22718, 22717])).
% 2.85/3.03 tff(22720,plain,
% 2.85/3.03 (~r(s(s(s(z))), s(s(z)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22719, 121, 22705, 22625, 1140])).
% 2.85/3.03 tff(22721,plain,
% 2.85/3.03 (b(s(s(s(z))), s(s(z)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[1368, 22720])).
% 2.85/3.03 tff(22722,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22723,plain,
% 2.85/3.03 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22724,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22723])).
% 2.85/3.03 tff(22725,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22724, 22722])).
% 2.85/3.03 tff(22726,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.85/3.03 inference(quant_inst,[status(thm)],[])).
% 2.85/3.03 tff(22727,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22726, 22725])).
% 2.85/3.03 tff(22728,plain,
% 2.85/3.03 (~b(s(s(z)), s(z))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22727, 271, 3871, 22721, 22713])).
% 2.85/3.03 tff(22729,plain,
% 2.85/3.03 (r(s(s(z)), s(z))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[4670, 22728])).
% 2.85/3.03 tff(22730,plain,
% 2.85/3.03 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22685])).
% 2.85/3.03 tff(22731,plain,
% 2.85/3.03 (~b(s(z), s(elem!1))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[3576, 22684, 317])).
% 2.85/3.03 tff(22732,plain,
% 2.85/3.03 (r(s(z), s(elem!1))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[444, 22731, 22412])).
% 2.85/3.03 tff(22733,plain,
% 2.85/3.03 (r(s(z), s(s(z)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22732, 22730])).
% 2.85/3.03 tff(22734,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22735,plain,
% 2.85/3.03 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22736,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22735])).
% 2.85/3.03 tff(22737,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22736, 22734])).
% 2.85/3.03 tff(22738,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.85/3.03 inference(quant_inst,[status(thm)],[])).
% 2.85/3.03 tff(22739,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22738, 22737])).
% 2.85/3.03 tff(22740,plain,
% 2.85/3.03 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22739, 121, 22733, 22729, 22703])).
% 2.85/3.03 tff(22741,plain,
% 2.85/3.03 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22740, 22700])).
% 2.85/3.03 tff(22742,plain,
% 2.85/3.03 (b(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[1995, 22741, 22698])).
% 2.85/3.03 tff(22743,plain,
% 2.85/3.03 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[17876, 22732, 22610, 22623])).
% 2.85/3.03 tff(22744,plain,
% 2.85/3.03 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22685])).
% 2.85/3.03 tff(22745,plain,
% 2.85/3.03 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22744])).
% 2.85/3.03 tff(22746,plain,
% 2.85/3.03 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22745])).
% 2.85/3.03 tff(22747,plain,
% 2.85/3.03 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[877, 22746])).
% 2.85/3.03 tff(22748,plain,
% 2.85/3.03 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[4138, 22747, 22743])).
% 2.85/3.03 tff(22749,plain,
% 2.85/3.03 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22684])).
% 2.85/3.03 tff(22750,plain,
% 2.85/3.03 (s(z) = elem!1),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[242, 22684])).
% 2.85/3.03 tff(22751,plain,
% 2.85/3.03 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[3049, 22750])).
% 2.85/3.03 tff(22752,plain,
% 2.85/3.03 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22686])).
% 2.85/3.03 tff(22753,plain,
% 2.85/3.03 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22752])).
% 2.85/3.03 tff(22754,plain,
% 2.85/3.03 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22753])).
% 2.85/3.03 tff(22755,plain,
% 2.85/3.03 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[4929, 22731, 3871])).
% 2.85/3.03 tff(22756,plain,
% 2.85/3.03 (~(s(elem!1) = s(s(s(z))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[2035, 22755])).
% 2.85/3.03 tff(22757,plain,
% 2.85/3.03 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22693])).
% 2.85/3.03 tff(22758,plain,
% 2.85/3.03 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22757])).
% 2.85/3.03 tff(22759,plain,
% 2.85/3.03 (~r(s(elem!1), s(s(s(z))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22712, 22758])).
% 2.85/3.03 tff(22760,plain,
% 2.85/3.03 (b(s(elem!1), s(s(s(z))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[2044, 22759, 22756])).
% 2.85/3.03 tff(22761,plain,
% 2.85/3.03 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22684])).
% 2.85/3.03 tff(22762,plain,
% 2.85/3.03 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22761])).
% 2.85/3.03 tff(22763,plain,
% 2.85/3.03 (r(s(z), s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22730, 22762])).
% 2.85/3.03 tff(22764,plain,
% 2.85/3.03 (r(elem!1, s(s(z)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22732, 22763])).
% 2.85/3.03 tff(22765,plain,
% 2.85/3.03 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(z))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22684])).
% 2.85/3.03 tff(22766,plain,
% 2.85/3.03 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.85/3.03 inference(symmetry,[status(thm)],[22765])).
% 2.85/3.03 tff(22767,plain,
% 2.85/3.03 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22766])).
% 2.85/3.03 tff(22768,plain,
% 2.85/3.03 (~(s(s(z)) = elem!1)),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[3595, 22767])).
% 2.85/3.03 tff(22769,plain,
% 2.85/3.03 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22684])).
% 2.85/3.03 tff(22770,plain,
% 2.85/3.03 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.85/3.03 inference(symmetry,[status(thm)],[22769])).
% 2.85/3.03 tff(22771,plain,
% 2.85/3.03 ((~b(s(s(z)), s(z))) <=> (~b(s(s(z)), elem!1))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22770])).
% 2.85/3.03 tff(22772,plain,
% 2.85/3.03 (~b(s(s(z)), elem!1)),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22728, 22771])).
% 2.85/3.03 tff(22773,plain,
% 2.85/3.03 (r(s(s(z)), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[3613, 22772, 22768])).
% 2.85/3.03 tff(22774,plain,
% 2.85/3.03 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[2376, 1226])).
% 2.85/3.03 tff(22775,plain,
% 2.85/3.03 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22774, 200])).
% 2.85/3.03 tff(22776,plain,
% 2.85/3.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22775])).
% 2.85/3.03 tff(22777,plain,
% 2.85/3.03 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22776])).
% 2.85/3.03 tff(22778,plain,
% 2.85/3.03 (~(s(s(z)) = s(s(s(s(z)))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[82, 22777])).
% 2.85/3.03 tff(22779,plain,
% 2.85/3.03 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[239])).
% 2.85/3.03 tff(22780,plain,
% 2.85/3.03 (r(s(s(z)), s(z))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[3600, 22779])).
% 2.85/3.03 tff(22781,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 2.85/3.03 tff(22782,plain,
% 2.85/3.03 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22739, 121, 22781, 22780, 911])).
% 2.85/3.03 tff(22783,plain,
% 2.85/3.03 (((~![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))))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22784,plain,
% 2.85/3.03 ((~![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))))))),
% 2.85/3.03 inference(quant_inst,[status(thm)],[])).
% 2.85/3.03 tff(22785,plain,
% 2.85/3.03 ((~![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)))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22784, 22783])).
% 2.85/3.03 tff(22786,plain,
% 2.85/3.03 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22785, 21, 22782])).
% 2.85/3.03 tff(22787,plain,
% 2.85/3.03 (b(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22786, 22778])).
% 2.85/3.03 tff(22788,plain,
% 2.85/3.03 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[1226])).
% 2.85/3.03 tff(22789,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22788])).
% 2.85/3.03 tff(22790,plain,
% 2.85/3.03 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22789])).
% 2.85/3.03 tff(22791,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 2.85/3.03 tff(22792,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[1234, 911, 239])).
% 2.85/3.03 tff(22793,plain,
% 2.85/3.03 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[14387, 22792, 22791, 3600])).
% 2.85/3.03 tff(22794,plain,
% 2.85/3.03 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22793, 22790])).
% 2.85/3.03 tff(22795,plain,
% 2.85/3.03 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[1226, 2376])).
% 2.85/3.03 tff(22796,plain,
% 2.85/3.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22795])).
% 2.85/3.03 tff(22797,plain,
% 2.85/3.03 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22796])).
% 2.85/3.03 tff(22798,plain,
% 2.85/3.03 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[82, 22797])).
% 2.85/3.03 tff(22799,plain,
% 2.85/3.03 (((~![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))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22800,plain,
% 2.85/3.03 ((~![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))))),
% 2.85/3.03 inference(quant_inst,[status(thm)],[])).
% 2.85/3.03 tff(22801,plain,
% 2.85/3.03 ((~![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)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22800, 22799])).
% 2.85/3.03 tff(22802,plain,
% 2.85/3.03 ((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)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22801, 21])).
% 2.85/3.03 tff(22803,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22802, 22798, 22794])).
% 2.85/3.03 tff(22804,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22805,plain,
% 2.85/3.03 (((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(22806,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(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, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22805])).
% 2.85/3.03 tff(22807,plain,
% 2.85/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(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, X3: $i, X2: $i, X1: $i] : ((~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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22806, 22804])).
% 2.85/3.03 tff(22808,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.85/3.03 inference(quant_inst,[status(thm)],[])).
% 2.85/3.03 tff(22809,plain,
% 2.85/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22808, 22807])).
% 2.85/3.03 tff(22810,plain,
% 2.85/3.03 ($false),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22809, 271, 22803, 22787, 6762, 11301])).
% 2.85/3.03 tff(22811,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~b(s(elem!1), s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.03 tff(22812,plain,
% 2.85/3.03 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22811, 22773, 22684, 22764, 82, 22703, 22760, 22733])).
% 2.85/3.03 tff(22813,plain,
% 2.85/3.03 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22812, 22754])).
% 2.85/3.03 tff(22814,plain,
% 2.85/3.03 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[556, 22813, 1])).
% 2.85/3.03 tff(22815,plain,
% 2.85/3.03 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22686])).
% 2.85/3.03 tff(22816,plain,
% 2.85/3.03 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22815])).
% 2.85/3.03 tff(22817,plain,
% 2.85/3.03 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22687])).
% 2.85/3.03 tff(22818,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22817])).
% 2.85/3.03 tff(22819,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22818, 22816])).
% 2.85/3.03 tff(22820,plain,
% 2.85/3.03 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22819])).
% 2.85/3.03 tff(22821,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22693])).
% 2.85/3.03 tff(22822,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22821])).
% 2.85/3.03 tff(22823,plain,
% 2.85/3.03 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22691, 10146])).
% 2.85/3.03 tff(22824,plain,
% 2.85/3.03 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22823])).
% 2.85/3.03 tff(22825,plain,
% 2.85/3.03 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22697, 22824])).
% 2.85/3.03 tff(22826,plain,
% 2.85/3.03 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22685])).
% 2.85/3.03 tff(22827,plain,
% 2.85/3.03 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22826])).
% 2.85/3.03 tff(22828,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22687])).
% 2.85/3.03 tff(22829,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22828, 22827])).
% 2.85/3.03 tff(22830,plain,
% 2.85/3.03 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22829])).
% 2.85/3.03 tff(22831,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22684])).
% 2.85/3.03 tff(22832,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.85/3.03 inference(symmetry,[status(thm)],[22831])).
% 2.85/3.03 tff(22833,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), elem!1)),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22144, 22832])).
% 2.85/3.03 tff(22834,plain,
% 2.85/3.03 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[14387, 22773, 22833, 22764])).
% 2.85/3.03 tff(22835,plain,
% 2.85/3.03 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22834, 22830])).
% 2.85/3.03 tff(22836,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(elem!1))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[1559, 22835, 22825])).
% 2.85/3.03 tff(22837,plain,
% 2.85/3.03 (b(s(s(s(s(z)))), s(s(z)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22836, 22822])).
% 2.85/3.03 tff(22838,plain,
% 2.85/3.03 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[21892, 271, 22721, 22713, 22837])).
% 2.85/3.03 tff(22839,plain,
% 2.85/3.03 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22838, 22820])).
% 2.85/3.03 tff(22840,plain,
% 2.85/3.03 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[586, 22839, 563])).
% 2.85/3.03 tff(22841,plain,
% 2.85/3.03 (~r(s(s(elem!1)), s(z))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[14540, 22840, 22145, 22814])).
% 2.85/3.03 tff(22842,plain,
% 2.85/3.03 (~r(s(s(elem!1)), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[6803, 22841, 22684])).
% 2.85/3.03 tff(22843,plain,
% 2.85/3.03 (b(s(s(elem!1)), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[862, 22842, 851])).
% 2.85/3.03 tff(22844,plain,
% 2.85/3.03 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22684])).
% 2.85/3.03 tff(22845,plain,
% 2.85/3.03 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22844])).
% 2.85/3.03 tff(22846,plain,
% 2.85/3.03 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[22686])).
% 2.85/3.03 tff(22847,plain,
% 2.85/3.03 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22846])).
% 2.85/3.03 tff(22848,plain,
% 2.85/3.03 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.85/3.03 inference(transitivity,[status(thm)],[22847, 22845])).
% 2.85/3.03 tff(22849,plain,
% 2.85/3.03 (b(elem!1, s(s(elem!1)))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[3871, 22848])).
% 2.85/3.03 tff(22850,plain,
% 2.85/3.03 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.85/3.03 inference(monotonicity,[status(thm)],[1224, 3029])).
% 2.85/3.03 tff(22851,plain,
% 2.85/3.03 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.85/3.03 inference(symmetry,[status(thm)],[22850])).
% 2.85/3.03 tff(22852,plain,
% 2.85/3.03 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[11383, 5606, 1326, 2359, 109, 588, 542])).
% 2.85/3.03 tff(22853,plain,
% 2.85/3.03 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[1494, 22852])).
% 2.85/3.03 tff(22854,plain,
% 2.85/3.03 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[22853, 22851])).
% 2.85/3.03 tff(22855,plain,
% 2.85/3.03 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[11438, 5606, 588, 542])).
% 2.85/3.03 tff(22856,plain,
% 2.85/3.03 ($false),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22855, 22854])).
% 2.85/3.03 tff(22857,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(elem!1 = s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.03 tff(22858,plain,
% 2.85/3.03 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[22857, 22684, 22849, 22843, 1326, 22625])).
% 2.85/3.03 tff(22859,plain,
% 2.85/3.03 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[8096, 22858, 22750])).
% 2.85/3.03 tff(22860,plain,
% 2.85/3.03 (r(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.03 inference(unit_resolution,[status(thm)],[840, 22859, 22751])).
% 2.85/3.04 tff(22861,plain,
% 2.85/3.04 (r(s(s(s(s(s(z))))), s(z))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22860, 22749])).
% 2.85/3.04 tff(22862,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(22863,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.85/3.04 inference(quant_inst,[status(thm)],[])).
% 2.85/3.04 tff(22864,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22863, 22862])).
% 2.85/3.04 tff(22865,plain,
% 2.85/3.04 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22864, 121, 22733, 22703, 22861])).
% 2.85/3.04 tff(22866,plain,
% 2.85/3.04 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[9512, 22865])).
% 2.85/3.04 tff(22867,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(22868,plain,
% 2.85/3.04 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(22869,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22868])).
% 2.85/3.04 tff(22870,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.85/3.04 inference(transitivity,[status(thm)],[22869, 22867])).
% 2.85/3.04 tff(22871,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.85/3.04 inference(quant_inst,[status(thm)],[])).
% 2.85/3.04 tff(22872,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22871, 22870])).
% 2.85/3.04 tff(22873,plain,
% 2.85/3.04 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22872, 121, 22733, 22703, 22861])).
% 2.85/3.04 tff(22874,plain,
% 2.85/3.04 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1777, 22873])).
% 2.85/3.04 tff(22875,plain,
% 2.85/3.04 ($false),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[14690, 22874, 22866, 22748, 22742])).
% 2.85/3.04 tff(22876,plain,(b(elem!1, s(elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.04 tff(22877,plain,
% 2.85/3.04 (b(elem!1, s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22876, 1391, 198, 1, 79, 3871, 6533, 22612, 3407, 1638, 1281, 1326])).
% 2.85/3.04 tff(22878,plain,
% 2.85/3.04 (~b(s(z), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[20382, 307, 1326, 1281])).
% 2.85/3.04 tff(22879,plain,
% 2.85/3.04 (r(s(z), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[236, 22616, 22878])).
% 2.85/3.04 tff(22880,plain,
% 2.85/3.04 (~r(s(elem!1), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1254, 22879, 412, 905])).
% 2.85/3.04 tff(22881,plain,
% 2.85/3.04 (b(s(elem!1), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[429, 22880, 22133])).
% 2.85/3.04 tff(22882,plain,
% 2.85/3.04 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2063, 22132])).
% 2.85/3.04 tff(22883,plain,
% 2.85/3.04 (~r(s(s(s(elem!1))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[18965, 21457, 572, 22613, 22878])).
% 2.85/3.04 tff(22884,plain,
% 2.85/3.04 (s(s(s(elem!1))) = elem!1),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[486, 22883, 22614])).
% 2.85/3.04 tff(22885,plain,
% 2.85/3.04 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2596, 22884])).
% 2.85/3.04 tff(22886,plain,
% 2.85/3.04 (~(s(elem!1) = s(s(s(z))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2035, 22885])).
% 2.85/3.04 tff(22887,plain,
% 2.85/3.04 (~r(s(s(s(z))), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[6541, 22879, 905, 6533])).
% 2.85/3.04 tff(22888,plain,
% 2.85/3.04 (b(s(s(s(z))), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2325, 22887])).
% 2.85/3.04 tff(22889,plain,
% 2.85/3.04 (~b(s(elem!1), s(s(s(z))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[3622, 22881, 3871, 22888])).
% 2.85/3.04 tff(22890,plain,
% 2.85/3.04 (r(s(elem!1), s(s(s(z))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2044, 22889, 22886])).
% 2.85/3.04 tff(22891,plain,
% 2.85/3.04 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[3865, 22890, 412, 6533])).
% 2.85/3.04 tff(22892,plain,
% 2.85/3.04 (b(s(s(s(z))), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1816, 22891, 22885])).
% 2.85/3.04 tff(22893,plain,
% 2.85/3.04 (~b(s(z), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[5698, 22892, 1326, 905, 22879, 22884, 22882, 22881])).
% 2.85/3.04 tff(22894,plain,
% 2.85/3.04 (r(elem!1, s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[299, 21457, 22613])).
% 2.85/3.04 tff(22895,plain,
% 2.85/3.04 (~b(z, s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[4122, 22881, 1326, 307])).
% 2.85/3.04 tff(22896,plain,
% 2.85/3.04 (r(z, s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1439, 22895])).
% 2.85/3.04 tff(22897,plain,
% 2.85/3.04 (b(s(s(s(z))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[6558, 22896, 3871, 1209, 22879, 22886, 22881, 905, 1326])).
% 2.85/3.04 tff(22898,plain,
% 2.85/3.04 (~b(s(elem!1), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[13140, 22897, 412, 6533, 307, 22885])).
% 2.85/3.04 tff(22899,plain,
% 2.85/3.04 (r(s(elem!1), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2243, 22898, 3500])).
% 2.85/3.04 tff(22900,plain,
% 2.85/3.04 (~r(s(z), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[6525, 22899, 22879, 22894])).
% 2.85/3.04 tff(22901,plain,
% 2.85/3.04 ($false),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[444, 22900, 22893, 22132])).
% 2.85/3.04 tff(22902,plain,(b(z, s(z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | b(z, s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.04 tff(22903,plain,
% 2.85/3.04 (b(z, s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22902, 22877, 22610, 1326, 3871, 1209, 3407, 22145, 1281, 219, 22410, 1391])).
% 2.85/3.04 tff(22904,plain,
% 2.85/3.04 (~r(s(s(s(elem!1))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[18965, 258, 22145, 294, 22878])).
% 2.85/3.04 tff(22905,plain,
% 2.85/3.04 (r(s(z), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[236, 1257, 22878])).
% 2.85/3.04 tff(22906,plain,
% 2.85/3.04 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[13328, 623, 22145, 22144, 944])).
% 2.85/3.04 tff(22907,plain,
% 2.85/3.04 (~r(s(z), s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[13318, 121, 623, 22145, 22144])).
% 2.85/3.04 tff(22908,plain,
% 2.85/3.04 (b(s(z), s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2167, 22907])).
% 2.85/3.04 tff(22909,plain,
% 2.85/3.04 (~r(s(s(elem!1)), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[13294, 121, 623, 22145, 22144])).
% 2.85/3.04 tff(22910,plain,
% 2.85/3.04 (b(s(s(elem!1)), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2143, 22909])).
% 2.85/3.04 tff(22911,plain,
% 2.85/3.04 (~b(s(s(elem!1)), z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[16949, 22910, 1281, 220])).
% 2.85/3.04 tff(22912,plain,
% 2.85/3.04 (r(s(s(elem!1)), z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2430, 22911])).
% 2.85/3.04 tff(22913,plain,
% 2.85/3.04 (~b(z, s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[12176, 22910, 220, 22908])).
% 2.85/3.04 tff(22914,plain,
% 2.85/3.04 (r(z, s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2106, 22913])).
% 2.85/3.04 tff(22915,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(22916,plain,
% 2.85/3.04 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(22917,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22916])).
% 2.85/3.04 tff(22918,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.85/3.04 inference(transitivity,[status(thm)],[22917, 22915])).
% 2.85/3.04 tff(22919,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.85/3.04 inference(quant_inst,[status(thm)],[])).
% 2.85/3.04 tff(22920,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22919, 22918])).
% 2.85/3.04 tff(22921,plain,
% 2.85/3.04 ($false),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22920, 271, 1326, 588, 504, 1638])).
% 2.85/3.04 tff(22922,plain,((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.04 tff(22923,plain,
% 2.85/3.04 (~b(elem!1, s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22922, 504, 1638, 1326])).
% 2.85/3.04 tff(22924,plain,
% 2.85/3.04 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[14498, 504, 3407, 2088, 2417, 331])).
% 2.85/3.04 tff(22925,plain,
% 2.85/3.04 ($false),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[599, 22924, 22923, 68])).
% 2.85/3.04 tff(22926,plain,((~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (z = elem!1) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.04 tff(22927,plain,
% 2.85/3.04 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22926, 22914, 3407, 68, 22912, 331, 1638, 1326])).
% 2.85/3.04 tff(22928,plain,
% 2.85/3.04 (s(s(s(elem!1))) = elem!1),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[486, 22927, 147])).
% 2.85/3.04 tff(22929,plain,
% 2.85/3.04 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2596, 22928])).
% 2.85/3.04 tff(22930,plain,
% 2.85/3.04 ($false),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[15148, 22929, 22928, 22910, 216, 351, 3456, 357, 412, 1140, 307, 22908, 907, 22906, 623])).
% 2.85/3.04 tff(22931,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (z = elem!1) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.04 tff(22932,plain,
% 2.85/3.04 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22931, 1256, 211, 22905, 412, 1140, 307, 907, 22904, 3407, 68, 331, 1638, 1326, 220, 1281, 19199])).
% 2.85/3.04 tff(22933,plain,
% 2.85/3.04 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[556, 22932, 1])).
% 2.85/3.04 tff(22934,plain,
% 2.85/3.04 (~b(s(s(elem!1)), z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[4735, 271, 22933, 3407, 1638])).
% 2.85/3.04 tff(22935,plain,
% 2.85/3.04 (r(s(s(elem!1)), z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2430, 22934])).
% 2.85/3.04 tff(22936,plain,
% 2.85/3.04 (~b(z, s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22456, 271, 22933, 3407, 1638])).
% 2.85/3.04 tff(22937,plain,
% 2.85/3.04 (r(z, s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2106, 22936])).
% 2.85/3.04 tff(22938,plain,
% 2.85/3.04 (~r(s(s(elem!1)), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[4880, 22937, 412, 22935])).
% 2.85/3.04 tff(22939,plain,
% 2.85/3.04 (b(s(s(elem!1)), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[701, 22938, 3313])).
% 2.85/3.04 tff(22940,plain,
% 2.85/3.04 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22926, 22937, 3407, 68, 22935, 331, 1638, 1326])).
% 2.85/3.04 tff(22941,plain,
% 2.85/3.04 (s(s(s(elem!1))) = elem!1),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[486, 22940, 22904])).
% 2.85/3.04 tff(22942,plain,
% 2.85/3.04 (b(s(s(elem!1)), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[8592, 22941, 22933])).
% 2.85/3.04 tff(22943,plain,
% 2.85/3.04 (~r(s(elem!1), s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[15072, 121, 22937, 412, 22935])).
% 2.85/3.04 tff(22944,plain,
% 2.85/3.04 (b(s(elem!1), s(s(elem!1)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[526, 22943, 211])).
% 2.85/3.04 tff(22945,plain,
% 2.85/3.04 ($false),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[857, 271, 307, 22944, 22942, 22939])).
% 2.85/3.04 tff(22946,plain,((elem!1 = s(z)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (z = elem!1) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.04 tff(22947,plain,
% 2.85/3.04 (elem!1 = s(z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22946, 22877, 22610, 3407, 68, 22411, 1638, 1326, 1, 6533, 22612, 22903, 1281, 22611])).
% 2.85/3.04 tff(22948,plain,
% 2.85/3.04 (s(elem!1) = s(s(z))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22947])).
% 2.85/3.04 tff(22949,plain,
% 2.85/3.04 (s(s(elem!1)) = s(s(s(z)))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22948])).
% 2.85/3.04 tff(22950,plain,
% 2.85/3.04 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22949])).
% 2.85/3.04 tff(22951,plain,
% 2.85/3.04 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22947])).
% 2.85/3.04 tff(22952,plain,
% 2.85/3.04 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22951])).
% 2.85/3.04 tff(22953,plain,
% 2.85/3.04 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22949])).
% 2.85/3.04 tff(22954,plain,
% 2.85/3.04 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22953])).
% 2.85/3.04 tff(22955,plain,
% 2.85/3.04 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.85/3.04 inference(transitivity,[status(thm)],[22954, 22952])).
% 2.85/3.04 tff(22956,plain,
% 2.85/3.04 (b(elem!1, s(s(elem!1)))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[3871, 22955])).
% 2.85/3.04 tff(22957,plain,
% 2.85/3.04 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22949])).
% 2.85/3.04 tff(22958,plain,
% 2.85/3.04 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22957])).
% 2.85/3.04 tff(22959,plain,
% 2.85/3.04 (r(z, s(s(elem!1)))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[6533, 22958])).
% 2.85/3.04 tff(22960,plain,
% 2.85/3.04 (~b(s(s(s(z))), z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[21058, 22903, 1281, 3871])).
% 2.85/3.04 tff(22961,plain,
% 2.85/3.04 (r(s(s(s(z))), z)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1155, 22960])).
% 2.85/3.04 tff(22962,plain,
% 2.85/3.04 (s(z) = elem!1),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[242, 22947])).
% 2.85/3.04 tff(22963,plain,
% 2.85/3.04 (b(s(z), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1276, 22962, 22877])).
% 2.85/3.04 tff(22964,plain,
% 2.85/3.04 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22949])).
% 2.85/3.04 tff(22965,plain,
% 2.85/3.04 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22964])).
% 2.85/3.04 tff(22966,plain,
% 2.85/3.04 (r(s(z), s(s(s(s(z)))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22145, 22965])).
% 2.85/3.04 tff(22967,plain,
% 2.85/3.04 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22964])).
% 2.85/3.04 tff(22968,plain,
% 2.85/3.04 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22967])).
% 2.85/3.04 tff(22969,plain,
% 2.85/3.04 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22968])).
% 2.85/3.04 tff(22970,plain,
% 2.85/3.04 (r(s(s(s(s(z)))), s(z))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22144, 22969])).
% 2.85/3.04 tff(22971,plain,
% 2.85/3.04 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22948, 22967])).
% 2.85/3.04 tff(22972,plain,
% 2.85/3.04 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.85/3.04 inference(transitivity,[status(thm)],[22971, 10493])).
% 2.85/3.04 tff(22973,plain,
% 2.85/3.04 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22972])).
% 2.85/3.04 tff(22974,plain,
% 2.85/3.04 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22973])).
% 2.85/3.04 tff(22975,plain,
% 2.85/3.04 (s(s(z)) = s(elem!1)),
% 2.85/3.04 inference(symmetry,[status(thm)],[22948])).
% 2.85/3.04 tff(22976,plain,
% 2.85/3.04 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22975])).
% 2.85/3.04 tff(22977,plain,
% 2.85/3.04 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22976])).
% 2.85/3.04 tff(22978,plain,
% 2.85/3.04 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[22977])).
% 2.85/3.04 tff(22979,plain,
% 2.85/3.04 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[79, 22978])).
% 2.85/3.04 tff(22980,plain,
% 2.85/3.04 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22979, 22974])).
% 2.85/3.04 tff(22981,plain,
% 2.85/3.04 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.04 inference(symmetry,[status(thm)],[10503])).
% 2.85/3.04 tff(22982,plain,
% 2.85/3.04 (~r(s(s(elem!1)), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[6803, 2128, 239])).
% 2.85/3.04 tff(22983,plain,
% 2.85/3.04 (b(s(s(elem!1)), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[862, 22982, 851])).
% 2.85/3.04 tff(22984,plain,
% 2.85/3.04 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22857, 22983, 239, 10359, 1326, 109])).
% 2.85/3.04 tff(22985,plain,
% 2.85/3.04 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[8096, 22984, 2359])).
% 2.85/3.04 tff(22986,plain,
% 2.85/3.04 (r(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[840, 22985, 10355])).
% 2.85/3.04 tff(22987,plain,
% 2.85/3.04 (r(s(s(s(s(s(z))))), s(z))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22986, 10354])).
% 2.85/3.04 tff(22988,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(22989,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(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)))))))),
% 2.85/3.04 inference(quant_inst,[status(thm)],[])).
% 2.85/3.04 tff(22990,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(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))))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[22989, 22988])).
% 2.85/3.04 tff(22991,plain,
% 2.85/3.04 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[22990, 121, 911, 22987, 1026])).
% 2.85/3.04 tff(22992,plain,
% 2.85/3.04 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[9512, 22991])).
% 2.85/3.04 tff(22993,plain,
% 2.85/3.04 (~r(s(s(s(z))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[6824, 2128, 2359])).
% 2.85/3.04 tff(22994,plain,
% 2.85/3.04 (b(s(s(s(z))), elem!1)),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[255, 22993, 907])).
% 2.85/3.04 tff(22995,plain,
% 2.85/3.04 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[239])).
% 2.85/3.04 tff(22996,plain,
% 2.85/3.04 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.85/3.04 inference(symmetry,[status(thm)],[22995])).
% 2.85/3.04 tff(22997,plain,
% 2.85/3.04 (b(s(z), s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.85/3.04 inference(transitivity,[status(thm)],[21548, 22996])).
% 2.85/3.04 tff(22998,plain,
% 2.85/3.04 (b(elem!1, s(s(z)))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[446, 22997])).
% 2.85/3.04 tff(22999,plain,
% 2.85/3.04 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[1223])).
% 2.85/3.04 tff(23000,plain,
% 2.85/3.04 ((s(s(s(z))) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 2.85/3.04 inference(transitivity,[status(thm)],[22999, 20097])).
% 2.85/3.04 tff(23001,plain,
% 2.85/3.04 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.85/3.04 inference(symmetry,[status(thm)],[23000])).
% 2.85/3.04 tff(23002,plain,
% 2.85/3.04 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[23001])).
% 2.85/3.04 tff(23003,plain,
% 2.85/3.04 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[1136, 23002])).
% 2.85/3.04 tff(23004,plain,
% 2.85/3.04 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.85/3.04 inference(transitivity,[status(thm)],[23001, 3547])).
% 2.85/3.04 tff(23005,plain,
% 2.85/3.04 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[23004])).
% 2.85/3.04 tff(23006,plain,
% 2.85/3.04 (~(s(elem!1) = s(s(s(z))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[1136, 23005])).
% 2.85/3.04 tff(23007,plain,
% 2.85/3.04 (~b(s(elem!1), s(s(s(z))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[3879, 22994, 3871, 446])).
% 2.85/3.04 tff(23008,plain,
% 2.85/3.04 (r(s(elem!1), s(s(s(z))))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[2044, 23007, 23006])).
% 2.85/3.04 tff(23009,plain,
% 2.85/3.04 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[3865, 23008, 412, 1140])).
% 2.85/3.04 tff(23010,plain,
% 2.85/3.04 (b(s(s(s(z))), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[1816, 23009, 23003])).
% 2.85/3.04 tff(23011,plain,
% 2.85/3.04 (b(s(s(s(z))), s(s(z)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[14223, 23010, 239])).
% 2.85/3.04 tff(23012,plain,
% 2.85/3.04 (~b(s(s(z)), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[6740, 23011, 22998, 22994])).
% 2.85/3.04 tff(23013,plain,
% 2.85/3.04 (r(s(s(z)), s(z))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[4670, 23012])).
% 2.85/3.04 tff(23014,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(23015,plain,
% 2.85/3.04 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(23016,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[23015])).
% 2.85/3.04 tff(23017,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.04 inference(transitivity,[status(thm)],[23016, 23014])).
% 2.85/3.04 tff(23018,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.85/3.04 inference(quant_inst,[status(thm)],[])).
% 2.85/3.04 tff(23019,plain,
% 2.85/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[23018, 23017])).
% 2.85/3.04 tff(23020,plain,
% 2.85/3.04 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[23019, 121, 23013, 22987, 1026])).
% 2.85/3.04 tff(23021,plain,
% 2.85/3.04 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[4270, 23020, 239])).
% 2.85/3.04 tff(23022,plain,
% 2.85/3.04 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[4138, 23021, 4262])).
% 2.85/3.04 tff(23023,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(23024,plain,
% 2.85/3.04 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(23025,plain,
% 2.85/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23024])).
% 2.85/3.05 tff(23026,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.05 inference(transitivity,[status(thm)],[23025, 23023])).
% 2.85/3.05 tff(23027,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.85/3.05 inference(quant_inst,[status(thm)],[])).
% 2.85/3.05 tff(23028,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23027, 23026])).
% 2.85/3.05 tff(23029,plain,
% 2.85/3.05 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23028, 121, 911, 22987, 1026])).
% 2.85/3.05 tff(23030,plain,
% 2.85/3.05 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1777, 23029])).
% 2.85/3.05 tff(23031,plain,
% 2.85/3.05 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[14690, 23030, 23022, 22992])).
% 2.85/3.05 tff(23032,plain,
% 2.85/3.05 (r(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1995, 23031, 2603])).
% 2.85/3.05 tff(23033,plain,
% 2.85/3.05 (r(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23032, 22981])).
% 2.85/3.05 tff(23034,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.05 inference(rewrite,[status(thm)],[])).
% 2.85/3.05 tff(23035,plain,
% 2.85/3.05 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.05 inference(rewrite,[status(thm)],[])).
% 2.85/3.05 tff(23036,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23035])).
% 2.85/3.05 tff(23037,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.85/3.05 inference(transitivity,[status(thm)],[23036, 23034])).
% 2.85/3.05 tff(23038,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.85/3.05 inference(quant_inst,[status(thm)],[])).
% 2.85/3.05 tff(23039,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23038, 23037])).
% 2.85/3.05 tff(23040,plain,
% 2.85/3.05 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23039, 121, 23013, 911, 1026])).
% 2.85/3.05 tff(23041,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23040, 23033])).
% 2.85/3.05 tff(23042,plain,(r(s(s(elem!1)), s(z)) | (~(elem!1 = s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23043,plain,
% 2.85/3.05 (r(s(s(elem!1)), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23042, 22947, 22980, 22970, 22966, 22610, 6533, 3871, 22963, 1326, 22961, 22612, 198])).
% 2.85/3.05 tff(23044,plain,
% 2.85/3.05 (~r(s(elem!1), s(s(elem!1)))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[5431, 23043, 22610, 22959])).
% 2.85/3.05 tff(23045,plain,
% 2.85/3.05 (b(s(elem!1), s(s(elem!1)))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[526, 23044, 211])).
% 2.85/3.05 tff(23046,plain,
% 2.85/3.05 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[9687, 23045, 22877, 22956])).
% 2.85/3.05 tff(23047,plain,
% 2.85/3.05 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[556, 23046, 1])).
% 2.85/3.05 tff(23048,plain,
% 2.85/3.05 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23047, 22950])).
% 2.85/3.05 tff(23049,plain,
% 2.85/3.05 (b(elem!1, s(s(s(z))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[11114, 22947, 3871])).
% 2.85/3.05 tff(23050,plain,
% 2.85/3.05 (b(s(elem!1), s(s(s(z))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2369, 23045, 22947])).
% 2.85/3.05 tff(23051,plain,
% 2.85/3.05 (~b(s(s(s(z))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[10690, 23050, 22877, 23049])).
% 2.85/3.05 tff(23052,plain,
% 2.85/3.05 (r(s(s(s(z))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2325, 23051])).
% 2.85/3.05 tff(23053,plain,
% 2.85/3.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[21540, 23052, 22966, 22970])).
% 2.85/3.05 tff(23054,plain,
% 2.85/3.05 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[8812, 23053, 22947])).
% 2.85/3.05 tff(23055,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23054, 23048])).
% 2.85/3.05 tff(23056,plain,(r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23057,plain,
% 2.85/3.05 (r(z, elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23056, 1326, 3871, 1, 3407, 68, 1638, 1281, 1209])).
% 2.85/3.05 tff(23058,plain,
% 2.85/3.05 (b(s(z), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1266, 21457, 22613, 378, 905])).
% 2.85/3.05 tff(23059,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[21030, 23058, 21458, 1281, 3407])).
% 2.85/3.05 tff(23060,plain,(b(z, s(z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (elem!1 = z) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23061,plain,
% 2.85/3.05 (b(z, s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23060, 23057, 3407, 1281, 22610, 219, 22410, 1326])).
% 2.85/3.05 tff(23062,plain,
% 2.85/3.05 (~b(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[21058, 23061, 1281, 3871])).
% 2.85/3.05 tff(23063,plain,
% 2.85/3.05 (r(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1155, 23062])).
% 2.85/3.05 tff(23064,plain,
% 2.85/3.05 (~b(elem!1, s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[22946, 258, 22610, 3407, 68, 22411, 1638, 1326, 1, 6533, 22612, 23061, 1281, 22611])).
% 2.85/3.05 tff(23065,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[22265, 23064, 258, 22610, 23057, 1209, 23063, 3871, 22412, 219])).
% 2.85/3.05 tff(23066,plain,((elem!1 = s(z)) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23067,plain,
% 2.85/3.05 (elem!1 = s(z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23066, 22608, 20246, 3407, 68, 1638, 22409, 1, 1281])).
% 2.85/3.05 tff(23068,plain,
% 2.85/3.05 (r(z, elem!1) <=> r(z, s(z))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23067])).
% 2.85/3.05 tff(23069,plain,
% 2.85/3.05 (r(z, elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23056, 22409, 20246, 1, 3407, 68, 1638, 1281, 22608])).
% 2.85/3.05 tff(23070,plain,
% 2.85/3.05 (r(z, s(z))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23069, 23068])).
% 2.85/3.05 tff(23071,plain,
% 2.85/3.05 (b(z, s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23060, 23069, 3407, 1281, 22607, 219, 22131, 22409])).
% 2.85/3.05 tff(23072,plain,
% 2.85/3.05 (~b(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[21058, 23071, 1281, 20246])).
% 2.85/3.05 tff(23073,plain,
% 2.85/3.05 (r(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1155, 23072])).
% 2.85/3.05 tff(23074,plain,
% 2.85/3.05 (s(elem!1) = s(s(z))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23067])).
% 2.85/3.05 tff(23075,plain,
% 2.85/3.05 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23074])).
% 2.85/3.05 tff(23076,plain,
% 2.85/3.05 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23067])).
% 2.85/3.05 tff(23077,plain,
% 2.85/3.05 (s(z) = elem!1),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[242, 23067])).
% 2.85/3.05 tff(23078,plain,
% 2.85/3.05 (r(elem!1, s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1045, 23077, 22145])).
% 2.85/3.05 tff(23079,plain,
% 2.85/3.05 (~r(s(elem!1), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[6817, 23078, 22607, 23069])).
% 2.85/3.05 tff(23080,plain,
% 2.85/3.05 (b(s(elem!1), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2243, 23079, 2207])).
% 2.85/3.05 tff(23081,plain,
% 2.85/3.05 (b(s(elem!1), s(z))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23080, 23076])).
% 2.85/3.05 tff(23082,plain,
% 2.85/3.05 (b(s(s(z)), s(z))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23081, 23075])).
% 2.85/3.05 tff(23083,plain,
% 2.85/3.05 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23074])).
% 2.85/3.05 tff(23084,plain,
% 2.85/3.05 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(z))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23083])).
% 2.85/3.05 tff(23085,plain,
% 2.85/3.05 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[3650, 23073, 22607, 23069])).
% 2.85/3.05 tff(23086,plain,
% 2.85/3.05 (~r(s(s(s(z))), s(s(z)))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23085, 23084])).
% 2.85/3.05 tff(23087,plain,
% 2.85/3.05 (b(s(s(s(z))), s(s(z)))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1368, 23086])).
% 2.85/3.05 tff(23088,plain,
% 2.85/3.05 (~b(s(s(s(z))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[19498, 23087, 1281, 23082])).
% 2.85/3.05 tff(23089,plain,
% 2.85/3.05 (r(s(s(s(z))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2325, 23088])).
% 2.85/3.05 tff(23090,plain,
% 2.85/3.05 (~(z = elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[364, 22131])).
% 2.85/3.05 tff(23091,plain,
% 2.85/3.05 (~(s(z) = s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[343, 23090])).
% 2.85/3.05 tff(23092,plain,
% 2.85/3.05 (~(s(s(s(z))) = elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[6548, 22409, 22608])).
% 2.85/3.05 tff(23093,plain,
% 2.85/3.05 (s(s(elem!1)) = s(s(s(z)))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23074])).
% 2.85/3.05 tff(23094,plain,
% 2.85/3.05 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23093])).
% 2.85/3.05 tff(23095,plain,
% 2.85/3.05 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23094])).
% 2.85/3.05 tff(23096,plain,
% 2.85/3.05 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23074, 23095])).
% 2.85/3.05 tff(23097,plain,
% 2.85/3.05 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.85/3.05 inference(transitivity,[status(thm)],[23096, 10493])).
% 2.85/3.05 tff(23098,plain,
% 2.85/3.05 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23097])).
% 2.85/3.05 tff(23099,plain,
% 2.85/3.05 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23098])).
% 2.85/3.05 tff(23100,plain,
% 2.85/3.05 (s(s(z)) = s(elem!1)),
% 2.85/3.05 inference(symmetry,[status(thm)],[23074])).
% 2.85/3.05 tff(23101,plain,
% 2.85/3.05 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23100])).
% 2.85/3.05 tff(23102,plain,
% 2.85/3.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23101])).
% 2.85/3.05 tff(23103,plain,
% 2.85/3.05 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23102])).
% 2.85/3.05 tff(23104,plain,
% 2.85/3.05 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[79, 23103])).
% 2.85/3.05 tff(23105,plain,
% 2.85/3.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23104, 23099])).
% 2.85/3.05 tff(23106,plain,
% 2.85/3.05 (r(z, s(s(s(z))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1214, 22608])).
% 2.85/3.05 tff(23107,plain,
% 2.85/3.05 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23094])).
% 2.85/3.05 tff(23108,plain,
% 2.85/3.05 (r(s(z), s(s(s(s(z)))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[22145, 23107])).
% 2.85/3.05 tff(23109,plain,
% 2.85/3.05 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23095])).
% 2.85/3.05 tff(23110,plain,
% 2.85/3.05 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23109])).
% 2.85/3.05 tff(23111,plain,
% 2.85/3.05 (r(s(s(s(s(z)))), s(z))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[22144, 23110])).
% 2.85/3.05 tff(23112,plain,
% 2.85/3.05 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23093])).
% 2.85/3.05 tff(23113,plain,
% 2.85/3.05 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23112])).
% 2.85/3.05 tff(23114,plain,
% 2.85/3.05 (r(z, s(s(elem!1)))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23106, 23113])).
% 2.85/3.05 tff(23115,plain,
% 2.85/3.05 (~r(s(s(elem!1)), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[8581, 23114, 22145, 23070])).
% 2.85/3.05 tff(23116,plain,
% 2.85/3.05 (~b(s(z), s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23042, 23115, 23067, 23111, 23108, 22607, 23106, 20246, 23105, 22409, 23073, 23092, 198])).
% 2.85/3.05 tff(23117,plain,
% 2.85/3.05 (r(s(z), s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[444, 23116, 23091])).
% 2.85/3.05 tff(23118,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[10317, 23117, 23089, 23073, 23070])).
% 2.85/3.05 tff(23119,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23120,plain,
% 2.85/3.05 (elem!1 = s(s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23119, 22123, 20244, 1281, 1, 100])).
% 2.85/3.05 tff(23121,plain,
% 2.85/3.05 (s(elem!1) = s(s(s(elem!1)))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23120])).
% 2.85/3.05 tff(23122,plain,
% 2.85/3.05 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23121])).
% 2.85/3.05 tff(23123,plain,
% 2.85/3.05 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.85/3.05 inference(symmetry,[status(thm)],[23122])).
% 2.85/3.05 tff(23124,plain,
% 2.85/3.05 (b(s(elem!1), z)),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[22123, 23123])).
% 2.85/3.05 tff(23125,plain,
% 2.85/3.05 (~b(s(elem!1), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[22605, 1, 20246, 20244, 1281, 22123])).
% 2.85/3.05 tff(23126,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23125, 23124])).
% 2.85/3.05 tff(23127,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | r(s(z), s(s(s(z)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23128,plain,
% 2.85/3.05 (r(z, s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23127, 20243, 1, 19197])).
% 2.85/3.05 tff(23129,plain,
% 2.85/3.05 (~b(s(s(s(elem!1))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[8132, 448, 504, 260])).
% 2.85/3.05 tff(23130,plain,
% 2.85/3.05 (r(s(s(s(elem!1))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[16580, 23129])).
% 2.85/3.05 tff(23131,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[19743, 121, 111, 19675, 909, 23130])).
% 2.85/3.05 tff(23132,plain,((~b(elem!1, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23133,plain,
% 2.85/3.05 (~b(elem!1, s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23132, 23128, 909, 20239, 20235])).
% 2.85/3.05 tff(23134,plain,
% 2.85/3.05 (r(elem!1, s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[299, 23133, 20233])).
% 2.85/3.05 tff(23135,plain,
% 2.85/3.05 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[19790, 23134, 909, 20228])).
% 2.85/3.05 tff(23136,plain,
% 2.85/3.05 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[760, 23135])).
% 2.85/3.05 tff(23137,plain,
% 2.85/3.05 ((~b(elem!1, s(z))) <=> (~b(s(s(s(z))), s(z)))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[10640])).
% 2.85/3.05 tff(23138,plain,
% 2.85/3.05 (~b(s(s(s(z))), s(z))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[294, 23137])).
% 2.85/3.05 tff(23139,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[222, 23138])).
% 2.85/3.05 tff(23140,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23141,plain,
% 2.85/3.05 (~b(s(s(s(z))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23140, 23133, 20224])).
% 2.85/3.05 tff(23142,plain,
% 2.85/3.05 (r(s(s(s(z))), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2325, 23141])).
% 2.85/3.05 tff(23143,plain,
% 2.85/3.05 (b(s(z), s(s(s(z))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[105, 20243])).
% 2.85/3.05 tff(23144,plain,
% 2.85/3.05 (s(elem!1) = s(s(s(s(z))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2605, 20224])).
% 2.85/3.05 tff(23145,plain,
% 2.85/3.05 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[9696])).
% 2.85/3.05 tff(23146,plain,
% 2.85/3.05 (b(z, s(s(s(s(s(z))))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[1894, 23145])).
% 2.85/3.05 tff(23147,plain,
% 2.85/3.05 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[4024])).
% 2.85/3.05 tff(23148,plain,
% 2.85/3.05 ((s(z) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 2.85/3.05 inference(transitivity,[status(thm)],[23147, 9523])).
% 2.85/3.05 tff(23149,plain,
% 2.85/3.05 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23148])).
% 2.85/3.05 tff(23150,plain,
% 2.85/3.05 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23149])).
% 2.85/3.05 tff(23151,plain,
% 2.85/3.05 (~(s(z) = s(elem!1))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[927, 23150])).
% 2.85/3.05 tff(23152,plain,
% 2.85/3.05 (~b(s(z), s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[19853, 1894, 1281, 394])).
% 2.85/3.05 tff(23153,plain,
% 2.85/3.05 (r(s(z), s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[444, 23152, 23151])).
% 2.85/3.05 tff(23154,plain,
% 2.85/3.05 (~r(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[10317, 23153, 909, 2327])).
% 2.85/3.05 tff(23155,plain,
% 2.85/3.05 (b(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1155, 23154])).
% 2.85/3.05 tff(23156,plain,
% 2.85/3.05 (~b(z, s(s(s(s(s(z))))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[4302, 23155, 1281, 3871])).
% 2.85/3.05 tff(23157,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23156, 23146])).
% 2.85/3.05 tff(23158,plain,((~b(z, s(s(elem!1)))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23159,plain,
% 2.85/3.05 (~b(z, s(s(elem!1)))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23158, 23144, 19197, 23143, 909, 23142, 394])).
% 2.85/3.05 tff(23160,plain,
% 2.85/3.05 (r(z, s(s(elem!1)))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2106, 23159])).
% 2.85/3.05 tff(23161,plain,
% 2.85/3.05 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23144])).
% 2.85/3.05 tff(23162,plain,
% 2.85/3.05 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23161])).
% 2.85/3.05 tff(23163,plain,
% 2.85/3.05 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 2.85/3.05 inference(symmetry,[status(thm)],[23162])).
% 2.85/3.05 tff(23164,plain,
% 2.85/3.05 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[20224])).
% 2.85/3.05 tff(23165,plain,
% 2.85/3.05 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.85/3.05 inference(transitivity,[status(thm)],[23164, 1836])).
% 2.85/3.05 tff(23166,plain,
% 2.85/3.05 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.85/3.05 inference(transitivity,[status(thm)],[23165, 1837])).
% 2.85/3.05 tff(23167,plain,
% 2.85/3.05 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23166])).
% 2.85/3.05 tff(23168,plain,
% 2.85/3.05 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[1489, 23167])).
% 2.85/3.05 tff(23169,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.85/3.05 inference(rewrite,[status(thm)],[])).
% 2.85/3.05 tff(23170,plain,
% 2.85/3.05 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.85/3.05 inference(rewrite,[status(thm)],[])).
% 2.85/3.05 tff(23171,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.85/3.05 inference(monotonicity,[status(thm)],[23170])).
% 2.85/3.05 tff(23172,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.85/3.05 inference(transitivity,[status(thm)],[23171, 23169])).
% 2.85/3.05 tff(23173,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.85/3.05 inference(quant_inst,[status(thm)],[])).
% 2.85/3.05 tff(23174,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23173, 23172])).
% 2.85/3.05 tff(23175,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23174, 271, 260, 750, 1849, 504])).
% 2.85/3.05 tff(23176,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23177,plain,
% 2.85/3.05 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23176, 20239, 23136, 20235])).
% 2.85/3.05 tff(23178,plain,
% 2.85/3.05 (r(elem!1, s(s(s(s(s(z))))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1847, 23177, 23168])).
% 2.85/3.05 tff(23179,plain,
% 2.85/3.05 (r(elem!1, s(s(elem!1)))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23178, 23163])).
% 2.85/3.05 tff(23180,plain,
% 2.85/3.05 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2502, 23179, 20228, 23160])).
% 2.85/3.05 tff(23181,plain,
% 2.85/3.05 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[556, 23180, 1])).
% 2.85/3.05 tff(23182,plain,
% 2.85/3.05 (~r(s(s(elem!1)), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[5075, 23179, 20228, 23160])).
% 2.85/3.05 tff(23183,plain,
% 2.85/3.05 (b(s(s(elem!1)), s(z))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2143, 23182])).
% 2.85/3.05 tff(23184,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[989, 23183, 23181, 20235, 23136])).
% 2.85/3.05 tff(23185,plain,((~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | r(s(s(s(elem!1))), elem!1) | b(z, elem!1) | b(z, s(z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23186,plain,
% 2.85/3.05 (~b(s(elem!1), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23185, 199, 909, 9983, 147, 1, 894, 82])).
% 2.85/3.05 tff(23187,plain,
% 2.85/3.05 (~(elem!1 = z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[20985, 23186, 19197])).
% 2.85/3.05 tff(23188,plain,
% 2.85/3.05 (~(z = elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[364, 23187])).
% 2.85/3.05 tff(23189,plain,
% 2.85/3.05 (r(z, elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[355, 23188, 199])).
% 2.85/3.05 tff(23190,plain,
% 2.85/3.05 (r(s(elem!1), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[409, 23186])).
% 2.85/3.05 tff(23191,plain,
% 2.85/3.05 (b(s(s(s(z))), s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[3724, 23188, 2207, 909, 23190, 199, 9983, 317])).
% 2.85/3.05 tff(23192,plain,
% 2.85/3.05 (~(s(s(s(z))) = elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[6165, 23191, 317])).
% 2.85/3.05 tff(23193,plain,
% 2.85/3.05 (b(elem!1, z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[21021, 23190, 219, 19197, 909, 23187])).
% 2.85/3.05 tff(23194,plain,
% 2.85/3.05 (~r(s(elem!1), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[3683, 23189, 9983, 23190])).
% 2.85/3.05 tff(23195,plain,
% 2.85/3.05 (b(s(elem!1), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[2243, 23194, 2207])).
% 2.85/3.05 tff(23196,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.85/3.05 inference(rewrite,[status(thm)],[])).
% 2.85/3.05 tff(23197,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.85/3.05 inference(quant_inst,[status(thm)],[])).
% 2.85/3.05 tff(23198,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23197, 23196])).
% 2.85/3.05 tff(23199,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23198, 271, 2618, 261, 1422, 257])).
% 2.85/3.05 tff(23200,plain,((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23201,plain,
% 2.85/3.05 (~b(s(s(s(z))), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23200, 23195, 23193, 23191])).
% 2.85/3.05 tff(23202,plain,
% 2.85/3.05 (r(s(s(s(z))), elem!1)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[255, 23201, 23192])).
% 2.85/3.05 tff(23203,plain,
% 2.85/3.05 (~r(z, s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[12090, 23189, 9983, 23190])).
% 2.85/3.05 tff(23204,plain,
% 2.85/3.05 (b(z, s(elem!1))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[1439, 23203])).
% 2.85/3.05 tff(23205,plain,
% 2.85/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))),
% 2.85/3.05 inference(rewrite,[status(thm)],[])).
% 2.85/3.05 tff(23206,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))),
% 2.85/3.05 inference(quant_inst,[status(thm)],[])).
% 2.85/3.05 tff(23207,plain,
% 2.85/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))),
% 2.85/3.05 inference(modus_ponens,[status(thm)],[23206, 23205])).
% 2.85/3.05 tff(23208,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23207, 271, 2618, 1422, 1421, 1935])).
% 2.85/3.05 tff(23209,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.05 tff(23210,plain,
% 2.85/3.05 (~b(s(s(s(z))), z)),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[23209, 23204, 23191, 23195])).
% 2.85/3.05 tff(23211,plain,
% 2.85/3.05 (r(s(s(s(z))), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1155, 23210])).
% 2.85/3.06 tff(23212,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[19765, 23211, 23202, 23189, 9983])).
% 2.85/3.06 tff(23213,plain,(b(z, elem!1) | b(elem!1, s(elem!1)) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23214,plain,
% 2.85/3.06 (b(z, elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23213, 82, 909, 147, 1, 894, 317])).
% 2.85/3.06 tff(23215,plain,
% 2.85/3.06 (~(elem!1 = s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1397, 23214, 894])).
% 2.85/3.06 tff(23216,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23217,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.85/3.06 inference(quant_inst,[status(thm)],[])).
% 2.85/3.06 tff(23218,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23217, 23216])).
% 2.85/3.06 tff(23219,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23218, 271, 1326, 394, 1281, 446])).
% 2.85/3.06 tff(23220,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23221,plain,
% 2.85/3.06 (~b(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23220, 394, 19197, 1326])).
% 2.85/3.06 tff(23222,plain,
% 2.85/3.06 (~b(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[9252, 271, 1326, 394, 19197])).
% 2.85/3.06 tff(23223,plain,
% 2.85/3.06 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[244])).
% 2.85/3.06 tff(23224,plain,
% 2.85/3.06 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.85/3.06 inference(symmetry,[status(thm)],[23223])).
% 2.85/3.06 tff(23225,plain,
% 2.85/3.06 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[379, 23224])).
% 2.85/3.06 tff(23226,plain,
% 2.85/3.06 (r(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[444, 9528, 439])).
% 2.85/3.06 tff(23227,plain,
% 2.85/3.06 (r(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[429, 9531, 424])).
% 2.85/3.06 tff(23228,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23229,plain,
% 2.85/3.06 (((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23230,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23229])).
% 2.85/3.06 tff(23231,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 2.85/3.06 inference(transitivity,[status(thm)],[23230, 23228])).
% 2.85/3.06 tff(23232,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 2.85/3.06 inference(quant_inst,[status(thm)],[])).
% 2.85/3.06 tff(23233,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23232, 23231])).
% 2.85/3.06 tff(23234,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23233, 121, 431, 1500, 411, 108])).
% 2.85/3.06 tff(23235,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23236,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23235, 23227, 23226, 15707, 23225])).
% 2.85/3.06 tff(23237,plain,((~(s(s(s(z))) = elem!1)) | b(s(elem!1), s(z)) | b(s(z), s(elem!1)) | (~r(elem!1, s(elem!1))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23238,plain,
% 2.85/3.06 (~(s(s(s(z))) = elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23237, 1242, 439, 379, 424])).
% 2.85/3.06 tff(23239,plain,
% 2.85/3.06 (~(s(z) = s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[19616, 23238, 1, 82, 379, 909, 147, 13988, 394])).
% 2.85/3.06 tff(23240,plain,
% 2.85/3.06 (~(s(elem!1) = s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[350, 23239])).
% 2.85/3.06 tff(23241,plain,
% 2.85/3.06 (r(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[429, 23240, 424])).
% 2.85/3.06 tff(23242,plain,
% 2.85/3.06 (r(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[444, 23239, 439])).
% 2.85/3.06 tff(23243,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[20297, 121, 379, 10603, 23242, 23241])).
% 2.85/3.06 tff(23244,plain,(b(s(z), elem!1) | (~r(elem!1, s(elem!1))) | b(s(elem!1), s(z)) | b(s(z), s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23245,plain,
% 2.85/3.06 (b(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23244, 23222, 379, 23221, 1, 82, 909, 147, 394, 1257])).
% 2.85/3.06 tff(23246,plain,
% 2.85/3.06 (~b(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[4760, 23245, 19197, 1326])).
% 2.85/3.06 tff(23247,plain,
% 2.85/3.06 (r(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[299, 23246, 258])).
% 2.85/3.06 tff(23248,plain,
% 2.85/3.06 (r(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[444, 348, 439])).
% 2.85/3.06 tff(23249,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[9263, 23248, 348, 1281, 379, 1326, 3456])).
% 2.85/3.06 tff(23250,plain,((s(z) = s(elem!1)) | (~b(s(z), z)) | (~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23251,plain,
% 2.85/3.06 (s(z) = s(elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23250, 23247, 379, 1326, 19197, 23221])).
% 2.85/3.06 tff(23252,plain,
% 2.85/3.06 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23251])).
% 2.85/3.06 tff(23253,plain,
% 2.85/3.06 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.06 inference(transitivity,[status(thm)],[23252, 1927])).
% 2.85/3.06 tff(23254,plain,
% 2.85/3.06 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 2.85/3.06 inference(symmetry,[status(thm)],[23253])).
% 2.85/3.06 tff(23255,plain,
% 2.85/3.06 (s(s(s(z))) = elem!1),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[19616, 23251, 1, 82, 379, 909, 147, 19200, 394])).
% 2.85/3.06 tff(23256,plain,
% 2.85/3.06 (s(elem!1) = s(s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2605, 23255])).
% 2.85/3.06 tff(23257,plain,
% 2.85/3.06 (s(s(s(s(z)))) = s(z)),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23256, 23254])).
% 2.85/3.06 tff(23258,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[927, 23257])).
% 2.85/3.06 tff(23259,plain,((~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23260,plain,
% 2.85/3.06 (~b(s(elem!1), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23259, 82, 1, 9983, 909, 147, 23214, 23215])).
% 2.85/3.06 tff(23261,plain,
% 2.85/3.06 (r(s(elem!1), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[409, 23260])).
% 2.85/3.06 tff(23262,plain,
% 2.85/3.06 (~(elem!1 = z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[20985, 23260, 19197])).
% 2.85/3.06 tff(23263,plain,
% 2.85/3.06 (b(elem!1, z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21021, 23262, 219, 19197, 909, 23261])).
% 2.85/3.06 tff(23264,plain,
% 2.85/3.06 (~b(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21813, 23261, 219, 19197, 23214, 23262])).
% 2.85/3.06 tff(23265,plain,
% 2.85/3.06 (~(elem!1 = z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[20985, 3498, 1281])).
% 2.85/3.06 tff(23266,plain,
% 2.85/3.06 (~b(z, s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[22622, 3501, 377, 1281, 894, 1326, 317, 1391, 23265])).
% 2.85/3.06 tff(23267,plain,
% 2.85/3.06 (r(z, s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[19736, 23266])).
% 2.85/3.06 tff(23268,plain,
% 2.85/3.06 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[11073, 23267, 1391])).
% 2.85/3.06 tff(23269,plain,
% 2.85/3.06 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[486, 23268, 147])).
% 2.85/3.06 tff(23270,plain,
% 2.85/3.06 (b(elem!1, z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21021, 3501, 377, 1281, 909, 23265])).
% 2.85/3.06 tff(23271,plain,
% 2.85/3.06 (~b(s(s(s(elem!1))), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[7080, 271, 1326, 23270, 23269])).
% 2.85/3.06 tff(23272,plain,
% 2.85/3.06 (r(s(s(s(elem!1))), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[8229, 23271])).
% 2.85/3.06 tff(23273,plain,
% 2.85/3.06 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[6215, 121, 23267, 3501, 23272])).
% 2.85/3.06 tff(23274,plain,
% 2.85/3.06 (b(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2293, 21, 23273, 2280])).
% 2.85/3.06 tff(23275,plain,
% 2.85/3.06 (~(z = elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[364, 23265])).
% 2.85/3.06 tff(23276,plain,
% 2.85/3.06 (~(s(z) = s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[343, 23275])).
% 2.85/3.06 tff(23277,plain,
% 2.85/3.06 (~(s(elem!1) = s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[350, 23276])).
% 2.85/3.06 tff(23278,plain,
% 2.85/3.06 (~b(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21813, 3501, 377, 1281, 1326, 23265])).
% 2.85/3.06 tff(23279,plain,
% 2.85/3.06 (~b(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3964, 23270, 1281, 1326])).
% 2.85/3.06 tff(23280,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23281,plain,
% 2.85/3.06 (((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23282,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23281])).
% 2.85/3.06 tff(23283,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.85/3.06 inference(transitivity,[status(thm)],[23282, 23280])).
% 2.85/3.06 tff(23284,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 2.85/3.06 inference(quant_inst,[status(thm)],[])).
% 2.85/3.06 tff(23285,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23284, 23283])).
% 2.85/3.06 tff(23286,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23285, 121, 379, 1244, 9232, 411])).
% 2.85/3.06 tff(23287,plain,((s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23288,plain,
% 2.85/3.06 (~r(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23287, 23279, 3502, 4012, 23278])).
% 2.85/3.06 tff(23289,plain,
% 2.85/3.06 (b(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[429, 23288, 23277])).
% 2.85/3.06 tff(23290,plain,
% 2.85/3.06 (r(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[299, 23278, 4011])).
% 2.85/3.06 tff(23291,plain,
% 2.85/3.06 (~r(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3709, 23290, 3502, 3501])).
% 2.85/3.06 tff(23292,plain,
% 2.85/3.06 (~b(s(s(s(elem!1))), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2310, 23288, 23276, 82, 23291, 23267, 3501])).
% 2.85/3.06 tff(23293,plain,
% 2.85/3.06 (r(s(s(s(elem!1))), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[16580, 23292])).
% 2.85/3.06 tff(23294,plain,
% 2.85/3.06 (~r(s(z), s(s(s(s(s(z))))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[19684, 23272, 909, 23293])).
% 2.85/3.06 tff(23295,plain,
% 2.85/3.06 (b(s(z), s(s(s(s(s(z))))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1756, 23294])).
% 2.85/3.06 tff(23296,plain,
% 2.85/3.06 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2063, 23276])).
% 2.85/3.06 tff(23297,plain,
% 2.85/3.06 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[11663, 23296])).
% 2.85/3.06 tff(23298,plain,
% 2.85/3.06 (~b(s(s(s(z))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[11686, 23269, 1326, 23270, 23297])).
% 2.85/3.06 tff(23299,plain,
% 2.85/3.06 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[8078, 3498, 377, 894])).
% 2.85/3.06 tff(23300,plain,
% 2.85/3.06 (r(s(s(s(z))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[255, 907, 2346])).
% 2.85/3.06 tff(23301,plain,
% 2.85/3.06 (b(elem!1, z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21021, 412, 377, 1281, 909, 259])).
% 2.85/3.06 tff(23302,plain,
% 2.85/3.06 (~b(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3964, 23301, 1281, 1326])).
% 2.85/3.06 tff(23303,plain,
% 2.85/3.06 (r(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[236, 23302, 4012])).
% 2.85/3.06 tff(23304,plain,
% 2.85/3.06 (~b(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21813, 412, 377, 1281, 1326, 259])).
% 2.85/3.06 tff(23305,plain,
% 2.85/3.06 (r(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[299, 23304, 4011])).
% 2.85/3.06 tff(23306,plain,
% 2.85/3.06 (~r(s(s(s(z))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[4112, 108, 3456, 357])).
% 2.85/3.06 tff(23307,plain,
% 2.85/3.06 (b(s(s(s(z))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[255, 23306, 907])).
% 2.85/3.06 tff(23308,plain,
% 2.85/3.06 (~b(z, s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1334, 23307, 1326, 261])).
% 2.85/3.06 tff(23309,plain,
% 2.85/3.06 (r(z, s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1214, 23308])).
% 2.85/3.06 tff(23310,plain,
% 2.85/3.06 (~b(s(s(s(z))), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1947, 23307, 1326, 261])).
% 2.85/3.06 tff(23311,plain,
% 2.85/3.06 (r(s(s(s(z))), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1155, 23310])).
% 2.85/3.06 tff(23312,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1148, 23311, 23309, 108, 909])).
% 2.85/3.06 tff(23313,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23314,plain,
% 2.85/3.06 (~r(s(z), s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23313, 907, 909, 1326, 23305, 23303, 23301])).
% 2.85/3.06 tff(23315,plain,
% 2.85/3.06 (b(s(z), s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[105, 23314])).
% 2.85/3.06 tff(23316,plain,
% 2.85/3.06 (~b(z, s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21465, 23315, 377, 1281, 894, 1326, 412, 23300, 259])).
% 2.85/3.06 tff(23317,plain,
% 2.85/3.06 (r(z, s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1214, 23316])).
% 2.85/3.06 tff(23318,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[4174, 121, 1258, 1256, 145, 2327])).
% 2.85/3.06 tff(23319,plain,((elem!1 = s(z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23320,plain,
% 2.85/3.06 (~r(s(s(s(z))), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23319, 23300, 4011, 23304, 23302])).
% 2.85/3.06 tff(23321,plain,
% 2.85/3.06 (b(s(s(s(z))), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2325, 23320])).
% 2.85/3.06 tff(23322,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23323,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.85/3.06 inference(quant_inst,[status(thm)],[])).
% 2.85/3.06 tff(23324,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23323, 23322])).
% 2.85/3.06 tff(23325,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23324, 271, 3871, 222, 1723, 5381])).
% 2.85/3.06 tff(23326,plain,((~b(s(s(s(s(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(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23327,plain,
% 2.85/3.06 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23326, 23315, 23321, 5381])).
% 2.85/3.06 tff(23328,plain,
% 2.85/3.06 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1733, 23327])).
% 2.85/3.06 tff(23329,plain,
% 2.85/3.06 (~r(z, s(s(s(s(s(z))))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[16283, 23328, 23300, 23317])).
% 2.85/3.06 tff(23330,plain,
% 2.85/3.06 (b(z, s(s(s(s(s(z))))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1658, 23329])).
% 2.85/3.06 tff(23331,plain,
% 2.85/3.06 (~b(z, s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[15001, 23330, 9894, 447])).
% 2.85/3.06 tff(23332,plain,
% 2.85/3.06 (r(z, s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1439, 23331])).
% 2.85/3.06 tff(23333,plain,
% 2.85/3.06 (s(elem!1) = s(s(s(z)))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[6558, 23332, 909, 1326, 23303, 2346, 23315, 447, 23316])).
% 2.85/3.06 tff(23334,plain,
% 2.85/3.06 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23333])).
% 2.85/3.06 tff(23335,plain,
% 2.85/3.06 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.06 inference(symmetry,[status(thm)],[23334])).
% 2.85/3.06 tff(23336,plain,
% 2.85/3.06 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23335])).
% 2.85/3.06 tff(23337,plain,
% 2.85/3.06 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23327, 23336])).
% 2.85/3.06 tff(23338,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[9894, 23337])).
% 2.85/3.06 tff(23339,plain,((s(s(s(z))) = elem!1) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(z))) | (~b(z, elem!1)) | b(s(s(s(z))), elem!1) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | b(z, s(z)) | (~r(s(elem!1), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23340,plain,
% 2.85/3.06 (s(s(s(z))) = elem!1),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23339, 23299, 909, 1326, 23298, 23289, 23295, 377, 1281, 894, 3501, 23265])).
% 2.85/3.06 tff(23341,plain,
% 2.85/3.06 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23340])).
% 2.85/3.06 tff(23342,plain,
% 2.85/3.06 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.85/3.06 inference(symmetry,[status(thm)],[23341])).
% 2.85/3.06 tff(23343,plain,
% 2.85/3.06 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23269, 23342])).
% 2.85/3.06 tff(23344,plain,
% 2.85/3.06 (~b(s(z), s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[6230, 23343, 23289, 23274])).
% 2.85/3.06 tff(23345,plain,
% 2.85/3.06 (r(s(z), s(s(s(elem!1))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[760, 23344])).
% 2.85/3.06 tff(23346,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23347,plain,
% 2.85/3.06 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.85/3.06 inference(rewrite,[status(thm)],[])).
% 2.85/3.06 tff(23348,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23347])).
% 2.85/3.06 tff(23349,plain,
% 2.85/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.85/3.06 inference(transitivity,[status(thm)],[23348, 23346])).
% 2.85/3.06 tff(23350,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 2.85/3.06 inference(quant_inst,[status(thm)],[])).
% 2.85/3.06 tff(23351,plain,
% 2.85/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[23350, 23349])).
% 2.85/3.06 tff(23352,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23351, 121, 23267, 23345, 909, 23272])).
% 2.85/3.06 tff(23353,plain,(b(s(elem!1), z) | (~r(z, s(z))) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | b(z, s(z)) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | r(z, elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23354,plain,
% 2.85/3.06 (r(z, elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23353, 23260, 23214, 219, 19197, 894, 147, 82, 909, 317])).
% 2.85/3.06 tff(23355,plain,
% 2.85/3.06 (b(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1266, 23354, 909, 23215, 23264])).
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% 2.85/3.06 inference(unit_resolution,[status(thm)],[3964, 23355, 23263, 19197, 23214])).
% 2.85/3.06 tff(23357,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(z))) | b(z, s(z)) | r(s(s(s(elem!1))), elem!1) | b(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23358,plain,
% 2.85/3.06 (s(s(s(elem!1))) = s(elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23357, 317, 894, 147, 909, 1])).
% 2.85/3.06 tff(23359,plain,
% 2.85/3.06 (elem!1 = s(s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[78, 23358])).
% 2.85/3.06 tff(23360,plain,
% 2.85/3.06 ((z = elem!1) <=> (z = s(s(elem!1)))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23359])).
% 2.85/3.06 tff(23361,plain,
% 2.85/3.06 ((z = elem!1) <=> (s(s(elem!1)) = z)),
% 2.85/3.06 inference(transitivity,[status(thm)],[23360, 2098])).
% 2.85/3.06 tff(23362,plain,
% 2.85/3.06 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.85/3.06 inference(symmetry,[status(thm)],[23361])).
% 2.85/3.06 tff(23363,plain,
% 2.85/3.06 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.85/3.06 inference(transitivity,[status(thm)],[23362, 361])).
% 2.85/3.06 tff(23364,plain,
% 2.85/3.06 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23363])).
% 2.85/3.06 tff(23365,plain,
% 2.85/3.06 (~(elem!1 = z)),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[59, 23364])).
% 2.85/3.06 tff(23366,plain,
% 2.85/3.06 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23362])).
% 2.85/3.06 tff(23367,plain,
% 2.85/3.06 (~(z = elem!1)),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[59, 23366])).
% 2.85/3.06 tff(23368,plain,
% 2.85/3.06 (b(s(elem!1), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[12364, 23359, 1, 147])).
% 2.85/3.06 tff(23369,plain,
% 2.85/3.06 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23359])).
% 2.85/3.06 tff(23370,plain,
% 2.85/3.06 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 2.85/3.06 inference(symmetry,[status(thm)],[23369])).
% 2.85/3.06 tff(23371,plain,
% 2.85/3.06 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23370])).
% 2.85/3.06 tff(23372,plain,
% 2.85/3.06 (~(s(z) = elem!1)),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[2137, 23371])).
% 2.85/3.06 tff(23373,plain,
% 2.85/3.06 (b(s(elem!1), s(s(elem!1)))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3787, 23359, 23368])).
% 2.85/3.06 tff(23374,plain,
% 2.85/3.06 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3790, 23359, 23368])).
% 2.85/3.06 tff(23375,plain,
% 2.85/3.06 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(elem!1))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23358])).
% 2.85/3.06 tff(23376,plain,
% 2.85/3.06 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(z))),
% 2.85/3.06 inference(transitivity,[status(thm)],[23375, 4396])).
% 2.85/3.06 tff(23377,plain,
% 2.85/3.06 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(z)))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23376])).
% 2.85/3.06 tff(23378,plain,
% 2.85/3.06 (~(s(elem!1) = s(z))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[61, 23377])).
% 2.85/3.06 tff(23379,plain,
% 2.85/3.06 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = s(elem!1)))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23375])).
% 2.85/3.06 tff(23380,plain,
% 2.85/3.06 (~(s(z) = s(elem!1))),
% 2.85/3.06 inference(modus_ponens,[status(thm)],[61, 23379])).
% 2.85/3.06 tff(23381,plain,
% 2.85/3.06 (~r(z, elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3673, 357, 909, 379])).
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% 2.85/3.06 (b(z, elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[355, 23381, 12082])).
% 2.85/3.06 tff(23383,plain,
% 2.85/3.06 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[3917, 348, 2470])).
% 2.85/3.06 tff(23384,plain,
% 2.85/3.06 (~(s(elem!1) = s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2035, 23383])).
% 2.85/3.06 tff(23385,plain,
% 2.85/3.06 (b(z, elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[355, 23381, 331])).
% 2.85/3.06 tff(23386,plain,
% 2.85/3.06 (~b(s(s(s(z))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[11686, 23301, 504, 23385, 11665])).
% 2.85/3.06 tff(23387,plain,
% 2.85/3.06 (r(s(s(s(z))), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[255, 23386, 907])).
% 2.85/3.06 tff(23388,plain,
% 2.85/3.06 (~b(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21813, 412, 377, 1281, 23385, 259])).
% 2.85/3.06 tff(23389,plain,
% 2.85/3.06 (r(elem!1, s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[299, 23388, 258])).
% 2.85/3.06 tff(23390,plain,
% 2.85/3.06 (~r(s(z), s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23313, 23389, 909, 357, 23385, 907, 23301])).
% 2.85/3.06 tff(23391,plain,
% 2.85/3.06 (b(s(z), s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[105, 23390])).
% 2.85/3.06 tff(23392,plain,
% 2.85/3.06 (b(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[5659, 412, 909, 379, 258, 331, 23385])).
% 2.85/3.06 tff(23393,plain,
% 2.85/3.06 (~b(z, s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[2905, 23392, 1281, 517])).
% 2.85/3.06 tff(23394,plain,
% 2.85/3.06 (r(z, s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1439, 23393])).
% 2.85/3.06 tff(23395,plain,
% 2.85/3.06 (~r(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1254, 412, 909, 357])).
% 2.85/3.06 tff(23396,plain,
% 2.85/3.06 (b(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[429, 23395, 422])).
% 2.85/3.06 tff(23397,plain,
% 2.85/3.06 (b(z, s(s(s(z))))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[6558, 23391, 909, 23385, 357, 23386, 2037, 23396, 23394])).
% 2.85/3.06 tff(23398,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[21465, 23397, 23391, 377, 1281, 894, 23385, 412, 23387, 259])).
% 2.85/3.06 tff(23399,plain,((~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | b(z, s(z)) | (elem!1 = z) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (s(elem!1) = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (s(elem!1) = s(z)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (elem!1 = s(z)) | (~r(elem!1, s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23400,plain,
% 2.85/3.06 (~r(s(elem!1), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23399, 357, 1281, 894, 12133, 909, 377, 23384, 3907, 422, 504, 15822, 517, 12075, 379, 12082])).
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% 2.85/3.06 inference(unit_resolution,[status(thm)],[409, 23400])).
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% 2.85/3.06 inference(unit_resolution,[status(thm)],[23220, 23401, 1281, 23382])).
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% 2.85/3.06 inference(unit_resolution,[status(thm)],[444, 23402, 348])).
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% 2.85/3.06 inference(modus_ponens,[status(thm)],[23382, 3935])).
% 2.85/3.06 tff(23406,plain,
% 2.85/3.06 (~b(s(elem!1), s(z))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[19933, 23401, 1281, 23405])).
% 2.85/3.06 tff(23407,plain,
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% 2.85/3.06 inference(unit_resolution,[status(thm)],[429, 23406, 422])).
% 2.85/3.06 tff(23408,plain,
% 2.85/3.06 (~r(z, s(elem!1))),
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% 2.85/3.06 tff(23409,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[1439, 23408, 23404])).
% 2.85/3.06 tff(23410,plain,((~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(elem!1, s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(z)) | b(z, s(z)) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23411,plain,
% 2.85/3.06 (~r(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23410, 9983, 19197, 909, 23359, 23380, 23378, 894, 219, 23374, 23373])).
% 2.85/3.06 tff(23412,plain,
% 2.85/3.06 (b(s(z), elem!1)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[236, 23411, 23372])).
% 2.85/3.06 tff(23413,plain,
% 2.85/3.06 (~r(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[6159, 412, 3500, 909, 260, 331, 379])).
% 2.85/3.06 tff(23414,plain,
% 2.85/3.06 (~b(s(z), s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[15307, 23301, 260, 2618])).
% 2.85/3.06 tff(23415,plain,
% 2.85/3.06 ($false),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[444, 23414, 23413, 348])).
% 2.85/3.06 tff(23416,plain,((~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(z))) | (z = elem!1) | (~r(elem!1, s(elem!1))) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.06 tff(23417,plain,
% 2.85/3.06 (~r(s(elem!1), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[23416, 23380, 23412, 23368, 909, 23367, 9983, 219, 19197, 23365])).
% 2.85/3.06 tff(23418,plain,
% 2.85/3.06 (b(s(elem!1), z)),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[409, 23417])).
% 2.85/3.06 tff(23419,plain,
% 2.85/3.06 (elem!1 = s(s(elem!1))),
% 2.85/3.06 inference(unit_resolution,[status(thm)],[78, 72])).
% 2.85/3.06 tff(23420,plain,
% 2.85/3.06 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 2.85/3.06 inference(monotonicity,[status(thm)],[23419])).
% 2.85/3.06 tff(23421,plain,
% 2.85/3.06 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 2.85/3.06 inference(symmetry,[status(thm)],[23420])).
% 2.85/3.06 tff(23422,plain,
% 2.85/3.06 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 2.85/3.06 inference(transitivity,[status(thm)],[23421, 1218])).
% 2.85/3.06 tff(23423,plain,
% 2.85/3.07 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23422])).
% 2.85/3.07 tff(23424,plain,
% 2.85/3.07 (~(elem!1 = s(z))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[2137, 23423])).
% 2.85/3.07 tff(23425,plain,
% 2.85/3.07 ((z = elem!1) <=> (z = s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23419])).
% 2.85/3.07 tff(23426,plain,
% 2.85/3.07 ((z = elem!1) <=> (s(s(elem!1)) = z)),
% 2.85/3.07 inference(transitivity,[status(thm)],[23425, 2098])).
% 2.85/3.07 tff(23427,plain,
% 2.85/3.07 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.85/3.07 inference(symmetry,[status(thm)],[23426])).
% 2.85/3.07 tff(23428,plain,
% 2.85/3.07 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.85/3.07 inference(transitivity,[status(thm)],[23427, 361])).
% 2.85/3.07 tff(23429,plain,
% 2.85/3.07 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23428])).
% 2.85/3.07 tff(23430,plain,
% 2.85/3.07 (~(elem!1 = z)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[59, 23429])).
% 2.85/3.07 tff(23431,plain,
% 2.85/3.07 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23427])).
% 2.85/3.07 tff(23432,plain,
% 2.85/3.07 (~(z = elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[59, 23431])).
% 2.85/3.07 tff(23433,plain,
% 2.85/3.07 (b(s(elem!1), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[12364, 23419, 1, 147])).
% 2.85/3.07 tff(23434,plain,
% 2.85/3.07 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[72])).
% 2.85/3.07 tff(23435,plain,
% 2.85/3.07 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23434])).
% 2.85/3.07 tff(23436,plain,
% 2.85/3.07 (~(s(z) = s(elem!1))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[61, 23435])).
% 2.85/3.07 tff(23437,plain,
% 2.85/3.07 (~r(s(elem!1), z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23416, 23436, 260, 23433, 909, 23432, 379, 219, 19197, 23430])).
% 2.85/3.07 tff(23438,plain,
% 2.85/3.07 (b(s(elem!1), z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[409, 23437])).
% 2.85/3.07 tff(23439,plain,
% 2.85/3.07 (~(s(s(s(z))) = elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[3906, 23419])).
% 2.85/3.07 tff(23440,plain,
% 2.85/3.07 (b(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[19773, 378, 23433, 19197, 379, 23439, 23436, 23438])).
% 2.85/3.07 tff(23441,plain,
% 2.85/3.07 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[3790, 23419, 23433])).
% 2.85/3.07 tff(23442,plain,
% 2.85/3.07 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2063, 23436])).
% 2.85/3.07 tff(23443,plain,
% 2.85/3.07 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[19800, 19792, 504, 19782])).
% 2.85/3.07 tff(23444,plain,
% 2.85/3.07 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2071, 23443, 23442])).
% 2.85/3.07 tff(23445,plain,
% 2.85/3.07 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23419])).
% 2.85/3.07 tff(23446,plain,
% 2.85/3.07 (b(s(s(s(z))), s(s(elem!1)))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[257, 23445])).
% 2.85/3.07 tff(23447,plain,
% 2.85/3.07 (~b(z, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[20471, 19782, 1281, 23446])).
% 2.85/3.07 tff(23448,plain,
% 2.85/3.07 (r(z, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1214, 23447])).
% 2.85/3.07 tff(23449,plain,
% 2.85/3.07 (~(elem!1 = s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1100, 23439])).
% 2.85/3.07 tff(23450,plain,
% 2.85/3.07 (~b(elem!1, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[20039, 19782, 260, 257])).
% 2.85/3.07 tff(23451,plain,
% 2.85/3.07 (r(elem!1, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1192, 23450, 23449])).
% 2.85/3.07 tff(23452,plain,
% 2.85/3.07 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[19919, 23451, 378, 23448])).
% 2.85/3.07 tff(23453,plain,
% 2.85/3.07 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[72])).
% 2.85/3.07 tff(23454,plain,
% 2.85/3.07 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23453])).
% 2.85/3.07 tff(23455,plain,
% 2.85/3.07 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23454])).
% 2.85/3.07 tff(23456,plain,
% 2.85/3.07 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[1510, 23455])).
% 2.85/3.07 tff(23457,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[5499, 23456])).
% 2.85/3.07 tff(23458,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23459,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23458, 23452, 23444, 72])).
% 2.85/3.07 tff(23460,plain,((~r(elem!1, s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23461,plain,
% 2.85/3.07 (~r(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23460, 378, 72, 23441, 260, 23440, 19197, 909])).
% 2.85/3.07 tff(23462,plain,
% 2.85/3.07 (b(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[299, 23461, 23424])).
% 2.85/3.07 tff(23463,plain,
% 2.85/3.07 ((s(s(s(elem!1))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[72])).
% 2.85/3.07 tff(23464,plain,
% 2.85/3.07 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23463, 2202])).
% 2.85/3.07 tff(23465,plain,
% 2.85/3.07 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = elem!1)),
% 2.85/3.07 inference(symmetry,[status(thm)],[23464])).
% 2.85/3.07 tff(23466,plain,
% 2.85/3.07 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23465, 654])).
% 2.85/3.07 tff(23467,plain,
% 2.85/3.07 ((~(elem!1 = s(elem!1))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23466])).
% 2.85/3.07 tff(23468,plain,
% 2.85/3.07 (~(elem!1 = s(s(s(elem!1))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[219, 23467])).
% 2.85/3.07 tff(23469,plain,
% 2.85/3.07 (s(s(elem!1)) = elem!1),
% 2.85/3.07 inference(symmetry,[status(thm)],[23419])).
% 2.85/3.07 tff(23470,plain,
% 2.85/3.07 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23469])).
% 2.85/3.07 tff(23471,plain,
% 2.85/3.07 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23470, 159])).
% 2.85/3.07 tff(23472,plain,
% 2.85/3.07 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23471])).
% 2.85/3.07 tff(23473,plain,
% 2.85/3.07 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23472])).
% 2.85/3.07 tff(23474,plain,
% 2.85/3.07 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23449, 23473])).
% 2.85/3.07 tff(23475,plain,
% 2.85/3.07 (~b(z, s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[13416, 23461, 909, 23474, 378, 147, 1, 379, 23438, 260, 23468, 23436, 23462])).
% 2.85/3.07 tff(23476,plain,
% 2.85/3.07 (~r(z, s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23132, 23462, 909, 260, 23441])).
% 2.85/3.07 tff(23477,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[19736, 23476, 23475])).
% 2.85/3.07 tff(23478,plain,((~r(z, elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23479,plain,
% 2.85/3.07 (~r(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23478, 23412, 909, 147, 1, 9983, 23358])).
% 2.85/3.07 tff(23480,plain,
% 2.85/3.07 (b(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[355, 23479, 23367])).
% 2.85/3.07 tff(23481,plain,
% 2.85/3.07 (~b(s(z), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23220, 23480, 19197, 23418])).
% 2.85/3.07 tff(23482,plain,
% 2.85/3.07 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23370, 1218])).
% 2.85/3.07 tff(23483,plain,
% 2.85/3.07 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23482])).
% 2.85/3.07 tff(23484,plain,
% 2.85/3.07 (~(elem!1 = s(z))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[2137, 23483])).
% 2.85/3.07 tff(23485,plain,
% 2.85/3.07 (r(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[20894, 23480, 19197, 23411, 23484])).
% 2.85/3.07 tff(23486,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23250, 23485, 23480, 9983, 23380, 19197, 23481])).
% 2.85/3.07 tff(23487,plain,(b(elem!1, s(elem!1)) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23488,plain,
% 2.85/3.07 (b(elem!1, s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23487, 147, 909, 1, 894])).
% 2.85/3.07 tff(23489,plain,
% 2.85/3.07 (~(z = elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1543, 23488, 894])).
% 2.85/3.07 tff(23490,plain,
% 2.85/3.07 (~(s(z) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[343, 23489])).
% 2.85/3.07 tff(23491,plain,
% 2.85/3.07 (~(s(elem!1) = s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[350, 23490])).
% 2.85/3.07 tff(23492,plain,
% 2.85/3.07 (b(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[355, 1391, 23489])).
% 2.85/3.07 tff(23493,plain,
% 2.85/3.07 (r(s(z), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[236, 5772, 1242])).
% 2.85/3.07 tff(23494,plain,
% 2.85/3.07 (~(elem!1 = z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[333, 23489])).
% 2.85/3.07 tff(23495,plain,
% 2.85/3.07 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2063, 23490])).
% 2.85/3.07 tff(23496,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[11663, 23495])).
% 2.85/3.07 tff(23497,plain,
% 2.85/3.07 (b(elem!1, z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[21021, 412, 219, 19197, 909, 23494])).
% 2.85/3.07 tff(23498,plain,
% 2.85/3.07 (~b(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[21813, 1326, 219, 19197, 412, 23494])).
% 2.85/3.07 tff(23499,plain,
% 2.85/3.07 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[12364, 147, 1, 2467])).
% 2.85/3.07 tff(23500,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[78, 23499])).
% 2.85/3.07 tff(23501,plain,
% 2.85/3.07 (r(s(s(s(elem!1))), z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[8229, 7703])).
% 2.85/3.07 tff(23502,plain,
% 2.85/3.07 (~b(z, s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[15671, 504, 307, 1326])).
% 2.85/3.07 tff(23503,plain,
% 2.85/3.07 (r(z, s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[19736, 23502])).
% 2.85/3.07 tff(23504,plain,
% 2.85/3.07 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[7238, 121, 23503, 412, 23501])).
% 2.85/3.07 tff(23505,plain,
% 2.85/3.07 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[6215, 121, 23503, 412, 23501])).
% 2.85/3.07 tff(23506,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[11152, 23505, 23504, 307, 82, 504])).
% 2.85/3.07 tff(23507,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23508,plain,
% 2.85/3.07 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23507, 23500, 307, 412, 1326])).
% 2.85/3.07 tff(23509,plain,
% 2.85/3.07 (s(s(s(elem!1))) = elem!1),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[486, 23508, 147])).
% 2.85/3.07 tff(23510,plain,
% 2.85/3.07 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23509])).
% 2.85/3.07 tff(23511,plain,
% 2.85/3.07 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23510])).
% 2.85/3.07 tff(23512,plain,
% 2.85/3.07 (~r(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[5343, 1256, 412, 8563])).
% 2.85/3.07 tff(23513,plain,
% 2.85/3.07 (~r(z, s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[11073, 23509, 23512])).
% 2.85/3.07 tff(23514,plain,
% 2.85/3.07 (r(s(z), s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23127, 23513, 1, 19197])).
% 2.85/3.07 tff(23515,plain,
% 2.85/3.07 (~r(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[4112, 23514, 357, 1256])).
% 2.85/3.07 tff(23516,plain,
% 2.85/3.07 (b(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[255, 23515, 907])).
% 2.85/3.07 tff(23517,plain,
% 2.85/3.07 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23516, 23511])).
% 2.85/3.07 tff(23518,plain,
% 2.85/3.07 (r(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[299, 294, 258])).
% 2.85/3.07 tff(23519,plain,
% 2.85/3.07 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[12364, 2467, 1, 147])).
% 2.85/3.07 tff(23520,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[78, 23519])).
% 2.85/3.07 tff(23521,plain,
% 2.85/3.07 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23507, 23520, 307, 412, 1326])).
% 2.85/3.07 tff(23522,plain,
% 2.85/3.07 (s(s(s(elem!1))) = elem!1),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[486, 23521, 147])).
% 2.85/3.07 tff(23523,plain,
% 2.85/3.07 (elem!1 = s(s(s(elem!1)))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[13222, 23522])).
% 2.85/3.07 tff(23524,plain,
% 2.85/3.07 (b(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[19808, 23523, 2073])).
% 2.85/3.07 tff(23525,plain,
% 2.85/3.07 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23522])).
% 2.85/3.07 tff(23526,plain,
% 2.85/3.07 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23525, 1218])).
% 2.85/3.07 tff(23527,plain,
% 2.85/3.07 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23526])).
% 2.85/3.07 tff(23528,plain,
% 2.85/3.07 (~(elem!1 = s(z))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[61, 23527])).
% 2.85/3.07 tff(23529,plain,
% 2.85/3.07 (r(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[299, 23528, 294])).
% 2.85/3.07 tff(23530,plain,
% 2.85/3.07 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23522])).
% 2.85/3.07 tff(23531,plain,
% 2.85/3.07 (~b(s(z), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[20382, 1326, 19197, 307])).
% 2.85/3.07 tff(23532,plain,
% 2.85/3.07 (~b(s(z), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2562, 23522, 23531])).
% 2.85/3.07 tff(23533,plain,
% 2.85/3.07 (r(s(z), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[760, 23532])).
% 2.85/3.07 tff(23534,plain,
% 2.85/3.07 (r(s(z), elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23533, 23530])).
% 2.85/3.07 tff(23535,plain,
% 2.85/3.07 (~r(s(elem!1), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[11219, 121, 8563, 23534, 23529])).
% 2.85/3.07 tff(23536,plain,
% 2.85/3.07 (b(s(elem!1), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[429, 23535, 422])).
% 2.85/3.07 tff(23537,plain,
% 2.85/3.07 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2596, 23522])).
% 2.85/3.07 tff(23538,plain,
% 2.85/3.07 (~b(z, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1978, 23524, 307, 1326])).
% 2.85/3.07 tff(23539,plain,
% 2.85/3.07 (r(z, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1214, 23538])).
% 2.85/3.07 tff(23540,plain,
% 2.85/3.07 (~b(s(s(s(z))), z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1940, 23524, 307, 1326])).
% 2.85/3.07 tff(23541,plain,
% 2.85/3.07 (r(s(s(s(z))), z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1155, 23540])).
% 2.85/3.07 tff(23542,plain,
% 2.85/3.07 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[22644, 121, 412, 23541, 23539])).
% 2.85/3.07 tff(23543,plain,
% 2.85/3.07 (b(s(s(s(z))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1816, 23542, 23537])).
% 2.85/3.07 tff(23544,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[6976, 271, 307, 23543, 23536, 23524])).
% 2.85/3.07 tff(23545,plain,(b(s(elem!1), elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | b(elem!1, s(z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23546,plain,
% 2.85/3.07 (~b(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23545, 294, 307, 422, 412, 2467, 2073, 147, 1])).
% 2.85/3.07 tff(23547,plain,
% 2.85/3.07 (r(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[355, 23546, 331])).
% 2.85/3.07 tff(23548,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[5343, 23547, 23518, 412, 8563])).
% 2.85/3.07 tff(23549,plain,(b(elem!1, s(z)) | (~r(s(elem!1), z)) | (z = elem!1) | (elem!1 = s(z)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23550,plain,
% 2.85/3.07 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23549, 147, 307, 331, 412, 422, 2467, 258, 294, 1])).
% 2.85/3.07 tff(23551,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23550, 23517])).
% 2.85/3.07 tff(23552,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = elem!1) | (~r(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (z = elem!1) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23553,plain,
% 2.85/3.07 (b(s(elem!1), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23552, 907, 23488, 1, 357, 412, 147, 23489, 23491, 1326, 258, 23498])).
% 2.85/3.07 tff(23554,plain,
% 2.85/3.07 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[11686, 257, 1326, 261, 11665])).
% 2.85/3.07 tff(23555,plain,
% 2.85/3.07 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23198, 271, 2618, 261, 257])).
% 2.85/3.07 tff(23556,plain,
% 2.85/3.07 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1816, 23555, 2033])).
% 2.85/3.07 tff(23557,plain,
% 2.85/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.85/3.07 inference(rewrite,[status(thm)],[])).
% 2.85/3.07 tff(23558,plain,
% 2.85/3.07 (((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.85/3.07 inference(rewrite,[status(thm)],[])).
% 2.85/3.07 tff(23559,plain,
% 2.85/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23558])).
% 2.85/3.07 tff(23560,plain,
% 2.85/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23559, 23557])).
% 2.85/3.07 tff(23561,plain,
% 2.85/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.85/3.07 inference(quant_inst,[status(thm)],[])).
% 2.85/3.07 tff(23562,plain,
% 2.85/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23561, 23560])).
% 2.85/3.07 tff(23563,plain,
% 2.85/3.07 (~b(s(elem!1), s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23562, 271, 2618, 261, 257])).
% 2.85/3.07 tff(23564,plain,
% 2.85/3.07 (r(s(elem!1), s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2044, 23563, 6284])).
% 2.85/3.07 tff(23565,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[3865, 23564, 23556, 17385, 11659])).
% 2.85/3.07 tff(23566,plain,((~b(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23567,plain,
% 2.85/3.07 (s(s(s(z))) = s(elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23566, 257, 2618, 1326, 261])).
% 2.85/3.07 tff(23568,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2596, 23567])).
% 2.85/3.07 tff(23569,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[486, 23568, 23554, 147])).
% 2.85/3.07 tff(23570,plain,((~b(s(s(s(z))), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23571,plain,
% 2.85/3.07 (~b(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23570, 23553, 147, 23497, 1326, 23496])).
% 2.85/3.07 tff(23572,plain,
% 2.85/3.07 (r(s(s(s(z))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[255, 23571, 907])).
% 2.85/3.07 tff(23573,plain,
% 2.85/3.07 (r(elem!1, s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[299, 23498, 258])).
% 2.85/3.07 tff(23574,plain,
% 2.85/3.07 (~r(s(z), s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23313, 907, 909, 357, 1326, 23573, 23497])).
% 2.85/3.07 tff(23575,plain,
% 2.85/3.07 (b(s(z), s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[105, 23574])).
% 2.85/3.07 tff(23576,plain,
% 2.85/3.07 (b(s(elem!1), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[429, 3793, 23491])).
% 2.85/3.07 tff(23577,plain,
% 2.85/3.07 (~b(z, s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[4122, 23576, 23488, 1326])).
% 2.85/3.07 tff(23578,plain,
% 2.85/3.07 (r(z, s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1439, 23577])).
% 2.85/3.07 tff(23579,plain,
% 2.85/3.07 (~(s(elem!1) = s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[8394, 23571, 23553])).
% 2.85/3.07 tff(23580,plain,
% 2.85/3.07 (b(z, s(s(s(z))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[6558, 23575, 909, 1326, 357, 23571, 23579, 23576, 23578])).
% 2.85/3.07 tff(23581,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[21465, 23580, 23575, 219, 19197, 894, 1326, 412, 23572, 23494])).
% 2.85/3.07 tff(23582,plain,((s(s(s(z))) = elem!1) | b(z, s(z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23583,plain,
% 2.85/3.07 (s(s(s(z))) = elem!1),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23582, 23492, 894, 412, 909, 23493, 147, 1, 5773])).
% 2.85/3.07 tff(23584,plain,
% 2.85/3.07 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[3906, 23583])).
% 2.85/3.07 tff(23585,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[78, 23584])).
% 2.85/3.07 tff(23586,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2611, 23583])).
% 2.85/3.07 tff(23587,plain,
% 2.85/3.07 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[486, 23586, 147])).
% 2.85/3.07 tff(23588,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23507, 23587, 23585, 23488, 412, 23492])).
% 2.85/3.07 tff(23589,plain,(r(z, elem!1) | (~r(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | b(z, s(z)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23590,plain,
% 2.85/3.07 (r(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23589, 3501, 147, 894, 909, 1, 1242])).
% 2.85/3.07 tff(23591,plain,
% 2.85/3.07 (elem!1 = s(z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1293, 23590, 19197, 909, 1242, 23491, 3501, 23488])).
% 2.85/3.07 tff(23592,plain,
% 2.85/3.07 (s(z) = elem!1),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[242, 23591])).
% 2.85/3.07 tff(23593,plain,
% 2.85/3.07 (b(elem!1, z)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[21021, 3501, 219, 19197, 909, 23494])).
% 2.85/3.07 tff(23594,plain,
% 2.85/3.07 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23592])).
% 2.85/3.07 tff(23595,plain,
% 2.85/3.07 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23594])).
% 2.85/3.07 tff(23596,plain,
% 2.85/3.07 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[2137, 23595])).
% 2.85/3.07 tff(23597,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[78, 23596])).
% 2.85/3.07 tff(23598,plain,
% 2.85/3.07 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.85/3.07 inference(transitivity,[status(thm)],[23594, 2212])).
% 2.85/3.07 tff(23599,plain,
% 2.85/3.07 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23598])).
% 2.85/3.07 tff(23600,plain,
% 2.85/3.07 (~(s(s(elem!1)) = elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[2137, 23599])).
% 2.85/3.07 tff(23601,plain,
% 2.85/3.07 (~b(z, elem!1)),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1397, 23591, 894])).
% 2.85/3.07 tff(23602,plain,
% 2.85/3.07 (s(s(z)) = s(elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23592])).
% 2.85/3.07 tff(23603,plain,
% 2.85/3.07 (s(s(s(z))) = s(s(elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23602])).
% 2.85/3.07 tff(23604,plain,
% 2.85/3.07 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23603])).
% 2.85/3.07 tff(23605,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23604])).
% 2.85/3.07 tff(23606,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23592])).
% 2.85/3.07 tff(23607,plain,
% 2.85/3.07 (~r(s(s(s(s(z)))), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1234, 23591, 147])).
% 2.85/3.07 tff(23608,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[932, 23607])).
% 2.85/3.07 tff(23609,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23608, 23606])).
% 2.85/3.07 tff(23610,plain,
% 2.85/3.07 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23609, 23605])).
% 2.85/3.07 tff(23611,plain,
% 2.85/3.07 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23603])).
% 2.85/3.07 tff(23612,plain,
% 2.85/3.07 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23592])).
% 2.85/3.07 tff(23613,plain,
% 2.85/3.07 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23612, 159])).
% 2.85/3.07 tff(23614,plain,
% 2.85/3.07 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.07 inference(transitivity,[status(thm)],[23613, 160])).
% 2.85/3.07 tff(23615,plain,
% 2.85/3.07 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23614])).
% 2.85/3.07 tff(23616,plain,
% 2.85/3.07 (~(s(s(s(z))) = elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[97, 23615])).
% 2.85/3.07 tff(23617,plain,
% 2.85/3.07 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23604])).
% 2.85/3.07 tff(23618,plain,
% 2.85/3.07 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23617])).
% 2.85/3.07 tff(23619,plain,
% 2.85/3.07 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[8078, 3498, 219, 894])).
% 2.85/3.07 tff(23620,plain,
% 2.85/3.07 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23619, 23618])).
% 2.85/3.07 tff(23621,plain,
% 2.85/3.07 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.85/3.07 inference(symmetry,[status(thm)],[2360])).
% 2.85/3.07 tff(23622,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2364])).
% 2.85/3.07 tff(23623,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23622, 23621])).
% 2.85/3.07 tff(23624,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23625,plain,
% 2.85/3.07 (~r(s(s(s(s(z)))), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1234, 239, 147])).
% 2.85/3.07 tff(23626,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), s(z))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[932, 23625])).
% 2.85/3.07 tff(23627,plain,
% 2.85/3.07 (b(s(s(s(s(z)))), elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23626, 23624])).
% 2.85/3.07 tff(23628,plain,
% 2.85/3.07 (b(s(s(s(elem!1))), s(z))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23627, 23623])).
% 2.85/3.07 tff(23629,plain,
% 2.85/3.07 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23630,plain,
% 2.85/3.07 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23629])).
% 2.85/3.07 tff(23631,plain,
% 2.85/3.07 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[2137, 23630])).
% 2.85/3.07 tff(23632,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[78, 23631])).
% 2.85/3.07 tff(23633,plain,
% 2.85/3.07 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23634,plain,
% 2.85/3.07 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23633])).
% 2.85/3.07 tff(23635,plain,
% 2.85/3.07 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23634])).
% 2.85/3.07 tff(23636,plain,
% 2.85/3.07 (~r(s(z), s(elem!1))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[2344, 23635])).
% 2.85/3.07 tff(23637,plain,
% 2.85/3.07 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23638,plain,
% 2.85/3.07 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23637])).
% 2.85/3.07 tff(23639,plain,
% 2.85/3.07 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(z)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23638])).
% 2.85/3.07 tff(23640,plain,
% 2.85/3.07 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23627, 23622])).
% 2.85/3.07 tff(23641,plain,
% 2.85/3.07 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2364])).
% 2.85/3.07 tff(23642,plain,
% 2.85/3.07 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23643,plain,
% 2.85/3.07 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23642, 159])).
% 2.85/3.07 tff(23644,plain,
% 2.85/3.07 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23643])).
% 2.85/3.07 tff(23645,plain,
% 2.85/3.07 (~(elem!1 = s(s(s(z))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[97, 23644])).
% 2.85/3.07 tff(23646,plain,
% 2.85/3.07 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1516, 23645])).
% 2.85/3.07 tff(23647,plain,
% 2.85/3.07 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[17419, 23646])).
% 2.85/3.07 tff(23648,plain,
% 2.85/3.07 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1045, 21747, 2359])).
% 2.85/3.07 tff(23649,plain,
% 2.85/3.07 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[760, 23648])).
% 2.85/3.07 tff(23650,plain,
% 2.85/3.07 (b(elem!1, s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[8233, 23649, 2359])).
% 2.85/3.07 tff(23651,plain,
% 2.85/3.07 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[747, 23650, 307, 23640])).
% 2.85/3.07 tff(23652,plain,
% 2.85/3.07 (b(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[14671, 14662])).
% 2.85/3.07 tff(23653,plain,
% 2.85/3.07 ($false),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[752, 23652])).
% 2.85/3.07 tff(23654,plain,((~b(s(elem!1), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.07 tff(23655,plain,
% 2.85/3.07 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[23654, 23651, 2359])).
% 2.85/3.07 tff(23656,plain,
% 2.85/3.07 (r(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[1995, 23655, 23647])).
% 2.85/3.07 tff(23657,plain,
% 2.85/3.07 (r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23656, 23641])).
% 2.85/3.07 tff(23658,plain,
% 2.85/3.07 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23659,plain,
% 2.85/3.07 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.85/3.07 inference(transitivity,[status(thm)],[23658, 653])).
% 2.85/3.07 tff(23660,plain,
% 2.85/3.07 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[23659])).
% 2.85/3.07 tff(23661,plain,
% 2.85/3.07 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[61, 23660])).
% 2.85/3.07 tff(23662,plain,
% 2.85/3.07 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23663,plain,
% 2.85/3.07 (r(s(elem!1), s(z))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[622, 23638])).
% 2.85/3.07 tff(23664,plain,
% 2.85/3.07 (~r(s(z), s(s(elem!1)))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[4423, 23663, 909, 412])).
% 2.85/3.07 tff(23665,plain,
% 2.85/3.07 (b(s(z), s(s(elem!1)))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[2167, 23664])).
% 2.85/3.07 tff(23666,plain,
% 2.85/3.07 (b(elem!1, s(s(elem!1)))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23665, 23662])).
% 2.85/3.07 tff(23667,plain,
% 2.85/3.07 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.07 inference(unit_resolution,[status(thm)],[18010, 23666, 147, 622, 23632, 23661, 23650, 23657])).
% 2.85/3.07 tff(23668,plain,
% 2.85/3.07 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23669,plain,
% 2.85/3.07 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23668])).
% 2.85/3.07 tff(23670,plain,
% 2.85/3.07 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2363])).
% 2.85/3.07 tff(23671,plain,
% 2.85/3.07 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23670])).
% 2.85/3.07 tff(23672,plain,
% 2.85/3.07 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.85/3.07 inference(transitivity,[status(thm)],[23662, 23671, 23669])).
% 2.85/3.07 tff(23673,plain,
% 2.85/3.07 (b(s(z), s(s(s(z))))),
% 2.85/3.07 inference(modus_ponens,[status(thm)],[23665, 23672])).
% 2.85/3.07 tff(23674,plain,
% 2.85/3.07 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.85/3.07 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.07 tff(23675,plain,
% 2.85/3.07 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.85/3.07 inference(symmetry,[status(thm)],[23674])).
% 2.85/3.08 tff(23676,plain,
% 2.85/3.08 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[2362])).
% 2.85/3.08 tff(23677,plain,
% 2.85/3.08 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.85/3.08 inference(symmetry,[status(thm)],[23676])).
% 2.85/3.08 tff(23678,plain,
% 2.85/3.08 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.85/3.08 inference(transitivity,[status(thm)],[23677, 23675])).
% 2.85/3.08 tff(23679,plain,
% 2.85/3.08 (b(s(z), s(s(z)))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[307, 23678])).
% 2.85/3.08 tff(23680,plain,
% 2.85/3.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[556, 23667, 1])).
% 2.85/3.08 tff(23681,plain,
% 2.85/3.08 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.85/3.08 inference(transitivity,[status(thm)],[23629, 2212])).
% 2.85/3.08 tff(23682,plain,
% 2.85/3.08 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23681])).
% 2.85/3.08 tff(23683,plain,
% 2.85/3.08 (~(s(s(elem!1)) = elem!1)),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[2137, 23682])).
% 2.85/3.08 tff(23684,plain,
% 2.85/3.08 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[3310, 23680, 2344, 331, 199, 23683, 23632])).
% 2.85/3.08 tff(23685,plain,
% 2.85/3.08 (b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[21604, 23684, 239, 622, 211, 23680, 23679, 23649, 23673, 145, 23667, 23632])).
% 2.85/3.08 tff(23686,plain,
% 2.85/3.08 (r(s(s(elem!1)), s(z))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6824, 145, 2359])).
% 2.85/3.08 tff(23687,plain,
% 2.85/3.08 (b(elem!1, z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[21021, 412, 219, 19197, 909, 358])).
% 2.85/3.08 tff(23688,plain,
% 2.85/3.08 (~b(z, s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[21421, 23673, 909, 412, 23687, 2359])).
% 2.85/3.08 tff(23689,plain,
% 2.85/3.08 (b(z, s(s(s(z))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[1894, 8835])).
% 2.85/3.08 tff(23690,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1209, 23689])).
% 2.85/3.08 tff(23691,plain,((~b(z, s(s(elem!1)))) | b(z, s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23692,plain,
% 2.85/3.08 (~b(z, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23691, 23688, 2359])).
% 2.85/3.08 tff(23693,plain,
% 2.85/3.08 (r(z, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2106, 23692])).
% 2.85/3.08 tff(23694,plain,
% 2.85/3.08 (~r(s(elem!1), s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[5431, 23693, 412, 23686])).
% 2.85/3.08 tff(23695,plain,
% 2.85/3.08 (b(s(elem!1), s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[526, 23694, 211])).
% 2.85/3.08 tff(23696,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[644, 271, 307, 23695, 23685, 23640])).
% 2.85/3.08 tff(23697,plain,((~r(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), elem!1)) | r(elem!1, s(elem!1)) | (z = elem!1) | b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23698,plain,
% 2.85/3.08 (~r(s(elem!1), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23697, 145, 412, 239, 307, 2344, 331, 199, 1, 909, 147, 378])).
% 2.85/3.08 tff(23699,plain,
% 2.85/3.08 (~r(s(elem!1), s(z))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23698, 23639])).
% 2.85/3.08 tff(23700,plain,
% 2.85/3.08 (~r(z, s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2310, 23699, 344, 23636, 23632, 23628, 412])).
% 2.85/3.08 tff(23701,plain,
% 2.85/3.08 (r(s(z), s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23127, 23700, 1, 19197])).
% 2.85/3.08 tff(23702,plain,
% 2.85/3.08 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.08 inference(monotonicity,[status(thm)],[2359])).
% 2.85/3.08 tff(23703,plain,
% 2.85/3.08 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.85/3.08 inference(symmetry,[status(thm)],[23702])).
% 2.85/3.08 tff(23704,plain,
% 2.85/3.08 (b(s(elem!1), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2243, 23698, 2207])).
% 2.85/3.08 tff(23705,plain,
% 2.85/3.08 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[2364])).
% 2.85/3.08 tff(23706,plain,
% 2.85/3.08 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.85/3.08 inference(symmetry,[status(thm)],[23705])).
% 2.85/3.08 tff(23707,plain,
% 2.85/3.08 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23706])).
% 2.85/3.08 tff(23708,plain,
% 2.85/3.08 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.85/3.08 inference(symmetry,[status(thm)],[23707])).
% 2.85/3.08 tff(23709,plain,
% 2.85/3.08 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[5001, 10355])).
% 2.85/3.08 tff(23710,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[20529, 271, 307, 2618, 1586, 19070])).
% 2.85/3.08 tff(23711,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23712,plain,
% 2.85/3.08 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23711, 23704, 307, 1586])).
% 2.85/3.08 tff(23713,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.85/3.08 tff(23714,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23713, 5602])).
% 2.85/3.08 tff(23715,plain,((~b(elem!1, s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(elem!1))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23716,plain,
% 2.85/3.08 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23715, 23712, 2359])).
% 2.85/3.08 tff(23717,plain,
% 2.85/3.08 (r(elem!1, s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1847, 23716, 23709])).
% 2.85/3.08 tff(23718,plain,
% 2.85/3.08 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23717, 23708])).
% 2.85/3.08 tff(23719,plain,
% 2.85/3.08 (r(s(s(elem!1)), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[14112, 145, 2359])).
% 2.85/3.08 tff(23720,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23721,plain,
% 2.85/3.08 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23722,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23721])).
% 2.85/3.08 tff(23723,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.85/3.08 inference(transitivity,[status(thm)],[23722, 23720])).
% 2.85/3.08 tff(23724,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 2.85/3.08 inference(quant_inst,[status(thm)],[])).
% 2.85/3.08 tff(23725,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23724, 23723])).
% 2.85/3.08 tff(23726,plain,
% 2.85/3.08 (~r(s(s(elem!1)), z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23725, 121, 378, 23719, 23718])).
% 2.85/3.08 tff(23727,plain,
% 2.85/3.08 (b(s(s(elem!1)), z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2430, 23726])).
% 2.85/3.08 tff(23728,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23729,plain,
% 2.85/3.08 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23730,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23729])).
% 2.85/3.08 tff(23731,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.85/3.08 inference(transitivity,[status(thm)],[23730, 23728])).
% 2.85/3.08 tff(23732,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.85/3.08 inference(quant_inst,[status(thm)],[])).
% 2.85/3.08 tff(23733,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23732, 23731])).
% 2.85/3.08 tff(23734,plain,
% 2.85/3.08 (~r(z, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23733, 121, 378, 23719, 23718])).
% 2.85/3.08 tff(23735,plain,
% 2.85/3.08 (b(z, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2106, 23734])).
% 2.85/3.08 tff(23736,plain,
% 2.85/3.08 (~b(elem!1, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[20129, 23735, 23727, 23687])).
% 2.85/3.08 tff(23737,plain,
% 2.85/3.08 (r(elem!1, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[599, 23736, 23631])).
% 2.85/3.08 tff(23738,plain,
% 2.85/3.08 (b(z, s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[19736, 23700])).
% 2.85/3.08 tff(23739,plain,
% 2.85/3.08 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[14530, 23738, 23735, 23727])).
% 2.85/3.08 tff(23740,plain,
% 2.85/3.08 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[586, 23739, 563])).
% 2.85/3.08 tff(23741,plain,
% 2.85/3.08 (~r(elem!1, s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[17619, 23740, 23719, 23737])).
% 2.85/3.08 tff(23742,plain,
% 2.85/3.08 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1045, 23741, 2359])).
% 2.85/3.08 tff(23743,plain,
% 2.85/3.08 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[760, 23742])).
% 2.85/3.08 tff(23744,plain,
% 2.85/3.08 (b(elem!1, s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[8233, 23743, 2359])).
% 2.85/3.08 tff(23745,plain,
% 2.85/3.08 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[19313, 23744, 23704, 1586])).
% 2.85/3.08 tff(23746,plain,
% 2.85/3.08 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[8096, 23745, 2359])).
% 2.85/3.08 tff(23747,plain,
% 2.85/3.08 (r(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[840, 23746, 10355])).
% 2.85/3.08 tff(23748,plain,
% 2.85/3.08 (r(s(s(s(s(s(z))))), s(z))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23747, 23703])).
% 2.85/3.08 tff(23749,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6313, 121, 145, 1736, 1660, 108])).
% 2.85/3.08 tff(23750,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23751,plain,
% 2.85/3.08 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23750, 23748, 145, 23701])).
% 2.85/3.08 tff(23752,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23753,plain,
% 2.85/3.08 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23754,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23753])).
% 2.85/3.08 tff(23755,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.85/3.08 inference(transitivity,[status(thm)],[23754, 23752])).
% 2.85/3.08 tff(23756,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.85/3.08 inference(quant_inst,[status(thm)],[])).
% 2.85/3.08 tff(23757,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23756, 23755])).
% 2.85/3.08 tff(23758,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23757, 121, 3061, 1826, 145, 1477])).
% 2.85/3.08 tff(23759,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23760,plain,
% 2.85/3.08 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23759, 23747, 145, 23717])).
% 2.85/3.08 tff(23761,plain,
% 2.85/3.08 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1494, 23760])).
% 2.85/3.08 tff(23762,plain,
% 2.85/3.08 (~r(z, s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[5017, 23747, 378, 23717])).
% 2.85/3.08 tff(23763,plain,
% 2.85/3.08 (b(z, s(s(s(s(s(z))))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1658, 23762])).
% 2.85/3.08 tff(23764,plain,
% 2.85/3.08 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.85/3.08 inference(monotonicity,[status(thm)],[2363])).
% 2.85/3.08 tff(23765,plain,
% 2.85/3.08 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.85/3.08 inference(symmetry,[status(thm)],[23764])).
% 2.85/3.08 tff(23766,plain,
% 2.85/3.08 ((~r(s(s(elem!1)), z)) <=> (~r(s(s(s(z))), z))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23765])).
% 2.85/3.08 tff(23767,plain,
% 2.85/3.08 (~r(s(s(s(z))), z)),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23726, 23766])).
% 2.85/3.08 tff(23768,plain,
% 2.85/3.08 (b(s(s(s(z))), z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1155, 23767])).
% 2.85/3.08 tff(23769,plain,
% 2.85/3.08 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[4072, 23768, 23763, 23761])).
% 2.85/3.08 tff(23770,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1733, 23769, 23751])).
% 2.85/3.08 tff(23771,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~(elem!1 = s(z))) | r(elem!1, s(elem!1)) | (z = elem!1) | b(z, elem!1) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23772,plain,
% 2.85/3.08 (~r(s(s(s(z))), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23771, 23590, 23620, 1, 3501, 23488, 23591, 2344, 23489, 23601, 909, 147])).
% 2.85/3.08 tff(23773,plain,
% 2.85/3.08 (b(s(s(s(z))), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[255, 23772, 23616])).
% 2.85/3.08 tff(23774,plain,
% 2.85/3.08 (b(s(s(elem!1)), elem!1)),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23773, 23611])).
% 2.85/3.08 tff(23775,plain,
% 2.85/3.08 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[8828, 23774, 1, 2344, 23489, 23610, 23601, 23600, 23597])).
% 2.85/3.08 tff(23776,plain,
% 2.85/3.08 (b(elem!1, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[599, 23775, 23596])).
% 2.85/3.08 tff(23777,plain,
% 2.85/3.08 (b(s(z), s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6679, 23776, 23591])).
% 2.85/3.08 tff(23778,plain,
% 2.85/3.08 (~b(z, s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[21421, 23777, 909, 3501, 23593, 23592])).
% 2.85/3.08 tff(23779,plain,
% 2.85/3.08 (~b(z, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23691, 23778, 23592])).
% 2.85/3.08 tff(23780,plain,
% 2.85/3.08 (r(z, s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2106, 23779])).
% 2.85/3.08 tff(23781,plain,
% 2.85/3.08 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23603])).
% 2.85/3.08 tff(23782,plain,
% 2.85/3.08 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23781])).
% 2.85/3.08 tff(23783,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23784,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.85/3.08 inference(quant_inst,[status(thm)],[])).
% 2.85/3.08 tff(23785,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23784, 23783])).
% 2.85/3.08 tff(23786,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23785, 271, 307, 2073, 257, 504])).
% 2.85/3.08 tff(23787,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23788,plain,
% 2.85/3.08 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23787, 23773, 23488, 23610])).
% 2.85/3.08 tff(23789,plain,
% 2.85/3.08 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23788, 23782])).
% 2.85/3.08 tff(23790,plain,
% 2.85/3.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[556, 23789, 1])).
% 2.85/3.08 tff(23791,plain,
% 2.85/3.08 (b(s(z), s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1276, 23592, 23488])).
% 2.85/3.08 tff(23792,plain,
% 2.85/3.08 (~b(s(elem!1), s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[3879, 23777, 23791, 23773])).
% 2.85/3.08 tff(23793,plain,
% 2.85/3.08 (~b(s(elem!1), s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2369, 23792, 23591])).
% 2.85/3.08 tff(23794,plain,
% 2.85/3.08 (r(s(elem!1), s(s(elem!1)))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[526, 23793, 211])).
% 2.85/3.08 tff(23795,plain,
% 2.85/3.08 (~r(z, s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6878, 23794, 23780, 23790])).
% 2.85/3.08 tff(23796,plain,
% 2.85/3.08 (b(z, s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1439, 23795])).
% 2.85/3.08 tff(23797,plain,
% 2.85/3.08 (~b(elem!1, s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6868, 23796, 23488, 3501, 23590, 23597, 23780, 23593])).
% 2.85/3.08 tff(23798,plain,
% 2.85/3.08 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23602])).
% 2.85/3.08 tff(23799,plain,
% 2.85/3.08 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.85/3.08 inference(transitivity,[status(thm)],[23798, 3535])).
% 2.85/3.08 tff(23800,plain,
% 2.85/3.08 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23799])).
% 2.85/3.08 tff(23801,plain,
% 2.85/3.08 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[1136, 23800])).
% 2.85/3.08 tff(23802,plain,
% 2.85/3.08 (r(z, s(s(s(z))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1214, 23778])).
% 2.85/3.08 tff(23803,plain,
% 2.85/3.08 (~b(s(elem!1), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[13140, 23802, 23488, 3501, 23773, 23801])).
% 2.85/3.08 tff(23804,plain,
% 2.85/3.08 (r(s(elem!1), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2243, 23803, 2207])).
% 2.85/3.08 tff(23805,plain,
% 2.85/3.08 (~r(elem!1, s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6817, 23804, 3501, 23590])).
% 2.85/3.08 tff(23806,plain,
% 2.85/3.08 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1045, 23805, 23592])).
% 2.85/3.08 tff(23807,plain,
% 2.85/3.08 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[760, 23806])).
% 2.85/3.08 tff(23808,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[8233, 23807, 23797, 23592])).
% 2.85/3.08 tff(23809,plain,(b(s(elem!1), z) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1)) | r(s(s(s(elem!1))), elem!1) | b(z, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23810,plain,
% 2.85/3.08 (b(s(elem!1), z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23809, 1242, 1, 2344, 147, 894, 909])).
% 2.85/3.08 tff(23811,plain,
% 2.85/3.08 (b(z, elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[355, 1391, 6509])).
% 2.85/3.08 tff(23812,plain,
% 2.85/3.08 (~(elem!1 = z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[333, 6509])).
% 2.85/3.08 tff(23813,plain,
% 2.85/3.08 (~b(s(z), s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23220, 23811, 1281, 394])).
% 2.85/3.08 tff(23814,plain,
% 2.85/3.08 (r(s(z), s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[444, 23813, 6510])).
% 2.85/3.08 tff(23815,plain,
% 2.85/3.08 (~b(s(elem!1), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[4598, 23811, 307, 394])).
% 2.85/3.08 tff(23816,plain,
% 2.85/3.08 (r(s(elem!1), elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[2243, 23815, 2564])).
% 2.85/3.08 tff(23817,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23818,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 2.85/3.08 inference(quant_inst,[status(thm)],[])).
% 2.85/3.08 tff(23819,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23818, 23817])).
% 2.85/3.08 tff(23820,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23819, 121, 622, 357, 1409, 431])).
% 2.85/3.08 tff(23821,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23822,plain,
% 2.85/3.08 (~r(elem!1, z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23821, 23816, 23493, 23814])).
% 2.85/3.08 tff(23823,plain,
% 2.85/3.08 (b(elem!1, z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[284, 23822, 23812])).
% 2.85/3.08 tff(23824,plain,
% 2.85/3.08 (~r(elem!1, s(z))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[6525, 23814, 23493, 23816])).
% 2.85/3.08 tff(23825,plain,
% 2.85/3.08 (b(elem!1, s(z))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[299, 23824, 5773])).
% 2.85/3.08 tff(23826,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[4775, 23825, 23823, 1281, 23811])).
% 2.85/3.08 tff(23827,plain,(r(z, elem!1) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | b(s(z), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.08 tff(23828,plain,
% 2.85/3.08 (r(z, elem!1)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23827, 23810, 2207, 19197, 23488, 1242, 894])).
% 2.85/3.08 tff(23829,plain,
% 2.85/3.08 (b(elem!1, s(z))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1266, 258, 909, 1242, 378])).
% 2.85/3.08 tff(23830,plain,
% 2.85/3.08 (~b(s(elem!1), s(z))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1290, 23829, 1281, 307])).
% 2.85/3.08 tff(23831,plain,
% 2.85/3.08 (r(s(elem!1), s(z))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[429, 23830, 422])).
% 2.85/3.08 tff(23832,plain,
% 2.85/3.08 (~r(z, s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[10675, 23831, 909, 1258])).
% 2.85/3.08 tff(23833,plain,
% 2.85/3.08 (b(z, s(elem!1))),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[1439, 23832])).
% 2.85/3.08 tff(23834,plain,
% 2.85/3.08 (~b(elem!1, z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[10660, 23833, 307, 394])).
% 2.85/3.08 tff(23835,plain,
% 2.85/3.08 (r(elem!1, z)),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[284, 23834, 259])).
% 2.85/3.08 tff(23836,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23837,plain,
% 2.85/3.08 (((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.85/3.08 inference(rewrite,[status(thm)],[])).
% 2.85/3.08 tff(23838,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 2.85/3.08 inference(monotonicity,[status(thm)],[23837])).
% 2.85/3.08 tff(23839,plain,
% 2.85/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.85/3.08 inference(transitivity,[status(thm)],[23838, 23836])).
% 2.85/3.08 tff(23840,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 2.85/3.08 inference(quant_inst,[status(thm)],[])).
% 2.85/3.08 tff(23841,plain,
% 2.85/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 2.85/3.08 inference(modus_ponens,[status(thm)],[23840, 23839])).
% 2.85/3.08 tff(23842,plain,
% 2.85/3.08 ($false),
% 2.85/3.08 inference(unit_resolution,[status(thm)],[23841, 121, 378, 1258, 909, 23835])).
% 2.85/3.08 tff(23843,plain,((elem!1 = s(z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (elem!1 = z) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23844,plain,
% 2.85/3.09 (elem!1 = s(z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23843, 23828, 909, 23494, 23488, 23810, 23491, 19197, 1242])).
% 2.85/3.09 tff(23845,plain,
% 2.85/3.09 (s(z) = elem!1),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[242, 23844])).
% 2.85/3.09 tff(23846,plain,
% 2.85/3.09 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23845])).
% 2.85/3.09 tff(23847,plain,
% 2.85/3.09 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23846])).
% 2.85/3.09 tff(23848,plain,
% 2.85/3.09 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[2137, 23847])).
% 2.85/3.09 tff(23849,plain,
% 2.85/3.09 (b(elem!1, z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[20120, 23845, 19197])).
% 2.85/3.09 tff(23850,plain,
% 2.85/3.09 (~b(z, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3404, 23849, 23488, 23810])).
% 2.85/3.09 tff(23851,plain,
% 2.85/3.09 (r(z, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2106, 23850])).
% 2.85/3.09 tff(23852,plain,
% 2.85/3.09 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23845])).
% 2.85/3.09 tff(23853,plain,
% 2.85/3.09 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.85/3.09 inference(transitivity,[status(thm)],[23852, 159])).
% 2.85/3.09 tff(23854,plain,
% 2.85/3.09 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.09 inference(transitivity,[status(thm)],[23853, 160])).
% 2.85/3.09 tff(23855,plain,
% 2.85/3.09 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23854])).
% 2.85/3.09 tff(23856,plain,
% 2.85/3.09 (~(s(s(s(z))) = elem!1)),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[97, 23855])).
% 2.85/3.09 tff(23857,plain,
% 2.85/3.09 (~b(z, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[10660, 23849, 23488, 23810])).
% 2.85/3.09 tff(23858,plain,
% 2.85/3.09 (r(z, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1439, 23857])).
% 2.85/3.09 tff(23859,plain,
% 2.85/3.09 (~b(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1315, 23849, 23488, 23810])).
% 2.85/3.09 tff(23860,plain,
% 2.85/3.09 (r(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1214, 23859])).
% 2.85/3.09 tff(23861,plain,
% 2.85/3.09 (b(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1276, 23845, 23488])).
% 2.85/3.09 tff(23862,plain,
% 2.85/3.09 (s(s(z)) = s(elem!1)),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23845])).
% 2.85/3.09 tff(23863,plain,
% 2.85/3.09 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23862])).
% 2.85/3.09 tff(23864,plain,
% 2.85/3.09 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.85/3.09 inference(transitivity,[status(thm)],[23863, 3535])).
% 2.85/3.09 tff(23865,plain,
% 2.85/3.09 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23864])).
% 2.85/3.09 tff(23866,plain,
% 2.85/3.09 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[1136, 23865])).
% 2.85/3.09 tff(23867,plain,
% 2.85/3.09 (~b(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[14857, 23866, 23488, 23810, 23861, 23860, 23858, 909])).
% 2.85/3.09 tff(23868,plain,
% 2.85/3.09 (r(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[255, 23867, 23856])).
% 2.85/3.09 tff(23869,plain,
% 2.85/3.09 (r(s(s(elem!1)), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[6824, 23868, 23845])).
% 2.85/3.09 tff(23870,plain,
% 2.85/3.09 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[5075, 23869, 23828, 23851])).
% 2.85/3.09 tff(23871,plain,
% 2.85/3.09 (b(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[599, 23870, 23848])).
% 2.85/3.09 tff(23872,plain,
% 2.85/3.09 (~b(s(s(elem!1)), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3324, 23871, 23488, 23810])).
% 2.85/3.09 tff(23873,plain,
% 2.85/3.09 (r(s(s(elem!1)), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[701, 23872, 3313])).
% 2.85/3.09 tff(23874,plain,
% 2.85/3.09 (s(s(s(z))) = s(s(elem!1))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23862])).
% 2.85/3.09 tff(23875,plain,
% 2.85/3.09 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23874])).
% 2.85/3.09 tff(23876,plain,
% 2.85/3.09 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23875])).
% 2.85/3.09 tff(23877,plain,
% 2.85/3.09 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23845])).
% 2.85/3.09 tff(23878,plain,
% 2.85/3.09 (~r(s(s(s(s(z)))), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1234, 23844, 147])).
% 2.85/3.09 tff(23879,plain,
% 2.85/3.09 (b(s(s(s(s(z)))), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[932, 23878])).
% 2.85/3.09 tff(23880,plain,
% 2.85/3.09 (b(s(s(s(s(z)))), elem!1)),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[23879, 23877])).
% 2.85/3.09 tff(23881,plain,
% 2.85/3.09 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[23880, 23876])).
% 2.85/3.09 tff(23882,plain,
% 2.85/3.09 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[78, 23848])).
% 2.85/3.09 tff(23883,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.85/3.09 inference(rewrite,[status(thm)],[])).
% 2.85/3.09 tff(23884,plain,
% 2.85/3.09 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.85/3.09 inference(rewrite,[status(thm)],[])).
% 2.85/3.09 tff(23885,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23884])).
% 2.85/3.09 tff(23886,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.85/3.09 inference(transitivity,[status(thm)],[23885, 23883])).
% 2.85/3.09 tff(23887,plain,
% 2.85/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.85/3.09 inference(quant_inst,[status(thm)],[])).
% 2.85/3.09 tff(23888,plain,
% 2.85/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[23887, 23886])).
% 2.85/3.09 tff(23889,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23888, 271, 394, 1281, 446, 1639])).
% 2.85/3.09 tff(23890,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23891,plain,
% 2.85/3.09 (~b(z, s(s(s(s(s(z))))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23890, 23861, 19197, 23810])).
% 2.85/3.09 tff(23892,plain,
% 2.85/3.09 (r(z, s(s(s(s(s(z))))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1658, 23891])).
% 2.85/3.09 tff(23893,plain,
% 2.85/3.09 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[11865, 23892, 23810, 23861, 909])).
% 2.85/3.09 tff(23894,plain,
% 2.85/3.09 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23862])).
% 2.85/3.09 tff(23895,plain,
% 2.85/3.09 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23894])).
% 2.85/3.09 tff(23896,plain,
% 2.85/3.09 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[877, 23895])).
% 2.85/3.09 tff(23897,plain,
% 2.85/3.09 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[4138, 23896, 23893])).
% 2.85/3.09 tff(23898,plain,
% 2.85/3.09 (~r(s(elem!1), s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[6368, 23897, 23858, 23892])).
% 2.85/3.09 tff(23899,plain,
% 2.85/3.09 (b(s(elem!1), s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[526, 23898, 211])).
% 2.85/3.09 tff(23900,plain,
% 2.85/3.09 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[9687, 23871, 23488, 23899])).
% 2.85/3.09 tff(23901,plain,
% 2.85/3.09 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[556, 23900, 1])).
% 2.85/3.09 tff(23902,plain,
% 2.85/3.09 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23875])).
% 2.85/3.09 tff(23903,plain,
% 2.85/3.09 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23853])).
% 2.85/3.09 tff(23904,plain,
% 2.85/3.09 (~(elem!1 = s(s(s(z))))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[97, 23903])).
% 2.85/3.09 tff(23905,plain,
% 2.85/3.09 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1516, 23904])).
% 2.85/3.09 tff(23906,plain,
% 2.85/3.09 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[17419, 23905])).
% 2.85/3.09 tff(23907,plain,
% 2.85/3.09 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[8581, 23869, 909, 23851])).
% 2.85/3.09 tff(23908,plain,
% 2.85/3.09 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[760, 23907])).
% 2.85/3.09 tff(23909,plain,
% 2.85/3.09 (b(elem!1, s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[8233, 23908, 23845])).
% 2.85/3.09 tff(23910,plain,
% 2.85/3.09 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[747, 23909, 23488, 23881])).
% 2.85/3.09 tff(23911,plain,
% 2.85/3.09 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23654, 23910, 23845])).
% 2.85/3.09 tff(23912,plain,
% 2.85/3.09 (r(s(elem!1), s(s(s(s(z)))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1995, 23911, 23906])).
% 2.85/3.09 tff(23913,plain,
% 2.85/3.09 (r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[23912, 23902])).
% 2.85/3.09 tff(23914,plain,
% 2.85/3.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3132, 23913, 23901, 23873])).
% 2.85/3.09 tff(23915,plain,
% 2.85/3.09 (~b(s(elem!1), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[10472, 23914, 23882, 23870, 23881])).
% 2.85/3.09 tff(23916,plain,
% 2.85/3.09 (r(s(elem!1), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2243, 23915, 2207])).
% 2.85/3.09 tff(23917,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.85/3.09 inference(rewrite,[status(thm)],[])).
% 2.85/3.09 tff(23918,plain,
% 2.85/3.09 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.85/3.09 inference(rewrite,[status(thm)],[])).
% 2.85/3.09 tff(23919,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 2.85/3.09 inference(monotonicity,[status(thm)],[23918])).
% 2.85/3.09 tff(23920,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.85/3.09 inference(transitivity,[status(thm)],[23919, 23917])).
% 2.85/3.09 tff(23921,plain,
% 2.85/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.85/3.09 inference(quant_inst,[status(thm)],[])).
% 2.85/3.09 tff(23922,plain,
% 2.85/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[23921, 23920])).
% 2.85/3.09 tff(23923,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23922, 121, 23916, 23858, 23851, 23873])).
% 2.85/3.09 tff(23924,plain,(b(s(z), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | b(z, s(z)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23925,plain,
% 2.85/3.09 (b(s(z), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23924, 2344, 909, 147, 894, 1])).
% 2.85/3.09 tff(23926,plain,
% 2.85/3.09 (~b(z, elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[20382, 260, 19197, 307])).
% 2.85/3.09 tff(23927,plain,
% 2.85/3.09 (r(z, elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[355, 23926, 331])).
% 2.85/3.09 tff(23928,plain,
% 2.85/3.09 (b(elem!1, z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[21021, 412, 219, 19197, 909, 259])).
% 2.85/3.09 tff(23929,plain,
% 2.85/3.09 (b(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[5347, 307, 412, 378, 909, 2564, 260, 348])).
% 2.85/3.09 tff(23930,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3435, 23929, 307, 2618, 260])).
% 2.85/3.09 tff(23931,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (s(elem!1) = elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23932,plain,
% 2.85/3.09 (~b(s(elem!1), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23931, 412, 909, 307, 260, 378, 2207, 348])).
% 2.85/3.09 tff(23933,plain,
% 2.85/3.09 (r(s(elem!1), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2243, 23932, 2207])).
% 2.85/3.09 tff(23934,plain,
% 2.85/3.09 (~r(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[5343, 23933, 412, 378])).
% 2.85/3.09 tff(23935,plain,
% 2.85/3.09 (b(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[299, 23934, 258])).
% 2.85/3.09 tff(23936,plain,
% 2.85/3.09 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[12364, 23932, 1, 147])).
% 2.85/3.09 tff(23937,plain,
% 2.85/3.09 (b(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[299, 293, 258])).
% 2.85/3.09 tff(23938,plain,
% 2.85/3.09 (b(s(z), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1293, 307, 1281, 412, 2282, 378, 258, 909])).
% 2.85/3.09 tff(23939,plain,
% 2.85/3.09 (b(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[5347, 307, 412, 378, 909, 2564, 23938, 348])).
% 2.85/3.09 tff(23940,plain,
% 2.85/3.09 (~b(s(elem!1), s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[4497, 23938, 307, 23939])).
% 2.85/3.09 tff(23941,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[5454, 23940, 23938, 412, 2088, 68, 448])).
% 2.85/3.09 tff(23942,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (s(elem!1) = elem!1) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23943,plain,
% 2.85/3.09 (~b(elem!1, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23942, 23937, 2088, 68, 412, 378, 909, 3500, 348, 1281, 258])).
% 2.85/3.09 tff(23944,plain,
% 2.85/3.09 (r(elem!1, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[392, 23943, 377])).
% 2.85/3.09 tff(23945,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3700, 23944, 23943, 412, 3500, 909, 258, 293, 199])).
% 2.85/3.09 tff(23946,plain,(r(elem!1, s(z)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (elem!1 = s(z)) | b(z, elem!1) | (elem!1 = s(elem!1)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23947,plain,
% 2.85/3.09 (~r(z, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23946, 23936, 19197, 909, 258, 219, 23926, 412, 378, 348, 23934])).
% 2.85/3.09 tff(23948,plain,
% 2.85/3.09 (b(z, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2106, 23947])).
% 2.85/3.09 tff(23949,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[5420, 23948, 23935, 19197, 23928])).
% 2.85/3.09 tff(23950,plain,((~r(s(elem!1), z)) | (elem!1 = s(z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (elem!1 = z) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23951,plain,
% 2.85/3.09 (~r(s(elem!1), z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23950, 258, 909, 23927, 344, 1, 147, 358, 307, 260])).
% 2.85/3.09 tff(23952,plain,
% 2.85/3.09 (b(s(elem!1), z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[409, 23951])).
% 2.85/3.09 tff(23953,plain,
% 2.85/3.09 (~r(z, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3387, 8563, 1409, 23927])).
% 2.85/3.09 tff(23954,plain,
% 2.85/3.09 (b(z, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1439, 23953])).
% 2.85/3.09 tff(23955,plain,
% 2.85/3.09 (~b(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19626, 271, 394, 19197, 23954])).
% 2.85/3.09 tff(23956,plain,
% 2.85/3.09 (r(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[444, 23955, 344])).
% 2.85/3.09 tff(23957,plain,
% 2.85/3.09 (~b(s(elem!1), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19636, 271, 394, 19197, 23954])).
% 2.85/3.09 tff(23958,plain,
% 2.85/3.09 (r(s(elem!1), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[429, 23957, 351])).
% 2.85/3.09 tff(23959,plain,
% 2.85/3.09 (~r(s(z), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23821, 8563, 431, 1409])).
% 2.85/3.09 tff(23960,plain,
% 2.85/3.09 (b(s(z), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[236, 23959, 231])).
% 2.85/3.09 tff(23961,plain,
% 2.85/3.09 (~b(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[13792, 11900, 307, 260, 411, 82])).
% 2.85/3.09 tff(23962,plain,
% 2.85/3.09 (r(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[299, 23961, 258])).
% 2.85/3.09 tff(23963,plain,
% 2.85/3.09 (~b(s(s(elem!1)), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[551, 11900, 307, 543])).
% 2.85/3.09 tff(23964,plain,
% 2.85/3.09 (r(s(s(elem!1)), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[862, 23963, 10064])).
% 2.85/3.09 tff(23965,plain,
% 2.85/3.09 (~r(s(elem!1), s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[18273, 23964, 8448, 23962])).
% 2.85/3.09 tff(23966,plain,
% 2.85/3.09 (b(s(elem!1), s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[526, 23965, 216])).
% 2.85/3.09 tff(23967,plain,
% 2.85/3.09 (~b(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[13752, 11900, 307, 260])).
% 2.85/3.09 tff(23968,plain,
% 2.85/3.09 (r(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[760, 23967])).
% 2.85/3.09 tff(23969,plain,
% 2.85/3.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[9617, 23968, 8448, 431])).
% 2.85/3.09 tff(23970,plain,
% 2.85/3.09 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[13884, 23965, 2344, 2467, 481, 23969])).
% 2.85/3.09 tff(23971,plain,
% 2.85/3.09 (b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[681, 23969, 82])).
% 2.85/3.09 tff(23972,plain,
% 2.85/3.09 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[673, 23971, 307, 481, 23970, 23966])).
% 2.85/3.09 tff(23973,plain,
% 2.85/3.09 (~b(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[9687, 23966, 307, 543])).
% 2.85/3.09 tff(23974,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[599, 23973, 23972, 10063])).
% 2.85/3.09 tff(23975,plain,((s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(elem!1, s(elem!1)) | b(s(elem!1), elem!1) | (s(elem!1) = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (elem!1 = s(z)) | (~b(s(z), elem!1)) | (~r(s(elem!1), s(z))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23976,plain,
% 2.85/3.09 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23975, 23960, 307, 2344, 431, 211, 481, 79, 258, 2467, 411, 147])).
% 2.85/3.09 tff(23977,plain,
% 2.85/3.09 (b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3326, 23976, 1, 394, 2344, 199, 2467])).
% 2.85/3.09 tff(23978,plain,
% 2.85/3.09 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[556, 23976, 1])).
% 2.85/3.09 tff(23979,plain,
% 2.85/3.09 (~r(s(s(elem!1)), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[10746, 23978, 307, 394, 8563, 1243, 358, 1409, 23977])).
% 2.85/3.09 tff(23980,plain,
% 2.85/3.09 (b(s(s(elem!1)), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[701, 23979, 3313])).
% 2.85/3.09 tff(23981,plain,
% 2.85/3.09 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3310, 23978, 2344, 331, 199, 198, 79])).
% 2.85/3.09 tff(23982,plain,
% 2.85/3.09 (b(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[599, 23981, 68])).
% 2.85/3.09 tff(23983,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3324, 23982, 23980, 307, 394])).
% 2.85/3.09 tff(23984,plain,(b(s(elem!1), elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (elem!1 = s(s(elem!1))) | r(elem!1, s(elem!1)) | (z = elem!1) | b(z, elem!1) | (~r(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(z)) | (~r(s(elem!1), s(z))) | r(s(s(s(elem!1))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23985,plain,
% 2.85/3.09 (s(s(s(elem!1))) = elem!1),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23984, 23958, 307, 147, 2344, 331, 394, 23956, 1, 2467, 68, 258, 23926, 1409, 1257])).
% 2.85/3.09 tff(23986,plain,
% 2.85/3.09 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2596, 23985])).
% 2.85/3.09 tff(23987,plain,
% 2.85/3.09 (~(s(s(s(z))) = elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2611, 23985])).
% 2.85/3.09 tff(23988,plain,
% 2.85/3.09 (~b(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3288, 1422, 307, 394])).
% 2.85/3.09 tff(23989,plain,
% 2.85/3.09 (r(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[255, 23988, 907])).
% 2.85/3.09 tff(23990,plain,
% 2.85/3.09 (~r(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19871, 23989, 1409, 378])).
% 2.85/3.09 tff(23991,plain,
% 2.85/3.09 (b(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1214, 23990])).
% 2.85/3.09 tff(23992,plain,
% 2.85/3.09 (~b(s(s(s(z))), z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[8279, 23991, 394, 1422])).
% 2.85/3.09 tff(23993,plain,
% 2.85/3.09 (r(s(s(s(z))), z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1155, 23992])).
% 2.85/3.09 tff(23994,plain,
% 2.85/3.09 (~b(elem!1, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1811, 1422, 307, 394])).
% 2.85/3.09 tff(23995,plain,
% 2.85/3.09 (r(elem!1, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1192, 23994, 1101])).
% 2.85/3.09 tff(23996,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[10776, 121, 378, 23995, 23989, 23993])).
% 2.85/3.09 tff(23997,plain,((~b(s(s(s(z))), s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(23998,plain,
% 2.85/3.09 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23997, 23987, 307, 394, 23927, 1409])).
% 2.85/3.09 tff(23999,plain,
% 2.85/3.09 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1816, 23998, 23986])).
% 2.85/3.09 tff(24000,plain,
% 2.85/3.09 (~r(s(z), s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23235, 23999, 23956, 23958])).
% 2.85/3.09 tff(24001,plain,
% 2.85/3.09 (b(s(z), s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[105, 24000])).
% 2.85/3.09 tff(24002,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[10652, 271, 307, 260, 3871, 257])).
% 2.85/3.09 tff(24003,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(24004,plain,
% 2.85/3.09 (~b(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24003, 24001, 307, 260])).
% 2.85/3.09 tff(24005,plain,
% 2.85/3.09 (r(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[255, 24004, 23987])).
% 2.85/3.09 tff(24006,plain,
% 2.85/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.85/3.09 inference(rewrite,[status(thm)],[])).
% 2.85/3.09 tff(24007,plain,
% 2.85/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.85/3.09 inference(quant_inst,[status(thm)],[])).
% 2.85/3.09 tff(24008,plain,
% 2.85/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 2.85/3.09 inference(modus_ponens,[status(thm)],[24007, 24006])).
% 2.85/3.09 tff(24009,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24008, 121, 8563, 1409, 24005, 23999])).
% 2.85/3.09 tff(24010,plain,(b(s(elem!1), elem!1) | (~r(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(24011,plain,
% 2.85/3.09 (b(s(elem!1), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24010, 10063, 307, 260, 394, 147, 2344, 331, 1, 1409, 258])).
% 2.85/3.09 tff(24012,plain,
% 2.85/3.09 (~b(s(elem!1), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3247, 271, 307, 24011, 260])).
% 2.85/3.09 tff(24013,plain,
% 2.85/3.09 (r(s(elem!1), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[429, 24012, 351])).
% 2.85/3.09 tff(24014,plain,
% 2.85/3.09 (~b(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3435, 24011, 307, 260])).
% 2.85/3.09 tff(24015,plain,
% 2.85/3.09 (r(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[444, 24014, 344])).
% 2.85/3.09 tff(24016,plain,
% 2.85/3.09 (r(s(s(s(elem!1))), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[16580, 2865])).
% 2.85/3.09 tff(24017,plain,
% 2.85/3.09 (r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[681, 3178, 82])).
% 2.85/3.09 tff(24018,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19655, 121, 24017, 24016, 431, 411])).
% 2.85/3.09 tff(24019,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(24020,plain,
% 2.85/3.09 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24019, 24013, 307, 82, 24011, 260, 24015])).
% 2.85/3.09 tff(24021,plain,
% 2.85/3.09 (s(s(s(elem!1))) = elem!1),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[486, 24020, 147])).
% 2.85/3.09 tff(24022,plain,
% 2.85/3.09 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2596, 24021])).
% 2.85/3.09 tff(24023,plain,
% 2.85/3.09 (~(s(s(s(z))) = elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2611, 24021])).
% 2.85/3.09 tff(24024,plain,
% 2.85/3.09 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23997, 24023, 307, 394, 23927, 1409])).
% 2.85/3.09 tff(24025,plain,
% 2.85/3.09 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1816, 24024, 24022])).
% 2.85/3.09 tff(24026,plain,
% 2.85/3.09 (~r(s(z), s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23235, 24025, 24015, 24013])).
% 2.85/3.09 tff(24027,plain,
% 2.85/3.09 (b(s(z), s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[105, 24026])).
% 2.85/3.09 tff(24028,plain,
% 2.85/3.09 (~b(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24003, 24027, 307, 260])).
% 2.85/3.09 tff(24029,plain,
% 2.85/3.09 (r(s(s(s(z))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[255, 24028, 24023])).
% 2.85/3.09 tff(24030,plain,
% 2.85/3.09 (~r(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19871, 24029, 23927, 1409])).
% 2.85/3.09 tff(24031,plain,
% 2.85/3.09 (b(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1214, 24030])).
% 2.85/3.09 tff(24032,plain,
% 2.85/3.09 (~b(s(s(s(z))), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[21149, 24031, 19197, 24027])).
% 2.85/3.09 tff(24033,plain,
% 2.85/3.09 (r(s(s(s(z))), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2325, 24032])).
% 2.85/3.09 tff(24034,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[8142, 121, 24015, 24025, 24013, 24033])).
% 2.85/3.09 tff(24035,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(24036,plain,
% 2.85/3.09 (s(s(s(elem!1))) = s(elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24035, 1409, 307, 260, 23952, 147, 2344, 331, 1, 258])).
% 2.85/3.09 tff(24037,plain,
% 2.85/3.09 (elem!1 = s(s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[78, 24036])).
% 2.85/3.09 tff(24038,plain,
% 2.85/3.09 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3917, 24037, 344])).
% 2.85/3.09 tff(24039,plain,
% 2.85/3.09 (~(s(s(s(z))) = elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3906, 24037])).
% 2.85/3.09 tff(24040,plain,
% 2.85/3.09 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23997, 24039, 307, 23952, 23927, 1409])).
% 2.85/3.09 tff(24041,plain,
% 2.85/3.09 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1816, 24040, 24038])).
% 2.85/3.09 tff(24042,plain,
% 2.85/3.09 (b(s(elem!1), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[12364, 24037, 1, 147])).
% 2.85/3.09 tff(24043,plain,
% 2.85/3.09 (~b(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3435, 24042, 307, 260])).
% 2.85/3.09 tff(24044,plain,
% 2.85/3.09 (r(s(z), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[444, 24043, 344])).
% 2.85/3.09 tff(24045,plain,
% 2.85/3.09 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3790, 24037, 24042])).
% 2.85/3.09 tff(24046,plain,
% 2.85/3.09 (~b(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[13752, 24045, 307, 260])).
% 2.85/3.09 tff(24047,plain,
% 2.85/3.09 (r(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[760, 24046])).
% 2.85/3.09 tff(24048,plain,
% 2.85/3.09 (~r(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19790, 24047, 909, 23927])).
% 2.85/3.09 tff(24049,plain,
% 2.85/3.09 (b(elem!1, s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[299, 24048, 258])).
% 2.85/3.09 tff(24050,plain,
% 2.85/3.09 (~b(s(elem!1), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1290, 24049, 19197, 307])).
% 2.85/3.09 tff(24051,plain,
% 2.85/3.09 (r(s(elem!1), s(z))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[429, 24050, 351])).
% 2.85/3.09 tff(24052,plain,
% 2.85/3.09 (~r(z, s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23132, 24049, 909, 260, 24045])).
% 2.85/3.09 tff(24053,plain,
% 2.85/3.09 (r(s(z), s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23127, 24052, 1, 19197])).
% 2.85/3.09 tff(24054,plain,
% 2.85/3.09 ($false),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[23235, 24053, 24051, 24044, 24041])).
% 2.85/3.09 tff(24055,plain,((~r(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (elem!1 = s(z)) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.09 tff(24056,plain,
% 2.85/3.09 (~r(elem!1, z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[24055, 258, 909, 260, 307, 1, 147, 2344, 331])).
% 2.85/3.09 tff(24057,plain,
% 2.85/3.09 (b(elem!1, z)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[284, 24056, 358])).
% 2.85/3.09 tff(24058,plain,
% 2.85/3.09 (~b(z, s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3415, 24057, 307, 23952])).
% 2.85/3.09 tff(24059,plain,
% 2.85/3.09 (r(z, s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19736, 24058])).
% 2.85/3.09 tff(24060,plain,
% 2.85/3.09 (~b(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1315, 24057, 307, 23952])).
% 2.85/3.09 tff(24061,plain,
% 2.85/3.09 (r(z, s(s(s(z))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1214, 24060])).
% 2.85/3.09 tff(24062,plain,
% 2.85/3.09 (~b(z, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[3404, 24057, 307, 23952])).
% 2.85/3.09 tff(24063,plain,
% 2.85/3.09 (r(z, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2106, 24062])).
% 2.85/3.09 tff(24064,plain,
% 2.85/3.09 (~b(z, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[10660, 24057, 307, 23952])).
% 2.85/3.09 tff(24065,plain,
% 2.85/3.09 (r(z, s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[1439, 24064])).
% 2.85/3.09 tff(24066,plain,
% 2.85/3.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[7694, 8563, 111, 1441])).
% 2.85/3.09 tff(24067,plain,
% 2.85/3.09 (b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[681, 23520, 24066])).
% 2.85/3.09 tff(24068,plain,
% 2.85/3.09 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2401, 271, 307, 394, 24067])).
% 2.85/3.09 tff(24069,plain,
% 2.85/3.09 (s(s(s(elem!1))) = elem!1),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[486, 24068, 147])).
% 2.85/3.09 tff(24070,plain,
% 2.85/3.09 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[19692, 24069, 260])).
% 2.85/3.09 tff(24071,plain,
% 2.85/3.09 (~r(elem!1, s(s(elem!1)))),
% 2.85/3.09 inference(unit_resolution,[status(thm)],[2580, 8563, 378, 1441])).
% 2.85/3.09 tff(24072,plain,
% 2.85/3.10 (b(elem!1, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[599, 24071, 23519])).
% 2.85/3.10 tff(24073,plain,
% 2.85/3.10 (~b(s(s(elem!1)), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3324, 24072, 307, 394])).
% 2.85/3.10 tff(24074,plain,
% 2.85/3.10 (r(s(s(elem!1)), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[701, 24073, 3313])).
% 2.85/3.10 tff(24075,plain,
% 2.85/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 2.85/3.10 inference(rewrite,[status(thm)],[])).
% 2.85/3.10 tff(24076,plain,
% 2.85/3.10 (((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 2.85/3.10 inference(rewrite,[status(thm)],[])).
% 2.85/3.10 tff(24077,plain,
% 2.85/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24076])).
% 2.85/3.10 tff(24078,plain,
% 2.85/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 2.85/3.10 inference(transitivity,[status(thm)],[24077, 24075])).
% 2.85/3.10 tff(24079,plain,
% 2.85/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 2.85/3.10 inference(quant_inst,[status(thm)],[])).
% 2.85/3.10 tff(24080,plain,
% 2.85/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24079, 24078])).
% 2.85/3.10 tff(24081,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24080, 121, 622, 378, 1441, 3456])).
% 2.85/3.10 tff(24082,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24083,plain,
% 2.85/3.10 (~r(elem!1, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24082, 8563, 378, 1441])).
% 2.85/3.10 tff(24084,plain,
% 2.85/3.10 (b(elem!1, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[299, 24083, 258])).
% 2.85/3.10 tff(24085,plain,
% 2.85/3.10 (~b(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1290, 24084, 19197, 307])).
% 2.85/3.10 tff(24086,plain,
% 2.85/3.10 (r(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[429, 24085, 2282])).
% 2.85/3.10 tff(24087,plain,
% 2.85/3.10 (~r(s(z), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2186, 24086, 909, 1441])).
% 2.85/3.10 tff(24088,plain,
% 2.85/3.10 (b(s(z), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[105, 24087])).
% 2.85/3.10 tff(24089,plain,
% 2.85/3.10 (~(s(s(s(z))) = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2611, 24069])).
% 2.85/3.10 tff(24090,plain,
% 2.85/3.10 (~(elem!1 = s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1100, 24089])).
% 2.85/3.10 tff(24091,plain,
% 2.85/3.10 (~r(s(s(s(elem!1))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[12809, 24083, 24069])).
% 2.85/3.10 tff(24092,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[16580, 24091])).
% 2.85/3.10 tff(24093,plain,
% 2.85/3.10 (r(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[10250, 24088, 24092, 147, 260, 24084])).
% 2.85/3.10 tff(24094,plain,
% 2.85/3.10 (~r(elem!1, s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[6723, 24093, 378, 1140])).
% 2.85/3.10 tff(24095,plain,
% 2.85/3.10 (b(elem!1, s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1192, 24094, 24090])).
% 2.85/3.10 tff(24096,plain,
% 2.85/3.10 (~b(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[11038, 24095, 24084, 24088])).
% 2.85/3.10 tff(24097,plain,
% 2.85/3.10 (r(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1155, 24096])).
% 2.85/3.10 tff(24098,plain,
% 2.85/3.10 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2596, 24069])).
% 2.85/3.10 tff(24099,plain,
% 2.85/3.10 (~(s(elem!1) = s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2035, 24098])).
% 2.85/3.10 tff(24100,plain,
% 2.85/3.10 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1811, 24095, 307, 394])).
% 2.85/3.10 tff(24101,plain,
% 2.85/3.10 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1816, 24100, 24098])).
% 2.85/3.10 tff(24102,plain,
% 2.85/3.10 (~r(s(elem!1), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[10701, 24101, 1441, 1140])).
% 2.85/3.10 tff(24103,plain,
% 2.85/3.10 (b(s(elem!1), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2044, 24102, 24099])).
% 2.85/3.10 tff(24104,plain,
% 2.85/3.10 (~b(s(s(s(z))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[10690, 24103, 307, 24095])).
% 2.85/3.10 tff(24105,plain,
% 2.85/3.10 (r(s(s(s(z))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2325, 24104])).
% 2.85/3.10 tff(24106,plain,
% 2.85/3.10 (~r(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[10317, 24105, 909, 24097])).
% 2.85/3.10 tff(24107,plain,
% 2.85/3.10 (b(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[444, 24106, 348])).
% 2.85/3.10 tff(24108,plain,
% 2.85/3.10 (~b(s(elem!1), s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[4497, 24107, 307, 260])).
% 2.85/3.10 tff(24109,plain,
% 2.85/3.10 (r(s(elem!1), s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[526, 24108, 211])).
% 2.85/3.10 tff(24110,plain,
% 2.85/3.10 (r(s(s(elem!1)), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2143, 5841])).
% 2.85/3.10 tff(24111,plain,
% 2.85/3.10 (~r(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[5431, 24110, 627, 2088])).
% 2.85/3.10 tff(24112,plain,
% 2.85/3.10 (b(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[409, 24111])).
% 2.85/3.10 tff(24113,plain,
% 2.85/3.10 (~r(z, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[17708, 24110, 627, 2088])).
% 2.85/3.10 tff(24114,plain,
% 2.85/3.10 (b(z, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1439, 24113])).
% 2.85/3.10 tff(24115,plain,
% 2.85/3.10 (~r(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3275, 5844, 627, 683])).
% 2.85/3.10 tff(24116,plain,
% 2.85/3.10 (~(z = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2488, 24112, 2467])).
% 2.85/3.10 tff(24117,plain,
% 2.85/3.10 (~(s(z) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[343, 24116])).
% 2.85/3.10 tff(24118,plain,
% 2.85/3.10 (b(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[444, 24117, 24115])).
% 2.85/3.10 tff(24119,plain,
% 2.85/3.10 (~b(z, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[9030, 24118, 24114, 24112])).
% 2.85/3.10 tff(24120,plain,
% 2.85/3.10 (r(z, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[902, 21, 24119, 898])).
% 2.85/3.10 tff(24121,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2445, 121, 5844, 2088, 24110, 24120])).
% 2.85/3.10 tff(24122,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | b(s(elem!1), elem!1) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24123,plain,
% 2.85/3.10 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24122, 24109, 2467, 24067, 24074, 2088, 24070])).
% 2.85/3.10 tff(24124,plain,
% 2.85/3.10 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[6878, 24109, 1441, 2088])).
% 2.85/3.10 tff(24125,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[556, 24124, 24123, 1])).
% 2.85/3.10 tff(24126,plain,(b(s(elem!1), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | r(s(s(s(elem!1))), elem!1) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24127,plain,
% 2.85/3.10 (b(s(elem!1), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24126, 24065, 1, 24063, 307, 260, 344, 909, 24061, 23952, 23927, 147, 258, 24059])).
% 2.85/3.10 tff(24128,plain,
% 2.85/3.10 (~b(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3247, 271, 307, 24127, 260])).
% 2.85/3.10 tff(24129,plain,
% 2.85/3.10 (r(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[429, 24128, 351])).
% 2.85/3.10 tff(24130,plain,
% 2.85/3.10 (~b(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3435, 24127, 307, 260])).
% 2.85/3.10 tff(24131,plain,
% 2.85/3.10 (r(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[444, 24130, 344])).
% 2.85/3.10 tff(24132,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[10292, 121, 24065, 909, 24131, 24129])).
% 2.85/3.10 tff(24133,plain,((elem!1 = s(z)) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24134,plain,
% 2.85/3.10 (elem!1 = s(z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24133, 23925, 23488, 909, 1, 147, 2344, 23489])).
% 2.85/3.10 tff(24135,plain,
% 2.85/3.10 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24134])).
% 2.85/3.10 tff(24136,plain,
% 2.85/3.10 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 2.85/3.10 inference(symmetry,[status(thm)],[24135])).
% 2.85/3.10 tff(24137,plain,
% 2.85/3.10 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24136])).
% 2.85/3.10 tff(24138,plain,
% 2.85/3.10 (~b(s(z), elem!1)),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[3529, 24137])).
% 2.85/3.10 tff(24139,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23925, 24138])).
% 2.85/3.10 tff(24140,plain,(r(elem!1, s(elem!1)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24141,plain,
% 2.85/3.10 (r(elem!1, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24140, 147, 1, 909, 894])).
% 2.85/3.10 tff(24142,plain,
% 2.85/3.10 (~r(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3673, 10603, 909, 24141])).
% 2.85/3.10 tff(24143,plain,
% 2.85/3.10 (~r(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23589, 24142, 147, 894, 909, 1, 1242])).
% 2.85/3.10 tff(24144,plain,
% 2.85/3.10 (~b(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23827, 24142, 2207, 19197, 23488, 1242, 894])).
% 2.85/3.10 tff(24145,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[409, 24144, 24143])).
% 2.85/3.10 tff(24146,plain,(b(s(z), elem!1) | b(z, s(z)) | r(s(s(s(elem!1))), elem!1) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24147,plain,
% 2.85/3.10 (b(s(z), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24146, 1257, 147, 909, 1, 894])).
% 2.85/3.10 tff(24148,plain,
% 2.85/3.10 (~b(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20382, 24147, 19197, 23488])).
% 2.85/3.10 tff(24149,plain,
% 2.85/3.10 (r(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[355, 24148, 23489])).
% 2.85/3.10 tff(24150,plain,
% 2.85/3.10 (~r(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23950, 24149, 909, 258, 23490, 1, 147, 23494, 23488, 24147])).
% 2.85/3.10 tff(24151,plain,
% 2.85/3.10 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23478, 24149, 909, 147, 1, 24141, 24147])).
% 2.85/3.10 tff(24152,plain,
% 2.85/3.10 (~b(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23185, 24151, 909, 24141, 147, 1, 894, 24148])).
% 2.85/3.10 tff(24153,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[409, 24152, 24150])).
% 2.85/3.10 tff(24154,plain,((elem!1 = s(z)) | (~r(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24155,plain,
% 2.85/3.10 (elem!1 = s(z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24154, 147, 909, 1, 894])).
% 2.85/3.10 tff(24156,plain,
% 2.85/3.10 (s(z) = elem!1),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[242, 24155])).
% 2.85/3.10 tff(24157,plain,
% 2.85/3.10 (r(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1402, 24156, 894])).
% 2.85/3.10 tff(24158,plain,
% 2.85/3.10 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24156])).
% 2.85/3.10 tff(24159,plain,
% 2.85/3.10 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24158])).
% 2.85/3.10 tff(24160,plain,
% 2.85/3.10 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[2137, 24159])).
% 2.85/3.10 tff(24161,plain,
% 2.85/3.10 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[78, 24160])).
% 2.85/3.10 tff(24162,plain,
% 2.85/3.10 (~b(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1397, 24155, 894])).
% 2.85/3.10 tff(24163,plain,
% 2.85/3.10 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24156])).
% 2.85/3.10 tff(24164,plain,
% 2.85/3.10 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.85/3.10 inference(transitivity,[status(thm)],[24163, 159])).
% 2.85/3.10 tff(24165,plain,
% 2.85/3.10 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.85/3.10 inference(transitivity,[status(thm)],[24164, 160])).
% 2.85/3.10 tff(24166,plain,
% 2.85/3.10 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24165])).
% 2.85/3.10 tff(24167,plain,
% 2.85/3.10 (~(s(s(s(z))) = elem!1)),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[97, 24166])).
% 2.85/3.10 tff(24168,plain,
% 2.85/3.10 (~b(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20223, 24167, 909, 24141, 1, 894, 147, 24162, 24161])).
% 2.85/3.10 tff(24169,plain,
% 2.85/3.10 (r(s(elem!1), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[409, 24168])).
% 2.85/3.10 tff(24170,plain,
% 2.85/3.10 (s(s(z)) = s(elem!1)),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24156])).
% 2.85/3.10 tff(24171,plain,
% 2.85/3.10 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24170])).
% 2.85/3.10 tff(24172,plain,
% 2.85/3.10 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.85/3.10 inference(transitivity,[status(thm)],[24171, 3535])).
% 2.85/3.10 tff(24173,plain,
% 2.85/3.10 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24172])).
% 2.85/3.10 tff(24174,plain,
% 2.85/3.10 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[1136, 24173])).
% 2.85/3.10 tff(24175,plain,
% 2.85/3.10 (~r(s(elem!1), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3683, 24169, 24141, 24157])).
% 2.85/3.10 tff(24176,plain,
% 2.85/3.10 (b(s(elem!1), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2243, 24175, 2207])).
% 2.85/3.10 tff(24177,plain,
% 2.85/3.10 (b(elem!1, z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20120, 24156, 19197])).
% 2.85/3.10 tff(24178,plain,
% 2.85/3.10 (b(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1276, 24156, 23488])).
% 2.85/3.10 tff(24179,plain,
% 2.85/3.10 (~r(z, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[12090, 24169, 24141, 24157])).
% 2.85/3.10 tff(24180,plain,
% 2.85/3.10 (b(z, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1439, 24179])).
% 2.85/3.10 tff(24181,plain,
% 2.85/3.10 (~b(s(elem!1), s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2905, 24180, 19197, 24178])).
% 2.85/3.10 tff(24182,plain,
% 2.85/3.10 (r(s(elem!1), s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[526, 24181, 211])).
% 2.85/3.10 tff(24183,plain,
% 2.85/3.10 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[1037])).
% 2.85/3.10 tff(24184,plain,
% 2.85/3.10 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 2.85/3.10 inference(symmetry,[status(thm)],[24183])).
% 2.85/3.10 tff(24185,plain,
% 2.85/3.10 (r(s(elem!1), s(s(s(z))))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[627, 24184])).
% 2.85/3.10 tff(24186,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2038, 24185])).
% 2.85/3.10 tff(24187,plain,((~r(s(elem!1), s(s(elem!1)))) | r(s(elem!1), s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24188,plain,
% 2.85/3.10 (r(s(elem!1), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24187, 24182, 24156])).
% 2.85/3.10 tff(24189,plain,
% 2.85/3.10 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24156])).
% 2.85/3.10 tff(24190,plain,
% 2.85/3.10 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.85/3.10 inference(symmetry,[status(thm)],[24189])).
% 2.85/3.10 tff(24191,plain,
% 2.85/3.10 (r(s(z), s(elem!1))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24141, 24190])).
% 2.85/3.10 tff(24192,plain,
% 2.85/3.10 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.85/3.10 inference(transitivity,[status(thm)],[24158, 2212])).
% 2.85/3.10 tff(24193,plain,
% 2.85/3.10 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24192])).
% 2.85/3.10 tff(24194,plain,
% 2.85/3.10 (~(s(s(elem!1)) = elem!1)),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[2137, 24193])).
% 2.85/3.10 tff(24195,plain,
% 2.85/3.10 (s(s(s(z))) = s(s(elem!1))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24170])).
% 2.85/3.10 tff(24196,plain,
% 2.85/3.10 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24195])).
% 2.85/3.10 tff(24197,plain,
% 2.85/3.10 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24196])).
% 2.85/3.10 tff(24198,plain,
% 2.85/3.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24156])).
% 2.85/3.10 tff(24199,plain,
% 2.85/3.10 (~r(s(s(s(s(z)))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1234, 24155, 147])).
% 2.85/3.10 tff(24200,plain,
% 2.85/3.10 (b(s(s(s(s(z)))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[932, 24199])).
% 2.85/3.10 tff(24201,plain,
% 2.85/3.10 (b(s(s(s(s(z)))), elem!1)),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24200, 24198])).
% 2.85/3.10 tff(24202,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24201, 24197])).
% 2.85/3.10 tff(24203,plain,
% 2.85/3.10 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3192, 24182, 23488, 24176, 24202, 24161])).
% 2.85/3.10 tff(24204,plain,
% 2.85/3.10 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[556, 24203, 1])).
% 2.85/3.10 tff(24205,plain,
% 2.85/3.10 (~b(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[551, 24204, 23488, 24202])).
% 2.85/3.10 tff(24206,plain,
% 2.85/3.10 (r(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[862, 24205, 24194])).
% 2.85/3.10 tff(24207,plain,
% 2.85/3.10 (~r(z, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19943, 24206, 24141, 24157])).
% 2.85/3.10 tff(24208,plain,
% 2.85/3.10 (b(z, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2106, 24207])).
% 2.85/3.10 tff(24209,plain,
% 2.85/3.10 (b(z, s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23691, 24208, 24156])).
% 2.85/3.10 tff(24210,plain,
% 2.85/3.10 (~b(s(z), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[21421, 24209, 909, 24156, 24177, 24169])).
% 2.85/3.10 tff(24211,plain,
% 2.85/3.10 (r(s(z), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[105, 24210])).
% 2.85/3.10 tff(24212,plain,
% 2.85/3.10 (~r(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3445, 24211, 24191, 24188])).
% 2.85/3.10 tff(24213,plain,
% 2.85/3.10 (b(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[255, 24212, 24167])).
% 2.85/3.10 tff(24214,plain,
% 2.85/3.10 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23200, 24213, 24177, 24176])).
% 2.85/3.10 tff(24215,plain,
% 2.85/3.10 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1816, 24214, 24174])).
% 2.85/3.10 tff(24216,plain,
% 2.85/3.10 (b(s(s(s(z))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[8109, 24213, 24156])).
% 2.85/3.10 tff(24217,plain,
% 2.85/3.10 (~b(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2650, 24216, 19197, 24208])).
% 2.85/3.10 tff(24218,plain,
% 2.85/3.10 (r(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1155, 24217])).
% 2.85/3.10 tff(24219,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3650, 24218, 24215, 24169, 24157])).
% 2.85/3.10 tff(24220,plain,(r(s(s(s(elem!1))), elem!1) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24221,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24220, 905, 894, 147, 1])).
% 2.85/3.10 tff(24222,plain,(b(z, s(z)) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24223,plain,
% 2.85/3.10 (b(z, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24222, 1, 147])).
% 2.85/3.10 tff(24224,plain,
% 2.85/3.10 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[9937])).
% 2.85/3.10 tff(24225,plain,
% 2.85/3.10 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.10 inference(symmetry,[status(thm)],[24224])).
% 2.85/3.10 tff(24226,plain,
% 2.85/3.10 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24225])).
% 2.85/3.10 tff(24227,plain,
% 2.85/3.10 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[179, 24226])).
% 2.85/3.10 tff(24228,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[5499, 24227])).
% 2.85/3.10 tff(24229,plain,((~(s(z) = s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24230,plain,
% 2.85/3.10 (~(s(z) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24229, 5499])).
% 2.85/3.10 tff(24231,plain,
% 2.85/3.10 (~(z = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[327, 317, 220])).
% 2.85/3.10 tff(24232,plain,
% 2.85/3.10 (~(s(z) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[343, 24231])).
% 2.85/3.10 tff(24233,plain,
% 2.85/3.10 (~(s(elem!1) = s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[350, 24232])).
% 2.85/3.10 tff(24234,plain,
% 2.85/3.10 (~b(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[16834, 271, 11211, 19197, 220])).
% 2.85/3.10 tff(24235,plain,
% 2.85/3.10 (r(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[429, 24234, 24233])).
% 2.85/3.10 tff(24236,plain,
% 2.85/3.10 (~b(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[9241, 11211, 19197, 220])).
% 2.85/3.10 tff(24237,plain,
% 2.85/3.10 (r(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[444, 24236, 24232])).
% 2.85/3.10 tff(24238,plain,
% 2.85/3.10 (~r(s(z), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20297, 121, 9983, 24237, 24235])).
% 2.85/3.10 tff(24239,plain,
% 2.85/3.10 (~r(elem!1, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19955, 121, 9983, 24237, 24235])).
% 2.85/3.10 tff(24240,plain,
% 2.85/3.10 (~b(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[16834, 271, 394, 19197, 220])).
% 2.85/3.10 tff(24241,plain,
% 2.85/3.10 (r(s(elem!1), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[429, 24240, 351])).
% 2.85/3.10 tff(24242,plain,
% 2.85/3.10 (~b(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[9241, 394, 19197, 220])).
% 2.85/3.10 tff(24243,plain,
% 2.85/3.10 (r(s(z), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[444, 24242, 344])).
% 2.85/3.10 tff(24244,plain,
% 2.85/3.10 (~r(s(z), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20297, 121, 379, 24243, 24241])).
% 2.85/3.10 tff(24245,plain,
% 2.85/3.10 (~r(elem!1, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19955, 121, 379, 24243, 24241])).
% 2.85/3.10 tff(24246,plain,
% 2.85/3.10 (~(s(s(s(z))) = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[250, 106, 24244])).
% 2.85/3.10 tff(24247,plain,
% 2.85/3.10 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23235, 106, 24243, 24241])).
% 2.85/3.10 tff(24248,plain,
% 2.85/3.10 (~b(s(s(s(s(z)))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[22548, 23626, 1281, 220])).
% 2.85/3.10 tff(24249,plain,
% 2.85/3.10 (r(s(s(s(s(z)))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1095, 24248])).
% 2.85/3.10 tff(24250,plain,
% 2.85/3.10 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, s(s(s(s(z))))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[21528])).
% 2.85/3.10 tff(24251,plain,
% 2.85/3.10 (b(elem!1, z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20120, 2359, 1281])).
% 2.85/3.10 tff(24252,plain,
% 2.85/3.10 (b(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[229, 2359, 220])).
% 2.85/3.10 tff(24253,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(symmetry,[status(thm)],[21507])).
% 2.85/3.10 tff(24254,plain,
% 2.85/3.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.85/3.10 inference(symmetry,[status(thm)],[21505])).
% 2.85/3.10 tff(24255,plain,
% 2.85/3.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(transitivity,[status(thm)],[24254, 24253])).
% 2.85/3.10 tff(24256,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[23626, 24255])).
% 2.85/3.10 tff(24257,plain,
% 2.85/3.10 (~b(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[7173, 24256, 24252, 24251])).
% 2.85/3.10 tff(24258,plain,
% 2.85/3.10 (~b(z, s(s(s(s(z)))))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24257, 24250])).
% 2.85/3.10 tff(24259,plain,
% 2.85/3.10 (r(z, s(s(s(s(z)))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1119, 21, 24258, 1114])).
% 2.85/3.10 tff(24260,plain,
% 2.85/3.10 (b(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1816, 23003, 1510])).
% 2.85/3.10 tff(24261,plain,
% 2.85/3.10 (~b(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1956, 24260, 394, 24252])).
% 2.85/3.10 tff(24262,plain,
% 2.85/3.10 (r(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1155, 24261])).
% 2.85/3.10 tff(24263,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[11616, 121, 24262, 24259, 24249, 21504])).
% 2.85/3.10 tff(24264,plain,((~(elem!1 = s(z))) | (~b(s(elem!1), z)) | r(s(s(s(z))), s(elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24265,plain,
% 2.85/3.10 (~(elem!1 = s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24264, 147, 1510, 19197, 220, 394, 5499])).
% 2.85/3.10 tff(24266,plain,
% 2.85/3.10 (~b(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[21984, 24265, 19197, 379, 24243, 8563, 344])).
% 2.85/3.10 tff(24267,plain,
% 2.85/3.10 (r(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[355, 24266, 331])).
% 2.85/3.10 tff(24268,plain,
% 2.85/3.10 (b(elem!1, s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[299, 24265, 24245])).
% 2.85/3.10 tff(24269,plain,
% 2.85/3.10 (~(s(z) = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1221, 24265])).
% 2.85/3.10 tff(24270,plain,
% 2.85/3.10 (b(s(z), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[236, 24269, 24244])).
% 2.85/3.10 tff(24271,plain,
% 2.85/3.10 (~b(elem!1, z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[8962, 24270, 220, 24268])).
% 2.85/3.10 tff(24272,plain,
% 2.85/3.10 (r(elem!1, z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[284, 24271, 358])).
% 2.85/3.10 tff(24273,plain,
% 2.85/3.10 (~r(z, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3387, 24272, 8563, 24267])).
% 2.85/3.10 tff(24274,plain,
% 2.85/3.10 (b(z, s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1439, 24273])).
% 2.85/3.10 tff(24275,plain,
% 2.85/3.10 (~(s(s(elem!1)) = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[197, 23499])).
% 2.85/3.10 tff(24276,plain,
% 2.85/3.10 (~(s(s(z)) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[960, 24269])).
% 2.85/3.10 tff(24277,plain,
% 2.85/3.10 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[953, 24276])).
% 2.85/3.10 tff(24278,plain,
% 2.85/3.10 (~b(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[5441, 981, 260, 448])).
% 2.85/3.10 tff(24279,plain,
% 2.85/3.10 (r(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[862, 24278, 851])).
% 2.85/3.10 tff(24280,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[8501, 24279, 22217, 379, 378])).
% 2.85/3.10 tff(24281,plain,((~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24282,plain,
% 2.85/3.10 (~b(s(s(elem!1)), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24281, 851, 378, 379, 260, 448, 1281, 220])).
% 2.85/3.10 tff(24283,plain,
% 2.85/3.10 (r(s(s(elem!1)), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2143, 24282])).
% 2.85/3.10 tff(24284,plain,
% 2.85/3.10 (~b(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20012, 24283, 944, 448, 257, 260])).
% 2.85/3.10 tff(24285,plain,
% 2.85/3.10 (r(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[862, 24284, 851])).
% 2.85/3.10 tff(24286,plain,
% 2.85/3.10 (~r(s(s(elem!1)), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[8501, 24285, 379, 378])).
% 2.85/3.10 tff(24287,plain,
% 2.85/3.10 (b(s(s(elem!1)), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2430, 24286])).
% 2.85/3.10 tff(24288,plain,
% 2.85/3.10 (~b(s(z), s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[17014, 24287, 1281, 220])).
% 2.85/3.10 tff(24289,plain,
% 2.85/3.10 (r(s(z), s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2167, 24288])).
% 2.85/3.10 tff(24290,plain,
% 2.85/3.10 (~r(s(s(elem!1)), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[16915, 121, 24289, 24283, 411])).
% 2.85/3.10 tff(24291,plain,
% 2.85/3.10 (b(s(s(elem!1)), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[701, 24290, 694])).
% 2.85/3.10 tff(24292,plain,
% 2.85/3.10 (~r(z, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19941, 121, 379, 378, 24285])).
% 2.85/3.10 tff(24293,plain,
% 2.85/3.10 (b(z, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2106, 24292])).
% 2.85/3.10 tff(24294,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2528, 24293, 24291, 394, 24287])).
% 2.85/3.10 tff(24295,plain,((s(s(elem!1)) = elem!1) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24296,plain,
% 2.85/3.10 (~b(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24295, 24277, 3313, 379, 24241, 394, 19197, 220, 24275, 24268, 24267, 24270])).
% 2.85/3.10 tff(24297,plain,
% 2.85/3.10 (r(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[255, 24296, 907])).
% 2.85/3.10 tff(24298,plain,
% 2.85/3.10 (~r(z, s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19871, 24272, 24297, 24267])).
% 2.85/3.10 tff(24299,plain,
% 2.85/3.10 (b(z, s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1214, 24298])).
% 2.85/3.10 tff(24300,plain,
% 2.85/3.10 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19710, 24299, 394, 24274])).
% 2.85/3.10 tff(24301,plain,
% 2.85/3.10 (s(s(s(z))) = s(elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1816, 24300, 1510])).
% 2.85/3.10 tff(24302,plain,
% 2.85/3.10 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24301])).
% 2.85/3.10 tff(24303,plain,
% 2.85/3.10 (r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[5499, 24302])).
% 2.85/3.10 tff(24304,plain,
% 2.85/3.10 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2596, 24301])).
% 2.85/3.10 tff(24305,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[486, 24304, 147])).
% 2.85/3.10 tff(24306,plain,
% 2.85/3.10 (~b(s(s(s(elem!1))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[8132, 24305, 24268, 24270])).
% 2.85/3.10 tff(24307,plain,
% 2.85/3.10 (r(s(s(s(elem!1))), s(z))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[16580, 24306])).
% 2.85/3.10 tff(24308,plain,
% 2.85/3.10 (~b(s(z), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[12821, 271, 24270, 24268, 24305])).
% 2.85/3.10 tff(24309,plain,
% 2.85/3.10 (r(s(z), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[760, 24308])).
% 2.85/3.10 tff(24310,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[13276, 121, 24309, 24307, 24241, 24303])).
% 2.85/3.10 tff(24311,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(z))), s(elem!1)) | (~b(s(elem!1), z)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24312,plain,
% 2.85/3.10 (r(s(s(s(elem!1))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24311, 24247, 5499, 394, 24246, 379, 220, 331, 1, 2467])).
% 2.85/3.10 tff(24313,plain,
% 2.85/3.10 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[23458, 24247, 5499])).
% 2.85/3.10 tff(24314,plain,
% 2.85/3.10 (~r(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[13607, 24313, 220, 379, 394, 24312])).
% 2.85/3.10 tff(24315,plain,
% 2.85/3.10 (b(z, elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[355, 24314, 331])).
% 2.85/3.10 tff(24316,plain,
% 2.85/3.10 (elem!1 = s(z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20894, 24315, 19197, 24245, 24244])).
% 2.85/3.10 tff(24317,plain,
% 2.85/3.10 (s(elem!1) = s(s(z))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24316])).
% 2.85/3.10 tff(24318,plain,
% 2.85/3.10 (s(s(elem!1)) = s(s(s(z)))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24317])).
% 2.85/3.10 tff(24319,plain,
% 2.85/3.10 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24318])).
% 2.85/3.10 tff(24320,plain,
% 2.85/3.10 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24318])).
% 2.85/3.10 tff(24321,plain,
% 2.85/3.10 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.10 inference(symmetry,[status(thm)],[24320])).
% 2.85/3.10 tff(24322,plain,
% 2.85/3.10 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[5499, 24321])).
% 2.85/3.10 tff(24323,plain,
% 2.85/3.10 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3520, 121, 379, 8563, 24312])).
% 2.85/3.10 tff(24324,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[681, 24313, 24323])).
% 2.85/3.10 tff(24325,plain,
% 2.85/3.10 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.85/3.10 inference(monotonicity,[status(thm)],[24316])).
% 2.85/3.10 tff(24326,plain,
% 2.85/3.10 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[7490, 24313])).
% 2.85/3.10 tff(24327,plain,
% 2.85/3.10 (~b(elem!1, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[6679, 24316, 71])).
% 2.85/3.10 tff(24328,plain,
% 2.85/3.10 (r(elem!1, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[599, 24327, 24326])).
% 2.85/3.10 tff(24329,plain,
% 2.85/3.10 (r(s(z), s(s(elem!1)))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24328, 24325])).
% 2.85/3.10 tff(24330,plain,
% 2.85/3.10 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[16699, 24322, 24312, 24329])).
% 2.85/3.10 tff(24331,plain,
% 2.85/3.10 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[760, 24330])).
% 2.85/3.10 tff(24332,plain,
% 2.85/3.10 (~b(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[21846, 24331, 19197, 24324])).
% 2.85/3.10 tff(24333,plain,
% 2.85/3.10 (r(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19736, 24332])).
% 2.85/3.10 tff(24334,plain,
% 2.85/3.10 (~r(z, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[3425, 24333, 24312, 24322])).
% 2.85/3.10 tff(24335,plain,
% 2.85/3.10 (b(z, s(s(elem!1)))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2106, 24334])).
% 2.85/3.10 tff(24336,plain,
% 2.85/3.10 (b(z, s(s(s(z))))),
% 2.85/3.10 inference(modus_ponens,[status(thm)],[24335, 24319])).
% 2.85/3.10 tff(24337,plain,
% 2.85/3.10 (s(z) = elem!1),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[11204, 24315, 219, 379, 220, 394, 344, 24244])).
% 2.85/3.10 tff(24338,plain,
% 2.85/3.10 (b(elem!1, z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20120, 24337, 19197])).
% 2.85/3.10 tff(24339,plain,
% 2.85/3.10 (~r(s(s(elem!1)), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[2670, 24322, 24312, 24328])).
% 2.85/3.10 tff(24340,plain,
% 2.85/3.10 (~r(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[14112, 24339, 24337])).
% 2.85/3.10 tff(24341,plain,
% 2.85/3.10 (b(s(s(s(z))), elem!1)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[255, 24340, 24246])).
% 2.85/3.10 tff(24342,plain,
% 2.85/3.10 (~b(z, s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1334, 24341, 24315, 24338])).
% 2.85/3.10 tff(24343,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24342, 24336])).
% 2.85/3.10 tff(24344,plain,(b(s(z), s(s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24345,plain,
% 2.85/3.10 (b(s(z), s(s(s(z))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24344, 2467, 9983, 220, 11211, 24231, 1, 5499])).
% 2.85/3.10 tff(24346,plain,
% 2.85/3.10 (b(s(s(s(elem!1))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[20978, 10994, 1, 19197, 3871, 3407])).
% 2.85/3.10 tff(24347,plain,
% 2.85/3.10 ($false),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[22605, 24346, 11211, 1, 19197, 3871, 3407])).
% 2.85/3.10 tff(24348,plain,(r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.10 tff(24349,plain,
% 2.85/3.10 (~b(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24348, 24345, 10994, 1])).
% 2.85/3.10 tff(24350,plain,
% 2.85/3.10 (r(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19736, 24349])).
% 2.85/3.10 tff(24351,plain,
% 2.85/3.10 (~b(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[24348, 3871, 10994, 1])).
% 2.85/3.10 tff(24352,plain,
% 2.85/3.10 (r(z, s(s(s(elem!1))))),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[19736, 24351])).
% 2.85/3.10 tff(24353,plain,
% 2.85/3.10 (~b(s(s(s(s(z)))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[22548, 937, 1281, 220])).
% 2.85/3.10 tff(24354,plain,
% 2.85/3.10 (r(s(s(s(s(z)))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1095, 24353])).
% 2.85/3.10 tff(24355,plain,
% 2.85/3.10 (~b(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[21058, 3871, 1281, 220])).
% 2.85/3.10 tff(24356,plain,
% 2.85/3.10 (r(s(s(s(z))), z)),
% 2.85/3.10 inference(unit_resolution,[status(thm)],[1155, 24355])).
% 2.85/3.10 tff(24357,plain,
% 2.85/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.85/3.10 inference(rewrite,[status(thm)],[])).
% 2.85/3.10 tff(24358,plain,
% 2.85/3.10 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24359,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24358])).
% 2.85/3.11 tff(24360,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.85/3.11 inference(transitivity,[status(thm)],[24359, 24357])).
% 2.85/3.11 tff(24361,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24362,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24361, 24360])).
% 2.85/3.11 tff(24363,plain,
% 2.85/3.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24362, 121, 111, 24356, 24354])).
% 2.85/3.11 tff(24364,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24365,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24366,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24365, 24364])).
% 2.85/3.11 tff(24367,plain,
% 2.85/3.11 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24366, 121, 111, 24356, 24354])).
% 2.85/3.11 tff(24368,plain,
% 2.85/3.11 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[10426, 24367])).
% 2.85/3.11 tff(24369,plain,
% 2.85/3.11 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[14911, 24368, 937, 3871])).
% 2.85/3.11 tff(24370,plain,
% 2.85/3.11 ($false),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1167, 21, 24369, 24363, 20146])).
% 2.85/3.11 tff(24371,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.11 tff(24372,plain,
% 2.85/3.11 (~b(s(s(s(s(z)))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24371, 24352, 3871, 19197, 220])).
% 2.85/3.11 tff(24373,plain,
% 2.85/3.11 (r(s(s(s(s(z)))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[932, 24372])).
% 2.85/3.11 tff(24374,plain,
% 2.85/3.11 (~(elem!1 = s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1234, 147, 24373])).
% 2.85/3.11 tff(24375,plain,
% 2.85/3.11 (~(s(z) = elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1221, 24374])).
% 2.85/3.11 tff(24376,plain,
% 2.85/3.11 (b(s(z), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[236, 24375, 24238])).
% 2.85/3.11 tff(24377,plain,
% 2.85/3.11 (~b(z, elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[11278, 24374, 220, 9983, 24232, 10994, 219, 3871, 11211])).
% 2.85/3.11 tff(24378,plain,
% 2.85/3.11 (r(z, elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[355, 24377, 24231])).
% 2.85/3.11 tff(24379,plain,
% 2.85/3.11 (b(elem!1, s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[299, 24374, 24239])).
% 2.85/3.11 tff(24380,plain,
% 2.85/3.11 (~b(s(elem!1), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[16834, 271, 394, 1281, 220])).
% 2.85/3.11 tff(24381,plain,
% 2.85/3.11 (r(s(elem!1), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[429, 24380, 2282])).
% 2.85/3.11 tff(24382,plain,
% 2.85/3.11 (~b(s(z), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[9241, 394, 1281, 220])).
% 2.85/3.11 tff(24383,plain,
% 2.85/3.11 (r(s(z), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[444, 24382, 348])).
% 2.85/3.11 tff(24384,plain,
% 2.85/3.11 (~r(elem!1, s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[19955, 121, 379, 24383, 24381])).
% 2.85/3.11 tff(24385,plain,
% 2.85/3.11 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13597, 271, 394, 220, 1638])).
% 2.85/3.11 tff(24386,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24387,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24388,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24387, 24386])).
% 2.85/3.11 tff(24389,plain,
% 2.85/3.11 (~b(s(s(s(elem!1))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24388, 271, 1281, 220, 1638])).
% 2.85/3.11 tff(24390,plain,
% 2.85/3.11 (r(s(s(s(elem!1))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[16580, 24389])).
% 2.85/3.11 tff(24391,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24392,plain,
% 2.85/3.11 (((~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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24393,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24392])).
% 2.85/3.11 tff(24394,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.85/3.11 inference(transitivity,[status(thm)],[24393, 24391])).
% 2.85/3.11 tff(24395,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24396,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24395, 24394])).
% 2.85/3.11 tff(24397,plain,
% 2.85/3.11 (~b(s(z), s(s(s(elem!1))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24396, 271, 1281, 220, 1638])).
% 2.85/3.11 tff(24398,plain,
% 2.85/3.11 (r(s(z), s(s(s(elem!1))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[760, 24397])).
% 2.85/3.11 tff(24399,plain,
% 2.85/3.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13251, 121, 24398, 24390, 24381])).
% 2.85/3.11 tff(24400,plain,
% 2.85/3.11 (s(s(s(elem!1))) = s(elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[681, 24399, 24385])).
% 2.85/3.11 tff(24401,plain,
% 2.85/3.11 (elem!1 = s(s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[78, 24400])).
% 2.85/3.11 tff(24402,plain,
% 2.85/3.11 (~r(s(s(elem!1)), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[12129, 24401, 24384])).
% 2.85/3.11 tff(24403,plain,
% 2.85/3.11 (b(s(s(elem!1)), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2143, 24402])).
% 2.85/3.11 tff(24404,plain,
% 2.85/3.11 (~b(s(s(elem!1)), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[16949, 24403, 1281, 220])).
% 2.85/3.11 tff(24405,plain,
% 2.85/3.11 (r(s(s(elem!1)), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2430, 24404])).
% 2.85/3.11 tff(24406,plain,
% 2.85/3.11 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24401])).
% 2.85/3.11 tff(24407,plain,
% 2.85/3.11 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13276, 121, 24398, 24390, 24381])).
% 2.85/3.11 tff(24408,plain,
% 2.85/3.11 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13604, 271, 394, 220, 1638])).
% 2.85/3.11 tff(24409,plain,
% 2.85/3.11 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2293, 21, 24408])).
% 2.85/3.11 tff(24410,plain,
% 2.85/3.11 (s(elem!1) = s(s(s(elem!1)))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24409, 24407])).
% 2.85/3.11 tff(24411,plain,
% 2.85/3.11 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24410])).
% 2.85/3.11 tff(24412,plain,
% 2.85/3.11 (r(elem!1, s(s(s(elem!1))))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[379, 24411])).
% 2.85/3.11 tff(24413,plain,
% 2.85/3.11 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24412, 24406])).
% 2.85/3.11 tff(24414,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24415,plain,
% 2.85/3.11 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24416,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24415])).
% 2.85/3.11 tff(24417,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.85/3.11 inference(transitivity,[status(thm)],[24416, 24414])).
% 2.85/3.11 tff(24418,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24419,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24418, 24417])).
% 2.85/3.11 tff(24420,plain,
% 2.85/3.11 ($false),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24419, 121, 24413, 111, 24390, 24405])).
% 2.85/3.11 tff(24421,plain,((~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.11 tff(24422,plain,
% 2.85/3.11 (~b(s(s(s(elem!1))), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24421, 24352, 9983, 19197, 220, 11211, 24232])).
% 2.85/3.11 tff(24423,plain,
% 2.85/3.11 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[12308, 24422, 11211])).
% 2.85/3.11 tff(24424,plain,
% 2.85/3.11 (~(s(s(elem!1)) = elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[197, 24423])).
% 2.85/3.11 tff(24425,plain,
% 2.85/3.11 (~(s(s(z)) = s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[960, 24375])).
% 2.85/3.11 tff(24426,plain,
% 2.85/3.11 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[953, 24425])).
% 2.85/3.11 tff(24427,plain,
% 2.85/3.11 (~b(s(s(s(z))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24295, 24426, 3313, 9983, 24235, 11211, 19197, 220, 24424, 24379, 24378, 24376])).
% 2.85/3.11 tff(24428,plain,
% 2.85/3.11 (~(elem!1 = z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[333, 24231])).
% 2.85/3.11 tff(24429,plain,
% 2.85/3.11 (~b(elem!1, z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[8962, 24376, 220, 24379])).
% 2.85/3.11 tff(24430,plain,
% 2.85/3.11 (r(elem!1, z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[284, 24429, 24428])).
% 2.85/3.11 tff(24431,plain,
% 2.85/3.11 (~b(s(s(s(z))), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[21058, 3871, 19197, 220])).
% 2.85/3.11 tff(24432,plain,
% 2.85/3.11 (r(s(s(s(z))), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1155, 24431])).
% 2.85/3.11 tff(24433,plain,
% 2.85/3.11 (~b(z, s(s(s(z))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[20322, 24377, 19197, 24231, 3871, 24432, 9983])).
% 2.85/3.11 tff(24434,plain,
% 2.85/3.11 (r(z, s(s(s(z))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1214, 24433])).
% 2.85/3.11 tff(24435,plain,
% 2.85/3.11 (~r(s(s(s(z))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[19871, 24434, 24430, 24378])).
% 2.85/3.11 tff(24436,plain,
% 2.85/3.11 (s(s(s(z))) = elem!1),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[255, 24435, 24427])).
% 2.85/3.11 tff(24437,plain,
% 2.85/3.11 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2611, 24436])).
% 2.85/3.11 tff(24438,plain,
% 2.85/3.11 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[486, 24437, 147])).
% 2.85/3.11 tff(24439,plain,
% 2.85/3.11 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24436])).
% 2.85/3.11 tff(24440,plain,
% 2.85/3.11 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.85/3.11 inference(symmetry,[status(thm)],[24439])).
% 2.85/3.11 tff(24441,plain,
% 2.85/3.11 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24438, 24440])).
% 2.85/3.11 tff(24442,plain,
% 2.85/3.11 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[78, 24423])).
% 2.85/3.11 tff(24443,plain,
% 2.85/3.11 (~b(s(s(s(z))), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[6165, 24436, 317])).
% 2.85/3.11 tff(24444,plain,
% 2.85/3.11 (~b(s(s(s(elem!1))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[10250, 24435, 3871, 147, 24379, 24376])).
% 2.85/3.11 tff(24445,plain,
% 2.85/3.11 (r(s(s(s(elem!1))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[16580, 24444])).
% 2.85/3.11 tff(24446,plain,
% 2.85/3.11 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24436])).
% 2.85/3.11 tff(24447,plain,
% 2.85/3.11 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 2.85/3.11 inference(symmetry,[status(thm)],[24446])).
% 2.85/3.11 tff(24448,plain,
% 2.85/3.11 (r(s(elem!1), s(s(s(z))))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[622, 24447])).
% 2.85/3.11 tff(24449,plain,
% 2.85/3.11 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24436])).
% 2.85/3.11 tff(24450,plain,
% 2.85/3.11 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 2.85/3.11 inference(symmetry,[status(thm)],[24449])).
% 2.85/3.11 tff(24451,plain,
% 2.85/3.11 (b(s(s(s(z))), s(z))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24379, 24450])).
% 2.85/3.11 tff(24452,plain,
% 2.85/3.11 (r(s(elem!1), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[429, 2282, 24234])).
% 2.85/3.11 tff(24453,plain,
% 2.85/3.11 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13276, 121, 572, 12761, 24452])).
% 2.85/3.11 tff(24454,plain,
% 2.85/3.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13251, 121, 572, 12761, 24452])).
% 2.85/3.11 tff(24455,plain,
% 2.85/3.11 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[11011, 10994, 24432])).
% 2.85/3.11 tff(24456,plain,
% 2.85/3.11 (r(s(s(s(z))), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1816, 3506, 24455])).
% 2.85/3.11 tff(24457,plain,
% 2.85/3.11 (~r(s(s(s(z))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[19641, 379, 24452, 1500])).
% 2.85/3.11 tff(24458,plain,
% 2.85/3.11 (r(s(z), s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[444, 348, 24236])).
% 2.85/3.11 tff(24459,plain,
% 2.85/3.11 (b(s(z), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[236, 20298, 1257])).
% 2.85/3.11 tff(24460,plain,
% 2.85/3.11 (b(elem!1, s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[299, 20299, 258])).
% 2.85/3.11 tff(24461,plain,
% 2.85/3.11 (~b(z, elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[11278, 379, 220, 3871, 10994, 11211, 377, 348, 258])).
% 2.85/3.11 tff(24462,plain,
% 2.85/3.11 (r(z, elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[355, 24461, 9297])).
% 2.85/3.11 tff(24463,plain,
% 2.85/3.11 (~r(s(s(s(elem!1))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[13607, 24462, 220, 82, 11211, 379])).
% 2.85/3.11 tff(24464,plain,
% 2.85/3.11 (~b(elem!1, z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[8962, 24459, 220, 24460])).
% 2.85/3.11 tff(24465,plain,
% 2.85/3.11 (r(elem!1, z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[284, 24464, 9298])).
% 2.85/3.11 tff(24466,plain,
% 2.85/3.11 (~r(s(s(s(z))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[19871, 24465, 24462, 1140])).
% 2.85/3.11 tff(24467,plain,
% 2.85/3.11 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[19657, 24460, 82, 431, 411, 2618, 24459])).
% 2.85/3.11 tff(24468,plain,
% 2.85/3.11 (s(s(s(elem!1))) = elem!1),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[486, 24467, 24463])).
% 2.85/3.11 tff(24469,plain,
% 2.85/3.11 (~r(s(s(s(elem!1))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[12809, 24468, 20299])).
% 2.85/3.11 tff(24470,plain,
% 2.85/3.11 (b(s(s(s(elem!1))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[16580, 24469])).
% 2.85/3.11 tff(24471,plain,
% 2.85/3.11 ($false),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[10250, 24470, 24466, 24463, 24460, 24459, 3871])).
% 2.85/3.11 tff(24472,plain,((~r(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(z)) | r(s(elem!1), z) | (elem!1 = s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.11 tff(24473,plain,
% 2.85/3.11 (~b(s(elem!1), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24472, 379, 1140, 220, 82, 24458, 24452, 3871, 258, 10994, 219, 348])).
% 2.85/3.11 tff(24474,plain,
% 2.85/3.11 (r(s(elem!1), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2243, 24473, 2207])).
% 2.85/3.11 tff(24475,plain,
% 2.85/3.11 (~r(s(z), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[17391, 24474, 24458, 379])).
% 2.85/3.11 tff(24476,plain,
% 2.85/3.11 (b(s(z), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[236, 24475, 1257])).
% 2.85/3.11 tff(24477,plain,
% 2.85/3.11 (~b(s(s(s(z))), elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[9017, 24476, 24458, 1500, 258, 24474, 379])).
% 2.85/3.11 tff(24478,plain,
% 2.85/3.11 (s(s(s(z))) = elem!1),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[255, 24477, 24457])).
% 2.85/3.11 tff(24479,plain,
% 2.85/3.11 (b(elem!1, s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[23140, 24478, 222])).
% 2.85/3.11 tff(24480,plain,
% 2.85/3.11 (s(elem!1) = s(s(s(s(z))))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2605, 24478])).
% 2.85/3.11 tff(24481,plain,
% 2.85/3.11 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24480])).
% 2.85/3.11 tff(24482,plain,
% 2.85/3.11 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24481])).
% 2.85/3.11 tff(24483,plain,
% 2.85/3.11 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.85/3.11 inference(symmetry,[status(thm)],[24482])).
% 2.85/3.11 tff(24484,plain,
% 2.85/3.11 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24478])).
% 2.85/3.11 tff(24485,plain,
% 2.85/3.11 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.85/3.11 inference(transitivity,[status(thm)],[24484, 1836])).
% 2.85/3.11 tff(24486,plain,
% 2.85/3.11 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24485])).
% 2.85/3.11 tff(24487,plain,
% 2.85/3.11 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[1489, 24486])).
% 2.85/3.11 tff(24488,plain,
% 2.85/3.11 (~b(elem!1, z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[8962, 24479, 220, 24476])).
% 2.85/3.11 tff(24489,plain,
% 2.85/3.11 (r(elem!1, z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[284, 24488, 9298])).
% 2.85/3.11 tff(24490,plain,
% 2.85/3.11 (~b(z, elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[11278, 379, 220, 3871, 10994, 11211, 219, 348, 258])).
% 2.85/3.11 tff(24491,plain,
% 2.85/3.11 (r(z, elem!1)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[355, 24490, 9297])).
% 2.85/3.11 tff(24492,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24493,plain,
% 2.85/3.11 (((~r(s(elem!1), s(z))) | (~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))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), z)))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24494,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), z))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24493])).
% 2.85/3.11 tff(24495,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), z)))),
% 2.85/3.11 inference(transitivity,[status(thm)],[24494, 24492])).
% 2.85/3.11 tff(24496,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24497,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), z))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24496, 24495])).
% 2.85/3.11 tff(24498,plain,
% 2.85/3.11 (~r(s(s(s(z))), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24497, 121, 1441, 1500, 411])).
% 2.85/3.11 tff(24499,plain,
% 2.85/3.11 (b(s(s(s(z))), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1155, 24498])).
% 2.85/3.11 tff(24500,plain,
% 2.85/3.11 (~r(s(s(s(z))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[19983, 121, 431, 1500, 411])).
% 2.85/3.11 tff(24501,plain,
% 2.85/3.11 (b(s(s(s(z))), s(z))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[2325, 24500])).
% 2.85/3.11 tff(24502,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24503,plain,
% 2.85/3.11 (((~r(s(elem!1), s(z))) | (~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(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24504,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[24503])).
% 2.85/3.11 tff(24505,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.85/3.11 inference(transitivity,[status(thm)],[24504, 24502])).
% 2.85/3.11 tff(24506,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24507,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24506, 24505])).
% 2.85/3.11 tff(24508,plain,
% 2.85/3.11 (~r(s(z), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24507, 121, 1441, 431, 411])).
% 2.85/3.11 tff(24509,plain,
% 2.85/3.11 (b(s(z), z)),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[25, 24508])).
% 2.85/3.11 tff(24510,plain,
% 2.85/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.85/3.11 inference(rewrite,[status(thm)],[])).
% 2.85/3.11 tff(24511,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.85/3.11 inference(quant_inst,[status(thm)],[])).
% 2.85/3.11 tff(24512,plain,
% 2.85/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.85/3.11 inference(modus_ponens,[status(thm)],[24511, 24510])).
% 2.85/3.11 tff(24513,plain,
% 2.85/3.11 ($false),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24512, 271, 24509, 220, 24501, 24499])).
% 2.85/3.11 tff(24514,plain,((~r(s(s(s(z))), s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.11 tff(24515,plain,
% 2.85/3.11 (~r(z, s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[24514, 1500, 220, 24452, 24458])).
% 2.85/3.11 tff(24516,plain,
% 2.85/3.11 (b(z, s(elem!1))),
% 2.85/3.11 inference(unit_resolution,[status(thm)],[1439, 24515])).
% 2.85/3.11 tff(24517,plain,
% 2.85/3.11 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.11 inference(monotonicity,[status(thm)],[4024, 9696])).
% 2.85/3.11 tff(24518,plain,
% 2.85/3.11 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.85/3.11 inference(symmetry,[status(thm)],[24517])).
% 2.85/3.11 tff(24519,plain,
% 2.85/3.11 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[4024])).
% 2.85/3.12 tff(24520,plain,
% 2.85/3.12 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.85/3.12 inference(transitivity,[status(thm)],[24519, 4032])).
% 2.85/3.12 tff(24521,plain,
% 2.85/3.12 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.12 inference(symmetry,[status(thm)],[24520])).
% 2.85/3.12 tff(24522,plain,
% 2.85/3.12 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24521])).
% 2.85/3.12 tff(24523,plain,
% 2.85/3.12 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[1772, 24522])).
% 2.85/3.12 tff(24524,plain,
% 2.85/3.12 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[4024])).
% 2.85/3.12 tff(24525,plain,
% 2.85/3.12 (r(elem!1, s(s(s(s(z)))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[379, 24524])).
% 2.85/3.12 tff(24526,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24527,plain,
% 2.85/3.12 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24528,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24527])).
% 2.85/3.12 tff(24529,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.85/3.12 inference(transitivity,[status(thm)],[24528, 24526])).
% 2.85/3.12 tff(24530,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24531,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24530, 24529])).
% 2.85/3.12 tff(24532,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24531, 121, 622, 3061, 4266, 16461])).
% 2.85/3.12 tff(24533,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24534,plain,
% 2.85/3.12 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24533, 3061, 622, 24525])).
% 2.85/3.12 tff(24535,plain,
% 2.85/3.12 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[4138, 24534, 24523])).
% 2.85/3.12 tff(24536,plain,
% 2.85/3.12 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[4024])).
% 2.85/3.12 tff(24537,plain,
% 2.85/3.12 (b(z, s(s(s(s(z)))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[1421, 24536])).
% 2.85/3.12 tff(24538,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24539,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24540,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z)))))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24539, 24538])).
% 2.85/3.12 tff(24541,plain,
% 2.85/3.12 (~r(z, s(s(s(s(s(z))))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24540, 121, 378, 1409, 3061])).
% 2.85/3.12 tff(24542,plain,
% 2.85/3.12 (b(z, s(s(s(s(s(z))))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[1658, 24541])).
% 2.85/3.12 tff(24543,plain,
% 2.85/3.12 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[14589, 24542, 24537, 24535])).
% 2.85/3.12 tff(24544,plain,
% 2.85/3.12 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[1777, 24543])).
% 2.85/3.12 tff(24545,plain,
% 2.85/3.12 (r(s(elem!1), s(s(elem!1)))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24544, 24518])).
% 2.85/3.12 tff(24546,plain,
% 2.85/3.12 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.12 inference(monotonicity,[status(thm)],[9696])).
% 2.85/3.12 tff(24547,plain,
% 2.85/3.12 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.85/3.12 inference(symmetry,[status(thm)],[24546])).
% 2.85/3.12 tff(24548,plain,
% 2.85/3.12 (r(s(s(elem!1)), elem!1)),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[3061, 24547])).
% 2.85/3.12 tff(24549,plain,
% 2.85/3.12 (~r(s(s(elem!1)), z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[8501, 24548, 379, 378])).
% 2.85/3.12 tff(24550,plain,
% 2.85/3.12 (b(s(s(elem!1)), z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[2430, 24549])).
% 2.85/3.12 tff(24551,plain,
% 2.85/3.12 (~b(s(z), s(s(elem!1)))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[17014, 24550, 1281, 220])).
% 2.85/3.12 tff(24552,plain,
% 2.85/3.12 (r(s(z), s(s(elem!1)))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[2167, 24551])).
% 2.85/3.12 tff(24553,plain,
% 2.85/3.12 (~b(s(s(elem!1)), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[2853, 24550, 1421, 394])).
% 2.85/3.12 tff(24554,plain,
% 2.85/3.12 (r(s(s(elem!1)), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[701, 24553, 694])).
% 2.85/3.12 tff(24555,plain,
% 2.85/3.12 (~r(s(elem!1), s(s(elem!1)))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[3275, 24554, 431, 24552])).
% 2.85/3.12 tff(24556,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24555, 24545])).
% 2.85/3.12 tff(24557,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24558,plain,
% 2.85/3.12 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24557, 24480, 24458, 3313, 24516, 11211, 19197, 220, 379, 24491, 24489, 24474])).
% 2.85/3.12 tff(24559,plain,
% 2.85/3.12 (b(s(s(s(s(s(z))))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[840, 24558, 24487])).
% 2.85/3.12 tff(24560,plain,
% 2.85/3.12 (b(s(s(elem!1)), elem!1)),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24559, 24483])).
% 2.85/3.12 tff(24561,plain,
% 2.85/3.12 (~b(s(s(elem!1)), s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[5441, 24560, 24476, 24479])).
% 2.85/3.12 tff(24562,plain,
% 2.85/3.12 (r(s(s(elem!1)), s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[2143, 24561])).
% 2.85/3.12 tff(24563,plain,
% 2.85/3.12 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24481])).
% 2.85/3.12 tff(24564,plain,
% 2.85/3.12 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.12 inference(symmetry,[status(thm)],[24563])).
% 2.85/3.12 tff(24565,plain,
% 2.85/3.12 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24564])).
% 2.85/3.12 tff(24566,plain,
% 2.85/3.12 (~(s(s(s(elem!1))) = elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[7179, 379, 676])).
% 2.85/3.12 tff(24567,plain,
% 2.85/3.12 (~r(s(s(s(elem!1))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[10227, 24491, 111, 379])).
% 2.85/3.12 tff(24568,plain,
% 2.85/3.12 (b(s(s(s(elem!1))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[486, 24567, 24566])).
% 2.85/3.12 tff(24569,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24570,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24571,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24570, 24569])).
% 2.85/3.12 tff(24572,plain,
% 2.85/3.12 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24571, 271, 24479, 24559, 24568])).
% 2.85/3.12 tff(24573,plain,
% 2.85/3.12 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24572, 24565])).
% 2.85/3.12 tff(24574,plain,
% 2.85/3.12 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[556, 24573, 1])).
% 2.85/3.12 tff(24575,plain,
% 2.85/3.12 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.85/3.12 inference(symmetry,[status(thm)],[24481])).
% 2.85/3.12 tff(24576,plain,
% 2.85/3.12 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24575])).
% 2.85/3.12 tff(24577,plain,
% 2.85/3.12 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24576])).
% 2.85/3.12 tff(24578,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24579,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24580,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24579, 24578])).
% 2.85/3.12 tff(24581,plain,
% 2.85/3.12 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24580, 271, 24479, 24559, 24568])).
% 2.85/3.12 tff(24582,plain,
% 2.85/3.12 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24581, 24577])).
% 2.85/3.12 tff(24583,plain,
% 2.85/3.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[586, 24582, 563])).
% 2.85/3.12 tff(24584,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[14540, 24583, 24574, 572, 24562])).
% 2.85/3.12 tff(24585,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (elem!1 = s(z)) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(elem!1)) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | r(s(elem!1), z) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24586,plain,
% 2.85/3.12 (~r(elem!1, s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24585, 258, 1, 220, 222, 24456, 572, 111, 24454, 1140, 82, 3871, 10994, 348])).
% 2.85/3.12 tff(24587,plain,
% 2.85/3.12 (b(elem!1, s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[392, 24586, 219])).
% 2.85/3.12 tff(24588,plain,
% 2.85/3.12 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[11152, 24587, 24454, 24453, 82])).
% 2.85/3.12 tff(24589,plain,
% 2.85/3.12 (~r(z, s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24514, 24456, 220, 24452, 24458])).
% 2.85/3.12 tff(24590,plain,
% 2.85/3.12 (b(z, s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[1439, 24589])).
% 2.85/3.12 tff(24591,plain,
% 2.85/3.12 (b(s(s(s(elem!1))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[681, 24454, 82])).
% 2.85/3.12 tff(24592,plain,
% 2.85/3.12 (~r(s(s(s(elem!1))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[3351, 24587, 9298, 24591, 11211, 24590])).
% 2.85/3.12 tff(24593,plain,
% 2.85/3.12 (s(s(s(elem!1))) = elem!1),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[486, 24592, 24588])).
% 2.85/3.12 tff(24594,plain,
% 2.85/3.12 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[6264, 24593, 19199])).
% 2.85/3.12 tff(24595,plain,
% 2.85/3.12 (r(elem!1, s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[12809, 24593, 12761])).
% 2.85/3.12 tff(24596,plain,
% 2.85/3.12 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[15185, 24593, 24455])).
% 2.85/3.12 tff(24597,plain,
% 2.85/3.12 (~(s(s(s(z))) = elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[4909, 24587, 3506])).
% 2.85/3.12 tff(24598,plain,
% 2.85/3.12 (~b(z, elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[9091, 24587, 11211, 24590])).
% 2.85/3.12 tff(24599,plain,
% 2.85/3.12 (r(z, elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[355, 24598, 9297])).
% 2.85/3.12 tff(24600,plain,
% 2.85/3.12 (~b(elem!1, z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[402, 24587, 11211, 220])).
% 2.85/3.12 tff(24601,plain,
% 2.85/3.12 (r(elem!1, z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[284, 24600, 9298])).
% 2.85/3.12 tff(24602,plain,
% 2.85/3.12 (~r(s(s(s(z))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[19871, 24601, 24599, 1140])).
% 2.85/3.12 tff(24603,plain,
% 2.85/3.12 (b(s(s(s(z))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[255, 24602, 24597])).
% 2.85/3.12 tff(24604,plain,
% 2.85/3.12 (~b(s(z), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24003, 24603, 3871, 24587])).
% 2.85/3.12 tff(24605,plain,
% 2.85/3.12 (r(s(z), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[236, 24604, 1257])).
% 2.85/3.12 tff(24606,plain,
% 2.85/3.12 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24593])).
% 2.85/3.12 tff(24607,plain,
% 2.85/3.12 (b(elem!1, s(s(s(z))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[6202, 24606])).
% 2.85/3.12 tff(24608,plain,
% 2.85/3.12 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[18462, 24607, 222, 24605, 24603, 24596, 24595, 3871])).
% 2.85/3.12 tff(24609,plain,
% 2.85/3.12 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[1733, 24608])).
% 2.85/3.12 tff(24610,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24611,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24612,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24611, 24610])).
% 2.85/3.12 tff(24613,plain,
% 2.85/3.12 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24612, 121, 24456, 24609, 2046])).
% 2.85/3.12 tff(24614,plain,
% 2.85/3.12 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[4138, 24613, 24594])).
% 2.85/3.12 tff(24615,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.85/3.12 tff(24616,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24617,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24618,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24617, 24616])).
% 2.85/3.12 tff(24619,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24618, 271, 394, 220, 9894, 24615])).
% 2.85/3.12 tff(24620,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24621,plain,
% 2.85/3.12 (~b(s(s(s(s(s(z))))), z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24620, 24614, 220, 11211])).
% 2.85/3.12 tff(24622,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24623,plain,
% 2.85/3.12 (((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.85/3.12 inference(rewrite,[status(thm)],[])).
% 2.85/3.12 tff(24624,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24623])).
% 2.85/3.12 tff(24625,plain,
% 2.85/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.85/3.12 inference(transitivity,[status(thm)],[24624, 24622])).
% 2.85/3.12 tff(24626,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.85/3.12 inference(quant_inst,[status(thm)],[])).
% 2.85/3.12 tff(24627,plain,
% 2.85/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24626, 24625])).
% 2.85/3.12 tff(24628,plain,
% 2.85/3.12 (~r(s(s(s(s(s(z))))), z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24627, 121, 24456, 24609, 1140])).
% 2.85/3.12 tff(24629,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[6593, 21, 711, 24628, 24621])).
% 2.85/3.12 tff(24630,plain,((elem!1 = s(z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(z))), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | r(s(elem!1), z) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24631,plain,
% 2.85/3.12 (~r(s(z), s(s(s(elem!1))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24630, 24451, 220, 3871, 24434, 24448, 24374, 24445, 24443, 24442, 1, 24441, 24352, 10994, 24232])).
% 2.85/3.12 tff(24632,plain,
% 2.85/3.12 (b(s(z), s(s(s(elem!1))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[760, 24631])).
% 2.85/3.12 tff(24633,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[12821, 271, 24376, 24632, 24379, 24438])).
% 2.85/3.12 tff(24634,plain,(r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(elem!1), z) | (~r(s(elem!1), elem!1)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24635,plain,
% 2.85/3.12 (r(s(s(s(elem!1))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24634, 24345, 220, 1, 10994, 8563, 317])).
% 2.85/3.12 tff(24636,plain,
% 2.85/3.12 (~r(z, elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[10227, 24635, 9983, 24350])).
% 2.85/3.12 tff(24637,plain,
% 2.85/3.12 (b(z, elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[355, 24636, 24231])).
% 2.85/3.12 tff(24638,plain,
% 2.85/3.12 (elem!1 = s(z)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[20894, 24637, 19197, 24239, 24238])).
% 2.85/3.12 tff(24639,plain,
% 2.85/3.12 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[8812, 24638, 5499])).
% 2.85/3.12 tff(24640,plain,
% 2.85/3.12 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24638])).
% 2.85/3.12 tff(24641,plain,
% 2.85/3.12 (r(s(s(s(z))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[11593, 24636, 2207, 220, 10994, 24345])).
% 2.85/3.12 tff(24642,plain,
% 2.85/3.12 (r(s(s(s(z))), s(z))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24641, 24640])).
% 2.85/3.12 tff(24643,plain,
% 2.85/3.12 (~b(s(s(s(s(z)))), s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24371, 24350, 24345, 19197, 220])).
% 2.85/3.12 tff(24644,plain,
% 2.85/3.12 (r(s(s(s(s(z)))), s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[932, 24643])).
% 2.85/3.12 tff(24645,plain,
% 2.85/3.12 (s(elem!1) = s(s(z))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24638])).
% 2.85/3.12 tff(24646,plain,
% 2.85/3.12 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.85/3.12 inference(monotonicity,[status(thm)],[24645])).
% 2.85/3.12 tff(24647,plain,
% 2.85/3.12 (r(s(z), s(s(z)))),
% 2.85/3.12 inference(modus_ponens,[status(thm)],[24237, 24646])).
% 2.85/3.12 tff(24648,plain,
% 2.85/3.12 ($false),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[20930, 121, 24647, 24644, 24642, 24639])).
% 2.85/3.12 tff(24649,plain,(b(s(elem!1), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.85/3.12 tff(24650,plain,
% 2.85/3.12 (b(s(elem!1), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24649, 10994, 220, 5499, 1, 317])).
% 2.85/3.12 tff(24651,plain,
% 2.85/3.12 (r(s(elem!1), s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[429, 24380, 351])).
% 2.85/3.12 tff(24652,plain,
% 2.85/3.12 (r(s(z), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[444, 24382, 344])).
% 2.85/3.12 tff(24653,plain,
% 2.85/3.12 (~r(s(s(s(z))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[23235, 108, 24652, 24651])).
% 2.85/3.12 tff(24654,plain,
% 2.85/3.12 (~r(elem!1, s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[19955, 121, 379, 24652, 24651])).
% 2.85/3.12 tff(24655,plain,
% 2.85/3.12 (~(elem!1 = s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[24264, 24653, 147, 1281, 220, 394, 5499])).
% 2.85/3.12 tff(24656,plain,
% 2.85/3.12 (b(elem!1, s(z))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[299, 24655, 24654])).
% 2.85/3.12 tff(24657,plain,
% 2.85/3.12 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[23458, 24653, 5499])).
% 2.85/3.12 tff(24658,plain,
% 2.85/3.12 (~r(s(z), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[20297, 121, 379, 24652, 24651])).
% 2.85/3.12 tff(24659,plain,
% 2.85/3.12 (~(s(z) = elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[1221, 24655])).
% 2.85/3.12 tff(24660,plain,
% 2.85/3.12 (b(s(z), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[236, 24659, 24658])).
% 2.85/3.12 tff(24661,plain,
% 2.85/3.12 (~b(s(s(s(elem!1))), elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[19657, 24660, 2618, 24652, 24657, 24651, 24656])).
% 2.85/3.12 tff(24662,plain,
% 2.85/3.12 (s(s(s(elem!1))) = elem!1),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[486, 24661, 147])).
% 2.85/3.12 tff(24663,plain,
% 2.85/3.12 (~(s(s(s(z))) = s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[2596, 24662])).
% 2.85/3.12 tff(24664,plain,
% 2.85/3.12 (b(s(s(s(z))), s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[1816, 24663, 24653])).
% 2.85/3.12 tff(24665,plain,
% 2.85/3.12 (~b(z, elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[20894, 24655, 1281, 24654, 24658])).
% 2.85/3.12 tff(24666,plain,
% 2.85/3.12 (r(z, elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[355, 24665, 331])).
% 2.85/3.12 tff(24667,plain,
% 2.85/3.12 (~(s(s(s(z))) = elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[250, 108, 24658])).
% 2.85/3.12 tff(24668,plain,
% 2.85/3.12 (~(elem!1 = s(s(elem!1)))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[7490, 24657])).
% 2.85/3.12 tff(24669,plain,
% 2.85/3.12 (~(s(s(elem!1)) = elem!1)),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[197, 24668])).
% 2.85/3.12 tff(24670,plain,
% 2.85/3.12 (~(s(s(z)) = s(elem!1))),
% 2.85/3.12 inference(unit_resolution,[status(thm)],[960, 24659])).
% 2.95/3.12 tff(24671,plain,
% 2.95/3.12 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[953, 24670])).
% 2.95/3.12 tff(24672,plain,
% 2.95/3.12 (~b(s(s(s(z))), elem!1)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[24295, 24671, 694, 379, 24651, 394, 1281, 220, 24669, 24656, 24666, 24660])).
% 2.95/3.12 tff(24673,plain,
% 2.95/3.12 (r(s(s(s(z))), elem!1)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[255, 24672, 24667])).
% 2.95/3.12 tff(24674,plain,
% 2.95/3.12 (~b(elem!1, z)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[8962, 24660, 220, 24656])).
% 2.95/3.12 tff(24675,plain,
% 2.95/3.12 (r(elem!1, z)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[284, 24674, 358])).
% 2.95/3.12 tff(24676,plain,
% 2.95/3.12 (~r(z, s(s(s(z))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[19871, 24675, 24673, 24666])).
% 2.95/3.12 tff(24677,plain,
% 2.95/3.12 (b(z, s(s(s(z))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[1214, 24676])).
% 2.95/3.12 tff(24678,plain,
% 2.95/3.12 (~b(s(s(s(z))), z)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[8279, 24677, 394, 24664])).
% 2.95/3.12 tff(24679,plain,
% 2.95/3.12 (r(s(s(s(z))), z)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[1155, 24678])).
% 2.95/3.12 tff(24680,plain,
% 2.95/3.12 ($false),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[10254, 121, 379, 24666, 24673, 24679])).
% 2.95/3.12 tff(24681,plain,((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.12 tff(24682,plain,
% 2.95/3.12 (~r(s(z), s(s(s(z))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[24681, 147, 11211, 379, 3313, 19197, 220, 2618, 331, 5499])).
% 2.95/3.12 tff(24683,plain,
% 2.95/3.12 (r(z, s(s(s(elem!1))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[23127, 24682, 1, 19197])).
% 2.95/3.12 tff(24684,plain,
% 2.95/3.12 (b(s(z), s(s(s(z))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[105, 24682])).
% 2.95/3.12 tff(24685,plain,
% 2.95/3.12 (~b(s(s(s(s(z)))), s(z))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[24371, 24684, 24683, 19197, 220])).
% 2.95/3.12 tff(24686,plain,
% 2.95/3.12 (r(s(s(s(s(z)))), s(z))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[932, 24685])).
% 2.95/3.13 tff(24687,plain,
% 2.95/3.13 (~(elem!1 = s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1234, 24686, 147])).
% 2.95/3.13 tff(24688,plain,
% 2.95/3.13 (r(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[429, 24234, 351])).
% 2.95/3.13 tff(24689,plain,
% 2.95/3.13 (r(s(z), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[444, 24236, 344])).
% 2.95/3.13 tff(24690,plain,
% 2.95/3.13 (~b(s(s(s(elem!1))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24421, 24683, 379, 19197, 220, 11211, 344])).
% 2.95/3.13 tff(24691,plain,
% 2.95/3.13 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[12308, 24690, 11211])).
% 2.95/3.13 tff(24692,plain,
% 2.95/3.13 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[78, 24691])).
% 2.95/3.13 tff(24693,plain,
% 2.95/3.13 (~r(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24472, 24692, 379, 220, 2618, 24684, 24689, 24688, 24687, 10994, 219, 344])).
% 2.95/3.13 tff(24694,plain,
% 2.95/3.13 (~b(s(s(s(z))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[21058, 24684, 19197, 220])).
% 2.95/3.13 tff(24695,plain,
% 2.95/3.13 (r(s(s(s(z))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1155, 24694])).
% 2.95/3.13 tff(24696,plain,
% 2.95/3.13 (~r(s(z), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20297, 121, 379, 24689, 24688])).
% 2.95/3.13 tff(24697,plain,
% 2.95/3.13 (~r(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[19955, 121, 379, 24689, 24688])).
% 2.95/3.13 tff(24698,plain,
% 2.95/3.13 (~b(z, elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20894, 24687, 19197, 24697, 24696])).
% 2.95/3.13 tff(24699,plain,
% 2.95/3.13 (~b(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20322, 24698, 19197, 331, 24684, 24695, 379])).
% 2.95/3.13 tff(24700,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1214, 24699, 24693])).
% 2.95/3.13 tff(24701,plain,(r(s(s(s(elem!1))), elem!1) | (z = elem!1) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24702,plain,
% 2.95/3.13 (r(s(s(s(elem!1))), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24701, 24650, 9983, 220, 24231, 10994, 1, 5499])).
% 2.95/3.13 tff(24703,plain,
% 2.95/3.13 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[13607, 378, 220, 379, 394, 139])).
% 2.95/3.13 tff(24704,plain,
% 2.95/3.13 (r(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23458, 24703, 5499])).
% 2.95/3.13 tff(24705,plain,
% 2.95/3.13 (~r(z, s(s(s(elem!1))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[10227, 378, 379, 139])).
% 2.95/3.13 tff(24706,plain,
% 2.95/3.13 (r(s(z), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23127, 24705, 1, 19197])).
% 2.95/3.13 tff(24707,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23235, 24706, 24704, 431, 411])).
% 2.95/3.13 tff(24708,plain,((~r(z, elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24709,plain,
% 2.95/3.13 (~r(z, elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24708, 24237, 24235, 1, 5499, 9983, 24702, 220, 11211])).
% 2.95/3.13 tff(24710,plain,
% 2.95/3.13 (b(z, elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[355, 24709, 24231])).
% 2.95/3.13 tff(24711,plain,
% 2.95/3.13 (s(z) = elem!1),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11204, 24710, 219, 9983, 220, 11211, 24232, 24238])).
% 2.95/3.13 tff(24712,plain,
% 2.95/3.13 (~b(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11634, 24710, 11211, 24650])).
% 2.95/3.13 tff(24713,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20120, 24712, 24711, 19197])).
% 2.95/3.13 tff(24714,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24715,plain,
% 2.95/3.13 (r(s(elem!1), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24714, 317, 1, 5499, 220])).
% 2.95/3.13 tff(24716,plain,
% 2.95/3.13 (~r(z, s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[12090, 1243, 379, 412])).
% 2.95/3.13 tff(24717,plain,
% 2.95/3.13 (b(z, s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1439, 24716])).
% 2.95/3.13 tff(24718,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[22213, 271, 1281, 220, 447, 1421])).
% 2.95/3.13 tff(24719,plain,((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24720,plain,
% 2.95/3.13 (~b(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24719, 24717, 220, 1281])).
% 2.95/3.13 tff(24721,plain,
% 2.95/3.13 (r(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[429, 24720, 351])).
% 2.95/3.13 tff(24722,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[4391, 121, 379, 378, 1409, 412])).
% 2.95/3.13 tff(24723,plain,((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24724,plain,
% 2.95/3.13 (~r(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24723, 1243, 379, 412])).
% 2.95/3.13 tff(24725,plain,
% 2.95/3.13 (b(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[284, 24724, 358])).
% 2.95/3.13 tff(24726,plain,
% 2.95/3.13 (~b(s(z), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[15307, 260, 2618, 261])).
% 2.95/3.13 tff(24727,plain,
% 2.95/3.13 (r(s(z), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[444, 24726, 348])).
% 2.95/3.13 tff(24728,plain,
% 2.95/3.13 (~b(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[8962, 260, 220, 261])).
% 2.95/3.13 tff(24729,plain,
% 2.95/3.13 (r(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[299, 24728, 258])).
% 2.95/3.13 tff(24730,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[3709, 24729, 24727, 379, 412])).
% 2.95/3.13 tff(24731,plain,((~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24732,plain,
% 2.95/3.13 (~b(s(z), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24731, 337, 412, 379, 344, 220, 24725, 2618])).
% 2.95/3.13 tff(24733,plain,
% 2.95/3.13 (b(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23287, 24732, 379, 230, 24721])).
% 2.95/3.13 tff(24734,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[22281, 271, 1281, 24725, 24733, 220])).
% 2.95/3.13 tff(24735,plain,(b(z, elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24736,plain,
% 2.95/3.13 (~b(s(elem!1), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24735, 199, 220, 379, 412, 1281, 331])).
% 2.95/3.13 tff(24737,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2243, 3718, 24736, 2564])).
% 2.95/3.13 tff(24738,plain,(b(z, elem!1) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24739,plain,
% 2.95/3.13 (b(z, elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24738, 9983, 2207, 24715, 220, 19197, 24231])).
% 2.95/3.13 tff(24740,plain,
% 2.95/3.13 (~b(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20398, 24739, 19197, 220])).
% 2.95/3.13 tff(24741,plain,
% 2.95/3.13 (~b(s(elem!1), s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[3922, 23419, 2467])).
% 2.95/3.13 tff(24742,plain,
% 2.95/3.13 (r(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23458, 72, 5499])).
% 2.95/3.13 tff(24743,plain,
% 2.95/3.13 (~r(elem!1, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[17626, 1500, 412, 379])).
% 2.95/3.13 tff(24744,plain,
% 2.95/3.13 (b(elem!1, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1192, 1101, 24743])).
% 2.95/3.13 tff(24745,plain,
% 2.95/3.13 (~b(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2020, 24744, 908, 1326])).
% 2.95/3.13 tff(24746,plain,
% 2.95/3.13 (r(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1214, 24745])).
% 2.95/3.13 tff(24747,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[21651, 121, 379, 1409, 412, 1140])).
% 2.95/3.13 tff(24748,plain,((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24749,plain,
% 2.95/3.13 (~r(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24748, 24746, 379, 412])).
% 2.95/3.13 tff(24750,plain,
% 2.95/3.13 (b(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[284, 24749, 259])).
% 2.95/3.13 tff(24751,plain,
% 2.95/3.13 (~b(s(s(s(z))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1947, 24750, 1326, 908])).
% 2.95/3.13 tff(24752,plain,
% 2.95/3.13 (r(s(s(s(z))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1155, 24751])).
% 2.95/3.13 tff(24753,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[22644, 121, 412, 1500, 24752, 24746])).
% 2.95/3.13 tff(24754,plain,((s(s(s(z))) = elem!1) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(z, elem!1)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24755,plain,
% 2.95/3.13 (r(s(s(s(z))), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24754, 24742, 379, 412, 259, 1326, 907])).
% 2.95/3.13 tff(24756,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24757,plain,
% 2.95/3.13 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24758,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24757])).
% 2.95/3.13 tff(24759,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.95/3.13 inference(transitivity,[status(thm)],[24758, 24756])).
% 2.95/3.13 tff(24760,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(24761,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[24760, 24759])).
% 2.95/3.13 tff(24762,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24761, 121, 379, 627, 145, 1500])).
% 2.95/3.13 tff(24763,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24764,plain,
% 2.95/3.13 (~r(s(elem!1), s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24763, 24742, 379, 24755])).
% 2.95/3.13 tff(24765,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[526, 24764, 24741, 216])).
% 2.95/3.13 tff(24766,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | b(s(elem!1), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24767,plain,
% 2.95/3.13 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24766, 907, 9983, 24715, 24428, 24739, 211, 2467, 5499])).
% 2.95/3.13 tff(24768,plain,
% 2.95/3.13 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[7490, 24767])).
% 2.95/3.13 tff(24769,plain,
% 2.95/3.13 (r(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[284, 279, 24428])).
% 2.95/3.13 tff(24770,plain,
% 2.95/3.13 (~r(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24748, 24769, 9983, 24715])).
% 2.95/3.13 tff(24771,plain,
% 2.95/3.13 (b(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1214, 24770])).
% 2.95/3.13 tff(24772,plain,
% 2.95/3.13 (~(s(z) = elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20120, 279, 19197])).
% 2.95/3.13 tff(24773,plain,
% 2.95/3.13 (~b(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20398, 1326, 1281, 220])).
% 2.95/3.13 tff(24774,plain,
% 2.95/3.13 (r(elem!1, s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[299, 243, 24773])).
% 2.95/3.13 tff(24775,plain,
% 2.95/3.13 (~r(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24748, 1409, 379, 412])).
% 2.95/3.13 tff(24776,plain,
% 2.95/3.13 (b(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1214, 24775])).
% 2.95/3.13 tff(24777,plain,
% 2.95/3.13 (~r(s(s(s(z))), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[15964, 357, 1409, 220, 24776])).
% 2.95/3.13 tff(24778,plain,
% 2.95/3.13 (~r(s(z), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[3709, 24774, 379, 412])).
% 2.95/3.13 tff(24779,plain,
% 2.95/3.13 (b(s(z), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[444, 24778, 24232])).
% 2.95/3.13 tff(24780,plain,
% 2.95/3.13 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[9276, 71, 24779])).
% 2.95/3.13 tff(24781,plain,
% 2.95/3.13 (~r(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24754, 907, 379, 412, 259, 1326, 221])).
% 2.95/3.13 tff(24782,plain,
% 2.95/3.13 (b(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1816, 24781, 2033])).
% 2.95/3.13 tff(24783,plain,
% 2.95/3.13 (~b(elem!1, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2020, 908, 1326, 1307])).
% 2.95/3.13 tff(24784,plain,
% 2.95/3.13 (r(elem!1, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1192, 24783, 1101])).
% 2.95/3.13 tff(24785,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24786,plain,
% 2.95/3.13 (((~r(s(z), s(s(s(z))))) | (~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(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24787,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24786])).
% 2.95/3.13 tff(24788,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[24787, 24785])).
% 2.95/3.13 tff(24789,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(24790,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[24789, 24788])).
% 2.95/3.13 tff(24791,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24790, 121, 1184, 3456, 2327, 108])).
% 2.95/3.13 tff(24792,plain,((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24793,plain,
% 2.95/3.13 (~r(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24792, 24784, 9232, 108])).
% 2.95/3.13 tff(24794,plain,
% 2.95/3.13 (b(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2325, 24793])).
% 2.95/3.13 tff(24795,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[5673, 271, 1422, 447, 222, 446])).
% 2.95/3.13 tff(24796,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24797,plain,
% 2.95/3.13 (~b(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24796, 24794, 446, 24782])).
% 2.95/3.13 tff(24798,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[16092, 271, 260, 220, 1307, 222])).
% 2.95/3.13 tff(24799,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24800,plain,
% 2.95/3.13 (~b(s(z), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24799, 24794, 220, 1307])).
% 2.95/3.13 tff(24801,plain,
% 2.95/3.13 (~r(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23287, 24800, 379, 294, 231])).
% 2.95/3.13 tff(24802,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[429, 24801, 24797, 422])).
% 2.95/3.13 tff(24803,plain,((s(s(s(z))) = elem!1) | (s(elem!1) = s(z)) | (~r(elem!1, s(elem!1))) | b(elem!1, s(z)) | (s(z) = elem!1) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (elem!1 = z) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24804,plain,
% 2.95/3.13 (s(s(s(z))) = elem!1),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24803, 106, 379, 24773, 231, 24779, 220, 24776, 24233, 24780, 1326, 412, 24428, 24777])).
% 2.95/3.13 tff(24805,plain,
% 2.95/3.13 (s(elem!1) = s(s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2605, 24804])).
% 2.95/3.13 tff(24806,plain,
% 2.95/3.13 (s(s(s(s(z)))) = s(elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[17419, 24805])).
% 2.95/3.13 tff(24807,plain,
% 2.95/3.13 (elem!1 = s(s(s(z)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1516, 24806])).
% 2.95/3.13 tff(24808,plain,
% 2.95/3.13 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24804])).
% 2.95/3.13 tff(24809,plain,
% 2.95/3.13 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 2.95/3.13 inference(symmetry,[status(thm)],[24808])).
% 2.95/3.13 tff(24810,plain,
% 2.95/3.13 (r(s(s(s(z))), z)),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[1409, 24809])).
% 2.95/3.13 tff(24811,plain,
% 2.95/3.13 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24805])).
% 2.95/3.13 tff(24812,plain,
% 2.95/3.13 (r(elem!1, s(s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[379, 24811])).
% 2.95/3.13 tff(24813,plain,
% 2.95/3.13 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24805])).
% 2.95/3.13 tff(24814,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[6165, 24804, 317])).
% 2.95/3.13 tff(24815,plain,
% 2.95/3.13 (r(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1816, 24814, 24780])).
% 2.95/3.13 tff(24816,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23140, 24804, 24773])).
% 2.95/3.13 tff(24817,plain,
% 2.95/3.13 (r(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2325, 24816])).
% 2.95/3.13 tff(24818,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24819,plain,
% 2.95/3.13 (((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24820,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24819])).
% 2.95/3.13 tff(24821,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[24820, 24818])).
% 2.95/3.13 tff(24822,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(24823,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[24822, 24821])).
% 2.95/3.13 tff(24824,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24823, 121, 357, 1500, 411, 2327])).
% 2.95/3.13 tff(24825,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24826,plain,
% 2.95/3.13 (~r(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24825, 24817, 357, 24815])).
% 2.95/3.13 tff(24827,plain,
% 2.95/3.13 (b(s(elem!1), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[429, 24826, 24233])).
% 2.95/3.13 tff(24828,plain,
% 2.95/3.13 (~b(z, s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24719, 24827, 220, 1281])).
% 2.95/3.13 tff(24829,plain,
% 2.95/3.13 (r(z, s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1439, 24828])).
% 2.95/3.13 tff(24830,plain,
% 2.95/3.13 (r(z, s(s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[24829, 24813])).
% 2.95/3.13 tff(24831,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[21213, 24830, 24812, 412, 24810, 24807])).
% 2.95/3.13 tff(24832,plain,(b(s(z), s(s(s(z)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | b(elem!1, s(elem!1)) | (s(z) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24833,plain,
% 2.95/3.13 (~r(s(z), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24832, 71, 379, 412, 220, 1281, 1409, 317, 231, 1326])).
% 2.95/3.13 tff(24834,plain,
% 2.95/3.13 (~b(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[12145, 237, 220, 1326])).
% 2.95/3.13 tff(24835,plain,
% 2.95/3.13 (r(elem!1, z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[284, 24834, 259])).
% 2.95/3.13 tff(24836,plain,
% 2.95/3.13 (~r(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24748, 24835, 379, 412])).
% 2.95/3.13 tff(24837,plain,
% 2.95/3.13 (b(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1214, 24836])).
% 2.95/3.13 tff(24838,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24799, 24837, 220, 237])).
% 2.95/3.13 tff(24839,plain,
% 2.95/3.13 (r(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2325, 24838])).
% 2.95/3.13 tff(24840,plain,
% 2.95/3.13 (~r(elem!1, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24792, 24839, 3456, 108])).
% 2.95/3.13 tff(24841,plain,
% 2.95/3.13 (b(elem!1, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1192, 24840, 2357])).
% 2.95/3.13 tff(24842,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24843,plain,
% 2.95/3.13 (((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(24844,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z)))))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[24843])).
% 2.95/3.13 tff(24845,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[24844, 24842])).
% 2.95/3.13 tff(24846,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(24847,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[24846, 24845])).
% 2.95/3.13 tff(24848,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24847, 271, 1326, 237, 1281, 24841])).
% 2.95/3.13 tff(24849,plain,(r(s(z), elem!1) | (~b(z, elem!1)) | (~b(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24850,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24849, 24833, 106, 1281, 24774, 1326, 220, 379, 412, 24428, 231])).
% 2.95/3.13 tff(24851,plain,(b(s(z), s(s(s(z)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (s(z) = elem!1) | (~r(elem!1, z)) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(24852,plain,
% 2.95/3.13 (b(s(z), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24851, 24772, 24739, 220, 9983, 24715, 19197, 24769, 317])).
% 2.95/3.13 tff(24853,plain,
% 2.95/3.13 (~b(s(s(s(z))), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[19416, 24852, 19197, 24771])).
% 2.95/3.13 tff(24854,plain,
% 2.95/3.13 (r(s(s(s(z))), elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[255, 24853, 907])).
% 2.95/3.13 tff(24855,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[20471, 24852, 19197, 24771])).
% 2.95/3.13 tff(24856,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[21149, 24852, 19197, 24771])).
% 2.95/3.13 tff(24857,plain,
% 2.95/3.13 (r(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[2325, 24856])).
% 2.95/3.13 tff(24858,plain,
% 2.95/3.13 (elem!1 = s(s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[21496, 24857, 1, 19197, 24715, 24739, 24852, 24854, 279, 220, 24853, 24855, 24428])).
% 2.95/3.13 tff(24859,plain,
% 2.95/3.13 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[7490, 24858])).
% 2.95/3.13 tff(24860,plain,
% 2.95/3.13 (r(s(s(s(z))), s(elem!1))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[23458, 24859, 5499])).
% 2.95/3.13 tff(24861,plain,
% 2.95/3.13 (~b(s(elem!1), s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[3922, 24858, 2467])).
% 2.95/3.13 tff(24862,plain,
% 2.95/3.13 (r(s(elem!1), s(s(elem!1)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[526, 24861, 211])).
% 2.95/3.13 tff(24863,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[24763, 24862, 24860, 9983, 24854])).
% 2.95/3.14 tff(24864,plain,(b(elem!1, z) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (s(s(s(z))) = elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(24865,plain,
% 2.95/3.14 (b(elem!1, z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24864, 907, 2467, 1, 220, 5499, 317])).
% 2.95/3.14 tff(24866,plain,
% 2.95/3.14 (~b(s(z), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[3964, 24865, 19197, 24739])).
% 2.95/3.14 tff(24867,plain,
% 2.95/3.14 (~r(z, elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[3683, 8563, 9983, 24715])).
% 2.95/3.14 tff(24868,plain,
% 2.95/3.14 (b(z, elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[355, 24867, 24231])).
% 2.95/3.14 tff(24869,plain,
% 2.95/3.14 (~r(s(z), s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[21984, 258, 19197, 379, 622, 1326, 348])).
% 2.95/3.14 tff(24870,plain,
% 2.95/3.14 (b(s(z), s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[444, 24869, 348])).
% 2.95/3.14 tff(24871,plain,
% 2.95/3.14 (~b(elem!1, s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[20398, 1326, 19197, 220])).
% 2.95/3.14 tff(24872,plain,
% 2.95/3.14 (r(elem!1, s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[299, 258, 24871])).
% 2.95/3.14 tff(24873,plain,
% 2.95/3.14 (r(s(z), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24849, 106, 1281, 3456, 1326, 220, 379, 412, 259, 231])).
% 2.95/3.14 tff(24874,plain,
% 2.95/3.14 (~r(s(s(s(z))), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[4112, 24873, 3456, 106])).
% 2.95/3.14 tff(24875,plain,
% 2.95/3.14 (~r(s(elem!1), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[9630, 121, 379, 622, 24873])).
% 2.95/3.14 tff(24876,plain,
% 2.95/3.14 (b(s(elem!1), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[429, 24875, 422])).
% 2.95/3.14 tff(24877,plain,
% 2.95/3.14 (~b(z, s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24719, 24876, 220, 1281])).
% 2.95/3.14 tff(24878,plain,
% 2.95/3.14 (r(z, s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1439, 24877])).
% 2.95/3.14 tff(24879,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24880,plain,
% 2.95/3.14 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24881,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24880])).
% 2.95/3.14 tff(24882,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)))),
% 2.95/3.14 inference(transitivity,[status(thm)],[24881, 24879])).
% 2.95/3.14 tff(24883,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24884,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24883, 24882])).
% 2.95/3.14 tff(24885,plain,
% 2.95/3.14 (~r(elem!1, z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24884, 121, 379, 622, 24878])).
% 2.95/3.14 tff(24886,plain,
% 2.95/3.14 (b(elem!1, z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[284, 24885, 259])).
% 2.95/3.14 tff(24887,plain,
% 2.95/3.14 (~r(z, elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[3683, 622, 379, 412])).
% 2.95/3.14 tff(24888,plain,
% 2.95/3.14 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[9276, 71, 446])).
% 2.95/3.14 tff(24889,plain,
% 2.95/3.14 (~b(s(s(s(elem!1))), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11686, 908, 1326, 261, 11665])).
% 2.95/3.14 tff(24890,plain,
% 2.95/3.14 (s(s(s(elem!1))) = elem!1),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[486, 24889, 147])).
% 2.95/3.14 tff(24891,plain,
% 2.95/3.14 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24890])).
% 2.95/3.14 tff(24892,plain,
% 2.95/3.14 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.14 inference(symmetry,[status(thm)],[24891])).
% 2.95/3.14 tff(24893,plain,
% 2.95/3.14 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[908, 24892])).
% 2.95/3.14 tff(24894,plain,
% 2.95/3.14 (~b(z, s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1334, 908, 1326, 261])).
% 2.95/3.14 tff(24895,plain,
% 2.95/3.14 (r(z, s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1214, 24894])).
% 2.95/3.14 tff(24896,plain,
% 2.95/3.14 (~r(z, s(s(s(elem!1))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11073, 24890, 1391])).
% 2.95/3.14 tff(24897,plain,
% 2.95/3.14 (b(z, s(s(s(elem!1))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[19736, 24896])).
% 2.95/3.14 tff(24898,plain,
% 2.95/3.14 (~r(elem!1, z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24748, 1140, 379, 412])).
% 2.95/3.14 tff(24899,plain,
% 2.95/3.14 (b(elem!1, z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[284, 24898, 259])).
% 2.95/3.14 tff(24900,plain,
% 2.95/3.14 (~b(s(s(s(z))), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1947, 24899, 1326, 257])).
% 2.95/3.14 tff(24901,plain,
% 2.95/3.14 (r(s(s(s(z))), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1155, 24900])).
% 2.95/3.14 tff(24902,plain,
% 2.95/3.14 (~b(z, s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[22213, 271, 1281, 220, 447])).
% 2.95/3.14 tff(24903,plain,
% 2.95/3.14 (r(z, s(elem!1))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1439, 24902])).
% 2.95/3.14 tff(24904,plain,
% 2.95/3.14 (~b(s(elem!1), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[23566, 24899, 257, 2033, 1326])).
% 2.95/3.14 tff(24905,plain,
% 2.95/3.14 (r(s(elem!1), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[2243, 24904, 2564])).
% 2.95/3.14 tff(24906,plain,
% 2.95/3.14 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[2590])).
% 2.95/3.14 tff(24907,plain,
% 2.95/3.14 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.95/3.14 inference(symmetry,[status(thm)],[24906])).
% 2.95/3.14 tff(24908,plain,
% 2.95/3.14 ((~r(elem!1, z)) <=> (~r(s(s(s(elem!1))), z))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[15941])).
% 2.95/3.14 tff(24909,plain,
% 2.95/3.14 (~r(s(s(s(elem!1))), z)),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24898, 24908])).
% 2.95/3.14 tff(24910,plain,
% 2.95/3.14 (b(s(s(s(elem!1))), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[8229, 24909])).
% 2.95/3.14 tff(24911,plain,
% 2.95/3.14 (r(s(s(s(elem!1))), s(z))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[3456, 12805])).
% 2.95/3.14 tff(24912,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24913,plain,
% 2.95/3.14 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24914,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24913])).
% 2.95/3.14 tff(24915,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.95/3.14 inference(transitivity,[status(thm)],[24914, 24912])).
% 2.95/3.14 tff(24916,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24917,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24916, 24915])).
% 2.95/3.14 tff(24918,plain,
% 2.95/3.14 (~r(z, s(s(s(s(z)))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24917, 121, 2327, 1140, 12542])).
% 2.95/3.14 tff(24919,plain,
% 2.95/3.14 (b(z, s(s(s(s(z)))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1121, 24918])).
% 2.95/3.14 tff(24920,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24921,plain,
% 2.95/3.14 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24922,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24921])).
% 2.95/3.14 tff(24923,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.14 inference(transitivity,[status(thm)],[24922, 24920])).
% 2.95/3.14 tff(24924,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24925,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24924, 24923])).
% 2.95/3.14 tff(24926,plain,
% 2.95/3.14 (~r(s(s(s(s(z)))), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24925, 121, 2327, 1140, 12542])).
% 2.95/3.14 tff(24927,plain,
% 2.95/3.14 (b(s(s(s(s(z)))), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1095, 24926])).
% 2.95/3.14 tff(24928,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24929,plain,
% 2.95/3.14 (((~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)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24930,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24929])).
% 2.95/3.14 tff(24931,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 2.95/3.14 inference(transitivity,[status(thm)],[24930, 24928])).
% 2.95/3.14 tff(24932,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24933,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24932, 24931])).
% 2.95/3.14 tff(24934,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24933, 271, 1281, 1067, 1157, 1103])).
% 2.95/3.14 tff(24935,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(24936,plain,
% 2.95/3.14 (~b(s(z), s(s(s(s(z)))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24935, 24927, 1281, 24919])).
% 2.95/3.14 tff(24937,plain,
% 2.95/3.14 (r(s(z), s(s(s(s(z)))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[16482, 24936])).
% 2.95/3.14 tff(24938,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24939,plain,
% 2.95/3.14 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24940,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24939])).
% 2.95/3.14 tff(24941,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.95/3.14 inference(transitivity,[status(thm)],[24940, 24938])).
% 2.95/3.14 tff(24942,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24943,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24942, 24941])).
% 2.95/3.14 tff(24944,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24943, 121, 911, 2327, 24937, 12542])).
% 2.95/3.14 tff(24945,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(24946,plain,
% 2.95/3.14 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24945, 911, 2327, 1281, 1140])).
% 2.95/3.14 tff(24947,plain,
% 2.95/3.14 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[10426, 24946])).
% 2.95/3.14 tff(24948,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~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)))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24949,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24950,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24949, 24948])).
% 2.95/3.14 tff(24951,plain,
% 2.95/3.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24950, 121, 357, 911, 2327])).
% 2.95/3.14 tff(24952,plain,
% 2.95/3.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1167, 21, 24951, 20146])).
% 2.95/3.14 tff(24953,plain,
% 2.95/3.14 (~r(elem!1, s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11254, 357, 2327, 3456])).
% 2.95/3.14 tff(24954,plain,
% 2.95/3.14 (b(elem!1, s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1192, 24953, 1102])).
% 2.95/3.14 tff(24955,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24956,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24957,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24956, 24955])).
% 2.95/3.14 tff(24958,plain,
% 2.95/3.14 (~b(s(s(s(s(z)))), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24957, 271, 24954, 13508, 24952])).
% 2.95/3.14 tff(24959,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24960,plain,
% 2.95/3.14 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24961,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24960])).
% 2.95/3.14 tff(24962,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.14 inference(transitivity,[status(thm)],[24961, 24959])).
% 2.95/3.14 tff(24963,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24964,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24963, 24962])).
% 2.95/3.14 tff(24965,plain,
% 2.95/3.14 (~r(s(s(s(s(z)))), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24964, 121, 357, 3456, 911])).
% 2.95/3.14 tff(24966,plain,
% 2.95/3.14 (((~![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))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(24967,plain,
% 2.95/3.14 ((~![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))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(24968,plain,
% 2.95/3.14 ((~![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)),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[24967, 24966])).
% 2.95/3.14 tff(24969,plain,
% 2.95/3.14 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24968, 21, 24965])).
% 2.95/3.14 tff(24970,plain,
% 2.95/3.14 (s(s(s(s(z)))) = elem!1),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[24969, 24958])).
% 2.95/3.14 tff(24971,plain,
% 2.95/3.14 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24970])).
% 2.95/3.14 tff(24972,plain,
% 2.95/3.14 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[24971])).
% 2.95/3.14 tff(24973,plain,
% 2.95/3.14 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.95/3.14 inference(symmetry,[status(thm)],[24972])).
% 2.95/3.14 tff(24974,plain,
% 2.95/3.14 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[24973])).
% 2.95/3.15 tff(24975,plain,
% 2.95/3.15 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[22629, 24974])).
% 2.95/3.15 tff(24976,plain,
% 2.95/3.15 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(elem!1))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[24971])).
% 2.95/3.15 tff(24977,plain,
% 2.95/3.15 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.95/3.15 inference(symmetry,[status(thm)],[24976])).
% 2.95/3.15 tff(24978,plain,
% 2.95/3.15 (b(s(s(s(s(z)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[24970])).
% 2.95/3.15 tff(24979,plain,
% 2.95/3.15 (b(elem!1, s(elem!1))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[1562, 24978])).
% 2.95/3.15 tff(24980,plain,
% 2.95/3.15 (b(elem!1, s(s(s(s(s(z))))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[24979, 24977])).
% 2.95/3.15 tff(24981,plain,
% 2.95/3.15 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1857, 24980, 257, 24954])).
% 2.95/3.15 tff(24982,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1733, 24981, 24975])).
% 2.95/3.15 tff(24983,plain,((~r(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(24984,plain,
% 2.95/3.15 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[24983, 24947, 412, 3456, 257, 1140, 109, 911, 2327, 357, 1102])).
% 2.95/3.15 tff(24985,plain,
% 2.95/3.15 (r(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1559, 24984, 1517])).
% 2.95/3.15 tff(24986,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(24987,plain,
% 2.95/3.15 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(24988,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[24987])).
% 2.95/3.15 tff(24989,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(transitivity,[status(thm)],[24988, 24986])).
% 2.95/3.15 tff(24990,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(24991,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[24990, 24989])).
% 2.95/3.15 tff(24992,plain,
% 2.95/3.15 (~r(s(s(s(s(z)))), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[24991, 121, 622, 1441, 24985])).
% 2.95/3.15 tff(24993,plain,
% 2.95/3.15 (b(s(s(s(s(z)))), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1095, 24992])).
% 2.95/3.15 tff(24994,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(24995,plain,
% 2.95/3.15 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(24996,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(z)))), z))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[24995])).
% 2.95/3.15 tff(24997,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 2.95/3.15 inference(transitivity,[status(thm)],[24996, 24994])).
% 2.95/3.15 tff(24998,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(24999,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[24998, 24997])).
% 2.95/3.15 tff(25000,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[24999, 271, 1281, 3407, 1067, 1103])).
% 2.95/3.15 tff(25001,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(25002,plain,
% 2.95/3.15 (~b(s(z), s(s(s(s(z)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25001, 24993, 1281, 3407])).
% 2.95/3.15 tff(25003,plain,
% 2.95/3.15 (r(s(z), s(s(s(s(z)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[16482, 25002])).
% 2.95/3.15 tff(25004,plain,
% 2.95/3.15 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[16499, 25003, 24911, 911])).
% 2.95/3.15 tff(25005,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.95/3.15 tff(25006,plain,
% 2.95/3.15 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[25005, 934])).
% 2.95/3.15 tff(25007,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1008, 25006])).
% 2.95/3.15 tff(25008,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(25009,plain,
% 2.95/3.15 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25008, 1008])).
% 2.95/3.15 tff(25010,assumption,(~r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.95/3.15 tff(25011,plain,
% 2.95/3.15 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1000, 21, 25010])).
% 2.95/3.15 tff(25012,plain,
% 2.95/3.15 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25011, 25009])).
% 2.95/3.15 tff(25013,plain,
% 2.95/3.15 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1014, 1008, 1007])).
% 2.95/3.15 tff(25014,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25015,plain,
% 2.95/3.15 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25016,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[25015])).
% 2.95/3.15 tff(25017,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[25016, 25014])).
% 2.95/3.15 tff(25018,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(25019,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[25018, 25017])).
% 2.95/3.15 tff(25020,plain,
% 2.95/3.15 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25019, 271, 2073, 25013, 25012])).
% 2.95/3.15 tff(25021,plain,
% 2.95/3.15 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[10426, 25020])).
% 2.95/3.15 tff(25022,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25023,plain,
% 2.95/3.15 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25024,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[25023])).
% 2.95/3.15 tff(25025,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[25024, 25022])).
% 2.95/3.15 tff(25026,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(25027,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[25026, 25025])).
% 2.95/3.15 tff(25028,plain,
% 2.95/3.15 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25027, 271, 2073, 25013, 25012])).
% 2.95/3.15 tff(25029,plain,
% 2.95/3.15 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1167, 21, 25028, 20146])).
% 2.95/3.15 tff(25030,plain,
% 2.95/3.15 (~r(s(s(s(s(z)))), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[21908, 121, 1140, 25029, 25021])).
% 2.95/3.15 tff(25031,plain,
% 2.95/3.15 (b(s(s(s(s(z)))), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1095, 25030])).
% 2.95/3.15 tff(25032,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25033,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(25034,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[25033, 25032])).
% 2.95/3.15 tff(25035,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25034, 271, 220, 1638, 25031, 25012])).
% 2.95/3.15 tff(25036,plain,((s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(25037,plain,
% 2.95/3.15 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25036, 25004, 220, 1140, 2073, 1008, 24910])).
% 2.95/3.15 tff(25038,plain,
% 2.95/3.15 (r(s(s(s(s(z)))), elem!1)),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[25037, 24907])).
% 2.95/3.15 tff(25039,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25040,plain,
% 2.95/3.15 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25041,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[25040])).
% 2.95/3.15 tff(25042,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.15 inference(transitivity,[status(thm)],[25041, 25039])).
% 2.95/3.15 tff(25043,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(25044,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[25043, 25042])).
% 2.95/3.15 tff(25045,plain,
% 2.95/3.15 (~r(s(s(s(s(z)))), elem!1)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25044, 121, 379, 622, 24985])).
% 2.95/3.15 tff(25046,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25045, 25038])).
% 2.95/3.15 tff(25047,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(25048,plain,
% 2.95/3.15 (~r(s(s(s(s(z)))), s(z))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[25047, 1140, 220, 2505, 2073, 1008, 1281, 3407, 24905, 24903, 379, 412, 3456, 257, 24901, 5675, 357, 1102])).
% 2.95/3.15 tff(25049,plain,
% 2.95/3.15 (b(s(s(s(s(z)))), s(z))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[932, 25048])).
% 2.95/3.15 tff(25050,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25051,plain,
% 2.95/3.15 (((~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), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(25052,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25051])).
% 2.95/3.16 tff(25053,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[25052, 25050])).
% 2.95/3.16 tff(25054,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25055,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25054, 25053])).
% 2.95/3.16 tff(25056,plain,
% 2.95/3.16 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25055, 271, 1281, 447, 25049])).
% 2.95/3.16 tff(25057,plain,
% 2.95/3.16 (~b(s(s(s(s(z)))), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[22548, 25049, 1281, 220])).
% 2.95/3.16 tff(25058,plain,
% 2.95/3.16 (r(s(s(s(s(z)))), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1095, 25057])).
% 2.95/3.16 tff(25059,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25060,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25061,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25060, 25059])).
% 2.95/3.16 tff(25062,plain,
% 2.95/3.16 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25061, 121, 24903, 412, 25058])).
% 2.95/3.16 tff(25063,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1559, 25062, 25056, 1517])).
% 2.95/3.16 tff(25064,plain,((~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (s(s(s(z))) = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(25065,plain,
% 2.95/3.16 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25064, 24897, 1281, 379, 220, 24890, 24782, 24895, 412, 447, 3456, 908, 357, 1101, 1008, 446, 2564, 1326, 2033, 259])).
% 2.95/3.16 tff(25066,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25065, 24893])).
% 2.95/3.16 tff(25067,plain,((s(s(s(z))) = elem!1) | (~b(s(z), z)) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(z), s(elem!1))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (s(s(s(z))) = s(elem!1)) | (elem!1 = z) | r(z, elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(25068,plain,
% 2.95/3.16 (s(s(s(z))) = elem!1),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25067, 24876, 379, 220, 412, 1281, 3456, 24873, 13988, 446, 2564, 1326, 24888, 259, 24887, 147, 24886, 11665, 24874])).
% 2.95/3.16 tff(25069,plain,
% 2.95/3.16 (~(s(s(s(elem!1))) = elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2611, 25068])).
% 2.95/3.16 tff(25070,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[486, 25069, 147])).
% 2.95/3.16 tff(25071,plain,
% 2.95/3.16 (~b(s(s(s(elem!1))), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[7080, 271, 1326, 24886, 25070])).
% 2.95/3.16 tff(25072,plain,
% 2.95/3.16 (r(s(s(s(elem!1))), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[8229, 25071])).
% 2.95/3.16 tff(25073,plain,
% 2.95/3.16 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25068])).
% 2.95/3.16 tff(25074,plain,
% 2.95/3.16 (r(elem!1, s(s(s(elem!1))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[5499, 25073])).
% 2.95/3.16 tff(25075,plain,
% 2.95/3.16 (s(elem!1) = s(s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2605, 25068])).
% 2.95/3.16 tff(25076,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25075])).
% 2.95/3.16 tff(25077,plain,
% 2.95/3.16 (~b(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[7173, 25070, 1326, 24886])).
% 2.95/3.16 tff(25078,plain,
% 2.95/3.16 (r(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[19736, 25077])).
% 2.95/3.16 tff(25079,plain,
% 2.95/3.16 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[7694, 25078, 622, 24878])).
% 2.95/3.16 tff(25080,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[681, 25079, 82])).
% 2.95/3.16 tff(25081,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25080, 25076])).
% 2.95/3.16 tff(25082,plain,
% 2.95/3.16 (b(s(z), s(s(s(s(z)))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[9597, 25075, 446])).
% 2.95/3.16 tff(25083,plain,
% 2.95/3.16 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25075])).
% 2.95/3.16 tff(25084,plain,
% 2.95/3.16 (b(s(s(s(s(z)))), s(z))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[24876, 25083])).
% 2.95/3.16 tff(25085,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25086,plain,
% 2.95/3.16 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25087,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25086])).
% 2.95/3.16 tff(25088,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[25087, 25085])).
% 2.95/3.16 tff(25089,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25090,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25089, 25088])).
% 2.95/3.16 tff(25091,plain,
% 2.95/3.16 (~b(s(z), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25090, 271, 25084, 25082, 25081])).
% 2.95/3.16 tff(25092,plain,
% 2.95/3.16 (r(s(z), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[760, 25091])).
% 2.95/3.16 tff(25093,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25094,plain,
% 2.95/3.16 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25095,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25094])).
% 2.95/3.16 tff(25096,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.95/3.16 inference(transitivity,[status(thm)],[25095, 25093])).
% 2.95/3.16 tff(25097,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25098,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25097, 25096])).
% 2.95/3.16 tff(25099,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25098, 121, 25092, 25074, 3456, 25072])).
% 2.95/3.16 tff(25100,plain,(b(s(z), s(s(s(z)))) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (elem!1 = z) | (s(s(s(elem!1))) = s(s(s(z)))) | (s(elem!1) = s(z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(25101,plain,
% 2.95/3.16 (b(s(z), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25100, 24872, 1326, 5499, 79, 622, 147, 24870, 379, 220, 412, 19197, 2207, 259, 15822, 2282, 1257])).
% 2.95/3.16 tff(25102,plain,
% 2.95/3.16 (~b(s(s(s(z))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[19416, 24837, 19197, 3871])).
% 2.95/3.16 tff(25103,plain,
% 2.95/3.16 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[20471, 24837, 19197, 3871])).
% 2.95/3.16 tff(25104,plain,
% 2.95/3.16 (~r(s(s(s(z))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[21496, 24839, 1, 19197, 412, 1326, 3871, 68, 24834, 220, 25102, 25103, 259])).
% 2.95/3.16 tff(25105,plain,
% 2.95/3.16 (s(s(s(z))) = elem!1),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[255, 25104, 25102])).
% 2.95/3.16 tff(25106,plain,
% 2.95/3.16 (s(elem!1) = s(s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2605, 25105])).
% 2.95/3.16 tff(25107,plain,
% 2.95/3.16 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25106])).
% 2.95/3.16 tff(25108,plain,
% 2.95/3.16 (r(s(s(s(s(z)))), z)),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[412, 25107])).
% 2.95/3.16 tff(25109,plain,
% 2.95/3.16 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25106])).
% 2.95/3.16 tff(25110,plain,
% 2.95/3.16 (r(elem!1, s(s(s(s(z)))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[379, 25109])).
% 2.95/3.16 tff(25111,plain,
% 2.95/3.16 (~r(s(z), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[24849, 232, 19197, 3456, 1326, 220, 379, 412, 259, 231])).
% 2.95/3.16 tff(25112,plain,
% 2.95/3.16 (r(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[23127, 25111, 1, 19197])).
% 2.95/3.16 tff(25113,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25114,plain,
% 2.95/3.16 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25115,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25114])).
% 2.95/3.16 tff(25116,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[25115, 25113])).
% 2.95/3.16 tff(25117,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25118,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25117, 25116])).
% 2.95/3.16 tff(25119,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25118, 121, 25112, 24835, 25110, 25108])).
% 2.95/3.16 tff(25120,plain,(r(s(z), elem!1) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (elem!1 = z) | (~r(elem!1, s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(25121,plain,
% 2.95/3.16 (r(s(z), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25120, 25101, 379, 1, 1326, 412, 68, 220, 259, 24872, 1257])).
% 2.95/3.16 tff(25122,plain,
% 2.95/3.16 (~r(s(elem!1), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[9630, 121, 379, 622, 25121])).
% 2.95/3.16 tff(25123,plain,
% 2.95/3.16 (b(s(elem!1), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[429, 25122, 2282])).
% 2.95/3.16 tff(25124,plain,
% 2.95/3.16 (~b(z, s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[24719, 25123, 220, 19197])).
% 2.95/3.16 tff(25125,plain,
% 2.95/3.16 (r(z, s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1439, 25124])).
% 2.95/3.16 tff(25126,plain,
% 2.95/3.16 (~r(elem!1, z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[24884, 121, 379, 622, 25125])).
% 2.95/3.16 tff(25127,plain,
% 2.95/3.16 (b(elem!1, z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[284, 25126, 259])).
% 2.95/3.16 tff(25128,plain,
% 2.95/3.16 (~b(s(z), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[3964, 25127, 19197, 1326])).
% 2.95/3.16 tff(25129,plain,
% 2.95/3.16 (~(s(s(s(z))) = elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[10599, 25128, 25101])).
% 2.95/3.16 tff(25130,plain,
% 2.95/3.16 (~b(s(s(s(elem!1))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2310, 111, 348, 24869, 9631, 79, 412])).
% 2.95/3.16 tff(25131,plain,
% 2.95/3.16 (r(s(s(s(elem!1))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[16580, 25130])).
% 2.95/3.16 tff(25132,plain,
% 2.95/3.16 (b(s(elem!1), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[429, 9631, 2282])).
% 2.95/3.16 tff(25133,plain,
% 2.95/3.16 (~b(z, s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[24719, 25132, 220, 19197])).
% 2.95/3.16 tff(25134,plain,
% 2.95/3.16 (r(z, s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1439, 25133])).
% 2.95/3.16 tff(25135,plain,
% 2.95/3.16 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[7694, 111, 622, 25134])).
% 2.95/3.16 tff(25136,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[681, 25135, 79])).
% 2.95/3.16 tff(25137,plain,
% 2.95/3.16 (~b(s(z), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[3984, 271, 25132, 24870, 25136])).
% 2.95/3.16 tff(25138,plain,
% 2.95/3.16 (r(s(z), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[760, 25137])).
% 2.95/3.16 tff(25139,plain,
% 2.95/3.16 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[13328, 25138, 5499, 19199, 25131])).
% 2.95/3.16 tff(25140,plain,
% 2.95/3.16 (~b(s(z), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[3964, 261, 19197, 1326])).
% 2.95/3.16 tff(25141,plain,
% 2.95/3.16 (~(s(s(s(z))) = elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[10599, 25140, 3871])).
% 2.95/3.16 tff(25142,plain,
% 2.95/3.16 (~(s(s(s(elem!1))) = elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11073, 111, 24887])).
% 2.95/3.16 tff(25143,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[486, 25142, 147])).
% 2.95/3.16 tff(25144,plain,
% 2.95/3.16 (~b(s(s(s(z))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11686, 25143, 1326, 261, 15822])).
% 2.95/3.16 tff(25145,plain,
% 2.95/3.16 (r(s(s(s(z))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[255, 25144, 25141])).
% 2.95/3.16 tff(25146,plain,
% 2.95/3.16 (~r(s(s(s(z))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[23319, 25145, 24871, 258, 25140])).
% 2.95/3.16 tff(25147,plain,
% 2.95/3.16 (b(s(s(s(z))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2325, 25146])).
% 2.95/3.16 tff(25148,plain,
% 2.95/3.16 (~b(s(s(s(z))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[24796, 25147, 24870, 25132])).
% 2.95/3.16 tff(25149,plain,
% 2.95/3.16 (~r(s(s(s(z))), s(elem!1))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[8370, 121, 379, 622, 25145])).
% 2.95/3.16 tff(25150,plain,
% 2.95/3.16 (s(s(s(z))) = s(elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1816, 25149, 25148])).
% 2.95/3.16 tff(25151,plain,
% 2.95/3.16 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25150])).
% 2.95/3.16 tff(25152,plain,
% 2.95/3.16 (s(s(z)) = elem!1),
% 2.95/3.16 inference(transitivity,[status(thm)],[92, 25151, 70])).
% 2.95/3.16 tff(25153,plain,
% 2.95/3.16 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25152])).
% 2.95/3.16 tff(25154,plain,
% 2.95/3.16 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.95/3.16 inference(symmetry,[status(thm)],[25153])).
% 2.95/3.16 tff(25155,plain,
% 2.95/3.16 (r(s(z), s(s(z)))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[357, 25154])).
% 2.95/3.16 tff(25156,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25157,plain,
% 2.95/3.16 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25158,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25157])).
% 2.95/3.16 tff(25159,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[25158, 25156])).
% 2.95/3.16 tff(25160,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25161,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25160, 25159])).
% 2.95/3.16 tff(25162,plain,
% 2.95/3.16 ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25161, 121])).
% 2.95/3.16 tff(25163,plain,
% 2.95/3.16 (~r(elem!1, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25162, 25155, 24872, 25131])).
% 2.95/3.16 tff(25164,plain,
% 2.95/3.16 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25150])).
% 2.95/3.16 tff(25165,plain,
% 2.95/3.16 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25164])).
% 2.95/3.16 tff(25166,plain,
% 2.95/3.16 (~b(s(s(s(s(z)))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[24371, 111, 3871, 19197, 220])).
% 2.95/3.16 tff(25167,plain,
% 2.95/3.16 (r(s(s(s(s(z)))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[932, 25166])).
% 2.95/3.16 tff(25168,plain,
% 2.95/3.16 (r(s(s(elem!1)), s(z))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25167, 25165])).
% 2.95/3.16 tff(25169,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25170,plain,
% 2.95/3.16 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(25171,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25170])).
% 2.95/3.16 tff(25172,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 2.95/3.16 inference(transitivity,[status(thm)],[25171, 25169])).
% 2.95/3.16 tff(25173,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(25174,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[25173, 25172])).
% 2.95/3.16 tff(25175,plain,
% 2.95/3.16 (~r(elem!1, s(s(elem!1)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25174, 121, 357, 25168, 24872])).
% 2.95/3.16 tff(25176,plain,
% 2.95/3.16 (b(elem!1, s(s(elem!1)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[599, 25175, 68])).
% 2.95/3.16 tff(25177,plain,
% 2.95/3.16 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11908, 25176, 147, 25142, 25163])).
% 2.95/3.16 tff(25178,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[556, 25177, 25139, 1])).
% 2.95/3.16 tff(25179,plain,((~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(25180,plain,
% 2.95/3.16 (~r(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25179, 25121, 147, 5499, 68, 1, 379, 622, 258, 1326, 25127, 348, 412, 25101, 220])).
% 2.95/3.16 tff(25181,plain,
% 2.95/3.16 (r(s(z), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[23127, 25180, 1, 19197])).
% 2.95/3.16 tff(25182,plain,
% 2.95/3.16 (~r(s(s(s(z))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[4112, 25181, 24872, 25121])).
% 2.95/3.16 tff(25183,plain,
% 2.95/3.16 (s(s(s(z))) = s(elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25067, 25182, 379, 220, 412, 19197, 24872, 25121, 19200, 24870, 2207, 1326, 25123, 259, 24887, 147, 25127, 15822, 25129])).
% 2.95/3.16 tff(25184,plain,
% 2.95/3.16 (b(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[19736, 25180])).
% 2.95/3.16 tff(25185,plain,
% 2.95/3.16 (~b(s(s(s(elem!1))), elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[7173, 25184, 1326, 25127])).
% 2.95/3.16 tff(25186,plain,
% 2.95/3.16 (s(s(s(elem!1))) = elem!1),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[486, 25185, 147])).
% 2.95/3.16 tff(25187,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2596, 25186, 25183])).
% 2.95/3.16 tff(25188,plain,((elem!1 = s(z)) | r(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(25189,plain,
% 2.95/3.16 (elem!1 = s(z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[25188, 24868, 9983, 220, 24715, 147, 24428, 1, 5499, 23519, 8563, 24232])).
% 2.95/3.16 tff(25190,plain,
% 2.95/3.16 (s(elem!1) = s(s(z))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25189])).
% 2.95/3.16 tff(25191,plain,
% 2.95/3.16 (s(s(z)) = s(elem!1)),
% 2.95/3.16 inference(symmetry,[status(thm)],[25190])).
% 2.95/3.16 tff(25192,plain,
% 2.95/3.16 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[25191])).
% 2.95/3.16 tff(25193,plain,
% 2.95/3.16 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25192])).
% 2.95/3.17 tff(25194,plain,
% 2.95/3.17 (~b(s(z), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3576, 25189, 317])).
% 2.95/3.17 tff(25195,plain,
% 2.95/3.17 (r(s(z), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[444, 25194, 24232])).
% 2.95/3.17 tff(25196,plain,
% 2.95/3.17 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[17876, 25195, 24715, 220])).
% 2.95/3.17 tff(25197,plain,
% 2.95/3.17 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190])).
% 2.95/3.17 tff(25198,plain,
% 2.95/3.17 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25197])).
% 2.95/3.17 tff(25199,plain,
% 2.95/3.17 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25198])).
% 2.95/3.17 tff(25200,plain,
% 2.95/3.17 (~(s(s(s(s(s(z))))) = s(elem!1))),
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% 2.95/3.17 tff(25201,plain,
% 2.95/3.17 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[4138, 25200, 25196])).
% 2.95/3.17 tff(25202,plain,
% 2.95/3.17 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25201, 25193])).
% 2.95/3.17 tff(25203,plain,
% 2.95/3.17 (s(s(elem!1)) = s(s(s(z)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190])).
% 2.95/3.17 tff(25204,plain,
% 2.95/3.17 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190, 25203])).
% 2.95/3.17 tff(25205,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[242, 25189])).
% 2.95/3.17 tff(25206,plain,
% 2.95/3.17 ((elem!1 = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25189])).
% 2.95/3.17 tff(25207,plain,
% 2.95/3.17 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 2.95/3.17 inference(transitivity,[status(thm)],[25206, 10339])).
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% 2.95/3.17 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25207])).
% 2.95/3.17 tff(25209,plain,
% 2.95/3.17 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.95/3.17 inference(transitivity,[status(thm)],[25208, 160])).
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% 2.95/3.17 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25209])).
% 2.95/3.17 tff(25211,plain,
% 2.95/3.17 (~(s(s(s(z))) = elem!1)),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[97, 25210])).
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% 2.95/3.17 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2063, 24232])).
% 2.95/3.17 tff(25213,plain,
% 2.95/3.17 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[11663, 25212])).
% 2.95/3.17 tff(25214,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[20120, 25205, 19197])).
% 2.95/3.17 tff(25215,plain,
% 2.95/3.17 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25189])).
% 2.95/3.17 tff(25216,plain,
% 2.95/3.17 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.95/3.17 inference(symmetry,[status(thm)],[25215])).
% 2.95/3.17 tff(25217,plain,
% 2.95/3.17 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25203])).
% 2.95/3.17 tff(25218,plain,
% 2.95/3.17 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25217])).
% 2.95/3.17 tff(25219,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25218])).
% 2.95/3.17 tff(25220,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
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% 2.95/3.17 tff(25221,plain,
% 2.95/3.17 (~r(s(s(s(s(z)))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1234, 25189, 147])).
% 2.95/3.17 tff(25222,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[932, 25221])).
% 2.95/3.17 tff(25223,plain,
% 2.95/3.17 (b(s(s(s(elem!1))), elem!1)),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25222, 25220])).
% 2.95/3.17 tff(25224,plain,
% 2.95/3.17 (~b(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[11686, 25223, 24868, 25214, 25213])).
% 2.95/3.17 tff(25225,plain,
% 2.95/3.17 (r(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[255, 25224, 25211])).
% 2.95/3.17 tff(25226,plain,
% 2.95/3.17 (~b(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[7173, 25223, 24868, 25214])).
% 2.95/3.17 tff(25227,plain,
% 2.95/3.17 (r(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[19736, 25226])).
% 2.95/3.17 tff(25228,plain,
% 2.95/3.17 (~b(s(z), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[24371, 25227, 25222, 19197, 220])).
% 2.95/3.17 tff(25229,plain,
% 2.95/3.17 (r(s(z), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[105, 25228])).
% 2.95/3.17 tff(25230,plain,
% 2.95/3.17 (~r(s(elem!1), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3445, 25229, 25195, 25225])).
% 2.95/3.17 tff(25231,plain,
% 2.95/3.17 (~r(s(elem!1), s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[24187, 25230, 25205])).
% 2.95/3.17 tff(25232,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[526, 25231, 211])).
% 2.95/3.17 tff(25233,plain,
% 2.95/3.17 (b(s(s(z)), s(s(s(z))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25232, 25204])).
% 2.95/3.17 tff(25234,plain,
% 2.95/3.17 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190])).
% 2.95/3.17 tff(25235,plain,
% 2.95/3.17 ((s(s(s(z))) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
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% 2.95/3.17 tff(25236,plain,
% 2.95/3.17 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25235])).
% 2.95/3.17 tff(25237,plain,
% 2.95/3.17 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25236])).
% 2.95/3.17 tff(25238,plain,
% 2.95/3.17 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[1136, 25237])).
% 2.95/3.17 tff(25239,plain,
% 2.95/3.17 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25189])).
% 2.95/3.17 tff(25240,plain,
% 2.95/3.17 (r(s(elem!1), s(z))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[8563, 25239])).
% 2.95/3.17 tff(25241,plain,
% 2.95/3.17 (~r(s(s(s(z))), s(elem!1))),
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% 2.95/3.17 tff(25242,plain,
% 2.95/3.17 (b(s(s(s(z))), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1816, 25241, 25238])).
% 2.95/3.17 tff(25243,plain,
% 2.95/3.17 (b(s(s(s(z))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[14223, 25242, 25189])).
% 2.95/3.17 tff(25244,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25191])).
% 2.95/3.17 tff(25245,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25244])).
% 2.95/3.17 tff(25246,plain,
% 2.95/3.17 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25217])).
% 2.95/3.17 tff(25247,plain,
% 2.95/3.17 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190, 25246])).
% 2.95/3.17 tff(25248,plain,
% 2.95/3.17 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.95/3.17 inference(transitivity,[status(thm)],[25247, 10493])).
% 2.95/3.17 tff(25249,plain,
% 2.95/3.17 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25248])).
% 2.95/3.17 tff(25250,plain,
% 2.95/3.17 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
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% 2.95/3.17 tff(25251,plain,
% 2.95/3.17 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25250])).
% 2.95/3.17 tff(25252,plain,
% 2.95/3.17 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25191])).
% 2.95/3.17 tff(25253,plain,
% 2.95/3.17 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25252])).
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% 2.95/3.17 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25253])).
% 2.95/3.17 tff(25255,plain,
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% 2.95/3.17 inference(modus_ponens,[status(thm)],[23520, 25254])).
% 2.95/3.17 tff(25256,plain,
% 2.95/3.17 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25255, 25251])).
% 2.95/3.17 tff(25257,plain,
% 2.95/3.17 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190])).
% 2.95/3.17 tff(25258,plain,
% 2.95/3.17 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25257])).
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% 2.95/3.17 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25258])).
% 2.95/3.17 tff(25260,plain,
% 2.95/3.17 (~b(s(s(s(s(z)))), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[22548, 25222, 19197, 220])).
% 2.95/3.17 tff(25261,plain,
% 2.95/3.17 (r(s(s(s(s(z)))), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1095, 25260])).
% 2.95/3.17 tff(25262,plain,
% 2.95/3.17 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25217])).
% 2.95/3.17 tff(25263,plain,
% 2.95/3.17 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, s(s(s(s(z))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25262])).
% 2.95/3.17 tff(25264,plain,
% 2.95/3.17 (~b(z, s(s(s(s(z)))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25226, 25263])).
% 2.95/3.17 tff(25265,plain,
% 2.95/3.17 (r(z, s(s(s(s(z)))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1119, 21, 25264, 1114])).
% 2.95/3.17 tff(25266,plain,
% 2.95/3.17 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25190])).
% 2.95/3.17 tff(25267,plain,
% 2.95/3.17 (r(s(s(z)), z)),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[24715, 25266])).
% 2.95/3.17 tff(25268,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25269,plain,
% 2.95/3.17 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25270,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25269])).
% 2.95/3.17 tff(25271,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.17 inference(transitivity,[status(thm)],[25270, 25268])).
% 2.95/3.17 tff(25272,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(25273,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25272, 25271])).
% 2.95/3.17 tff(25274,plain,
% 2.95/3.17 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25273, 121, 25267, 25265, 25261])).
% 2.95/3.17 tff(25275,plain,
% 2.95/3.17 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25274, 25259])).
% 2.95/3.17 tff(25276,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1559, 25275, 25256])).
% 2.95/3.17 tff(25277,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(s(z)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25276, 25245])).
% 2.95/3.17 tff(25278,plain,
% 2.95/3.17 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[21892, 271, 25243, 25233, 25277])).
% 2.95/3.17 tff(25279,plain,
% 2.95/3.17 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[10426, 25278])).
% 2.95/3.17 tff(25280,plain,
% 2.95/3.17 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25189])).
% 2.95/3.17 tff(25281,plain,
% 2.95/3.17 (r(s(s(s(z))), s(z))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25225, 25280])).
% 2.95/3.17 tff(25282,plain,
% 2.95/3.17 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25249])).
% 2.95/3.17 tff(25283,plain,
% 2.95/3.17 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25255, 25282])).
% 2.95/3.17 tff(25284,plain,
% 2.95/3.17 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25191])).
% 2.95/3.17 tff(25285,plain,
% 2.95/3.17 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25284])).
% 2.95/3.17 tff(25286,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25287,plain,
% 2.95/3.17 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25288,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25287])).
% 2.95/3.17 tff(25289,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.95/3.17 inference(transitivity,[status(thm)],[25288, 25286])).
% 2.95/3.17 tff(25290,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(25291,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25290, 25289])).
% 2.95/3.17 tff(25292,plain,
% 2.95/3.17 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25291, 121, 25267, 25265, 25261])).
% 2.95/3.17 tff(25293,plain,
% 2.95/3.17 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25292, 25285])).
% 2.95/3.17 tff(25294,plain,
% 2.95/3.17 (b(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1995, 25293, 25283])).
% 2.95/3.17 tff(25295,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25296,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(25297,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25296, 25295])).
% 2.95/3.17 tff(25298,plain,
% 2.95/3.17 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25297, 121, 1736, 2327, 12542])).
% 2.95/3.17 tff(25299,plain,
% 2.95/3.17 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[9512, 25298])).
% 2.95/3.17 tff(25300,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25301,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(25302,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25301, 25300])).
% 2.95/3.17 tff(25303,plain,
% 2.95/3.17 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25302, 121, 1736, 2327, 12542])).
% 2.95/3.17 tff(25304,plain,
% 2.95/3.17 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1777, 25303])).
% 2.95/3.17 tff(25305,plain,
% 2.95/3.17 ($false),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[14690, 25304, 25299, 9894, 14671])).
% 2.95/3.17 tff(25306,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(25307,plain,
% 2.95/3.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25306, 25201, 25294, 25281, 25279])).
% 2.95/3.17 tff(25308,plain,
% 2.95/3.17 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1733, 25307])).
% 2.95/3.17 tff(25309,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25310,plain,
% 2.95/3.17 (((~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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(25311,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25310])).
% 2.95/3.17 tff(25312,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.95/3.17 inference(transitivity,[status(thm)],[25311, 25309])).
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% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
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% 2.95/3.17 inference(modus_ponens,[status(thm)],[25313, 25312])).
% 2.95/3.17 tff(25315,plain,
% 2.95/3.17 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25314, 271, 25308, 25243, 25233])).
% 2.95/3.17 tff(25316,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[25315, 25202])).
% 2.95/3.17 tff(25317,plain,(b(s(elem!1), elem!1) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1) | b(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(25318,plain,
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% 2.95/3.17 tff(25319,plain,
% 2.95/3.17 (~r(z, s(s(s(z))))),
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% 2.95/3.17 tff(25320,plain,
% 2.95/3.17 (b(z, s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1214, 25319])).
% 2.95/3.17 tff(25321,plain,
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% 2.95/3.17 tff(25322,plain,
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% 2.95/3.17 tff(25323,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[299, 243, 25322])).
% 2.95/3.17 tff(25324,plain,
% 2.95/3.17 (~r(s(z), s(s(s(z))))),
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% 2.95/3.17 tff(25325,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[105, 25324])).
% 2.95/3.17 tff(25326,plain,
% 2.95/3.17 (elem!1 = s(s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25120, 25325, 9983, 1, 25321, 412, 25323, 220, 24428, 232, 231])).
% 2.95/3.17 tff(25327,plain,
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% 2.95/3.17 tff(25328,plain,
% 2.95/3.17 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
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% 2.95/3.17 tff(25330,plain,
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% 2.95/3.17 tff(25332,plain,
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% 2.95/3.17 tff(25333,plain,
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% 2.95/3.17 inference(unit_resolution,[status(thm)],[1439, 25332])).
% 2.95/3.17 tff(25334,plain,
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% 2.95/3.17 tff(25336,plain,
% 2.95/3.17 ($false),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12518, 25335, 21162, 3456, 1625])).
% 2.95/3.17 tff(25337,plain,((~b(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(25338,plain,
% 2.95/3.17 (~r(s(z), s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25337, 25334, 19197, 1307, 25325, 25323])).
% 2.95/3.17 tff(25339,plain,
% 2.95/3.17 (b(s(z), s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2167, 25338])).
% 2.95/3.17 tff(25340,plain,
% 2.95/3.17 (~b(s(s(elem!1)), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[17014, 25339, 19197, 220])).
% 2.95/3.17 tff(25341,plain,
% 2.95/3.17 (r(s(s(elem!1)), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2430, 25340])).
% 2.95/3.17 tff(25342,plain,
% 2.95/3.17 (~r(s(s(elem!1)), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[14657, 25341, 412, 25333])).
% 2.95/3.17 tff(25343,plain,
% 2.95/3.17 (b(s(s(elem!1)), s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[701, 25342, 3313])).
% 2.95/3.17 tff(25344,plain,
% 2.95/3.17 (b(elem!1, s(elem!1))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25343, 25328])).
% 2.95/3.17 tff(25345,plain,
% 2.95/3.17 ($false),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[317, 25344])).
% 2.95/3.17 tff(25346,plain,(r(s(z), elem!1) | b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(25347,plain,
% 2.95/3.17 (r(s(z), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25346, 25320, 412, 220, 317, 2618, 1, 24772])).
% 2.95/3.17 tff(25348,plain,
% 2.95/3.17 (b(s(z), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[24832, 24769, 9983, 412, 220, 19197, 25347, 317, 24772, 25321])).
% 2.95/3.17 tff(25349,plain,
% 2.95/3.17 (~b(s(s(s(z))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[21149, 25348, 19197, 25320])).
% 2.95/3.17 tff(25350,plain,
% 2.95/3.17 (r(s(s(s(z))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2325, 25349])).
% 2.95/3.17 tff(25351,plain,
% 2.95/3.17 (~r(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[15964, 25347, 24769, 220, 25320])).
% 2.95/3.17 tff(25352,plain,
% 2.95/3.17 (~b(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[19416, 25348, 19197, 25320])).
% 2.95/3.17 tff(25353,plain,
% 2.95/3.17 (s(s(s(z))) = elem!1),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[255, 25352, 25351])).
% 2.95/3.17 tff(25354,plain,
% 2.95/3.17 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25353])).
% 2.95/3.17 tff(25355,plain,
% 2.95/3.17 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25354])).
% 2.95/3.17 tff(25356,plain,
% 2.95/3.17 (r(s(s(s(z))), s(elem!1))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[9983, 25355])).
% 2.95/3.17 tff(25357,plain,
% 2.95/3.17 (s(elem!1) = s(s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2605, 25353])).
% 2.95/3.17 tff(25358,plain,
% 2.95/3.17 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[25357])).
% 2.95/3.17 tff(25359,plain,
% 2.95/3.17 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 2.95/3.17 inference(symmetry,[status(thm)],[25358])).
% 2.95/3.17 tff(25360,plain,
% 2.95/3.17 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3906, 25353])).
% 2.95/3.17 tff(25361,plain,
% 2.95/3.17 (~b(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[21391, 25360, 1, 19197, 25320, 412, 25351, 24428, 25348])).
% 2.95/3.17 tff(25362,plain,
% 2.95/3.17 (r(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[19736, 25361])).
% 2.95/3.17 tff(25363,plain,
% 2.95/3.17 (~b(s(s(s(s(z)))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[24371, 25362, 25348, 19197, 220])).
% 2.95/3.17 tff(25364,plain,
% 2.95/3.17 (r(s(s(s(s(z)))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[932, 25363])).
% 2.95/3.17 tff(25365,plain,
% 2.95/3.17 (r(s(elem!1), s(z))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[25364, 25359])).
% 2.95/3.17 tff(25366,plain,
% 2.95/3.17 ($false),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[24825, 25365, 25356, 25347, 25350])).
% 2.95/3.17 tff(25367,plain,(b(elem!1, z) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | b(elem!1, s(elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(25368,plain,
% 2.95/3.17 (b(elem!1, z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[25367, 25318, 1, 24715, 317, 220])).
% 2.95/3.17 tff(25369,plain,
% 2.95/3.17 (b(z, elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[24735, 2618, 220, 379, 412, 1281, 24231])).
% 2.95/3.17 tff(25370,plain,
% 2.95/3.17 (~b(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[23570, 147, 25369, 261, 25213, 2618])).
% 2.95/3.17 tff(25371,plain,
% 2.95/3.17 (r(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[255, 907, 25370])).
% 2.95/3.17 tff(25372,plain,
% 2.95/3.17 (r(s(s(elem!1)), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[6824, 223, 145])).
% 2.95/3.18 tff(25373,plain,
% 2.95/3.18 (r(s(z), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[444, 11359, 24232])).
% 2.95/3.18 tff(25374,plain,
% 2.95/3.18 (~r(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3709, 25373, 379, 412])).
% 2.95/3.18 tff(25375,plain,
% 2.95/3.18 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12129, 25374, 25372])).
% 2.95/3.18 tff(25376,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[78, 25375])).
% 2.95/3.18 tff(25377,plain,
% 2.95/3.18 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 2.95/3.18 inference(monotonicity,[status(thm)],[1038])).
% 2.95/3.18 tff(25378,plain,
% 2.95/3.18 (~b(s(s(s(s(z)))), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[22548, 20316, 1281, 220])).
% 2.95/3.18 tff(25379,plain,
% 2.95/3.18 (r(s(s(s(s(z)))), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1095, 25378])).
% 2.95/3.18 tff(25380,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), z)),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25379, 25377])).
% 2.95/3.18 tff(25381,plain,
% 2.95/3.18 (~b(z, s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3747, 271, 2618, 25369, 261])).
% 2.95/3.18 tff(25382,plain,
% 2.95/3.18 (r(z, s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1439, 25381])).
% 2.95/3.18 tff(25383,plain,
% 2.95/3.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[7087, 121, 25382, 412, 25380])).
% 2.95/3.18 tff(25384,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[7075, 271, 2618, 261, 20318])).
% 2.95/3.18 tff(25385,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[681, 25384, 25383, 25376])).
% 2.95/3.18 tff(25386,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | r(s(s(s(elem!1))), elem!1) | b(elem!1, s(elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25387,plain,
% 2.95/3.18 (~(s(z) = elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25386, 25371, 261, 412, 1281, 220, 379, 147, 317, 2618])).
% 2.95/3.18 tff(25388,plain,
% 2.95/3.18 (~(elem!1 = s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[242, 25387])).
% 2.95/3.18 tff(25389,plain,
% 2.95/3.18 (~b(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[20398, 25369, 1281, 220])).
% 2.95/3.18 tff(25390,plain,
% 2.95/3.18 (~b(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3964, 261, 1281, 25369])).
% 2.95/3.18 tff(25391,plain,
% 2.95/3.18 (~r(s(elem!1), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[23287, 25387, 379, 25389, 25390])).
% 2.95/3.18 tff(25392,plain,
% 2.95/3.18 (b(s(elem!1), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[429, 25391, 24233])).
% 2.95/3.18 tff(25393,plain,
% 2.95/3.18 (~r(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3709, 431, 379, 412])).
% 2.95/3.18 tff(25394,plain,
% 2.95/3.18 (b(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[299, 25393, 258])).
% 2.95/3.18 tff(25395,plain,
% 2.95/3.18 (~b(s(z), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4775, 25394, 1326, 261])).
% 2.95/3.18 tff(25396,plain,
% 2.95/3.18 (r(s(z), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25, 25395])).
% 2.95/3.18 tff(25397,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4611, 121, 1441, 25396, 412, 431])).
% 2.95/3.18 tff(25398,plain,((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25399,plain,
% 2.95/3.18 (~r(s(z), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25398, 25388, 379, 412, 25382, 25369, 261])).
% 2.95/3.18 tff(25400,plain,
% 2.95/3.18 (b(s(z), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[444, 25399, 24232])).
% 2.95/3.18 tff(25401,plain,
% 2.95/3.18 (r(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[236, 25387, 25390])).
% 2.95/3.18 tff(25402,plain,
% 2.95/3.18 (r(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[299, 25388, 25389])).
% 2.95/3.18 tff(25403,plain,
% 2.95/3.18 (~r(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4112, 25402, 25371, 25401])).
% 2.95/3.18 tff(25404,plain,
% 2.95/3.18 (b(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[105, 25403])).
% 2.95/3.18 tff(25405,plain,
% 2.95/3.18 (~r(s(s(s(z))), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[23319, 17770, 1242, 294, 258])).
% 2.95/3.18 tff(25406,plain,
% 2.95/3.18 (b(s(s(s(z))), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2325, 25405])).
% 2.95/3.18 tff(25407,plain,
% 2.95/3.18 (~b(s(s(s(z))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[24796, 25406, 446, 447])).
% 2.95/3.18 tff(25408,plain,
% 2.95/3.18 (~b(s(elem!1), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3622, 25406, 3871, 447])).
% 2.95/3.18 tff(25409,plain,
% 2.95/3.18 (r(s(elem!1), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2044, 25408, 8606])).
% 2.95/3.18 tff(25410,plain,
% 2.95/3.18 (~b(z, s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[15813, 25406, 220, 3871])).
% 2.95/3.18 tff(25411,plain,
% 2.95/3.18 (r(z, s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1214, 25410])).
% 2.95/3.18 tff(25412,plain,
% 2.95/3.18 (~r(s(s(s(z))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3865, 25411, 412, 25409])).
% 2.95/3.18 tff(25413,plain,
% 2.95/3.18 (s(s(s(z))) = s(elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1816, 25412, 25407])).
% 2.95/3.18 tff(25414,plain,
% 2.95/3.18 (s(elem!1) = s(s(s(z)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25413, 3547])).
% 2.95/3.18 tff(25415,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[8606, 25414])).
% 2.95/3.18 tff(25416,plain,(b(s(s(s(z))), elem!1) | (~r(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | b(s(z), elem!1) | b(elem!1, s(z)) | (elem!1 = s(z)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25417,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25416, 25404, 25400, 412, 25370, 25392, 220, 25390, 25389, 25388, 907, 2618])).
% 2.95/3.18 tff(25418,plain,((s(s(s(z))) = elem!1) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), z)) | r(s(s(s(elem!1))), elem!1) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25419,plain,
% 2.95/3.18 (s(s(s(z))) = elem!1),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25418, 25318, 220, 24715, 9983, 25368, 19197, 147, 317])).
% 2.95/3.18 tff(25420,plain,
% 2.95/3.18 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3906, 25419])).
% 2.95/3.18 tff(25421,plain,
% 2.95/3.18 (~(s(s(elem!1)) = elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[197, 25420])).
% 2.95/3.18 tff(25422,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[78, 25420])).
% 2.95/3.18 tff(25423,plain,
% 2.95/3.18 (s(elem!1) = s(s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2605, 25419])).
% 2.95/3.18 tff(25424,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25423])).
% 2.95/3.18 tff(25425,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25424])).
% 2.95/3.18 tff(25426,plain,
% 2.95/3.18 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25425])).
% 2.95/3.18 tff(25427,plain,
% 2.95/3.18 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25423])).
% 2.95/3.18 tff(25428,plain,
% 2.95/3.18 (b(s(s(s(s(z)))), elem!1)),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25318, 25427])).
% 2.95/3.18 tff(25429,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2611, 25419])).
% 2.95/3.18 tff(25430,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[486, 25429, 147])).
% 2.95/3.18 tff(25431,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(25432,plain,
% 2.95/3.18 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(25433,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25432])).
% 2.95/3.18 tff(25434,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25433, 25431])).
% 2.95/3.18 tff(25435,plain,
% 2.95/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(25436,plain,
% 2.95/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25435, 25434])).
% 2.95/3.18 tff(25437,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25436, 271, 25368, 25430, 25428])).
% 2.95/3.18 tff(25438,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25437, 25426])).
% 2.95/3.18 tff(25439,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[681, 25438, 25422])).
% 2.95/3.18 tff(25440,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25419])).
% 2.95/3.18 tff(25441,plain,
% 2.95/3.18 (r(elem!1, s(s(s(elem!1))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[5499, 25440])).
% 2.95/3.18 tff(25442,plain,
% 2.95/3.18 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25423])).
% 2.95/3.18 tff(25443,plain,
% 2.95/3.18 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25442])).
% 2.95/3.18 tff(25444,plain,
% 2.95/3.18 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25423])).
% 2.95/3.18 tff(25445,plain,
% 2.95/3.18 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25444])).
% 2.95/3.18 tff(25446,plain,
% 2.95/3.18 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25445])).
% 2.95/3.18 tff(25447,plain,
% 2.95/3.18 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25446, 25443])).
% 2.95/3.18 tff(25448,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25419])).
% 2.95/3.18 tff(25449,plain,
% 2.95/3.18 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25448])).
% 2.95/3.18 tff(25450,plain,
% 2.95/3.18 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25423])).
% 2.95/3.18 tff(25451,plain,
% 2.95/3.18 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25450, 25449])).
% 2.95/3.18 tff(25452,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[9983, 25451])).
% 2.95/3.18 tff(25453,plain,
% 2.95/3.18 (b(z, elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[24735, 25318, 220, 9983, 24715, 19197, 24231])).
% 2.95/3.18 tff(25454,plain,
% 2.95/3.18 (~b(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3964, 25368, 19197, 25453])).
% 2.95/3.18 tff(25455,plain,
% 2.95/3.18 (~b(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[10599, 25419, 25454])).
% 2.95/3.18 tff(25456,plain,
% 2.95/3.18 (r(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[105, 25455])).
% 2.95/3.18 tff(25457,plain,
% 2.95/3.18 (r(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[250, 25456, 25419])).
% 2.95/3.18 tff(25458,plain,
% 2.95/3.18 (r(s(z), elem!1) <=> r(s(z), s(z))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[239])).
% 2.95/3.18 tff(25459,plain,
% 2.95/3.18 (r(s(z), s(z)) <=> r(s(z), elem!1)),
% 2.95/3.18 inference(symmetry,[status(thm)],[25458])).
% 2.95/3.18 tff(25460,plain,
% 2.95/3.18 ((~r(s(z), s(z))) <=> (~r(s(z), elem!1))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25459])).
% 2.95/3.18 tff(25461,plain,
% 2.95/3.18 (~r(s(z), elem!1)),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[11590, 25460])).
% 2.95/3.18 tff(25462,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[357, 25461])).
% 2.95/3.18 tff(25463,plain,((~(elem!1 = s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25464,plain,
% 2.95/3.18 (~(elem!1 = s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25463, 25457])).
% 2.95/3.18 tff(25465,plain,
% 2.95/3.18 (~(s(z) = elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1221, 25464])).
% 2.95/3.18 tff(25466,plain,
% 2.95/3.18 (~(s(s(z)) = s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[960, 25465])).
% 2.95/3.18 tff(25467,plain,
% 2.95/3.18 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[953, 25466])).
% 2.95/3.18 tff(25468,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[946, 25467])).
% 2.95/3.18 tff(25469,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1014, 25437, 25468])).
% 2.95/3.18 tff(25470,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(25471,plain,
% 2.95/3.18 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(25472,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25471])).
% 2.95/3.18 tff(25473,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25472, 25470])).
% 2.95/3.18 tff(25474,plain,
% 2.95/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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))))))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(25475,plain,
% 2.95/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25474, 25473])).
% 2.95/3.18 tff(25476,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25475, 121, 1758, 5499, 18818, 13550])).
% 2.95/3.18 tff(25477,plain,((~r(s(s(s(s(z)))), s(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))))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25478,plain,
% 2.95/3.18 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25477, 25469, 5499, 25452])).
% 2.95/3.18 tff(25479,plain,
% 2.95/3.18 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1777, 25478])).
% 2.95/3.18 tff(25480,plain,
% 2.95/3.18 (b(s(elem!1), s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25479, 25447])).
% 2.95/3.18 tff(25481,plain,
% 2.95/3.18 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25444])).
% 2.95/3.18 tff(25482,plain,
% 2.95/3.18 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25481])).
% 2.95/3.18 tff(25483,plain,
% 2.95/3.18 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25419])).
% 2.95/3.18 tff(25484,plain,
% 2.95/3.18 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.95/3.18 inference(transitivity,[status(thm)],[25483, 1836])).
% 2.95/3.18 tff(25485,plain,
% 2.95/3.18 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25484, 1837])).
% 2.95/3.18 tff(25486,plain,
% 2.95/3.18 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25485])).
% 2.95/3.18 tff(25487,plain,
% 2.95/3.18 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[1489, 25486])).
% 2.95/3.18 tff(25488,plain,
% 2.95/3.18 (~b(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[20398, 25453, 19197, 220])).
% 2.95/3.18 tff(25489,plain,
% 2.95/3.18 (r(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[299, 25464, 25488])).
% 2.95/3.18 tff(25490,plain,
% 2.95/3.18 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25444])).
% 2.95/3.18 tff(25491,plain,
% 2.95/3.18 (~b(z, s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3747, 271, 25318, 25453, 25368])).
% 2.95/3.18 tff(25492,plain,
% 2.95/3.18 (r(z, s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1439, 25491])).
% 2.95/3.18 tff(25493,plain,
% 2.95/3.18 (~r(s(z), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25398, 25464, 9983, 24715, 25492, 25453, 25368])).
% 2.95/3.18 tff(25494,plain,
% 2.95/3.18 (b(s(z), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[444, 25493, 24232])).
% 2.95/3.18 tff(25495,plain,
% 2.95/3.18 (~b(s(s(elem!1)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[22224, 25494, 19197, 3313, 220, 24715, 25318, 25492])).
% 2.95/3.18 tff(25496,plain,
% 2.95/3.18 (r(s(s(elem!1)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2143, 25495])).
% 2.95/3.18 tff(25497,plain,
% 2.95/3.18 (r(s(s(s(s(s(z))))), s(z))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25496, 25490])).
% 2.95/3.18 tff(25498,plain,
% 2.95/3.18 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[16014, 25497, 25489, 25457])).
% 2.95/3.18 tff(25499,plain,
% 2.95/3.18 (b(elem!1, s(s(s(s(s(z))))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1847, 25498, 25487])).
% 2.95/3.18 tff(25500,plain,
% 2.95/3.18 (b(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25499, 25482])).
% 2.95/3.18 tff(25501,plain,
% 2.95/3.18 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[14419, 25500, 25480, 25318])).
% 2.95/3.18 tff(25502,plain,
% 2.95/3.18 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[556, 25501, 1])).
% 2.95/3.18 tff(25503,plain,
% 2.95/3.18 (~r(s(s(elem!1)), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[10103, 25502, 25441, 25439])).
% 2.95/3.18 tff(25504,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[7080, 271, 25453, 25368, 25430])).
% 2.95/3.18 tff(25505,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[8229, 25504])).
% 2.95/3.18 tff(25506,plain,
% 2.95/3.18 (~r(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[6850, 25439, 24715, 25505])).
% 2.95/3.18 tff(25507,plain,
% 2.95/3.18 (b(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2106, 25506])).
% 2.95/3.18 tff(25508,plain,
% 2.95/3.18 (~b(s(s(elem!1)), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2222, 25507, 25500, 25453])).
% 2.95/3.18 tff(25509,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[862, 25508, 25503, 25421])).
% 2.95/3.18 tff(25510,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25511,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25510, 317, 5499, 220, 1])).
% 2.95/3.18 tff(25512,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3821, 121, 379, 684, 139, 412])).
% 2.95/3.18 tff(25513,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25514,plain,
% 2.95/3.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25513, 25511, 9983, 24715])).
% 2.95/3.18 tff(25515,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[681, 24767, 25514])).
% 2.95/3.18 tff(25516,plain,
% 2.95/3.18 (~r(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[9637, 25515, 9983, 24232, 25511, 8563])).
% 2.95/3.18 tff(25517,plain,
% 2.95/3.18 (s(z) = elem!1),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[236, 25516, 24866])).
% 2.95/3.18 tff(25518,plain,
% 2.95/3.18 (s(s(z)) = s(elem!1)),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25517])).
% 2.95/3.18 tff(25519,plain,
% 2.95/3.18 (s(s(s(z))) = s(s(elem!1))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25518])).
% 2.95/3.18 tff(25520,plain,
% 2.95/3.18 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25519])).
% 2.95/3.18 tff(25521,plain,
% 2.95/3.18 (~b(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3964, 261, 1281, 1326])).
% 2.95/3.18 tff(25522,plain,
% 2.95/3.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25513, 139, 379, 412])).
% 2.95/3.18 tff(25523,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[9637, 1244, 379, 348, 139, 622])).
% 2.95/3.18 tff(25524,plain,
% 2.95/3.18 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[681, 25523, 25522])).
% 2.95/3.18 tff(25525,plain,
% 2.95/3.18 (~r(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4112, 1244, 9232, 108])).
% 2.95/3.18 tff(25526,plain,
% 2.95/3.18 (~r(s(s(s(z))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[24754, 25525, 379, 412, 259, 1326, 907])).
% 2.95/3.18 tff(25527,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[23458, 25526, 25524, 5499])).
% 2.95/3.18 tff(25528,plain,((s(z) = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25529,plain,
% 2.95/3.18 (s(z) = elem!1),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25528, 108, 379, 412, 259, 1326, 907, 5499, 348, 139, 622, 294, 25521])).
% 2.95/3.18 tff(25530,plain,
% 2.95/3.18 (s(s(z)) = s(elem!1)),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25529])).
% 2.95/3.18 tff(25531,plain,
% 2.95/3.18 (s(s(s(z))) = s(s(elem!1))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25530])).
% 2.95/3.18 tff(25532,plain,
% 2.95/3.18 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25531])).
% 2.95/3.18 tff(25533,plain,
% 2.95/3.18 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25532])).
% 2.95/3.18 tff(25534,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25531])).
% 2.95/3.18 tff(25535,plain,
% 2.95/3.18 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[5499, 25534])).
% 2.95/3.18 tff(25536,plain,
% 2.95/3.18 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25529])).
% 2.95/3.18 tff(25537,plain,
% 2.95/3.18 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.95/3.18 inference(symmetry,[status(thm)],[25536])).
% 2.95/3.18 tff(25538,plain,
% 2.95/3.18 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25531])).
% 2.95/3.18 tff(25539,plain,
% 2.95/3.18 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25538, 25537])).
% 2.95/3.18 tff(25540,plain,
% 2.95/3.18 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25529])).
% 2.95/3.18 tff(25541,plain,
% 2.95/3.18 (r(elem!1, s(s(s(z))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[108, 25540])).
% 2.95/3.18 tff(25542,plain,
% 2.95/3.18 (r(s(z), s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25541, 25539])).
% 2.95/3.18 tff(25543,plain,
% 2.95/3.18 (~r(s(z), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[16699, 25535, 139, 25542])).
% 2.95/3.18 tff(25544,plain,
% 2.95/3.18 (b(s(z), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[760, 25543])).
% 2.95/3.18 tff(25545,plain,
% 2.95/3.18 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25531])).
% 2.95/3.18 tff(25546,plain,
% 2.95/3.18 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25545])).
% 2.95/3.18 tff(25547,plain,
% 2.95/3.18 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.18 inference(transitivity,[status(thm)],[25546, 200])).
% 2.95/3.18 tff(25548,plain,
% 2.95/3.18 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25547])).
% 2.95/3.18 tff(25549,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[19205, 25548])).
% 2.95/3.18 tff(25550,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[681, 25549, 25522])).
% 2.95/3.18 tff(25551,plain,
% 2.95/3.18 (~b(z, s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[21846, 25550, 1281, 25544])).
% 2.95/3.18 tff(25552,plain,
% 2.95/3.18 (r(z, s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[19736, 25551])).
% 2.95/3.18 tff(25553,plain,
% 2.95/3.18 (~r(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3425, 25552, 139, 25535])).
% 2.95/3.18 tff(25554,plain,
% 2.95/3.18 (b(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2106, 25553])).
% 2.95/3.18 tff(25555,plain,
% 2.95/3.18 (b(z, s(s(s(z))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25554, 25533])).
% 2.95/3.18 tff(25556,plain,
% 2.95/3.18 (r(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25541, 25538])).
% 2.95/3.18 tff(25557,plain,
% 2.95/3.18 (~r(s(s(elem!1)), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2670, 25556, 139, 25535])).
% 2.95/3.18 tff(25558,plain,
% 2.95/3.18 (~r(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[14112, 25557, 25529])).
% 2.95/3.18 tff(25559,plain,
% 2.95/3.18 (b(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[255, 25558, 907])).
% 2.95/3.18 tff(25560,plain,
% 2.95/3.18 (~b(z, s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1334, 25559, 1326, 261])).
% 2.95/3.18 tff(25561,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25560, 25555])).
% 2.95/3.18 tff(25562,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = z) | (s(z) = s(elem!1)) | (~r(s(elem!1), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25563,plain,
% 2.95/3.18 (~r(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25562, 24865, 24739, 25511, 907, 19197, 5499, 9983, 24715, 24428, 24232, 8563, 24740])).
% 2.95/3.18 tff(25564,plain,
% 2.95/3.18 (b(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[105, 25563])).
% 2.95/3.18 tff(25565,plain,
% 2.95/3.18 (elem!1 = s(z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1221, 25517])).
% 2.95/3.18 tff(25566,plain,
% 2.95/3.18 (b(elem!1, s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[11114, 25565, 25564])).
% 2.95/3.18 tff(25567,plain,
% 2.95/3.18 (b(elem!1, s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[25566, 25520])).
% 2.95/3.18 tff(25568,plain,
% 2.95/3.18 (~b(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2238, 25567, 9983, 8563, 24739, 24768])).
% 2.95/3.18 tff(25569,plain,
% 2.95/3.18 (r(z, s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[23127, 25563, 1, 19197])).
% 2.95/3.18 tff(25570,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[25519])).
% 2.95/3.18 tff(25571,plain,
% 2.95/3.18 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[5499, 25570])).
% 2.95/3.18 tff(25572,plain,
% 2.95/3.18 (~r(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3425, 25571, 25511, 25569])).
% 2.95/3.18 tff(25573,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2106, 25572, 25568])).
% 2.95/3.18 tff(25574,plain,((s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(25575,plain,
% 2.95/3.18 (s(s(s(z))) = elem!1),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25574, 2467, 5499, 1, 220, 317])).
% 2.95/3.18 tff(25576,plain,
% 2.95/3.18 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3906, 25575])).
% 2.95/3.18 tff(25577,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[78, 25576])).
% 2.95/3.18 tff(25578,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[681, 25577, 25514])).
% 2.95/3.18 tff(25579,plain,
% 2.95/3.18 (~r(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[9637, 25578, 9983, 24232, 25511, 8563])).
% 2.95/3.18 tff(25580,plain,
% 2.95/3.18 (~r(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[250, 25579, 25575])).
% 2.95/3.18 tff(25581,plain,
% 2.95/3.18 (b(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[105, 25580])).
% 2.95/3.18 tff(25582,plain,
% 2.95/3.18 (b(s(z), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[10599, 25581, 25575])).
% 2.95/3.18 tff(25583,plain,
% 2.95/3.18 (~b(elem!1, z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12145, 25582, 220, 24739])).
% 2.95/3.18 tff(25584,plain,
% 2.95/3.18 (~(s(z) = elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[20120, 25583, 19197])).
% 2.95/3.18 tff(25585,plain,
% 2.95/3.18 (~(elem!1 = s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[242, 25584])).
% 2.95/3.18 tff(25586,plain,
% 2.95/3.18 (~r(elem!1, s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[25120, 25584, 9983, 1, 24739, 24715, 25576, 220, 24428, 25581, 25579])).
% 2.95/3.18 tff(25587,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[299, 25586, 25585, 24740])).
% 2.95/3.18 tff(25588,plain,(b(s(elem!1), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25589,plain,
% 2.95/3.19 (b(s(elem!1), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25588, 317, 220, 5499, 1])).
% 2.95/3.19 tff(25590,plain,
% 2.95/3.19 (b(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25367, 25589, 1, 24715, 317, 220])).
% 2.95/3.19 tff(25591,plain,
% 2.95/3.19 (~b(s(z), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3964, 25590, 19197, 24739])).
% 2.95/3.19 tff(25592,plain,
% 2.95/3.19 (~r(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23287, 231, 379, 294, 1242])).
% 2.95/3.19 tff(25593,plain,
% 2.95/3.19 (b(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[429, 25592, 2282])).
% 2.95/3.19 tff(25594,plain,
% 2.95/3.19 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3823, 25593, 379, 139, 412, 1244])).
% 2.95/3.19 tff(25595,plain,
% 2.95/3.19 (r(s(s(s(z))), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23458, 25594, 5499])).
% 2.95/3.19 tff(25596,plain,
% 2.95/3.19 (r(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[24754, 25595, 379, 412, 259, 1326, 907])).
% 2.95/3.19 tff(25597,plain,
% 2.95/3.19 (~r(s(z), s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[4112, 25596, 9232, 1244])).
% 2.95/3.19 tff(25598,plain,
% 2.95/3.19 (~r(s(z), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3709, 9232, 379, 412])).
% 2.95/3.19 tff(25599,plain,
% 2.95/3.19 (b(s(z), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[444, 25598, 348])).
% 2.95/3.19 tff(25600,plain,
% 2.95/3.19 (elem!1 = s(s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[78, 25594])).
% 2.95/3.19 tff(25601,plain,
% 2.95/3.19 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3917, 25600, 348])).
% 2.95/3.19 tff(25602,plain,
% 2.95/3.19 (~b(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23566, 25601, 2618, 1326, 261])).
% 2.95/3.19 tff(25603,plain,
% 2.95/3.19 (~b(s(z), s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25416, 25602, 412, 2618, 1242, 220, 25593, 294, 243, 907, 25599])).
% 2.95/3.19 tff(25604,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[105, 25603, 25597])).
% 2.95/3.19 tff(25605,plain,((s(z) = elem!1) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | b(s(z), elem!1) | (~b(z, s(z))) | b(elem!1, s(z)) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(elem!1))) | (elem!1 = z) | (s(z) = s(elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25606,plain,
% 2.95/3.19 (s(z) = elem!1),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25605, 907, 2618, 1242, 220, 294, 412, 1326, 261, 379, 259, 348, 5499, 139])).
% 2.95/3.19 tff(25607,plain,
% 2.95/3.19 (s(s(z)) = s(elem!1)),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25606])).
% 2.95/3.19 tff(25608,plain,
% 2.95/3.19 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25607])).
% 2.95/3.19 tff(25609,plain,
% 2.95/3.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.95/3.19 inference(transitivity,[status(thm)],[25608, 3535])).
% 2.95/3.19 tff(25610,plain,
% 2.95/3.19 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25609])).
% 2.95/3.19 tff(25611,plain,
% 2.95/3.19 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[1136, 25610])).
% 2.95/3.19 tff(25612,plain,
% 2.95/3.19 (~b(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23566, 25611, 2618, 1326, 261])).
% 2.95/3.19 tff(25613,plain,
% 2.95/3.19 (r(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[255, 25612, 907])).
% 2.95/3.19 tff(25614,plain,
% 2.95/3.19 (r(s(s(elem!1)), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[14112, 25613, 25606])).
% 2.95/3.19 tff(25615,plain,
% 2.95/3.19 (s(s(s(z))) = s(s(elem!1))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25607])).
% 2.95/3.19 tff(25616,plain,
% 2.95/3.19 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25615])).
% 2.95/3.19 tff(25617,plain,
% 2.95/3.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[5499, 25616])).
% 2.95/3.19 tff(25618,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[13178, 121, 379, 25617, 139, 25614])).
% 2.95/3.19 tff(25619,plain,((s(s(s(z))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(s(z), elem!1) | (~b(z, s(z))) | b(elem!1, s(z)) | (~r(s(elem!1), z)) | (elem!1 = z) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25620,plain,
% 2.95/3.19 (s(s(s(z))) = elem!1),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25619, 9983, 25511, 25589, 24739, 25590, 5499, 25591, 220, 24740, 24715, 24428, 24232])).
% 2.95/3.19 tff(25621,plain,
% 2.95/3.19 (~b(s(z), s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[10599, 25620, 25591])).
% 2.95/3.19 tff(25622,plain,
% 2.95/3.19 (r(s(z), s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[105, 25621])).
% 2.95/3.19 tff(25623,plain,
% 2.95/3.19 (r(s(z), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[250, 25622, 25620])).
% 2.95/3.19 tff(25624,plain,
% 2.95/3.19 (~(elem!1 = s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25463, 25623])).
% 2.95/3.19 tff(25625,plain,
% 2.95/3.19 (~(s(z) = elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1221, 25624])).
% 2.95/3.19 tff(25626,plain,
% 2.95/3.19 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3906, 25620])).
% 2.95/3.19 tff(25627,plain,
% 2.95/3.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[78, 25626])).
% 2.95/3.19 tff(25628,plain,
% 2.95/3.19 (~b(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3823, 25623, 9983, 25511, 24715, 25627])).
% 2.95/3.19 tff(25629,plain,
% 2.95/3.19 (r(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[429, 25628, 24233])).
% 2.95/3.19 tff(25630,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23287, 25629, 25625, 9983, 24740, 25591])).
% 2.95/3.19 tff(25631,plain,(b(elem!1, s(elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25632,plain,
% 2.95/3.19 (b(elem!1, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25631, 5499, 220, 1])).
% 2.95/3.19 tff(25633,plain,
% 2.95/3.19 (~(z = elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[500, 24230])).
% 2.95/3.19 tff(25634,plain,
% 2.95/3.19 (~(elem!1 = z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[333, 25633])).
% 2.95/3.19 tff(25635,plain,
% 2.95/3.19 (r(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[429, 22133, 24234])).
% 2.95/3.19 tff(25636,plain,
% 2.95/3.19 (r(s(z), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[444, 22132, 24236])).
% 2.95/3.19 tff(25637,plain,
% 2.95/3.19 (~b(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[402, 11211, 25632, 220])).
% 2.95/3.19 tff(25638,plain,
% 2.95/3.19 (r(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[284, 259, 25637])).
% 2.95/3.19 tff(25639,plain,
% 2.95/3.19 (~b(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[402, 394, 307, 220])).
% 2.95/3.19 tff(25640,plain,
% 2.95/3.19 (r(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[284, 3328, 25639])).
% 2.95/3.19 tff(25641,plain,
% 2.95/3.19 (~(s(z) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[343, 2489])).
% 2.95/3.19 tff(25642,plain,
% 2.95/3.19 (r(s(z), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[444, 25641, 24382])).
% 2.95/3.19 tff(25643,plain,
% 2.95/3.19 (~(s(elem!1) = s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[350, 25641])).
% 2.95/3.19 tff(25644,plain,
% 2.95/3.19 (r(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[429, 25643, 24380])).
% 2.95/3.19 tff(25645,plain,
% 2.95/3.19 (~(s(z) = elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1276, 24382, 307])).
% 2.95/3.19 tff(25646,plain,
% 2.95/3.19 (~r(s(z), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23821, 8448, 25640, 25642])).
% 2.95/3.19 tff(25647,plain,
% 2.95/3.19 (b(s(z), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[236, 25646, 25645])).
% 2.95/3.19 tff(25648,plain,
% 2.95/3.19 (~r(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[10721, 3871, 220, 307, 394, 259, 378])).
% 2.95/3.19 tff(25649,plain,
% 2.95/3.19 (~b(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[24003, 3871, 307, 260])).
% 2.95/3.19 tff(25650,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[255, 25649, 25648, 907])).
% 2.95/3.19 tff(25651,plain,((~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25652,plain,
% 2.95/3.19 (~b(s(z), s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25651, 25647, 307, 907, 220, 394, 3328, 3379])).
% 2.95/3.19 tff(25653,plain,
% 2.95/3.19 (r(s(z), s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[105, 25652])).
% 2.95/3.19 tff(25654,plain,
% 2.95/3.19 (~r(s(s(s(z))), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23235, 25653, 25644, 25642])).
% 2.95/3.19 tff(25655,plain,
% 2.95/3.19 (b(z, s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[19736, 6933])).
% 2.95/3.19 tff(25656,plain,
% 2.95/3.19 (~r(s(s(s(elem!1))), z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[13798, 121, 378, 1409, 139])).
% 2.95/3.19 tff(25657,plain,
% 2.95/3.19 (b(s(s(s(elem!1))), z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[8229, 25656])).
% 2.95/3.19 tff(25658,plain,
% 2.95/3.19 (s(elem!1) = s(s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[22147, 25657, 1281, 2282, 394, 25655])).
% 2.95/3.19 tff(25659,plain,
% 2.95/3.19 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[84, 25658])).
% 2.95/3.19 tff(25660,plain,
% 2.95/3.19 (elem!1 = s(s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[78, 25659])).
% 2.95/3.19 tff(25661,plain,
% 2.95/3.19 (s(elem!1) = s(s(s(elem!1)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25660])).
% 2.95/3.19 tff(25662,plain,
% 2.95/3.19 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25661])).
% 2.95/3.19 tff(25663,plain,
% 2.95/3.19 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 2.95/3.19 inference(symmetry,[status(thm)],[25662])).
% 2.95/3.19 tff(25664,plain,
% 2.95/3.19 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(elem!1)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25663])).
% 2.95/3.19 tff(25665,plain,
% 2.95/3.19 (~r(z, s(elem!1))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[6933, 25664])).
% 2.95/3.19 tff(25666,plain,
% 2.95/3.19 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3917, 25660, 348])).
% 2.95/3.19 tff(25667,plain,
% 2.95/3.19 (b(s(s(s(z))), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1816, 25666, 1510])).
% 2.95/3.19 tff(25668,plain,
% 2.95/3.19 (~b(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3288, 25667, 307, 394])).
% 2.95/3.19 tff(25669,plain,
% 2.95/3.19 (r(s(s(s(z))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[255, 25668, 907])).
% 2.95/3.19 tff(25670,plain,
% 2.95/3.19 (~b(elem!1, s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1811, 25667, 307, 394])).
% 2.95/3.19 tff(25671,plain,
% 2.95/3.19 (r(elem!1, s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1192, 25670, 1101])).
% 2.95/3.19 tff(25672,plain,
% 2.95/3.19 (~r(z, s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[6723, 25671, 378, 25669])).
% 2.95/3.19 tff(25673,plain,
% 2.95/3.19 (b(z, s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1214, 25672])).
% 2.95/3.19 tff(25674,plain,
% 2.95/3.19 (~b(z, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[19710, 25673, 394, 25667])).
% 2.95/3.19 tff(25675,plain,
% 2.95/3.19 (r(z, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1439, 25674])).
% 2.95/3.19 tff(25676,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25675, 25665])).
% 2.95/3.19 tff(25677,plain,((~r(z, elem!1)) | (~b(s(elem!1), z)) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(elem!1))) | r(s(s(s(z))), s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25678,plain,
% 2.95/3.19 (~r(s(s(s(elem!1))), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25677, 25654, 307, 394, 907, 25641, 1281, 3379, 25640])).
% 2.95/3.19 tff(25679,plain,
% 2.95/3.19 (~(elem!1 = s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[242, 25645])).
% 2.95/3.19 tff(25680,plain,
% 2.95/3.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23458, 25654, 5499])).
% 2.95/3.19 tff(25681,plain,
% 2.95/3.19 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[612])).
% 2.95/3.19 tff(25682,plain,
% 2.95/3.19 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.19 inference(symmetry,[status(thm)],[25681])).
% 2.95/3.19 tff(25683,plain,
% 2.95/3.19 (~b(elem!1, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2479, 3891, 2469])).
% 2.95/3.19 tff(25684,plain,
% 2.95/3.19 (elem!1 = s(elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[392, 25683, 2344])).
% 2.95/3.19 tff(25685,plain,
% 2.95/3.19 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[4025])).
% 2.95/3.19 tff(25686,plain,
% 2.95/3.19 (s(s(s(z))) = s(elem!1)),
% 2.95/3.19 inference(transitivity,[status(thm)],[775, 25685, 70, 212])).
% 2.95/3.19 tff(25687,plain,
% 2.95/3.19 (s(elem!1) = s(s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[218, 212])).
% 2.95/3.19 tff(25688,plain,
% 2.95/3.19 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[210, 25687])).
% 2.95/3.19 tff(25689,plain,
% 2.95/3.19 (s(s(s(elem!1))) = elem!1),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3895, 25688])).
% 2.95/3.19 tff(25690,plain,
% 2.95/3.19 (~(s(s(s(z))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2596, 25689])).
% 2.95/3.19 tff(25691,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25690, 25686])).
% 2.95/3.19 tff(25692,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25693,plain,
% 2.95/3.19 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25692, 25684])).
% 2.95/3.19 tff(25694,plain,
% 2.95/3.19 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[612])).
% 2.95/3.19 tff(25695,plain,
% 2.95/3.19 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25694])).
% 2.95/3.19 tff(25696,plain,
% 2.95/3.19 (elem!1 = s(s(s(elem!1)))),
% 2.95/3.19 inference(transitivity,[status(thm)],[3891, 601])).
% 2.95/3.19 tff(25697,plain,
% 2.95/3.19 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25696])).
% 2.95/3.19 tff(25698,plain,
% 2.95/3.19 ((~r(elem!1, s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25697])).
% 2.95/3.19 tff(25699,plain,
% 2.95/3.19 (~r(s(s(s(elem!1))), s(z))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[293, 25698])).
% 2.95/3.19 tff(25700,plain,
% 2.95/3.19 (b(s(s(s(elem!1))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[66, 21, 25699, 63])).
% 2.95/3.19 tff(25701,plain,
% 2.95/3.19 (s(elem!1) = s(s(s(elem!1)))),
% 2.95/3.19 inference(transitivity,[status(thm)],[609, 601])).
% 2.95/3.19 tff(25702,plain,
% 2.95/3.19 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25701])).
% 2.95/3.19 tff(25703,plain,
% 2.95/3.19 (b(s(s(s(elem!1))), z)),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[394, 25702])).
% 2.95/3.19 tff(25704,plain,
% 2.95/3.19 (~b(z, s(s(s(s(z)))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[19379, 25703, 1281, 25700])).
% 2.95/3.19 tff(25705,plain,
% 2.95/3.19 (r(z, s(s(s(s(z)))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1119, 21, 25704, 1114])).
% 2.95/3.19 tff(25706,plain,
% 2.95/3.19 (b(s(s(elem!1)), z) <=> b(s(s(s(elem!1))), z)),
% 2.95/3.19 inference(monotonicity,[status(thm)],[601])).
% 2.95/3.19 tff(25707,plain,
% 2.95/3.19 (b(s(s(s(elem!1))), z) <=> b(s(s(elem!1)), z)),
% 2.95/3.19 inference(symmetry,[status(thm)],[25706])).
% 2.95/3.19 tff(25708,plain,
% 2.95/3.19 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 2.95/3.19 inference(transitivity,[status(thm)],[25702, 25707])).
% 2.95/3.19 tff(25709,plain,
% 2.95/3.19 (b(s(s(elem!1)), z)),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[394, 25708])).
% 2.95/3.19 tff(25710,plain,
% 2.95/3.19 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[601])).
% 2.95/3.19 tff(25711,plain,
% 2.95/3.19 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.95/3.19 inference(symmetry,[status(thm)],[25710])).
% 2.95/3.19 tff(25712,plain,
% 2.95/3.19 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.95/3.19 inference(transitivity,[status(thm)],[25697, 25711])).
% 2.95/3.19 tff(25713,plain,
% 2.95/3.19 ((~r(elem!1, s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25712])).
% 2.95/3.19 tff(25714,plain,
% 2.95/3.19 (~r(s(s(elem!1)), s(z))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[293, 25713])).
% 2.95/3.19 tff(25715,plain,
% 2.95/3.19 (b(s(s(elem!1)), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2143, 25714])).
% 2.95/3.19 tff(25716,plain,
% 2.95/3.19 (~b(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[16949, 25715, 25709, 1281])).
% 2.95/3.19 tff(25717,plain,
% 2.95/3.19 (r(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[902, 21, 25716, 898])).
% 2.95/3.19 tff(25718,plain,
% 2.95/3.19 (s(s(s(elem!1))) = elem!1),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3895, 601])).
% 2.95/3.19 tff(25719,plain,
% 2.95/3.19 (~b(s(z), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2562, 25718, 1242])).
% 2.95/3.19 tff(25720,plain,
% 2.95/3.19 (r(s(z), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[760, 25719])).
% 2.95/3.19 tff(25721,plain,
% 2.95/3.19 (~r(s(s(s(s(z)))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[9490, 25720, 25717, 25705])).
% 2.95/3.19 tff(25722,plain,
% 2.95/3.19 (b(s(s(s(s(z)))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[930, 21, 927, 25721])).
% 2.95/3.19 tff(25723,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(25724,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(25725,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25724, 25723])).
% 2.95/3.19 tff(25726,plain,
% 2.95/3.19 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25725, 271, 1281, 25700, 25722])).
% 2.95/3.19 tff(25727,plain,
% 2.95/3.19 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25726, 25695])).
% 2.95/3.19 tff(25728,plain,
% 2.95/3.19 (r(s(elem!1), s(s(s(s(z)))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1995, 25727, 25693])).
% 2.95/3.19 tff(25729,plain,
% 2.95/3.19 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25728, 25682])).
% 2.95/3.19 tff(25730,plain,
% 2.95/3.19 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[612])).
% 2.95/3.19 tff(25731,plain,
% 2.95/3.19 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.19 inference(symmetry,[status(thm)],[25730])).
% 2.95/3.19 tff(25732,plain,
% 2.95/3.19 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[14008, 25693])).
% 2.95/3.19 tff(25733,plain,
% 2.95/3.19 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[609])).
% 2.95/3.19 tff(25734,plain,
% 2.95/3.19 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.19 inference(symmetry,[status(thm)],[25733])).
% 2.95/3.19 tff(25735,plain,
% 2.95/3.19 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[611])).
% 2.95/3.19 tff(25736,plain,
% 2.95/3.19 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.19 inference(transitivity,[status(thm)],[25735, 25734])).
% 2.95/3.19 tff(25737,plain,
% 2.95/3.19 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25736])).
% 2.95/3.19 tff(25738,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(25739,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(25740,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25739, 25738])).
% 2.95/3.19 tff(25741,plain,
% 2.95/3.19 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25740, 271, 1281, 25700, 25722])).
% 2.95/3.19 tff(25742,plain,
% 2.95/3.19 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25741, 25737])).
% 2.95/3.19 tff(25743,plain,
% 2.95/3.19 (r(s(s(s(s(z)))), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1559, 25742, 25732])).
% 2.95/3.19 tff(25744,plain,
% 2.95/3.19 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25743, 25731])).
% 2.95/3.19 tff(25745,plain,
% 2.95/3.19 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25696])).
% 2.95/3.19 tff(25746,plain,
% 2.95/3.19 (r(z, s(s(s(elem!1))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[378, 25745])).
% 2.95/3.19 tff(25747,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(25748,plain,
% 2.95/3.19 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(25749,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[25748])).
% 2.95/3.19 tff(25750,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.95/3.19 inference(transitivity,[status(thm)],[25749, 25747])).
% 2.95/3.19 tff(25751,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(25752,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25751, 25750])).
% 2.95/3.19 tff(25753,plain,
% 2.95/3.19 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25752, 121, 25746, 25705, 25744])).
% 2.95/3.19 tff(25754,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25753, 25729])).
% 2.95/3.19 tff(25755,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | r(elem!1, s(z)) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | r(elem!1, s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25756,plain,
% 2.95/3.19 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25755, 1242, 293, 3379, 394, 2344, 2469, 1281])).
% 2.95/3.19 tff(25757,plain,
% 2.95/3.19 (~(s(elem!1) = s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[210, 25756])).
% 2.95/3.19 tff(25758,plain,
% 2.95/3.19 (~(elem!1 = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[218, 25757])).
% 2.95/3.19 tff(25759,plain,
% 2.95/3.19 (b(elem!1, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[392, 25758, 2344])).
% 2.95/3.19 tff(25760,plain,
% 2.95/3.19 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2479, 25759, 2469])).
% 2.95/3.19 tff(25761,plain,
% 2.95/3.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[78, 25760])).
% 2.95/3.19 tff(25762,plain,
% 2.95/3.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[556, 25756, 2469])).
% 2.95/3.19 tff(25763,plain,
% 2.95/3.19 (~(s(s(elem!1)) = elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[197, 25760])).
% 2.95/3.19 tff(25764,plain,
% 2.95/3.19 (~r(elem!1, s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3310, 25763, 199, 2489, 25762, 2344, 25761])).
% 2.95/3.19 tff(25765,plain,
% 2.95/3.19 (b(elem!1, s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[599, 25764, 25760])).
% 2.95/3.19 tff(25766,plain,
% 2.95/3.19 (~(elem!1 = s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[6679, 25765, 71])).
% 2.95/3.19 tff(25767,plain,
% 2.95/3.19 (b(elem!1, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[299, 25766, 293])).
% 2.95/3.19 tff(25768,plain,
% 2.95/3.19 (~b(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1290, 25767, 1281, 25759])).
% 2.95/3.19 tff(25769,plain,
% 2.95/3.19 (r(s(elem!1), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[429, 25768, 25643])).
% 2.95/3.19 tff(25770,plain,
% 2.95/3.19 (~(s(z) = elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1221, 25766])).
% 2.95/3.19 tff(25771,plain,
% 2.95/3.19 (r(s(z), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[236, 25770, 1242])).
% 2.95/3.19 tff(25772,plain,
% 2.95/3.19 (~(s(elem!1) = elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2206, 25758])).
% 2.95/3.19 tff(25773,plain,
% 2.95/3.19 (r(s(elem!1), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2243, 25772, 2467])).
% 2.95/3.19 tff(25774,plain,
% 2.95/3.19 (~r(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[10675, 1441, 357, 411])).
% 2.95/3.19 tff(25775,plain,
% 2.95/3.19 (b(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[902, 21, 25774, 898])).
% 2.95/3.19 tff(25776,plain,
% 2.95/3.19 (~b(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[22281, 271, 1281, 448, 25775])).
% 2.95/3.19 tff(25777,plain,
% 2.95/3.19 (r(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[284, 25776, 259])).
% 2.95/3.19 tff(25778,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3385, 121, 622, 378, 1441, 25777])).
% 2.95/3.19 tff(25779,plain,((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25780,plain,
% 2.95/3.19 (~r(z, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25779, 25773, 3379, 3328, 1281, 25767, 25771, 25769])).
% 2.95/3.19 tff(25781,plain,
% 2.95/3.19 (b(z, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1439, 25780])).
% 2.95/3.19 tff(25782,plain,
% 2.95/3.19 (~b(s(z), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[19626, 271, 394, 1281, 25781])).
% 2.95/3.19 tff(25783,plain,
% 2.95/3.19 (r(s(z), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[444, 25782, 25641])).
% 2.95/3.19 tff(25784,plain,
% 2.95/3.19 (~b(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2892, 271, 25759, 394, 25781])).
% 2.95/3.19 tff(25785,plain,
% 2.95/3.19 (r(elem!1, z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[284, 25784, 3328])).
% 2.95/3.19 tff(25786,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[23819, 121, 25773, 25771, 25785, 25783])).
% 2.95/3.19 tff(25787,plain,(b(s(z), elem!1) | (~b(s(elem!1), z)) | (~b(s(z), z)) | r(elem!1, s(z)) | b(s(z), s(s(s(z)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25788,plain,
% 2.95/3.19 (b(s(z), elem!1)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25787, 293, 1281, 394, 71, 199, 2344, 2469, 2467])).
% 2.95/3.19 tff(25789,plain,
% 2.95/3.19 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[212])).
% 2.95/3.19 tff(25790,plain,
% 2.95/3.19 (b(s(z), s(elem!1))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[260, 25789])).
% 2.95/3.19 tff(25791,plain,
% 2.95/3.19 (~b(z, s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[19761, 25790, 394, 1281])).
% 2.95/3.19 tff(25792,plain,
% 2.95/3.19 (r(z, s(s(s(z))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1214, 25791])).
% 2.95/3.19 tff(25793,plain,
% 2.95/3.19 (~b(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[9241, 25790, 394, 1281])).
% 2.95/3.19 tff(25794,plain,
% 2.95/3.19 (r(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[902, 21, 25793, 898])).
% 2.95/3.19 tff(25795,plain,
% 2.95/3.19 (~r(s(s(s(z))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2335, 25794, 25792, 108])).
% 2.95/3.19 tff(25796,plain,
% 2.95/3.19 (b(s(s(s(z))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2325, 25795])).
% 2.95/3.19 tff(25797,plain,
% 2.95/3.19 (~r(s(s(s(z))), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1508, 25794, 108, 25792])).
% 2.95/3.19 tff(25798,plain,
% 2.95/3.19 (b(s(s(s(z))), s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1816, 25797, 25690])).
% 2.95/3.19 tff(25799,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(25800,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(25801,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[25800, 25799])).
% 2.95/3.19 tff(25802,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25801, 271, 394, 25798, 25796, 25790])).
% 2.95/3.19 tff(25803,plain,((~(elem!1 = s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(25804,plain,
% 2.95/3.19 (~(elem!1 = s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[25803, 25788, 106, 1281, 394])).
% 2.95/3.19 tff(25805,plain,
% 2.95/3.19 (b(elem!1, s(elem!1))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[392, 25804, 2344])).
% 2.95/3.19 tff(25806,plain,
% 2.95/3.19 (~(elem!1 = s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[2479, 25805, 2469])).
% 2.95/3.19 tff(25807,plain,
% 2.95/3.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[78, 25806])).
% 2.95/3.20 tff(25808,plain,
% 2.95/3.20 (~(s(s(elem!1)) = elem!1)),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[197, 25806])).
% 2.95/3.20 tff(25809,plain,
% 2.95/3.20 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[614, 25807])).
% 2.95/3.20 tff(25810,plain,
% 2.95/3.20 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[556, 25809, 2469])).
% 2.95/3.20 tff(25811,plain,
% 2.95/3.20 (~r(elem!1, s(s(elem!1)))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[3310, 25810, 199, 2489, 25808, 2344, 25807])).
% 2.95/3.20 tff(25812,plain,
% 2.95/3.20 (b(elem!1, s(s(elem!1)))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[599, 25811, 25806])).
% 2.95/3.20 tff(25813,plain,
% 2.95/3.20 (~(elem!1 = s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[6679, 25812, 71])).
% 2.95/3.20 tff(25814,plain,
% 2.95/3.20 (b(elem!1, s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[299, 25813, 293])).
% 2.95/3.20 tff(25815,plain,
% 2.95/3.20 (~b(s(elem!1), s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[1290, 25814, 1281, 25805])).
% 2.95/3.20 tff(25816,plain,
% 2.95/3.20 (r(s(elem!1), s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[429, 25815, 25643])).
% 2.95/3.20 tff(25817,plain,
% 2.95/3.20 (b(s(s(s(elem!1))), s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[3326, 25809, 199, 2344, 394, 2469, 2467])).
% 2.95/3.20 tff(25818,plain,
% 2.95/3.20 (~(s(elem!1) = s(s(elem!1)))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[210, 25809])).
% 2.95/3.20 tff(25819,plain,
% 2.95/3.20 (~(s(s(elem!1)) = s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[620, 25818])).
% 2.95/3.20 tff(25820,plain,
% 2.95/3.20 (~b(s(s(elem!1)), s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[3324, 25812, 394, 25805])).
% 2.95/3.20 tff(25821,plain,
% 2.95/3.20 (r(s(s(elem!1)), s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[701, 25820, 25819])).
% 2.95/3.20 tff(25822,plain,
% 2.95/3.20 (~(s(elem!1) = elem!1)),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[2206, 25804])).
% 2.95/3.20 tff(25823,plain,
% 2.95/3.20 (r(s(elem!1), elem!1)),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[2243, 25822, 2467])).
% 2.95/3.20 tff(25824,plain,
% 2.95/3.20 (~b(z, s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[3359, 25823, 25821, 3328, 25805, 394, 25810, 25817])).
% 2.95/3.20 tff(25825,plain,
% 2.95/3.20 (r(z, s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[1439, 25824])).
% 2.95/3.20 tff(25826,plain,
% 2.95/3.20 (~r(z, s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[2186, 25825, 25816, 106])).
% 2.95/3.20 tff(25827,plain,
% 2.95/3.20 (b(z, s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[902, 21, 25826, 898])).
% 2.95/3.20 tff(25828,plain,
% 2.95/3.20 (~b(elem!1, z)),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[8962, 25827, 25788, 25814])).
% 2.95/3.20 tff(25829,plain,
% 2.95/3.20 (r(elem!1, z)),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[284, 25828, 3328])).
% 2.95/3.20 tff(25830,plain,
% 2.95/3.20 ($false),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[3385, 121, 25823, 3379, 25825, 25829])).
% 2.95/3.20 tff(25831,plain,(r(elem!1, s(z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | b(s(z), s(s(s(z)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.20 tff(25832,plain,
% 2.95/3.20 (r(elem!1, s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[25831, 1281, 394, 71, 199, 2344, 2469, 2467])).
% 2.95/3.20 tff(25833,plain,
% 2.95/3.20 (~r(z, s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[3464, 25832, 106, 3379])).
% 2.95/3.20 tff(25834,plain,
% 2.95/3.20 (b(z, s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[902, 21, 25833, 898])).
% 2.95/3.20 tff(25835,plain,
% 2.95/3.20 (~b(s(elem!1), s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[16834, 271, 394, 1281, 25834])).
% 2.95/3.20 tff(25836,plain,
% 2.95/3.20 (r(s(elem!1), s(z))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[429, 25835, 25643])).
% 2.95/3.20 tff(25837,plain,
% 2.95/3.20 (~b(s(z), s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[9241, 25834, 394, 1281])).
% 2.95/3.20 tff(25838,plain,
% 2.95/3.20 (r(s(z), s(elem!1))),
% 2.95/3.20 inference(unit_resolution,[status(thm)],[444, 25837, 25641])).
% 2.95/3.20 tff(25839,plain,
% 2.95/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25840,plain,
% 3.03/3.20 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25841,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25840])).
% 3.03/3.20 tff(25842,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[25841, 25839])).
% 3.03/3.20 tff(25843,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(25844,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25843, 25842])).
% 3.03/3.20 tff(25845,plain,
% 3.03/3.20 (~r(s(elem!1), elem!1)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25844, 121, 25832, 25838, 25836])).
% 3.03/3.20 tff(25846,plain,
% 3.03/3.20 (s(elem!1) = elem!1),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[2243, 25845, 2467])).
% 3.03/3.20 tff(25847,plain,
% 3.03/3.20 (elem!1 = s(elem!1)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[2206, 25846])).
% 3.03/3.20 tff(25848,plain,
% 3.03/3.20 (s(elem!1) = s(s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[218, 25847])).
% 3.03/3.20 tff(25849,plain,
% 3.03/3.20 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[210, 25848])).
% 3.03/3.20 tff(25850,plain,
% 3.03/3.20 (s(s(s(elem!1))) = elem!1),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[3895, 25849])).
% 3.03/3.20 tff(25851,plain,
% 3.03/3.20 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.03/3.20 inference(transitivity,[status(thm)],[3042, 2590])).
% 3.03/3.20 tff(25852,plain,
% 3.03/3.20 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25851])).
% 3.03/3.20 tff(25853,plain,
% 3.03/3.20 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.03/3.20 inference(transitivity,[status(thm)],[872, 25852, 55, 601])).
% 3.03/3.20 tff(25854,plain,
% 3.03/3.20 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25853])).
% 3.03/3.20 tff(25855,plain,
% 3.03/3.20 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 3.03/3.20 inference(symmetry,[status(thm)],[25854])).
% 3.03/3.20 tff(25856,plain,
% 3.03/3.20 (elem!1 = s(s(s(z)))),
% 3.03/3.20 inference(transitivity,[status(thm)],[2590, 611, 56, 25855, 774])).
% 3.03/3.20 tff(25857,plain,
% 3.03/3.20 (s(elem!1) = elem!1),
% 3.03/3.20 inference(transitivity,[status(thm)],[609, 601, 2505])).
% 3.03/3.20 tff(25858,plain,
% 3.03/3.20 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = elem!1)),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25857])).
% 3.03/3.20 tff(25859,plain,
% 3.03/3.20 ((s(s(s(z))) = s(elem!1)) <=> (elem!1 = s(s(s(z))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[25858, 159])).
% 3.03/3.20 tff(25860,plain,
% 3.03/3.20 ((~(s(s(s(z))) = s(elem!1))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25859])).
% 3.03/3.20 tff(25861,plain,
% 3.03/3.20 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[21129])).
% 3.03/3.20 tff(25862,plain,
% 3.03/3.20 (~(z = elem!1)),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[30, 25861])).
% 3.03/3.20 tff(25863,plain,
% 3.03/3.20 (~(s(z) = s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[343, 25862])).
% 3.03/3.20 tff(25864,plain,
% 3.03/3.20 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[3917, 3891, 25863])).
% 3.03/3.20 tff(25865,plain,
% 3.03/3.20 (~(elem!1 = s(s(s(z))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25864, 25860])).
% 3.03/3.20 tff(25866,plain,
% 3.03/3.20 ($false),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25865, 25856])).
% 3.03/3.20 tff(25867,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.20 tff(25868,plain,
% 3.03/3.20 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25867, 25849, 25850])).
% 3.03/3.20 tff(25869,plain,
% 3.03/3.20 (s(s(elem!1)) = s(elem!1)),
% 3.03/3.20 inference(symmetry,[status(thm)],[25848])).
% 3.03/3.20 tff(25870,plain,
% 3.03/3.20 (s(s(elem!1)) = elem!1),
% 3.03/3.20 inference(transitivity,[status(thm)],[25869, 25846])).
% 3.03/3.20 tff(25871,plain,
% 3.03/3.20 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25870])).
% 3.03/3.20 tff(25872,plain,
% 3.03/3.20 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 3.03/3.20 inference(symmetry,[status(thm)],[25871])).
% 3.03/3.20 tff(25873,plain,
% 3.03/3.20 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25846])).
% 3.03/3.20 tff(25874,plain,
% 3.03/3.20 (r(s(z), elem!1)),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25838, 25873])).
% 3.03/3.20 tff(25875,plain,
% 3.03/3.20 (r(s(z), s(s(elem!1)))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25874, 25872])).
% 3.03/3.20 tff(25876,plain,
% 3.03/3.20 (r(z, s(elem!1)) <=> r(z, elem!1)),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25846])).
% 3.03/3.20 tff(25877,plain,
% 3.03/3.20 (r(z, elem!1) <=> r(z, s(elem!1))),
% 3.03/3.20 inference(symmetry,[status(thm)],[25876])).
% 3.03/3.20 tff(25878,plain,
% 3.03/3.20 (r(z, s(elem!1))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[3379, 25877])).
% 3.03/3.20 tff(25879,plain,
% 3.03/3.20 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[212])).
% 3.03/3.20 tff(25880,plain,
% 3.03/3.20 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[3061, 25879])).
% 3.03/3.20 tff(25881,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25882,plain,
% 3.03/3.20 (((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25883,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25882])).
% 3.03/3.20 tff(25884,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[25883, 25881])).
% 3.03/3.20 tff(25885,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(25886,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25885, 25884])).
% 3.03/3.20 tff(25887,plain,
% 3.03/3.20 (~r(s(s(s(s(s(z))))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25886, 121, 1441, 411, 25880])).
% 3.03/3.20 tff(25888,plain,
% 3.03/3.20 (b(s(s(s(s(s(z))))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[6593, 21, 711, 25887])).
% 3.03/3.20 tff(25889,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25890,plain,
% 3.03/3.20 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25891,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25890])).
% 3.03/3.20 tff(25892,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[25891, 25889])).
% 3.03/3.20 tff(25893,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(25894,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25893, 25892])).
% 3.03/3.20 tff(25895,plain,
% 3.03/3.20 ($false),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25894, 121, 1625, 3456, 3061, 1660])).
% 3.03/3.20 tff(25896,plain,((~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.20 tff(25897,plain,
% 3.03/3.20 (~r(s(s(s(s(s(z))))), s(z))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25896, 3061, 3456, 1625])).
% 3.03/3.20 tff(25898,plain,
% 3.03/3.20 (b(s(s(s(s(s(z))))), s(z))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1682, 25897])).
% 3.03/3.20 tff(25899,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25900,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(25901,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25900, 25899])).
% 3.03/3.20 tff(25902,plain,
% 3.03/3.20 ($false),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25901, 271, 1281, 220, 25898, 25888])).
% 3.03/3.20 tff(25903,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~(elem!1 = s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.20 tff(25904,plain,
% 3.03/3.20 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25903, 25878, 25834, 1281, 25836, 25847, 25832, 25875])).
% 3.03/3.20 tff(25905,plain,
% 3.03/3.20 (b(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[840, 25904, 25868])).
% 3.03/3.20 tff(25906,plain,
% 3.03/3.20 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[212])).
% 3.03/3.20 tff(25907,plain,
% 3.03/3.20 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[831, 25906])).
% 3.03/3.20 tff(25908,plain,
% 3.03/3.20 ($false),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[3499, 25907])).
% 3.03/3.20 tff(25909,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.20 tff(25910,plain,
% 3.03/3.20 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25909, 25905, 25847])).
% 3.03/3.20 tff(25911,plain,
% 3.03/3.20 (~b(s(s(s(s(s(z))))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[24620, 25910, 25834, 394])).
% 3.03/3.20 tff(25912,plain,
% 3.03/3.20 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[2596, 25850])).
% 3.03/3.20 tff(25913,plain,
% 3.03/3.20 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[24514, 25878, 25838, 25836, 25834])).
% 3.03/3.20 tff(25914,plain,
% 3.03/3.20 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1816, 25913, 25912])).
% 3.03/3.20 tff(25915,plain,
% 3.03/3.20 (~(s(elem!1) = s(s(s(z))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[2035, 25912])).
% 3.03/3.20 tff(25916,plain,
% 3.03/3.20 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25867, 25688, 25689])).
% 3.03/3.20 tff(25917,plain,
% 3.03/3.20 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[5001, 25916])).
% 3.03/3.20 tff(25918,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25919,plain,
% 3.03/3.20 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25920,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[25919])).
% 3.03/3.20 tff(25921,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[25920, 25918])).
% 3.03/3.20 tff(25922,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(25923,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25922, 25921])).
% 3.03/3.20 tff(25924,plain,
% 3.03/3.20 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25923, 271, 394, 1422, 9894])).
% 3.03/3.20 tff(25925,plain,
% 3.03/3.20 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1494, 25924])).
% 3.03/3.20 tff(25926,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25927,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(25928,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[25927, 25926])).
% 3.03/3.20 tff(25929,plain,
% 3.03/3.20 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[25928, 271, 394, 1422, 9894])).
% 3.03/3.20 tff(25930,plain,
% 3.03/3.20 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1733, 25929])).
% 3.03/3.20 tff(25931,plain,
% 3.03/3.20 (~b(s(s(s(z))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[8279, 1307, 1422, 394])).
% 3.03/3.20 tff(25932,plain,
% 3.03/3.20 (r(s(s(s(z))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1155, 25931])).
% 3.03/3.20 tff(25933,plain,
% 3.03/3.20 (~r(z, s(s(s(s(s(z))))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[5135, 25932, 25930, 25925])).
% 3.03/3.20 tff(25934,plain,
% 3.03/3.20 (b(z, s(s(s(s(s(z))))))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1658, 25933])).
% 3.03/3.20 tff(25935,plain,
% 3.03/3.20 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[213])).
% 3.03/3.20 tff(25936,plain,
% 3.03/3.20 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 3.03/3.20 inference(symmetry,[status(thm)],[25935])).
% 3.03/3.20 tff(25937,plain,
% 3.03/3.20 (b(s(elem!1), s(s(s(s(s(z))))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[1849, 25936])).
% 3.03/3.20 tff(25938,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25939,plain,
% 3.03/3.20 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(25940,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[25939])).
% 3.03/3.21 tff(25941,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[25940, 25938])).
% 3.03/3.21 tff(25942,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(25943,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[25942, 25941])).
% 3.03/3.21 tff(25944,plain,
% 3.03/3.21 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25943, 271, 394, 1639, 9894])).
% 3.03/3.21 tff(25945,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25944, 25937])).
% 3.03/3.21 tff(25946,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~(elem!1 = s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(25947,plain,
% 3.03/3.21 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25946, 25934, 394, 212, 9894])).
% 3.03/3.21 tff(25948,plain,
% 3.03/3.21 (r(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1847, 25947, 25917])).
% 3.03/3.21 tff(25949,plain,
% 3.03/3.21 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[213])).
% 3.03/3.21 tff(25950,plain,
% 3.03/3.21 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 3.03/3.21 inference(symmetry,[status(thm)],[25949])).
% 3.03/3.21 tff(25951,plain,
% 3.03/3.21 (r(s(elem!1), s(s(s(s(s(z))))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[1826, 25950])).
% 3.03/3.21 tff(25952,assumption,(~r(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 3.03/3.21 tff(25953,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25952, 25951])).
% 3.03/3.21 tff(25954,plain,(r(s(elem!1), s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(25955,plain,
% 3.03/3.21 (r(s(elem!1), s(s(s(s(s(z))))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25954, 25948, 212])).
% 3.03/3.21 tff(25956,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25957,plain,
% 3.03/3.21 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25958,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[25957])).
% 3.03/3.21 tff(25959,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[25958, 25956])).
% 3.03/3.21 tff(25960,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(25961,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[25960, 25959])).
% 3.03/3.21 tff(25962,plain,
% 3.03/3.21 (~r(s(elem!1), s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25961, 121, 25925, 25930, 25955])).
% 3.03/3.21 tff(25963,plain,
% 3.03/3.21 (b(s(elem!1), s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[2044, 25962, 2037])).
% 3.03/3.21 tff(25964,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25965,plain,
% 3.03/3.21 (((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25966,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[25965])).
% 3.03/3.21 tff(25967,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[25966, 25964])).
% 3.03/3.21 tff(25968,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(25969,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[25968, 25967])).
% 3.03/3.21 tff(25970,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25969, 271, 394, 1422, 1307, 25963])).
% 3.03/3.21 tff(25971,plain,((~b(z, s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~(elem!1 = s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(25972,plain,
% 3.03/3.21 (~b(z, s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25971, 25910, 394, 25915, 25847, 25914])).
% 3.03/3.21 tff(25973,plain,
% 3.03/3.21 (r(z, s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1214, 25972])).
% 3.03/3.21 tff(25974,plain,
% 3.03/3.21 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25692, 25847])).
% 3.03/3.21 tff(25975,plain,
% 3.03/3.21 (~(s(s(s(z))) = elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[2605, 25974])).
% 3.03/3.21 tff(25976,plain,
% 3.03/3.21 (~r(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[4112, 25874, 106, 25832])).
% 3.03/3.21 tff(25977,plain,
% 3.03/3.21 (b(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[255, 25976, 25975])).
% 3.03/3.21 tff(25978,plain,
% 3.03/3.21 (b(s(elem!1), z) <=> b(elem!1, z)),
% 3.03/3.21 inference(monotonicity,[status(thm)],[25846])).
% 3.03/3.21 tff(25979,plain,
% 3.03/3.21 (b(elem!1, z)),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[394, 25978])).
% 3.03/3.21 tff(25980,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25981,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(25982,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[25981, 25980])).
% 3.03/3.21 tff(25983,plain,
% 3.03/3.21 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25982, 271, 25979, 25905, 25977])).
% 3.03/3.21 tff(25984,plain,
% 3.03/3.21 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1733, 25983])).
% 3.03/3.21 tff(25985,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25986,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(25987,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[25986, 25985])).
% 3.03/3.21 tff(25988,plain,
% 3.03/3.21 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25987, 271, 25979, 25905, 25977])).
% 3.03/3.21 tff(25989,plain,
% 3.03/3.21 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1494, 25988])).
% 3.03/3.21 tff(25990,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25991,plain,
% 3.03/3.21 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(25992,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[25991])).
% 3.03/3.21 tff(25993,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[25992, 25990])).
% 3.03/3.21 tff(25994,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(25995,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[25994, 25993])).
% 3.03/3.21 tff(25996,plain,
% 3.03/3.21 (~r(s(s(s(s(s(z))))), z)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25995, 121, 25989, 25984, 25973])).
% 3.03/3.21 tff(25997,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[6593, 21, 711, 25996, 25911])).
% 3.03/3.21 tff(25998,plain,((~b(s(z), z)) | (~b(s(elem!1), z)) | b(s(elem!1), elem!1) | b(s(z), s(s(s(z)))) | b(z, elem!1) | r(elem!1, s(elem!1)) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(25999,plain,
% 3.03/3.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[25998, 25652, 1281, 2344, 394, 2467, 199])).
% 3.03/3.21 tff(26000,plain,
% 3.03/3.21 (s(s(s(elem!1))) = elem!1),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[23975, 25999, 307, 2344, 2467, 216, 25680, 25642, 25679, 25647, 25644, 25678])).
% 3.03/3.21 tff(26001,plain,
% 3.03/3.21 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[2596, 26000])).
% 3.03/3.21 tff(26002,plain,
% 3.03/3.21 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1816, 26001, 25654])).
% 3.03/3.21 tff(26003,plain,
% 3.03/3.21 (~b(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[3288, 26002, 307, 394])).
% 3.03/3.21 tff(26004,plain,
% 3.03/3.21 (r(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[255, 26003, 907])).
% 3.03/3.21 tff(26005,plain,
% 3.03/3.21 (~r(z, s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[3387, 3379, 8448, 25640])).
% 3.03/3.21 tff(26006,plain,
% 3.03/3.21 (b(z, s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1439, 26005])).
% 3.03/3.21 tff(26007,plain,
% 3.03/3.21 (~b(z, s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[19710, 26002, 394, 26006])).
% 3.03/3.21 tff(26008,plain,
% 3.03/3.21 (r(z, s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1214, 26007])).
% 3.03/3.21 tff(26009,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[19871, 26008, 26004, 25640, 3379])).
% 3.03/3.21 tff(26010,plain,(b(s(elem!1), elem!1) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | r(elem!1, s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(z, elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(26011,plain,
% 3.03/3.21 (b(s(elem!1), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26010, 907, 11211, 25632, 2344, 211, 19197, 5499, 199, 220])).
% 3.03/3.21 tff(26012,plain,
% 3.03/3.21 (~(s(z) = elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1276, 24236, 25632])).
% 3.03/3.21 tff(26013,plain,
% 3.03/3.21 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[11663, 22882])).
% 3.03/3.21 tff(26014,plain,
% 3.03/3.21 (r(s(elem!1), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[429, 22133, 24380])).
% 3.03/3.21 tff(26015,plain,
% 3.03/3.21 (r(s(z), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[444, 22132, 24382])).
% 3.03/3.21 tff(26016,plain,
% 3.03/3.21 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[23235, 108, 26014, 26015])).
% 3.03/3.21 tff(26017,plain,
% 3.03/3.21 (~r(elem!1, s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[4112, 145, 108, 357])).
% 3.03/3.21 tff(26018,plain,
% 3.03/3.21 (b(elem!1, s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[299, 26017, 258])).
% 3.03/3.21 tff(26019,plain,
% 3.03/3.21 (~b(elem!1, z)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[22281, 271, 1281, 26018, 220])).
% 3.03/3.21 tff(26020,plain,
% 3.03/3.21 (r(elem!1, z)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[284, 26019, 259])).
% 3.03/3.21 tff(26021,plain,
% 3.03/3.21 (~b(z, s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[15964, 26020, 357, 220, 145])).
% 3.03/3.21 tff(26022,plain,
% 3.03/3.21 (~r(z, s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[19871, 26020, 145, 378])).
% 3.03/3.21 tff(26023,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1214, 26022, 26021])).
% 3.03/3.21 tff(26024,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (~b(s(z), z)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(26025,plain,
% 3.03/3.21 (~r(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26024, 108, 378, 220, 259, 1281, 25679, 357])).
% 3.03/3.21 tff(26026,plain,
% 3.03/3.21 (b(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[255, 26025, 907])).
% 3.03/3.21 tff(26027,plain,
% 3.03/3.21 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[3288, 26026, 307, 394])).
% 3.03/3.21 tff(26028,plain,
% 3.03/3.21 (s(s(s(z))) = s(elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1816, 26027, 26016])).
% 3.03/3.21 tff(26029,plain,
% 3.03/3.21 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[2596, 26028])).
% 3.03/3.21 tff(26030,plain,
% 3.03/3.21 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[486, 26029, 147])).
% 3.03/3.21 tff(26031,plain,
% 3.03/3.21 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[3177, 271, 307, 2618, 26030])).
% 3.03/3.21 tff(26032,plain,
% 3.03/3.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[14823, 26031, 307, 394, 2618, 365, 147, 2344])).
% 3.03/3.21 tff(26033,plain,
% 3.03/3.21 (r(elem!1, z)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[284, 259, 25639])).
% 3.03/3.21 tff(26034,plain,
% 3.03/3.21 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[23458, 26016, 5499])).
% 3.03/3.21 tff(26035,plain,
% 3.03/3.21 (~(elem!1 = s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[7490, 26034])).
% 3.03/3.21 tff(26036,plain,
% 3.03/3.21 (~(s(s(elem!1)) = elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[197, 26035])).
% 3.03/3.21 tff(26037,plain,
% 3.03/3.21 (~b(s(s(elem!1)), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[551, 26032, 307, 26030])).
% 3.03/3.21 tff(26038,plain,
% 3.03/3.21 (r(s(s(elem!1)), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[862, 26037, 26036])).
% 3.03/3.21 tff(26039,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(26040,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(26041,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[26040, 26039])).
% 3.03/3.21 tff(26042,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26041, 121, 357, 2117, 1409, 1624])).
% 3.03/3.21 tff(26043,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(26044,plain,
% 3.03/3.21 (~r(s(s(elem!1)), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26043, 26038, 26033, 357])).
% 3.03/3.21 tff(26045,plain,
% 3.03/3.21 (b(s(s(elem!1)), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[2143, 26044])).
% 3.03/3.21 tff(26046,plain,
% 3.03/3.21 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[989, 26045, 26030, 26032])).
% 3.03/3.21 tff(26047,plain,
% 3.03/3.21 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[760, 26046])).
% 3.03/3.21 tff(26048,plain,
% 3.03/3.21 (r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[681, 26031, 26034])).
% 3.03/3.21 tff(26049,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(26050,plain,
% 3.03/3.21 (((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(26051,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[26050])).
% 3.03/3.21 tff(26052,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[26051, 26049])).
% 3.03/3.21 tff(26053,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(26054,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[26053, 26052])).
% 3.03/3.21 tff(26055,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26054, 121, 26048, 26047, 26015, 26014])).
% 3.03/3.21 tff(26056,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(26057,plain,
% 3.03/3.21 (~r(s(z), s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26056, 357, 25632, 11211, 2618, 147, 2344, 907, 5499, 378, 220, 259, 19197])).
% 3.03/3.21 tff(26058,plain,
% 3.03/3.21 (r(z, s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[23127, 26057, 1, 19197])).
% 3.03/3.21 tff(26059,plain,
% 3.03/3.21 (b(s(z), s(s(s(z))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[105, 26057])).
% 3.03/3.21 tff(26060,plain,
% 3.03/3.21 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[24371, 26059, 26058, 19197, 220])).
% 3.03/3.21 tff(26061,plain,
% 3.03/3.21 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[932, 26060])).
% 3.03/3.21 tff(26062,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(26063,plain,
% 3.03/3.21 (((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(26064,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[26063])).
% 3.03/3.21 tff(26065,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[26064, 26062])).
% 3.03/3.21 tff(26066,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(26067,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[26066, 26065])).
% 3.03/3.21 tff(26068,plain,
% 3.03/3.21 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[26067, 121, 357, 26061, 25635])).
% 3.03/3.21 tff(26069,plain,
% 3.03/3.21 (b(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1559, 26068, 19204])).
% 3.03/3.21 tff(26070,plain,
% 3.03/3.21 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[4929, 26059, 24236])).
% 3.03/3.21 tff(26071,plain,
% 3.03/3.21 (~r(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[10721, 26059, 220, 25632, 11211, 259, 378])).
% 3.03/3.21 tff(26072,plain,
% 3.03/3.21 (b(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[255, 26071, 907])).
% 3.03/3.21 tff(26073,plain,
% 3.03/3.21 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[3288, 26072, 25632, 11211])).
% 3.03/3.21 tff(26074,plain,
% 3.03/3.21 (r(s(s(s(z))), s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1816, 26073, 26070])).
% 3.03/3.22 tff(26075,plain,
% 3.03/3.22 (~r(z, s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24514, 26074, 220, 25636, 25635])).
% 3.03/3.22 tff(26076,plain,
% 3.03/3.22 (b(z, s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1439, 26075])).
% 3.03/3.22 tff(26077,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26078,plain,
% 3.03/3.22 (((~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(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26079,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26078])).
% 3.03/3.22 tff(26080,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.22 inference(transitivity,[status(thm)],[26079, 26077])).
% 3.03/3.22 tff(26081,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26082,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26081, 26080])).
% 3.03/3.22 tff(26083,plain,
% 3.03/3.22 (~b(s(s(s(s(z)))), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26082, 271, 2618, 26076, 26069])).
% 3.03/3.22 tff(26084,plain,
% 3.03/3.22 (r(s(s(s(s(z)))), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1095, 26083])).
% 3.03/3.22 tff(26085,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26086,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26087,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26086, 26085])).
% 3.03/3.22 tff(26088,plain,
% 3.03/3.22 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26087, 121, 357, 26061, 25635])).
% 3.03/3.22 tff(26089,plain,
% 3.03/3.22 (~b(z, s(s(s(s(z)))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[14020, 26088, 26076, 19205, 26068])).
% 3.03/3.22 tff(26090,plain,
% 3.03/3.22 (r(z, s(s(s(s(z)))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1121, 26089])).
% 3.03/3.22 tff(26091,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26092,plain,
% 3.03/3.22 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26093,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26092])).
% 3.03/3.22 tff(26094,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(transitivity,[status(thm)],[26093, 26091])).
% 3.03/3.22 tff(26095,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26096,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26095, 26094])).
% 3.03/3.22 tff(26097,plain,
% 3.03/3.22 (~r(s(s(s(s(z)))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26096, 121, 25638, 26090, 26084])).
% 3.03/3.22 tff(26098,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26099,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26100,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26099, 26098])).
% 3.03/3.22 tff(26101,plain,
% 3.03/3.22 (~b(s(s(s(s(z)))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26100, 271, 25632, 2618, 26069])).
% 3.03/3.22 tff(26102,plain,
% 3.03/3.22 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24968, 21, 26101])).
% 3.03/3.22 tff(26103,plain,
% 3.03/3.22 (s(s(s(s(z)))) = elem!1),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26102, 26097])).
% 3.03/3.22 tff(26104,plain,
% 3.03/3.22 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26103])).
% 3.03/3.22 tff(26105,plain,
% 3.03/3.22 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26104])).
% 3.03/3.22 tff(26106,plain,
% 3.03/3.22 (~(s(s(z)) = s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[960, 26012])).
% 3.03/3.22 tff(26107,plain,
% 3.03/3.22 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[953, 26106])).
% 3.03/3.22 tff(26108,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[946, 26107])).
% 3.03/3.22 tff(26109,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26108, 26105])).
% 3.03/3.22 tff(26110,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[486, 26109, 147])).
% 3.03/3.22 tff(26111,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26112,plain,
% 3.03/3.22 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26113,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26112])).
% 3.03/3.22 tff(26114,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 3.03/3.22 inference(transitivity,[status(thm)],[26113, 26111])).
% 3.03/3.22 tff(26115,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26116,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26115, 26114])).
% 3.03/3.22 tff(26117,plain,
% 3.03/3.22 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26116, 271, 25632, 26072, 26110])).
% 3.03/3.22 tff(26118,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[6237, 21, 26117, 26013])).
% 3.03/3.22 tff(26119,plain,
% 3.03/3.22 (~b(z, s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24348, 26059, 10994, 1])).
% 3.03/3.22 tff(26120,plain,
% 3.03/3.22 (~(elem!1 = s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[6491, 26076, 26119])).
% 3.03/3.22 tff(26121,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[78, 26120])).
% 3.03/3.22 tff(26122,plain,
% 3.03/3.22 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[3177, 271, 25632, 2618, 26110])).
% 3.03/3.22 tff(26123,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[681, 26122, 26121])).
% 3.03/3.22 tff(26124,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26125,plain,
% 3.03/3.22 (((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26126,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26125])).
% 3.03/3.22 tff(26127,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.03/3.22 inference(transitivity,[status(thm)],[26126, 26124])).
% 3.03/3.22 tff(26128,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26129,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26128, 26127])).
% 3.03/3.22 tff(26130,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26129, 121, 26123, 26074, 25635, 26118])).
% 3.03/3.22 tff(26131,plain,((~r(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (s(s(s(z))) = elem!1) | (elem!1 = z) | (~r(z, elem!1)) | r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(26132,plain,
% 3.03/3.22 (~r(s(z), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26131, 147, 2618, 220, 907, 259, 378, 10994, 1, 2344, 5499])).
% 3.03/3.22 tff(26133,plain,
% 3.03/3.22 (b(s(z), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[236, 26132, 26012])).
% 3.03/3.22 tff(26134,plain,
% 3.03/3.22 (~b(s(z), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[25651, 26133, 25632, 907, 220, 11211, 259, 378])).
% 3.03/3.22 tff(26135,plain,
% 3.03/3.22 (r(s(z), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[105, 26134])).
% 3.03/3.22 tff(26136,plain,
% 3.03/3.22 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[23235, 26135, 25635, 25636])).
% 3.03/3.22 tff(26137,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[23458, 26136, 5499])).
% 3.03/3.22 tff(26138,plain,
% 3.03/3.22 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24019, 26137, 25635, 25636, 25632, 26133, 2618])).
% 3.03/3.22 tff(26139,plain,
% 3.03/3.22 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[23997, 378, 11211, 25638, 907, 25632])).
% 3.03/3.22 tff(26140,plain,
% 3.03/3.22 (s(s(s(z))) = s(elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1816, 26136, 26139])).
% 3.03/3.22 tff(26141,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[2596, 26140])).
% 3.03/3.22 tff(26142,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[486, 26141, 26138, 147])).
% 3.03/3.22 tff(26143,plain,(r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (elem!1 = z) | (~r(z, elem!1)) | r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(26144,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26143, 259, 5499, 907, 220, 26011, 366, 10994, 1, 2344])).
% 3.03/3.22 tff(26145,plain,
% 3.03/3.22 (r(s(s(s(z))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[25677, 26144, 25632, 11211, 907, 22132, 19197, 366, 25638])).
% 3.03/3.22 tff(26146,plain,
% 3.03/3.22 (~r(s(z), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[23235, 26145, 25635, 25636])).
% 3.03/3.22 tff(26147,plain,
% 3.03/3.22 (r(z, s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[23127, 26146, 1, 19197])).
% 3.03/3.22 tff(26148,plain,
% 3.03/3.22 (b(s(z), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[105, 26146])).
% 3.03/3.22 tff(26149,plain,
% 3.03/3.22 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24371, 26148, 26147, 19197, 220])).
% 3.03/3.22 tff(26150,plain,
% 3.03/3.22 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[932, 26149])).
% 3.03/3.22 tff(26151,plain,
% 3.03/3.22 (~b(s(z), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[25651, 26148, 25632, 907, 220, 11211, 259, 366])).
% 3.03/3.22 tff(26152,plain,
% 3.03/3.22 (r(s(z), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[236, 26151, 26012])).
% 3.03/3.22 tff(26153,plain,
% 3.03/3.22 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26067, 121, 26152, 26150, 25635])).
% 3.03/3.22 tff(26154,plain,
% 3.03/3.22 (b(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1559, 26153, 19204])).
% 3.03/3.22 tff(26155,plain,
% 3.03/3.22 (~r(z, s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24514, 26145, 220, 25636, 25635])).
% 3.03/3.22 tff(26156,plain,
% 3.03/3.22 (b(z, s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1439, 26155])).
% 3.03/3.22 tff(26157,plain,
% 3.03/3.22 (~b(s(s(s(s(z)))), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26082, 271, 26011, 26156, 26154])).
% 3.03/3.22 tff(26158,plain,
% 3.03/3.22 (r(s(s(s(s(z)))), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1095, 26157])).
% 3.03/3.22 tff(26159,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26160,plain,
% 3.03/3.22 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26161,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26160])).
% 3.03/3.22 tff(26162,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(transitivity,[status(thm)],[26161, 26159])).
% 3.03/3.22 tff(26163,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26164,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26163, 26162])).
% 3.03/3.22 tff(26165,plain,
% 3.03/3.22 (~r(s(s(s(s(z)))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26164, 121, 366, 25638, 26158])).
% 3.03/3.22 tff(26166,plain,
% 3.03/3.22 (~b(s(s(s(s(z)))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26100, 271, 25632, 26011, 26154])).
% 3.03/3.22 tff(26167,plain,
% 3.03/3.22 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[24968, 21, 26166])).
% 3.03/3.22 tff(26168,plain,
% 3.03/3.22 (s(s(s(s(z)))) = elem!1),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26167, 26165])).
% 3.03/3.22 tff(26169,plain,
% 3.03/3.22 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26168])).
% 3.03/3.22 tff(26170,plain,
% 3.03/3.22 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.03/3.22 inference(symmetry,[status(thm)],[26169])).
% 3.03/3.22 tff(26171,plain,
% 3.03/3.22 ((~r(elem!1, s(z))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26170])).
% 3.03/3.22 tff(26172,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[16580, 7033])).
% 3.03/3.22 tff(26173,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26174,plain,
% 3.03/3.22 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(26175,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[26174])).
% 3.03/3.22 tff(26176,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 3.03/3.22 inference(transitivity,[status(thm)],[26175, 26173])).
% 3.03/3.22 tff(26177,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(26178,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[26177, 26176])).
% 3.03/3.22 tff(26179,plain,
% 3.03/3.22 (~r(z, s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[26178, 121, 378, 139, 3456])).
% 3.03/3.22 tff(26180,plain,
% 3.03/3.22 (b(z, s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[19736, 26179])).
% 3.03/3.22 tff(26181,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[17333, 26180, 26172, 220, 7036])).
% 3.03/3.22 tff(26182,plain,((~r(elem!1, s(z))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26183,plain,
% 3.03/3.23 (~r(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26182, 26152, 366, 26144, 220])).
% 3.03/3.23 tff(26184,plain,
% 3.03/3.23 (~r(s(s(s(s(z)))), s(z))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26183, 26171])).
% 3.03/3.23 tff(26185,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26150, 26184])).
% 3.03/3.23 tff(26186,plain,((elem!1 = z) | (~b(z, s(z))) | (s(s(s(z))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(elem!1), z) | r(elem!1, s(elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26187,plain,
% 3.03/3.23 (b(z, elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26186, 10994, 220, 1, 5499, 25634, 2344, 907])).
% 3.03/3.23 tff(26188,plain,
% 3.03/3.23 (~b(s(elem!1), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[4598, 1326, 307, 394])).
% 3.03/3.23 tff(26189,plain,
% 3.03/3.23 (r(s(elem!1), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2243, 26188, 3500])).
% 3.03/3.23 tff(26190,plain,
% 3.03/3.23 (r(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[299, 24773, 25679])).
% 3.03/3.23 tff(26191,plain,
% 3.03/3.23 (r(s(z), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[9267, 24773, 377, 1281, 25645, 24383, 348, 1326])).
% 3.03/3.23 tff(26192,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[6525, 26191, 26190, 24383, 26189])).
% 3.03/3.23 tff(26193,plain,((~b(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26194,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26193, 26187, 11211, 19197, 25632, 24230, 219, 220])).
% 3.03/3.23 tff(26195,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(elem!1, s(elem!1)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26196,plain,
% 3.03/3.23 (r(s(elem!1), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26195, 907, 1, 5499, 2344, 220])).
% 3.03/3.23 tff(26197,plain,
% 3.03/3.23 (r(z, elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[355, 199, 25633])).
% 3.03/3.23 tff(26198,plain,
% 3.03/3.23 (~(s(elem!1) = s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[350, 24230])).
% 3.03/3.23 tff(26199,plain,
% 3.03/3.23 (~r(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[5343, 1243, 412, 622])).
% 3.03/3.23 tff(26200,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[299, 26199, 337, 294])).
% 3.03/3.23 tff(26201,plain,(b(z, elem!1) | b(elem!1, s(z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (z = elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26202,plain,
% 3.03/3.23 (b(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26201, 199, 412, 622, 25633, 220])).
% 3.03/3.23 tff(26203,plain,
% 3.03/3.23 (~r(elem!1, z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[5358, 26197, 412, 622])).
% 3.03/3.23 tff(26204,plain,
% 3.03/3.23 (b(elem!1, z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[284, 26203, 25634])).
% 3.03/3.23 tff(26205,plain,
% 3.03/3.23 (~b(s(z), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[8962, 26204, 220, 26202])).
% 3.03/3.23 tff(26206,plain,
% 3.03/3.23 (r(s(z), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[236, 26205, 230])).
% 3.03/3.23 tff(26207,plain,
% 3.03/3.23 (~b(s(elem!1), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1290, 26202, 1281, 307])).
% 3.03/3.23 tff(26208,plain,
% 3.03/3.23 (r(s(elem!1), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[429, 26207, 26198])).
% 3.03/3.23 tff(26209,plain,
% 3.03/3.23 (~r(z, s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[25779, 26206, 1281, 622, 25634, 26208, 26197, 26202])).
% 3.03/3.23 tff(26210,plain,
% 3.03/3.23 (b(z, s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1439, 26209])).
% 3.03/3.23 tff(26211,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[16768])).
% 3.03/3.23 tff(26212,plain,
% 3.03/3.23 (r(s(elem!1), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.23 inference(symmetry,[status(thm)],[26211])).
% 3.03/3.23 tff(26213,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[411, 26212])).
% 3.03/3.23 tff(26214,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[16768])).
% 3.03/3.23 tff(26215,plain,
% 3.03/3.23 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.23 inference(symmetry,[status(thm)],[26214])).
% 3.03/3.23 tff(26216,plain,
% 3.03/3.23 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[16767])).
% 3.03/3.23 tff(26217,plain,
% 3.03/3.23 (b(z, s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[1421, 26216])).
% 3.03/3.23 tff(26218,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[16767])).
% 3.03/3.23 tff(26219,plain,
% 3.03/3.23 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[13202])).
% 3.03/3.23 tff(26220,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[307, 26219])).
% 3.03/3.23 tff(26221,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26220, 26218])).
% 3.03/3.23 tff(26222,plain,
% 3.03/3.23 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 3.03/3.23 inference(monotonicity,[status(thm)],[13202])).
% 3.03/3.23 tff(26223,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), z)),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[261, 26222])).
% 3.03/3.23 tff(26224,plain,
% 3.03/3.23 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[16768])).
% 3.03/3.23 tff(26225,plain,
% 3.03/3.23 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.23 inference(symmetry,[status(thm)],[26224])).
% 3.03/3.23 tff(26226,plain,
% 3.03/3.23 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[14671, 26225])).
% 3.03/3.23 tff(26227,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.03/3.23 tff(26228,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26229,plain,
% 3.03/3.23 (((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26230,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26229])).
% 3.03/3.23 tff(26231,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[26230, 26228])).
% 3.03/3.23 tff(26232,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(26233,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26232, 26231])).
% 3.03/3.23 tff(26234,plain,
% 3.03/3.23 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26233, 271, 1638, 18789, 26227])).
% 3.03/3.23 tff(26235,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26234, 26226])).
% 3.03/3.23 tff(26236,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26237,plain,
% 3.03/3.23 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26236, 26223, 13202, 26221, 26217])).
% 3.03/3.23 tff(26238,plain,
% 3.03/3.23 (r(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1995, 26237, 2603])).
% 3.03/3.23 tff(26239,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26238, 26215])).
% 3.03/3.23 tff(26240,plain,
% 3.03/3.23 (~b(z, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[13207, 13202, 199])).
% 3.03/3.23 tff(26241,plain,
% 3.03/3.23 (r(z, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[19736, 26240])).
% 3.03/3.23 tff(26242,plain,
% 3.03/3.23 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[13202])).
% 3.03/3.23 tff(26243,plain,
% 3.03/3.23 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.03/3.23 inference(symmetry,[status(thm)],[26242])).
% 3.03/3.23 tff(26244,plain,
% 3.03/3.23 (r(s(s(s(z))), elem!1)),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[5499, 26243])).
% 3.03/3.23 tff(26245,plain,
% 3.03/3.23 (~r(s(z), s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26024, 26244, 26197, 220, 25634, 1281, 337, 357])).
% 3.03/3.23 tff(26246,plain,
% 3.03/3.23 (b(s(z), s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[105, 26245])).
% 3.03/3.23 tff(26247,plain,
% 3.03/3.23 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[24371, 26246, 26241, 1281, 220])).
% 3.03/3.23 tff(26248,plain,
% 3.03/3.23 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[932, 26247])).
% 3.03/3.23 tff(26249,plain,
% 3.03/3.23 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[13202])).
% 3.03/3.23 tff(26250,plain,
% 3.03/3.23 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[357, 26249])).
% 3.03/3.23 tff(26251,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26252,plain,
% 3.03/3.23 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(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(s(z))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26253,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26252])).
% 3.03/3.23 tff(26254,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[26253, 26251])).
% 3.03/3.23 tff(26255,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(26256,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26255, 26254])).
% 3.03/3.23 tff(26257,plain,
% 3.03/3.23 ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26256, 121, 26250, 26248])).
% 3.03/3.23 tff(26258,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26257, 26239, 26213])).
% 3.03/3.23 tff(26259,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(z, s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26260,plain,
% 3.03/3.23 (~(elem!1 = s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26259, 26208, 1281, 220, 2603, 26206, 26210, 5499, 26204, 307, 199])).
% 3.03/3.23 tff(26261,plain,
% 3.03/3.23 (~r(elem!1, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[6817, 26197, 412, 622])).
% 3.03/3.23 tff(26262,plain,
% 3.03/3.23 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[660, 21, 26261])).
% 3.03/3.23 tff(26263,plain,
% 3.03/3.23 (b(elem!1, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26262, 26260])).
% 3.03/3.23 tff(26264,plain,
% 3.03/3.23 (b(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[299, 21722, 258])).
% 3.03/3.23 tff(26265,plain,
% 3.03/3.23 (~b(s(elem!1), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1290, 26264, 1281, 307])).
% 3.03/3.23 tff(26266,plain,
% 3.03/3.23 (r(s(elem!1), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[429, 26265, 422])).
% 3.03/3.23 tff(26267,plain,
% 3.03/3.23 (~r(z, s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[25779, 26266, 1281, 378, 259, 622, 357, 26264])).
% 3.03/3.23 tff(26268,plain,
% 3.03/3.23 (~b(z, s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[5420, 21724, 1281, 26264])).
% 3.03/3.23 tff(26269,plain,
% 3.03/3.23 (r(z, s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2106, 26268])).
% 3.03/3.23 tff(26270,plain,
% 3.03/3.23 (~b(z, s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[6868, 26269, 307, 412, 738, 82, 378, 21724])).
% 3.03/3.23 tff(26271,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1439, 26270, 26267])).
% 3.03/3.23 tff(26272,plain,((~r(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~b(s(z), z)) | (elem!1 = z) | (~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26273,plain,
% 3.03/3.23 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26272, 26263, 307, 412, 622, 26206, 1281, 25634, 26197, 26198, 337])).
% 3.03/3.23 tff(26274,plain,
% 3.03/3.23 (elem!1 = s(s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[78, 26273])).
% 3.03/3.23 tff(26275,plain,
% 3.03/3.23 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26274])).
% 3.03/3.23 tff(26276,plain,
% 3.03/3.23 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 3.03/3.23 inference(symmetry,[status(thm)],[26275])).
% 3.03/3.23 tff(26277,plain,
% 3.03/3.23 ((~b(s(s(elem!1)), z)) <=> (~b(elem!1, z))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26276])).
% 3.03/3.23 tff(26278,plain,
% 3.03/3.23 (~r(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[5343, 26197, 412, 622])).
% 3.03/3.23 tff(26279,plain,
% 3.03/3.23 (~r(s(s(elem!1)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12129, 26274, 26278])).
% 3.03/3.23 tff(26280,plain,
% 3.03/3.23 (b(s(s(elem!1)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2143, 26279])).
% 3.03/3.23 tff(26281,plain,
% 3.03/3.23 (~b(s(s(elem!1)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[16949, 26280, 1281, 220])).
% 3.03/3.23 tff(26282,plain,
% 3.03/3.23 (~b(elem!1, z)),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26281, 26277])).
% 3.03/3.23 tff(26283,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26204, 26282])).
% 3.03/3.23 tff(26284,plain,(b(z, elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26285,plain,
% 3.03/3.23 (b(z, elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26284, 8563, 220, 25632, 26196, 19197, 19205, 5499])).
% 3.03/3.23 tff(26286,plain,
% 3.03/3.23 (~b(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[20398, 26285, 19197, 220])).
% 3.03/3.23 tff(26287,plain,
% 3.03/3.23 (b(z, elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26284, 622, 220, 25632, 26196, 19197, 19205, 5499])).
% 3.03/3.23 tff(26288,plain,
% 3.03/3.23 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[1038])).
% 3.03/3.23 tff(26289,plain,
% 3.03/3.23 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.23 inference(transitivity,[status(thm)],[26288, 200])).
% 3.03/3.23 tff(26290,plain,
% 3.03/3.23 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26289])).
% 3.03/3.23 tff(26291,plain,
% 3.03/3.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[19205, 26290])).
% 3.03/3.23 tff(26292,plain,
% 3.03/3.23 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[23507, 26291, 25632, 26196, 26287])).
% 3.03/3.23 tff(26293,plain,
% 3.03/3.23 (r(s(s(s(elem!1))), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[486, 26292, 5087])).
% 3.03/3.23 tff(26294,plain,
% 3.03/3.23 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[5499, 1378])).
% 3.03/3.23 tff(26295,plain,
% 3.03/3.23 (~r(s(elem!1), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[635, 624, 623, 622])).
% 3.03/3.23 tff(26296,plain,
% 3.03/3.23 (b(s(elem!1), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[526, 26295, 216])).
% 3.03/3.23 tff(26297,plain,
% 3.03/3.23 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[720, 624, 622, 139])).
% 3.03/3.23 tff(26298,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[681, 26297, 82])).
% 3.03/3.23 tff(26299,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[673, 26298, 26296, 307, 481, 623, 624])).
% 3.03/3.23 tff(26300,plain,((~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26301,plain,
% 3.03/3.23 (~r(elem!1, s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26300, 5087, 25632, 26294, 26291, 211, 622, 26293])).
% 3.03/3.23 tff(26302,plain,
% 3.03/3.23 (b(elem!1, s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[599, 26301, 5038])).
% 3.03/3.23 tff(26303,plain,
% 3.03/3.23 (b(s(z), s(s(elem!1)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26302, 17792])).
% 3.03/3.23 tff(26304,plain,
% 3.03/3.23 (~b(s(s(elem!1)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[17014, 26303, 19197, 220])).
% 3.03/3.23 tff(26305,plain,
% 3.03/3.23 (r(s(s(elem!1)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2430, 26304])).
% 3.03/3.23 tff(26306,plain,
% 3.03/3.23 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26293, 6658])).
% 3.03/3.23 tff(26307,plain,
% 3.03/3.23 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[8812, 1222, 5499])).
% 3.03/3.23 tff(26308,plain,
% 3.03/3.23 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 3.03/3.23 inference(monotonicity,[status(thm)],[223])).
% 3.03/3.23 tff(26309,plain,
% 3.03/3.23 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 3.03/3.23 inference(symmetry,[status(thm)],[26308])).
% 3.03/3.23 tff(26310,plain,
% 3.03/3.23 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 3.03/3.23 inference(symmetry,[status(thm)],[4949])).
% 3.03/3.23 tff(26311,plain,
% 3.03/3.23 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 3.03/3.23 inference(transitivity,[status(thm)],[26310, 26309])).
% 3.03/3.23 tff(26312,plain,
% 3.03/3.23 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 3.03/3.23 inference(transitivity,[status(thm)],[7870, 17792])).
% 3.03/3.23 tff(26313,plain,
% 3.03/3.23 (b(elem!1, s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[11114, 20246, 1222])).
% 3.03/3.23 tff(26314,plain,
% 3.03/3.23 (b(s(z), s(s(elem!1)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26313, 26312])).
% 3.03/3.23 tff(26315,plain,
% 3.03/3.23 (~b(s(s(elem!1)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[17014, 26314, 19197, 220])).
% 3.03/3.23 tff(26316,plain,
% 3.03/3.23 (r(s(s(elem!1)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2430, 26315])).
% 3.03/3.23 tff(26317,plain,
% 3.03/3.23 (r(z, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[23127, 100, 1, 19197])).
% 3.03/3.23 tff(26318,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26319,plain,
% 3.03/3.23 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26320,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26319])).
% 3.03/3.23 tff(26321,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z)))),
% 3.03/3.23 inference(transitivity,[status(thm)],[26320, 26318])).
% 3.03/3.23 tff(26322,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(26323,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), z))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26322, 26321])).
% 3.03/3.23 tff(26324,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26323, 121, 623, 26317, 139, 26316])).
% 3.03/3.23 tff(26325,plain,(r(s(z), s(s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(26326,plain,
% 3.03/3.23 (r(s(z), s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26325, 26294, 26293, 220, 223, 1])).
% 3.03/3.23 tff(26327,plain,
% 3.03/3.23 (b(s(z), s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1276, 223, 25632])).
% 3.03/3.23 tff(26328,plain,
% 3.03/3.23 (b(s(z), s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[6679, 26302, 1222])).
% 3.03/3.23 tff(26329,plain,
% 3.03/3.23 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[3057])).
% 3.03/3.23 tff(26330,plain,
% 3.03/3.23 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(symmetry,[status(thm)],[26329])).
% 3.03/3.23 tff(26331,plain,
% 3.03/3.23 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[5001, 7890])).
% 3.03/3.23 tff(26332,plain,
% 3.03/3.23 (b(elem!1, s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[11114, 3871, 1222])).
% 3.03/3.23 tff(26333,plain,
% 3.03/3.23 (~b(z, s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[19416, 257, 1281, 3871])).
% 3.03/3.23 tff(26334,plain,
% 3.03/3.23 (r(z, s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1214, 26333])).
% 3.03/3.23 tff(26335,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26336,plain,
% 3.03/3.23 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26337,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[26336])).
% 3.03/3.23 tff(26338,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[26337, 26335])).
% 3.03/3.23 tff(26339,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(26340,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[26339, 26338])).
% 3.03/3.23 tff(26341,plain,
% 3.03/3.23 (~r(s(s(s(s(s(z))))), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[26340, 121, 1736, 109, 1140])).
% 3.03/3.23 tff(26342,plain,
% 3.03/3.23 (b(s(s(s(s(s(z))))), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[6593, 21, 711, 26341])).
% 3.03/3.23 tff(26343,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(26344,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~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))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(26345,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26344, 26343])).
% 3.03/3.24 tff(26346,plain,
% 3.03/3.24 (~r(s(s(s(s(s(z))))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26345, 121, 1736, 109, 108])).
% 3.03/3.24 tff(26347,plain,
% 3.03/3.24 (b(s(s(s(s(s(z))))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1682, 26346])).
% 3.03/3.24 tff(26348,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[25901, 271, 1281, 220, 26347, 26342])).
% 3.03/3.24 tff(26349,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26350,plain,
% 3.03/3.24 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26349, 26334, 220, 108, 24356, 1281])).
% 3.03/3.24 tff(26351,plain,
% 3.03/3.24 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1733, 26350])).
% 3.03/3.24 tff(26352,plain,
% 3.03/3.24 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1857, 26351, 257, 26332])).
% 3.03/3.24 tff(26353,plain,
% 3.03/3.24 (r(elem!1, s(s(s(s(s(z))))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1847, 26352, 26331])).
% 3.03/3.24 tff(26354,plain,
% 3.03/3.24 (r(elem!1, s(s(s(s(elem!1)))))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26353, 26330])).
% 3.03/3.24 tff(26355,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26356,plain,
% 3.03/3.24 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26357,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26356])).
% 3.03/3.24 tff(26358,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 3.03/3.24 inference(transitivity,[status(thm)],[26357, 26355])).
% 3.03/3.24 tff(26359,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(26360,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26359, 26358])).
% 3.03/3.24 tff(26361,plain,
% 3.03/3.24 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26360, 121, 622, 139, 26354])).
% 3.03/3.24 tff(26362,plain,
% 3.03/3.24 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[681, 26361, 26291])).
% 3.03/3.24 tff(26363,plain,
% 3.03/3.24 (~b(z, s(s(elem!1)))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26333, 17671])).
% 3.03/3.24 tff(26364,plain,
% 3.03/3.24 (r(z, s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2106, 26363])).
% 3.03/3.24 tff(26365,plain,
% 3.03/3.24 (~r(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3425, 26364, 623, 139])).
% 3.03/3.24 tff(26366,plain,
% 3.03/3.24 (b(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[19736, 26365])).
% 3.03/3.24 tff(26367,plain,
% 3.03/3.24 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[21846, 26366, 1281, 26362])).
% 3.03/3.24 tff(26368,plain,
% 3.03/3.24 (~b(s(elem!1), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2369, 12496, 1222])).
% 3.03/3.24 tff(26369,plain,
% 3.03/3.24 (r(s(elem!1), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[526, 26368, 216])).
% 3.03/3.24 tff(26370,plain,
% 3.03/3.24 (~r(s(s(elem!1)), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[5431, 26364, 412, 26369])).
% 3.03/3.24 tff(26371,plain,
% 3.03/3.24 (~r(s(z), s(s(s(s(z)))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[23042, 26370, 412, 1222, 6796, 6659, 26334, 3871, 446, 1326, 24356, 907, 19205])).
% 3.03/3.24 tff(26372,plain,
% 3.03/3.24 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1053, 26371, 223])).
% 3.03/3.24 tff(26373,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[760, 26372, 26367])).
% 3.03/3.24 tff(26374,plain,((~b(s(s(s(z))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(z), z)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26375,plain,
% 3.03/3.24 (~b(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26374, 223, 19197, 26196, 26328, 26327, 26287, 907, 26294, 26293, 622, 211, 220, 26326])).
% 3.03/3.24 tff(26376,plain,
% 3.03/3.24 (r(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[255, 26375, 907])).
% 3.03/3.24 tff(26377,plain,
% 3.03/3.24 (r(s(s(elem!1)), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[14112, 26376, 223])).
% 3.03/3.24 tff(26378,plain,
% 3.03/3.24 (r(s(s(s(z))), s(z))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26377, 26311])).
% 3.03/3.24 tff(26379,plain,
% 3.03/3.24 (~r(s(z), s(s(s(s(z)))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[21540, 26378, 26307, 26306])).
% 3.03/3.24 tff(26380,plain,
% 3.03/3.24 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1053, 26379, 223])).
% 3.03/3.24 tff(26381,plain,
% 3.03/3.24 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[760, 26380])).
% 3.03/3.24 tff(26382,plain,
% 3.03/3.24 (b(s(z), s(s(z)))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[25632, 7921])).
% 3.03/3.24 tff(26383,plain,
% 3.03/3.24 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[17419, 1548])).
% 3.03/3.24 tff(26384,plain,
% 3.03/3.24 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26383, 26290])).
% 3.03/3.24 tff(26385,plain,
% 3.03/3.24 (r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[681, 675, 26384])).
% 3.03/3.24 tff(26386,plain,
% 3.03/3.24 (b(elem!1, s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[599, 4435, 5038])).
% 3.03/3.24 tff(26387,plain,
% 3.03/3.24 (b(s(z), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[6679, 26386, 1222])).
% 3.03/3.24 tff(26388,plain,
% 3.03/3.24 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[21604, 675, 1222, 622, 216, 623, 6763, 750, 26387, 145, 4435, 26384])).
% 3.03/3.24 tff(26389,plain,
% 3.03/3.24 (~b(s(elem!1), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[16735, 26388, 2344, 622, 5038, 479, 26385])).
% 3.03/3.24 tff(26390,plain,
% 3.03/3.24 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[4478, 675, 622, 5038, 4435, 623, 5087])).
% 3.03/3.24 tff(26391,plain,
% 3.03/3.24 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[586, 26390, 6943])).
% 3.03/3.24 tff(26392,plain,
% 3.03/3.24 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[1038])).
% 3.03/3.24 tff(26393,plain,
% 3.03/3.24 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[1562, 26392])).
% 3.03/3.24 tff(26394,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[675, 26393])).
% 3.03/3.24 tff(26395,plain,((~b(s(s(s(s(z)))), s(elem!1))) | b(s(s(s(elem!1))), s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26396,plain,
% 3.03/3.24 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26395, 675, 223])).
% 3.03/3.24 tff(26397,plain,
% 3.03/3.24 (r(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1559, 26396, 1548])).
% 3.03/3.24 tff(26398,plain,
% 3.03/3.24 (~r(s(elem!1), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2395, 26397, 1222, 26391, 145])).
% 3.03/3.24 tff(26399,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[526, 26398, 26389, 216])).
% 3.03/3.24 tff(26400,plain,(b(s(s(s(elem!1))), s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | r(elem!1, s(elem!1)) | (~r(s(elem!1), elem!1)) | b(s(s(s(elem!1))), elem!1) | (s(s(s(s(z)))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | r(elem!1, s(s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26401,plain,
% 3.03/3.24 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26400, 26376, 211, 2344, 622, 26292, 19204, 563, 26294, 26382, 26381, 26301, 223])).
% 3.03/3.24 tff(26402,plain,
% 3.03/3.24 (~b(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[21846, 26401, 19197, 26381])).
% 3.03/3.24 tff(26403,plain,
% 3.03/3.24 (r(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[19736, 26402])).
% 3.03/3.24 tff(26404,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26323, 121, 26294, 26403, 26293, 26305])).
% 3.03/3.24 tff(26405,plain,((~(s(z) = elem!1)) | r(elem!1, s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26406,plain,
% 3.03/3.24 (~(s(z) = elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26405, 8563, 2344, 907, 220, 1, 5499])).
% 3.03/3.24 tff(26407,plain,
% 3.03/3.24 (~(elem!1 = s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[242, 26406])).
% 3.03/3.24 tff(26408,plain,
% 3.03/3.24 (r(elem!1, s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[299, 26407, 26286])).
% 3.03/3.24 tff(26409,plain,
% 3.03/3.24 (~b(s(z), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[20382, 26285, 19197, 25632])).
% 3.03/3.24 tff(26410,plain,
% 3.03/3.24 (r(s(z), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[236, 26406, 26409])).
% 3.03/3.24 tff(26411,plain,
% 3.03/3.24 (r(s(s(s(elem!1))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[23552, 26410, 907, 1, 25632, 26196, 26285, 25633, 26198, 2467, 26407, 26286])).
% 3.03/3.24 tff(26412,plain,
% 3.03/3.24 (~r(s(s(s(elem!1))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[4618, 121, 26410, 26411, 26408])).
% 3.03/3.24 tff(26413,plain,
% 3.03/3.24 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[16580, 26412])).
% 3.03/3.24 tff(26414,plain,
% 3.03/3.24 (~r(s(elem!1), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[11219, 121, 8563, 26410, 26408])).
% 3.03/3.24 tff(26415,plain,
% 3.03/3.24 (~r(s(z), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[6525, 26408, 8563, 26410])).
% 3.03/3.24 tff(26416,plain,
% 3.03/3.24 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[18965, 26411, 26286, 26407, 26409])).
% 3.03/3.24 tff(26417,plain,
% 3.03/3.24 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[760, 26416])).
% 3.03/3.24 tff(26418,plain,
% 3.03/3.24 (~b(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[17333, 26413, 220, 26417])).
% 3.03/3.24 tff(26419,plain,
% 3.03/3.24 (r(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[19736, 26418])).
% 3.03/3.24 tff(26420,plain,
% 3.03/3.24 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2310, 26419, 24230, 26415, 26414, 26413, 26196])).
% 3.03/3.24 tff(26421,plain,
% 3.03/3.24 (r(s(s(s(z))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[23458, 26420, 5499])).
% 3.03/3.24 tff(26422,plain,
% 3.03/3.24 (elem!1 = s(s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[78, 26420])).
% 3.03/3.24 tff(26423,plain,
% 3.03/3.24 (~b(s(elem!1), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3922, 26422, 2467])).
% 3.03/3.24 tff(26424,plain,
% 3.03/3.24 (r(s(elem!1), s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[526, 26423, 211])).
% 3.03/3.24 tff(26425,plain,
% 3.03/3.24 (b(s(elem!1), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[429, 26414, 26198])).
% 3.03/3.24 tff(26426,plain,
% 3.03/3.24 (~b(z, s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[24719, 26425, 220, 19197])).
% 3.03/3.24 tff(26427,plain,
% 3.03/3.24 (r(z, s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1439, 26426])).
% 3.03/3.24 tff(26428,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26429,plain,
% 3.03/3.24 (((~r(s(elem!1), s(s(elem!1)))) | (~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(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26430,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26429])).
% 3.03/3.24 tff(26431,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.03/3.24 inference(transitivity,[status(thm)],[26430, 26428])).
% 3.03/3.24 tff(26432,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(26433,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26432, 26431])).
% 3.03/3.24 tff(26434,plain,
% 3.03/3.24 (~r(s(s(s(z))), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26433, 121, 26427, 26424, 26421])).
% 3.03/3.24 tff(26435,plain,
% 3.03/3.24 (b(s(s(s(z))), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1155, 26434])).
% 3.03/3.24 tff(26436,plain,
% 3.03/3.24 (~b(s(z), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[21058, 26435, 19197, 220])).
% 3.03/3.24 tff(26437,plain,
% 3.03/3.24 (r(s(z), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[105, 26436])).
% 3.03/3.24 tff(26438,plain,
% 3.03/3.24 (~b(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1940, 26435, 25632, 26285])).
% 3.03/3.24 tff(26439,plain,
% 3.03/3.24 (r(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[255, 26438, 907])).
% 3.03/3.24 tff(26440,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[4112, 26439, 26437, 26410, 26408])).
% 3.03/3.24 tff(26441,plain,(b(s(elem!1), elem!1) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26442,plain,
% 3.03/3.24 (b(s(elem!1), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26441, 907, 220, 5499, 1, 2344])).
% 3.03/3.24 tff(26443,plain,
% 3.03/3.24 (~r(s(elem!1), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26284, 199, 220, 25632, 26196, 19197, 19205, 5499])).
% 3.03/3.24 tff(26444,plain,
% 3.03/3.24 (~b(s(s(s(z))), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[21058, 20246, 19197, 220])).
% 3.03/3.24 tff(26445,plain,
% 3.03/3.24 (r(s(s(s(z))), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1155, 26444])).
% 3.03/3.24 tff(26446,plain,
% 3.03/3.24 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3650, 26445, 412, 378])).
% 3.03/3.24 tff(26447,plain,
% 3.03/3.24 (~b(s(z), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[4613, 21154, 307, 2618, 348])).
% 3.03/3.24 tff(26448,plain,
% 3.03/3.24 (~(s(s(s(z))) = elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[10599, 26447, 3871])).
% 3.03/3.24 tff(26449,plain,
% 3.03/3.24 (b(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[255, 26448, 221])).
% 3.03/3.24 tff(26450,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1976, 271, 307, 21154, 1307, 26449])).
% 3.03/3.24 tff(26451,plain,(r(s(s(s(z))), elem!1) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26452,plain,
% 3.03/3.24 (~b(z, s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26451, 221, 1281, 307, 2618, 24230, 3871])).
% 3.03/3.24 tff(26453,plain,
% 3.03/3.24 (r(z, s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1214, 26452])).
% 3.03/3.24 tff(26454,plain,
% 3.03/3.24 (s(s(s(z))) = s(elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[13140, 26453, 307, 412, 2618, 5469])).
% 3.03/3.24 tff(26455,plain,
% 3.03/3.24 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26454])).
% 3.03/3.24 tff(26456,plain,
% 3.03/3.24 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26455])).
% 3.03/3.24 tff(26457,plain,
% 3.03/3.24 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26456])).
% 3.03/3.24 tff(26458,plain,
% 3.03/3.24 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.24 inference(symmetry,[status(thm)],[26457])).
% 3.03/3.24 tff(26459,plain,
% 3.03/3.24 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2596, 26454])).
% 3.03/3.24 tff(26460,plain,
% 3.03/3.24 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[486, 26459, 147])).
% 3.03/3.24 tff(26461,plain,
% 3.03/3.24 (b(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26460, 26458])).
% 3.03/3.24 tff(26462,plain,
% 3.03/3.24 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[5007, 26461, 307, 5469])).
% 3.03/3.24 tff(26463,plain,
% 3.03/3.24 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[9660, 26454, 5499])).
% 3.03/3.24 tff(26464,plain,
% 3.03/3.24 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26456])).
% 3.03/3.24 tff(26465,plain,
% 3.03/3.24 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 3.03/3.24 inference(symmetry,[status(thm)],[26464])).
% 3.03/3.24 tff(26466,plain,
% 3.03/3.24 (r(z, s(s(s(s(s(z))))))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[111, 26465])).
% 3.03/3.24 tff(26467,plain,
% 3.03/3.24 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[5135, 26466, 109, 26463])).
% 3.03/3.24 tff(26468,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1733, 26467, 26462])).
% 3.03/3.24 tff(26469,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26470,plain,
% 3.03/3.24 (r(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26469, 26445, 25632, 26317, 147, 5499, 412, 2618, 19197, 20246, 907])).
% 3.03/3.24 tff(26471,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[10776, 121, 378, 1184, 145, 109])).
% 3.03/3.24 tff(26472,plain,((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26473,plain,
% 3.03/3.24 (~r(elem!1, s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26472, 26470, 378, 26445])).
% 3.03/3.24 tff(26474,plain,
% 3.03/3.24 (b(elem!1, s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1192, 26473, 1101])).
% 3.03/3.24 tff(26475,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26476,plain,
% 3.03/3.24 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26477,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z)))))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26476])).
% 3.03/3.24 tff(26478,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(z))))))),
% 3.03/3.24 inference(transitivity,[status(thm)],[26477, 26475])).
% 3.03/3.24 tff(26479,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(26480,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z)))))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26479, 26478])).
% 3.03/3.24 tff(26481,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26480, 271, 307, 2618, 1195, 1422])).
% 3.03/3.24 tff(26482,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26483,plain,
% 3.03/3.24 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26482, 26474, 2618, 25632])).
% 3.03/3.24 tff(26484,plain,
% 3.03/3.24 (s(s(s(z))) = s(elem!1)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1816, 26483, 26446])).
% 3.03/3.24 tff(26485,plain,
% 3.03/3.24 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26484])).
% 3.03/3.24 tff(26486,plain,
% 3.03/3.24 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(symmetry,[status(thm)],[26485])).
% 3.03/3.24 tff(26487,plain,
% 3.03/3.24 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26486])).
% 3.03/3.24 tff(26488,plain,
% 3.03/3.24 (~r(s(s(s(z))), elem!1)),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[15091, 26487])).
% 3.03/3.24 tff(26489,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26470, 26488])).
% 3.03/3.24 tff(26490,plain,(r(s(z), s(s(s(z)))) | r(s(elem!1), elem!1) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26491,plain,
% 3.03/3.24 (r(s(z), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26490, 26443, 26442, 26197, 147, 5499, 26196, 907, 220, 1])).
% 3.03/3.24 tff(26492,plain,
% 3.03/3.24 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[13128, 271, 25632, 26442, 257])).
% 3.03/3.24 tff(26493,plain,
% 3.03/3.24 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3917, 23419, 24230])).
% 3.03/3.24 tff(26494,plain,
% 3.03/3.24 (~r(z, s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[13140, 26493, 307, 412, 2618, 257])).
% 3.03/3.24 tff(26495,plain,
% 3.03/3.24 (b(z, s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1214, 26494])).
% 3.03/3.24 tff(26496,plain,
% 3.03/3.24 (~r(s(s(s(z))), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3650, 24742, 412, 378])).
% 3.03/3.24 tff(26497,plain,
% 3.03/3.24 (b(s(s(s(z))), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[1155, 26496])).
% 3.03/3.24 tff(26498,plain,
% 3.03/3.24 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2063, 24230])).
% 3.03/3.24 tff(26499,plain,
% 3.03/3.24 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12235, 23419, 26498])).
% 3.03/3.24 tff(26500,plain,
% 3.03/3.24 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[23419])).
% 3.03/3.24 tff(26501,plain,
% 3.03/3.24 (r(z, s(s(elem!1)))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[378, 26500])).
% 3.03/3.24 tff(26502,plain,
% 3.03/3.24 (~r(s(s(s(z))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2640, 1500, 412, 431])).
% 3.03/3.24 tff(26503,plain,
% 3.03/3.24 (b(s(s(s(z))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[2325, 26502])).
% 3.03/3.24 tff(26504,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26505,plain,
% 3.03/3.24 (((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(26506,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z)))))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[26505])).
% 3.03/3.24 tff(26507,plain,
% 3.03/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))))),
% 3.03/3.24 inference(transitivity,[status(thm)],[26506, 26504])).
% 3.03/3.24 tff(26508,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(26509,plain,
% 3.03/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z)))))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[26508, 26507])).
% 3.03/3.24 tff(26510,plain,
% 3.03/3.24 (~r(s(z), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26509, 121, 412, 431, 1500])).
% 3.03/3.24 tff(26511,plain,
% 3.03/3.24 (b(s(z), s(s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[103, 21, 26510, 99])).
% 3.03/3.24 tff(26512,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[11263, 271, 220, 26511, 26503, 1935])).
% 3.03/3.24 tff(26513,plain,((~r(s(s(s(z))), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(26514,plain,
% 3.03/3.24 (~r(s(z), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[26513, 26497, 412, 24742, 220])).
% 3.03/3.24 tff(26515,plain,
% 3.03/3.24 (b(s(z), s(elem!1))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[444, 26514, 24230])).
% 3.03/3.24 tff(26516,plain,
% 3.03/3.24 (~b(elem!1, s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3019, 26515, 307, 2618])).
% 3.03/3.24 tff(26517,plain,
% 3.03/3.25 (r(elem!1, s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[299, 26516, 243])).
% 3.03/3.25 tff(26518,plain,
% 3.03/3.25 (~b(s(z), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3435, 26515, 307, 2618])).
% 3.03/3.25 tff(26519,plain,
% 3.03/3.25 (r(s(z), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[236, 26518, 231])).
% 3.03/3.25 tff(26520,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26521,plain,
% 3.03/3.25 (((~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))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26522,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(s(s(z))), z))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26521])).
% 3.03/3.25 tff(26523,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.03/3.25 inference(transitivity,[status(thm)],[26522, 26520])).
% 3.03/3.25 tff(26524,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26525,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(z))) | (~b(s(s(s(z))), z))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26524, 26523])).
% 3.03/3.25 tff(26526,plain,
% 3.03/3.25 (~b(s(s(s(z))), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26525, 271, 1281, 26495, 26497])).
% 3.03/3.25 tff(26527,plain,
% 3.03/3.25 (r(s(s(s(z))), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2325, 26526])).
% 3.03/3.25 tff(26528,plain,
% 3.03/3.25 (~r(elem!1, s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[11254, 26527, 26519, 26517])).
% 3.03/3.25 tff(26529,plain,
% 3.03/3.25 (b(elem!1, s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1192, 26528, 1102])).
% 3.03/3.25 tff(26530,plain,
% 3.03/3.25 (b(s(s(elem!1)), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[5482, 26529, 23419])).
% 3.03/3.25 tff(26531,plain,
% 3.03/3.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[13534, 26530, 26501, 26499, 26497, 23446, 26495])).
% 3.03/3.25 tff(26532,plain,
% 3.03/3.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[10426, 26531])).
% 3.03/3.25 tff(26533,plain,
% 3.03/3.25 (s(elem!1) = s(s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[23419])).
% 3.03/3.25 tff(26534,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26533])).
% 3.03/3.25 tff(26535,plain,
% 3.03/3.25 (~(s(elem!1) = s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2035, 26493])).
% 3.03/3.25 tff(26536,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2044, 26535, 13137])).
% 3.03/3.25 tff(26537,plain,
% 3.03/3.25 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26536, 26534])).
% 3.03/3.25 tff(26538,plain,
% 3.03/3.25 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[13558, 26532, 26537, 26527])).
% 3.03/3.25 tff(26539,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1014, 26538, 13988])).
% 3.03/3.25 tff(26540,plain,
% 3.03/3.25 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26533])).
% 3.03/3.25 tff(26541,plain,
% 3.03/3.25 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26515, 26540])).
% 3.03/3.25 tff(26542,plain,
% 3.03/3.25 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26533])).
% 3.03/3.25 tff(26543,plain,
% 3.03/3.25 (r(s(s(s(elem!1))), z)),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[412, 26542])).
% 3.03/3.25 tff(26544,plain,
% 3.03/3.25 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[25008, 13988])).
% 3.03/3.25 tff(26545,plain,
% 3.03/3.25 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26533])).
% 3.03/3.25 tff(26546,plain,
% 3.03/3.25 (b(s(elem!1), s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3787, 23419, 2618])).
% 3.03/3.25 tff(26547,plain,
% 3.03/3.25 (~b(z, s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2905, 26515, 1281, 26546])).
% 3.03/3.25 tff(26548,plain,
% 3.03/3.25 (r(z, s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1439, 26547])).
% 3.03/3.25 tff(26549,plain,
% 3.03/3.25 (r(z, s(s(s(elem!1))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26548, 26545])).
% 3.03/3.25 tff(26550,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 3.03/3.25 tff(26551,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26552,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26553,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26552, 26551])).
% 3.03/3.25 tff(26554,plain,
% 3.03/3.25 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26553, 121, 111, 6842, 24354])).
% 3.03/3.25 tff(26555,plain,
% 3.03/3.25 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12570, 937, 750, 1066])).
% 3.03/3.25 tff(26556,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1000, 21, 26555, 26554, 26550])).
% 3.03/3.25 tff(26557,plain,((~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(26558,plain,
% 3.03/3.25 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26557, 26549, 26544, 26543, 26541, 26539, 1281, 220])).
% 3.03/3.25 tff(26559,plain,
% 3.03/3.25 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[932, 26558])).
% 3.03/3.25 tff(26560,plain,
% 3.03/3.25 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[23419])).
% 3.03/3.25 tff(26561,plain,
% 3.03/3.25 (r(s(z), s(s(elem!1)))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26519, 26560])).
% 3.03/3.25 tff(26562,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~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))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26563,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26564,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26563, 26562])).
% 3.03/3.25 tff(26565,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26564, 121, 26561, 26559, 26527, 26532])).
% 3.03/3.25 tff(26566,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(s(s(z)))) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(26567,plain,
% 3.03/3.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26566, 257, 220, 1101, 26196, 19197, 26197, 230, 25632, 26442, 5499])).
% 3.03/3.25 tff(26568,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2293, 21, 3179, 2280])).
% 3.03/3.25 tff(26569,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26570,plain,
% 3.03/3.25 (((~r(s(s(s(elem!1))), s(elem!1))) | (~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(s(s(elem!1))), 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))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26571,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26570])).
% 3.03/3.25 tff(26572,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[26571, 26569])).
% 3.03/3.25 tff(26573,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26574,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26573, 26572])).
% 3.03/3.25 tff(26575,plain,
% 3.03/3.25 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26574, 121, 24017, 26568, 5499])).
% 3.03/3.25 tff(26576,plain,
% 3.03/3.25 (s(s(s(z))) = s(elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1816, 26575, 3506])).
% 3.03/3.25 tff(26577,plain,
% 3.03/3.25 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26576])).
% 3.03/3.25 tff(26578,plain,
% 3.03/3.25 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26577])).
% 3.03/3.25 tff(26579,plain,
% 3.03/3.25 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26578])).
% 3.03/3.25 tff(26580,plain,
% 3.03/3.25 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26579])).
% 3.03/3.25 tff(26581,plain,
% 3.03/3.25 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[24017, 26580])).
% 3.03/3.25 tff(26582,plain,
% 3.03/3.25 (~b(s(z), s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[9276, 26576, 71])).
% 3.03/3.25 tff(26583,plain,
% 3.03/3.25 (r(s(z), s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[444, 26582, 24230])).
% 3.03/3.25 tff(26584,plain,
% 3.03/3.25 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[17876, 26583, 412, 220])).
% 3.03/3.25 tff(26585,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26584, 26581])).
% 3.03/3.25 tff(26586,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(z))) | b(s(z), s(s(s(z)))) | b(s(s(s(z))), s(elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(26587,plain,
% 3.03/3.25 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26586, 71, 220, 26567, 26492, 5499, 26196, 25632, 26442])).
% 3.03/3.25 tff(26588,plain,
% 3.03/3.25 (~r(elem!1, z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[5358, 8563, 412, 378])).
% 3.03/3.25 tff(26589,plain,
% 3.03/3.25 (b(elem!1, z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[284, 26588, 259])).
% 3.03/3.25 tff(26590,plain,
% 3.03/3.25 (~r(elem!1, s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[5343, 8563, 412, 378])).
% 3.03/3.25 tff(26591,plain,
% 3.03/3.25 (b(elem!1, s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[299, 26590, 243])).
% 3.03/3.25 tff(26592,plain,
% 3.03/3.25 (~b(z, s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[5420, 26591, 19197, 26589])).
% 3.03/3.25 tff(26593,plain,
% 3.03/3.25 (r(z, s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2106, 26592])).
% 3.03/3.25 tff(26594,plain,
% 3.03/3.25 (~b(s(z), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[8962, 26591, 220, 26589])).
% 3.03/3.25 tff(26595,plain,
% 3.03/3.25 (r(s(z), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[236, 26594, 231])).
% 3.03/3.25 tff(26596,plain,
% 3.03/3.25 (~b(s(elem!1), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1290, 26591, 19197, 307])).
% 3.03/3.25 tff(26597,plain,
% 3.03/3.25 (r(s(elem!1), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[429, 26596, 422])).
% 3.03/3.25 tff(26598,plain,
% 3.03/3.25 (~r(z, s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[25779, 26597, 19197, 378, 259, 8563, 26595, 26591])).
% 3.03/3.25 tff(26599,plain,
% 3.03/3.25 (b(z, s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1439, 26598])).
% 3.03/3.25 tff(26600,plain,
% 3.03/3.25 (~b(elem!1, s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[6868, 26599, 307, 412, 378, 23520, 26593, 26589])).
% 3.03/3.25 tff(26601,plain,
% 3.03/3.25 (~r(elem!1, s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[6817, 8563, 412, 378])).
% 3.03/3.25 tff(26602,plain,
% 3.03/3.25 (elem!1 = s(s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[660, 21, 26601, 26600])).
% 3.03/3.25 tff(26603,plain,
% 3.03/3.25 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26602])).
% 3.03/3.25 tff(26604,plain,
% 3.03/3.25 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26603])).
% 3.03/3.25 tff(26605,plain,
% 3.03/3.25 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26604])).
% 3.03/3.25 tff(26606,plain,
% 3.03/3.25 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26605])).
% 3.03/3.25 tff(26607,plain,
% 3.03/3.25 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26606])).
% 3.03/3.25 tff(26608,plain,
% 3.03/3.25 (r(z, s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26593, 26607])).
% 3.03/3.25 tff(26609,plain,
% 3.03/3.25 (s(s(s(s(elem!1)))) = s(elem!1)),
% 3.03/3.25 inference(symmetry,[status(thm)],[26603])).
% 3.03/3.25 tff(26610,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26609])).
% 3.03/3.25 tff(26611,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26610])).
% 3.03/3.25 tff(26612,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26603, 26605])).
% 3.03/3.25 tff(26613,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26612])).
% 3.03/3.25 tff(26614,plain,
% 3.03/3.25 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26603])).
% 3.03/3.25 tff(26615,plain,
% 3.03/3.25 (~b(s(elem!1), s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2905, 26599, 19197, 446])).
% 3.03/3.25 tff(26616,plain,
% 3.03/3.25 (r(s(elem!1), s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[526, 26615, 211])).
% 3.03/3.25 tff(26617,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26616, 26614])).
% 3.03/3.25 tff(26618,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26617, 26613])).
% 3.03/3.25 tff(26619,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26618, 26611])).
% 3.03/3.25 tff(26620,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26609])).
% 3.03/3.25 tff(26621,plain,
% 3.03/3.25 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 3.03/3.25 inference(symmetry,[status(thm)],[26620])).
% 3.03/3.25 tff(26622,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), z)),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[412, 26621])).
% 3.03/3.25 tff(26623,plain,
% 3.03/3.25 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26605])).
% 3.03/3.25 tff(26624,plain,
% 3.03/3.25 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.03/3.25 inference(transitivity,[status(thm)],[26623, 9849])).
% 3.03/3.25 tff(26625,plain,
% 3.03/3.25 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26624])).
% 3.03/3.25 tff(26626,plain,
% 3.03/3.25 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(z)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26625])).
% 3.03/3.25 tff(26627,plain,
% 3.03/3.25 (~(s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[3504, 26626])).
% 3.03/3.25 tff(26628,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26603])).
% 3.03/3.25 tff(26629,plain,
% 3.03/3.25 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26602])).
% 3.03/3.25 tff(26630,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[307, 26629])).
% 3.03/3.25 tff(26631,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26630, 26628])).
% 3.03/3.25 tff(26632,plain,
% 3.03/3.25 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26604])).
% 3.03/3.25 tff(26633,plain,
% 3.03/3.25 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26604])).
% 3.03/3.25 tff(26634,plain,
% 3.03/3.25 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26633])).
% 3.03/3.25 tff(26635,plain,
% 3.03/3.25 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26634])).
% 3.03/3.25 tff(26636,plain,
% 3.03/3.25 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[16767])).
% 3.03/3.25 tff(26637,plain,
% 3.03/3.25 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26636])).
% 3.03/3.25 tff(26638,plain,
% 3.03/3.25 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(elem!1)))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26637])).
% 3.03/3.25 tff(26639,plain,
% 3.03/3.25 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26638])).
% 3.03/3.25 tff(26640,plain,
% 3.03/3.25 (r(z, s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[2088, 26639])).
% 3.03/3.25 tff(26641,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[16768])).
% 3.03/3.25 tff(26642,plain,
% 3.03/3.25 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[26641])).
% 3.03/3.25 tff(26643,plain,
% 3.03/3.25 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[18328, 26642])).
% 3.03/3.25 tff(26644,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26645,plain,
% 3.03/3.25 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26646,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26645])).
% 3.03/3.25 tff(26647,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[26646, 26644])).
% 3.03/3.25 tff(26648,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26649,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26648, 26647])).
% 3.03/3.25 tff(26650,plain,
% 3.03/3.25 ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26649, 121, 6026])).
% 3.03/3.25 tff(26651,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26650, 26643, 16771, 26640])).
% 3.03/3.25 tff(26652,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(26653,plain,
% 3.03/3.25 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26652, 26593, 26602, 26618, 412])).
% 3.03/3.25 tff(26654,plain,
% 3.03/3.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26653, 26635])).
% 3.03/3.25 tff(26655,plain,
% 3.03/3.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[556, 26654, 1])).
% 3.03/3.25 tff(26656,plain,
% 3.03/3.25 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26655, 26632])).
% 3.03/3.25 tff(26657,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26658,plain,
% 3.03/3.25 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26659,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[26658])).
% 3.03/3.25 tff(26660,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[26659, 26657])).
% 3.03/3.25 tff(26661,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26662,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[26661, 26660])).
% 3.03/3.25 tff(26663,plain,
% 3.03/3.25 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[26662, 271, 2073, 26656, 26631])).
% 3.03/3.25 tff(26664,plain,
% 3.03/3.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(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(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(26665,plain,
% 3.03/3.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(26666,plain,
% 3.03/3.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26665, 26664])).
% 3.03/3.26 tff(26667,plain,
% 3.03/3.26 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26666, 21, 26663])).
% 3.03/3.26 tff(26668,plain,
% 3.03/3.26 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26667, 26627])).
% 3.03/3.26 tff(26669,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26670,plain,
% 3.03/3.26 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26671,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[26670])).
% 3.03/3.26 tff(26672,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[26671, 26669])).
% 3.03/3.26 tff(26673,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(26674,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26673, 26672])).
% 3.03/3.26 tff(26675,plain,
% 3.03/3.26 ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26674, 121, 26668])).
% 3.03/3.26 tff(26676,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26675, 26622, 26619, 26608])).
% 3.03/3.26 tff(26677,plain,(b(s(elem!1), elem!1) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(s(z), s(elem!1))) | (elem!1 = z) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26678,plain,
% 3.03/3.26 (b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26677, 446, 2073, 1, 307, 1243, 412, 358, 230, 422, 220, 147])).
% 3.03/3.26 tff(26679,plain,
% 3.03/3.26 (b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2243, 22302, 2564])).
% 3.03/3.26 tff(26680,plain,
% 3.03/3.26 (~b(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3435, 26679, 307, 446])).
% 3.03/3.26 tff(26681,plain,
% 3.03/3.26 (~r(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[19871, 1409, 145, 378])).
% 3.03/3.26 tff(26682,plain,
% 3.03/3.26 (b(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1214, 26681])).
% 3.03/3.26 tff(26683,plain,
% 3.03/3.26 (~r(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[15964, 26682, 1409, 220, 145])).
% 3.03/3.26 tff(26684,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[236, 26683, 26680, 231])).
% 3.03/3.26 tff(26685,plain,((~r(elem!1, z)) | (s(z) = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26686,plain,
% 3.03/3.26 (~r(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26685, 17770, 220, 231, 307, 446, 2564, 378, 412])).
% 3.03/3.26 tff(26687,plain,
% 3.03/3.26 (b(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[284, 26686, 259])).
% 3.03/3.26 tff(26688,plain,
% 3.03/3.26 (~b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[15307, 260, 446, 261])).
% 3.03/3.26 tff(26689,plain,
% 3.03/3.26 (r(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2243, 26688, 2564])).
% 3.03/3.26 tff(26690,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[5343, 24729, 26689, 412, 378])).
% 3.03/3.26 tff(26691,plain,((~b(s(z), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (s(elem!1) = elem!1) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26692,plain,
% 3.03/3.26 (~b(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26691, 26687, 378, 243, 2564, 220, 412, 446])).
% 3.03/3.26 tff(26693,plain,
% 3.03/3.26 (r(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[236, 26692, 231])).
% 3.03/3.26 tff(26694,plain,
% 3.03/3.26 (~r(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[4112, 26693, 108, 17770])).
% 3.03/3.26 tff(26695,plain,
% 3.03/3.26 (~(elem!1 = s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[19808, 2346, 2073])).
% 3.03/3.26 tff(26696,plain,
% 3.03/3.26 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13222, 26695])).
% 3.03/3.26 tff(26697,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[486, 26696, 147])).
% 3.03/3.26 tff(26698,plain,
% 3.03/3.26 (~b(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26691, 261, 378, 243, 2564, 220, 412, 446])).
% 3.03/3.26 tff(26699,plain,
% 3.03/3.26 (r(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[236, 26698, 231])).
% 3.03/3.26 tff(26700,plain,
% 3.03/3.26 (~r(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[4112, 26699, 108, 145])).
% 3.03/3.26 tff(26701,plain,
% 3.03/3.26 (b(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[299, 26700, 243])).
% 3.03/3.26 tff(26702,plain,
% 3.03/3.26 (~b(z, s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[5420, 26701, 1281, 261])).
% 3.03/3.26 tff(26703,plain,
% 3.03/3.26 (r(z, s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2106, 26702])).
% 3.03/3.26 tff(26704,plain,
% 3.03/3.26 (~b(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1290, 26701, 1281, 307])).
% 3.03/3.26 tff(26705,plain,
% 3.03/3.26 (r(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[429, 26704, 422])).
% 3.03/3.26 tff(26706,plain,
% 3.03/3.26 (~b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3019, 26701, 307, 446])).
% 3.03/3.26 tff(26707,plain,
% 3.03/3.26 (r(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2243, 26706, 2564])).
% 3.03/3.26 tff(26708,plain,
% 3.03/3.26 (~r(z, s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[25779, 26707, 1281, 378, 259, 26705, 26699, 26701])).
% 3.03/3.26 tff(26709,plain,
% 3.03/3.26 (b(z, s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1439, 26708])).
% 3.03/3.26 tff(26710,plain,
% 3.03/3.26 (~b(elem!1, s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[6868, 26709, 307, 412, 378, 82, 26703, 261])).
% 3.03/3.26 tff(26711,plain,
% 3.03/3.26 (~r(elem!1, s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[6817, 26707, 412, 378])).
% 3.03/3.26 tff(26712,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[660, 21, 26711, 4358, 26710])).
% 3.03/3.26 tff(26713,plain,((~b(elem!1, z)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (elem!1 = z) | (s(elem!1) = elem!1) | (s(elem!1) = s(z)) | (~b(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26714,plain,
% 3.03/3.26 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26713, 26687, 307, 412, 378, 26695, 1281, 259, 2564, 422, 446, 108, 17770, 231, 220])).
% 3.03/3.26 tff(26715,plain,
% 3.03/3.26 (b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[7281, 26714, 26697])).
% 3.03/3.26 tff(26716,plain,
% 3.03/3.26 (~b(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3019, 26715, 307, 446])).
% 3.03/3.26 tff(26717,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[299, 26716, 26694, 243])).
% 3.03/3.26 tff(26718,plain,(b(s(s(s(z))), elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~b(s(z), z)) | (elem!1 = z) | (s(elem!1) = elem!1) | (s(elem!1) = s(z)) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26719,plain,
% 3.03/3.26 (b(s(s(s(z))), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26718, 446, 307, 108, 230, 412, 1243, 19197, 358, 2207, 422, 220, 147, 2073, 907])).
% 3.03/3.26 tff(26720,plain,
% 3.03/3.26 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[23787, 26719, 2073, 307])).
% 3.03/3.26 tff(26721,plain,
% 3.03/3.26 (~(elem!1 = s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3790, 26720, 26678])).
% 3.03/3.26 tff(26722,plain,
% 3.03/3.26 (~(s(s(elem!1)) = elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[197, 26721])).
% 3.03/3.26 tff(26723,plain,
% 3.03/3.26 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[9276, 446, 71])).
% 3.03/3.26 tff(26724,plain,
% 3.03/3.26 (~r(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13140, 26678, 307, 412, 26723, 26719])).
% 3.03/3.26 tff(26725,plain,
% 3.03/3.26 (b(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1214, 26724])).
% 3.03/3.26 tff(26726,plain,
% 3.03/3.26 (~b(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3019, 26678, 307, 446])).
% 3.03/3.26 tff(26727,plain,
% 3.03/3.26 (r(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[299, 26726, 337])).
% 3.03/3.26 tff(26728,plain,
% 3.03/3.26 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13128, 271, 307, 26678, 26719])).
% 3.03/3.26 tff(26729,plain,
% 3.03/3.26 (r(s(s(s(z))), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1816, 26728, 26723])).
% 3.03/3.26 tff(26730,plain,
% 3.03/3.26 (~r(s(s(s(z))), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3650, 26729, 412, 1243])).
% 3.03/3.26 tff(26731,plain,
% 3.03/3.26 (b(s(s(s(z))), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1155, 26730])).
% 3.03/3.26 tff(26732,plain,
% 3.03/3.26 (~b(s(s(s(z))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26525, 271, 19197, 26725, 26731])).
% 3.03/3.26 tff(26733,plain,
% 3.03/3.26 (r(s(s(s(z))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2325, 26732])).
% 3.03/3.26 tff(26734,plain,
% 3.03/3.26 (~r(elem!1, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[24792, 26733, 26727, 108])).
% 3.03/3.26 tff(26735,plain,
% 3.03/3.26 (b(elem!1, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1192, 26734, 1101])).
% 3.03/3.26 tff(26736,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26737,plain,
% 3.03/3.26 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26738,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z)))))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[26737])).
% 3.03/3.26 tff(26739,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[26738, 26736])).
% 3.03/3.26 tff(26740,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(26741,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26740, 26739])).
% 3.03/3.26 tff(26742,plain,
% 3.03/3.26 (~b(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26741, 271, 26735, 26725, 2073])).
% 3.03/3.26 tff(26743,plain,
% 3.03/3.26 (r(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[284, 26742, 358])).
% 3.03/3.26 tff(26744,plain,
% 3.03/3.26 (~(s(elem!1) = s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2035, 26723])).
% 3.03/3.26 tff(26745,plain,
% 3.03/3.26 (~b(s(elem!1), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13136, 271, 307, 26678, 26719])).
% 3.03/3.26 tff(26746,plain,
% 3.03/3.26 (r(s(elem!1), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2044, 26745, 26744])).
% 3.03/3.26 tff(26747,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[8939, 121, 1500, 411, 108, 2046])).
% 3.03/3.26 tff(26748,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26749,plain,
% 3.03/3.26 (~r(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26748, 26729, 26746, 108])).
% 3.03/3.26 tff(26750,plain,
% 3.03/3.26 (b(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[429, 26749, 422])).
% 3.03/3.26 tff(26751,plain,
% 3.03/3.26 (~b(z, s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[24719, 26750, 220, 19197])).
% 3.03/3.26 tff(26752,plain,
% 3.03/3.26 (r(z, s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1439, 26751])).
% 3.03/3.26 tff(26753,plain,
% 3.03/3.26 (~b(s(s(elem!1)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[22224, 26752, 19197, 3313, 220, 412, 446, 26678])).
% 3.03/3.26 tff(26754,plain,
% 3.03/3.26 (r(s(s(elem!1)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2143, 26753])).
% 3.03/3.26 tff(26755,plain,
% 3.03/3.26 (~b(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3435, 26678, 307, 446])).
% 3.03/3.26 tff(26756,plain,
% 3.03/3.26 (r(s(z), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[236, 26755, 230])).
% 3.03/3.26 tff(26757,plain,
% 3.03/3.26 (~r(s(s(elem!1)), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26043, 26756, 26754, 26743])).
% 3.03/3.26 tff(26758,plain,
% 3.03/3.26 (b(s(s(elem!1)), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[862, 26757, 26722])).
% 3.03/3.26 tff(26759,plain,
% 3.03/3.26 (~b(s(s(elem!1)), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[6807, 26758, 307, 26678])).
% 3.03/3.26 tff(26760,plain,
% 3.03/3.26 (r(s(s(elem!1)), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[701, 26759, 3313])).
% 3.03/3.26 tff(26761,plain,
% 3.03/3.26 (~(s(s(z)) = s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[960, 230])).
% 3.03/3.26 tff(26762,plain,
% 3.03/3.26 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[953, 26761])).
% 3.03/3.26 tff(26763,plain,
% 3.03/3.26 (~r(s(s(elem!1)), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[14657, 26760, 412, 26752])).
% 3.03/3.26 tff(26764,plain,
% 3.03/3.26 (b(s(s(elem!1)), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2430, 26763])).
% 3.03/3.26 tff(26765,plain,
% 3.03/3.26 (s(s(s(elem!1))) = elem!1),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[486, 26720, 147])).
% 3.03/3.26 tff(26766,plain,
% 3.03/3.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2511, 26757, 26765])).
% 3.03/3.26 tff(26767,plain,
% 3.03/3.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[556, 26766, 1])).
% 3.03/3.26 tff(26768,plain,
% 3.03/3.26 (~r(z, s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[17205, 26764, 337, 26721, 220, 331, 26767])).
% 3.03/3.26 tff(26769,plain,
% 3.03/3.26 (b(z, s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2106, 26768])).
% 3.03/3.26 tff(26770,plain,
% 3.03/3.26 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2454, 26769, 26731, 26764])).
% 3.03/3.26 tff(26771,plain,
% 3.03/3.26 (r(s(s(s(z))), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2462, 21, 26770, 26762])).
% 3.03/3.26 tff(26772,plain,
% 3.03/3.26 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[78, 26721])).
% 3.03/3.26 tff(26773,plain,
% 3.03/3.26 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2830, 26765, 2344])).
% 3.03/3.26 tff(26774,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[681, 26773, 26772])).
% 3.03/3.26 tff(26775,plain,
% 3.03/3.26 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2562, 26765, 26755])).
% 3.03/3.26 tff(26776,plain,
% 3.03/3.26 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[760, 26775])).
% 3.03/3.26 tff(26777,plain,
% 3.03/3.26 (elem!1 = s(s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13222, 26765])).
% 3.03/3.26 tff(26778,plain,
% 3.03/3.26 (~b(z, s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13207, 26777, 199])).
% 3.03/3.26 tff(26779,plain,
% 3.03/3.26 (r(z, s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[19736, 26778])).
% 3.03/3.26 tff(26780,plain,
% 3.03/3.26 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[10857, 26764, 26779, 26776])).
% 3.03/3.26 tff(26781,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[586, 26780, 563])).
% 3.03/3.26 tff(26782,plain,
% 3.03/3.26 (~b(s(elem!1), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1459, 26781, 26774, 26767])).
% 3.03/3.26 tff(26783,plain,
% 3.03/3.26 (r(s(elem!1), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[526, 26782, 211])).
% 3.03/3.26 tff(26784,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3927, 121, 26783, 26729, 26771, 26760])).
% 3.03/3.26 tff(26785,plain,((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (z = elem!1) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | b(z, elem!1) | r(elem!1, s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (s(s(s(z))) = elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26786,plain,
% 3.03/3.26 (~b(s(z), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26785, 199, 9297, 412, 1, 307, 220, 2344, 147, 2073, 108, 2282, 907, 71])).
% 3.03/3.26 tff(26787,plain,
% 3.03/3.26 (r(s(z), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[444, 26786, 348])).
% 3.03/3.26 tff(26788,plain,
% 3.03/3.26 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[946, 26762])).
% 3.03/3.26 tff(26789,plain,
% 3.03/3.26 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[25008, 26788])).
% 3.03/3.26 tff(26790,plain,
% 3.03/3.26 (b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2243, 22198, 2564])).
% 3.03/3.26 tff(26791,plain,
% 3.03/3.26 (~r(s(elem!1), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3445, 17770, 108, 431])).
% 3.03/3.26 tff(26792,plain,
% 3.03/3.26 (b(s(elem!1), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2044, 26791, 8606])).
% 3.03/3.26 tff(26793,plain,
% 3.03/3.26 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13752, 26697, 307, 260])).
% 3.03/3.26 tff(26794,plain,
% 3.03/3.26 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[760, 26793])).
% 3.03/3.26 tff(26795,plain,
% 3.03/3.26 (~r(s(s(s(z))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12657, 26794, 3456, 17770])).
% 3.03/3.26 tff(26796,plain,
% 3.03/3.26 (b(s(s(s(z))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2325, 26795])).
% 3.03/3.26 tff(26797,plain,
% 3.03/3.26 (~b(elem!1, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[10690, 26796, 307, 26792])).
% 3.03/3.26 tff(26798,plain,
% 3.03/3.26 (r(elem!1, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1192, 26797, 1101])).
% 3.03/3.26 tff(26799,plain,
% 3.03/3.26 (~b(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[24799, 26796, 220, 260])).
% 3.03/3.26 tff(26800,plain,
% 3.03/3.26 (r(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1214, 26799])).
% 3.03/3.26 tff(26801,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[6723, 26800, 26798, 378, 17770])).
% 3.03/3.26 tff(26802,plain,(b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26803,plain,
% 3.03/3.26 (b(s(s(s(z))), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26802, 3456, 220, 260, 307, 378, 147, 108, 431, 26790, 2073, 907])).
% 3.03/3.26 tff(26804,plain,
% 3.03/3.26 (~b(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3247, 271, 307, 26790, 260])).
% 3.03/3.26 tff(26805,plain,
% 3.03/3.26 (r(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[429, 26804, 422])).
% 3.03/3.26 tff(26806,plain,
% 3.03/3.26 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[23235, 26805, 431, 108])).
% 3.03/3.26 tff(26807,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[486, 4328, 147])).
% 3.03/3.26 tff(26808,plain,
% 3.03/3.26 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[1997])).
% 3.03/3.26 tff(26809,plain,
% 3.03/3.26 (b(s(elem!1), s(s(s(elem!1))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[2073, 26808])).
% 3.03/3.26 tff(26810,plain,
% 3.03/3.26 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 3.03/3.26 inference(monotonicity,[status(thm)],[1997])).
% 3.03/3.26 tff(26811,plain,
% 3.03/3.26 (b(s(elem!1), elem!1)),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[257, 26810])).
% 3.03/3.26 tff(26812,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2930, 271, 307, 26811, 26809, 26807])).
% 3.03/3.26 tff(26813,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26814,plain,
% 3.03/3.26 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26813, 26803, 307, 2073, 147])).
% 3.03/3.26 tff(26815,plain,
% 3.03/3.26 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1816, 26814, 26806])).
% 3.03/3.26 tff(26816,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13128, 271, 307, 26790, 26815, 26803])).
% 3.03/3.26 tff(26817,plain,((~r(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (s(s(s(z))) = elem!1) | (s(elem!1) = s(z)) | (s(elem!1) = elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26818,plain,
% 3.03/3.26 (~r(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26817, 260, 2073, 147, 220, 307, 378, 108, 431, 907, 2282, 2564, 412])).
% 3.03/3.26 tff(26819,plain,
% 3.03/3.26 (b(elem!1, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[299, 26818, 258])).
% 3.03/3.26 tff(26820,plain,
% 3.03/3.26 (~b(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[8962, 26819, 220, 260])).
% 3.03/3.26 tff(26821,plain,
% 3.03/3.26 (r(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[284, 26820, 9298])).
% 3.03/3.26 tff(26822,plain,
% 3.03/3.26 (~r(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[5358, 26821, 412, 378])).
% 3.03/3.26 tff(26823,plain,
% 3.03/3.26 (b(s(elem!1), elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2243, 26822, 2564])).
% 3.03/3.26 tff(26824,plain,
% 3.03/3.26 (~b(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1290, 448, 1281, 307])).
% 3.03/3.26 tff(26825,plain,
% 3.03/3.26 (r(s(elem!1), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[429, 26824, 2282])).
% 3.03/3.26 tff(26826,plain,
% 3.03/3.26 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[19657, 26697, 431, 260, 448, 26825, 2618])).
% 3.03/3.26 tff(26827,plain,
% 3.03/3.26 (elem!1 = s(s(elem!1))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[78, 26826])).
% 3.03/3.26 tff(26828,plain,
% 3.03/3.26 (s(elem!1) = s(s(s(elem!1)))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[26827])).
% 3.03/3.26 tff(26829,plain,
% 3.03/3.26 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 3.03/3.26 inference(monotonicity,[status(thm)],[26828])).
% 3.03/3.26 tff(26830,plain,
% 3.03/3.26 (r(s(s(s(elem!1))), z)),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[412, 26829])).
% 3.03/3.26 tff(26831,plain,
% 3.03/3.26 (~b(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[8962, 448, 220, 260])).
% 3.03/3.26 tff(26832,plain,
% 3.03/3.26 (r(elem!1, z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[284, 26831, 9298])).
% 3.03/3.26 tff(26833,plain,
% 3.03/3.26 (~r(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[19871, 17770, 26832, 378])).
% 3.03/3.26 tff(26834,plain,
% 3.03/3.26 (b(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1214, 26833])).
% 3.03/3.26 tff(26835,plain,
% 3.03/3.26 (~b(s(s(s(z))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[24799, 26834, 220, 260])).
% 3.03/3.26 tff(26836,plain,
% 3.03/3.26 (r(s(s(s(z))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2325, 26835])).
% 3.03/3.26 tff(26837,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[26827])).
% 3.03/3.26 tff(26838,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26697, 26837])).
% 3.03/3.26 tff(26839,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.03/3.26 tff(26840,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26841,plain,
% 3.03/3.26 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26842,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[26841])).
% 3.03/3.26 tff(26843,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[26842, 26840])).
% 3.03/3.26 tff(26844,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(26845,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26844, 26843])).
% 3.03/3.26 tff(26846,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26845, 121, 572, 911, 6842, 26839])).
% 3.03/3.26 tff(26847,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26848,plain,
% 3.03/3.26 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26847, 911, 6842, 572])).
% 3.03/3.26 tff(26849,plain,
% 3.03/3.26 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1000, 21, 26848, 26550])).
% 3.03/3.26 tff(26850,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~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))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26851,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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))))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(26852,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~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)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26851, 26850])).
% 3.03/3.26 tff(26853,plain,
% 3.03/3.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26852, 121, 572, 911, 2327])).
% 3.03/3.26 tff(26854,plain,
% 3.03/3.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[10426, 26853])).
% 3.03/3.26 tff(26855,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(26856,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(26857,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[26856, 26855])).
% 3.03/3.26 tff(26858,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26857, 271, 589, 2073, 26854, 26849])).
% 3.03/3.26 tff(26859,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(26860,plain,
% 3.03/3.26 (~r(s(s(s(s(z)))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[26859, 26838, 2073, 26550, 26794, 26836, 26830])).
% 3.03/3.26 tff(26861,plain,
% 3.03/3.26 (b(s(s(s(s(z)))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[932, 26860])).
% 3.03/3.26 tff(26862,plain,
% 3.03/3.26 (~b(s(s(s(s(z)))), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[22548, 26861, 1281, 220])).
% 3.03/3.26 tff(26863,plain,
% 3.03/3.26 (r(s(s(s(s(z)))), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1095, 26862])).
% 3.03/3.26 tff(26864,plain,
% 3.03/3.26 (~r(s(s(elem!1)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12129, 26827, 293])).
% 3.03/3.26 tff(26865,plain,
% 3.03/3.26 (b(s(s(elem!1)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2143, 26864])).
% 3.03/3.27 tff(26866,plain,
% 3.03/3.27 (~b(s(s(elem!1)), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[16949, 26865, 1281, 220])).
% 3.03/3.27 tff(26867,plain,
% 3.03/3.27 (r(s(s(elem!1)), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2430, 26866])).
% 3.03/3.27 tff(26868,plain,
% 3.03/3.27 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[23235, 26825, 431, 108])).
% 3.03/3.27 tff(26869,plain,
% 3.03/3.27 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3917, 26827, 348])).
% 3.03/3.27 tff(26870,plain,
% 3.03/3.27 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1816, 26869, 26868])).
% 3.03/3.27 tff(26871,plain,
% 3.03/3.27 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26828])).
% 3.03/3.27 tff(26872,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26792, 26871])).
% 3.03/3.27 tff(26873,plain,
% 3.03/3.27 (~b(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[5687, 26872, 26834, 26870])).
% 3.03/3.27 tff(26874,plain,
% 3.03/3.27 (r(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19736, 26873])).
% 3.03/3.27 tff(26875,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(26876,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(26877,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26876, 26875])).
% 3.03/3.27 tff(26878,plain,
% 3.03/3.27 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26877, 121, 26874, 26867, 26863])).
% 3.03/3.27 tff(26879,plain,
% 3.03/3.27 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[12235, 26827, 9149])).
% 3.03/3.27 tff(26880,plain,
% 3.03/3.27 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26827])).
% 3.03/3.27 tff(26881,plain,
% 3.03/3.27 (b(s(z), s(s(elem!1)))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[260, 26880])).
% 3.03/3.27 tff(26882,plain,
% 3.03/3.27 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[12249, 271, 26881, 26865, 26861])).
% 3.03/3.27 tff(26883,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[12253, 21, 26882, 26879, 26878])).
% 3.03/3.27 tff(26884,plain,(b(s(s(s(z))), elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(s(z), elem!1)) | r(elem!1, s(z)) | (s(z) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26885,plain,
% 3.03/3.27 (b(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26884, 260, 220, 2073, 26550, 412, 1281, 26818, 348, 431, 26819, 26823, 307, 147, 378, 108, 907])).
% 3.03/3.27 tff(26886,plain,
% 3.03/3.27 (~b(s(elem!1), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1290, 26819, 1281, 307])).
% 3.03/3.27 tff(26887,plain,
% 3.03/3.27 (r(s(elem!1), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[429, 26886, 2282])).
% 3.03/3.27 tff(26888,plain,
% 3.03/3.27 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[23235, 26887, 431, 108])).
% 3.03/3.27 tff(26889,plain,
% 3.03/3.27 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26813, 26885, 307, 2073, 147])).
% 3.03/3.27 tff(26890,plain,
% 3.03/3.27 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1816, 26889, 26888])).
% 3.03/3.27 tff(26891,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13128, 271, 307, 26823, 26890, 26885])).
% 3.03/3.27 tff(26892,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (s(elem!1) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26893,plain,
% 3.03/3.27 (~b(s(z), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26892, 26789, 2073, 147, 220, 307, 412, 19197, 348, 26787, 10219, 108, 907, 2207, 337])).
% 3.03/3.27 tff(26894,plain,
% 3.03/3.27 (r(s(z), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[236, 26893, 230])).
% 3.03/3.27 tff(26895,plain,
% 3.03/3.27 (~r(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26024, 10219, 26894, 220, 9298, 19197, 337, 108])).
% 3.03/3.27 tff(26896,plain,
% 3.03/3.27 (b(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[255, 26895, 907])).
% 3.03/3.27 tff(26897,plain,
% 3.03/3.27 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26813, 26896, 307, 2073, 147])).
% 3.03/3.27 tff(26898,plain,
% 3.03/3.27 (b(elem!1, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[299, 26590, 337])).
% 3.03/3.27 tff(26899,plain,
% 3.03/3.27 (~b(z, s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[5420, 26589, 19197, 26898])).
% 3.03/3.27 tff(26900,plain,
% 3.03/3.27 (r(z, s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2106, 26899])).
% 3.03/3.27 tff(26901,plain,
% 3.03/3.27 (r(s(z), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[236, 1242, 230])).
% 3.03/3.27 tff(26902,plain,
% 3.03/3.27 (~b(s(elem!1), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1290, 26898, 19197, 307])).
% 3.03/3.27 tff(26903,plain,
% 3.03/3.27 (r(s(elem!1), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[429, 26902, 422])).
% 3.03/3.27 tff(26904,plain,
% 3.03/3.27 (~r(z, s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[25779, 26903, 19197, 378, 259, 8563, 26901, 26898])).
% 3.03/3.27 tff(26905,plain,
% 3.03/3.27 (b(z, s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1439, 26904])).
% 3.03/3.27 tff(26906,plain,
% 3.03/3.27 (~b(elem!1, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[6868, 26905, 307, 412, 378, 23520, 26900, 26589])).
% 3.03/3.27 tff(26907,plain,
% 3.03/3.27 (elem!1 = s(s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[660, 21, 26601, 26906])).
% 3.03/3.27 tff(26908,plain,
% 3.03/3.27 (s(elem!1) = s(s(s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26907])).
% 3.03/3.27 tff(26909,plain,
% 3.03/3.27 (s(s(s(s(elem!1)))) = s(elem!1)),
% 3.03/3.27 inference(symmetry,[status(thm)],[26908])).
% 3.03/3.27 tff(26910,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26909])).
% 3.03/3.27 tff(26911,plain,
% 3.03/3.27 (r(s(elem!1), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.27 inference(symmetry,[status(thm)],[26910])).
% 3.03/3.27 tff(26912,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26903, 26911])).
% 3.03/3.27 tff(26913,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26909])).
% 3.03/3.27 tff(26914,plain,
% 3.03/3.27 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[26913])).
% 3.03/3.27 tff(26915,plain,
% 3.03/3.27 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26908])).
% 3.03/3.27 tff(26916,plain,
% 3.03/3.27 (b(z, s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26905, 26915])).
% 3.03/3.27 tff(26917,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26908])).
% 3.03/3.27 tff(26918,plain,
% 3.03/3.27 (b(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19808, 26907, 2073])).
% 3.03/3.27 tff(26919,plain,
% 3.03/3.27 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[23787, 26918, 2073, 307])).
% 3.03/3.27 tff(26920,plain,
% 3.03/3.27 (s(s(s(elem!1))) = elem!1),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[486, 26919, 147])).
% 3.03/3.27 tff(26921,plain,
% 3.03/3.27 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2830, 26920, 2344])).
% 3.03/3.27 tff(26922,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[681, 26921, 23520])).
% 3.03/3.27 tff(26923,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26922, 26917])).
% 3.03/3.27 tff(26924,plain,
% 3.03/3.27 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26907])).
% 3.03/3.27 tff(26925,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), z)),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26589, 26924])).
% 3.03/3.27 tff(26926,plain,
% 3.03/3.27 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26236, 26907, 26925, 26923, 26916])).
% 3.03/3.27 tff(26927,plain,
% 3.03/3.27 (r(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1995, 26926, 2603])).
% 3.03/3.27 tff(26928,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26927, 26914])).
% 3.03/3.27 tff(26929,plain,
% 3.03/3.27 (~b(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13207, 26907, 199])).
% 3.03/3.27 tff(26930,plain,
% 3.03/3.27 (r(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19736, 26929])).
% 3.03/3.27 tff(26931,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[2002, 26215])).
% 3.03/3.27 tff(26932,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(26933,plain,
% 3.03/3.27 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(26934,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26933])).
% 3.03/3.27 tff(26935,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 3.03/3.27 inference(transitivity,[status(thm)],[26934, 26932])).
% 3.03/3.27 tff(26936,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(26937,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26936, 26935])).
% 3.03/3.27 tff(26938,plain,
% 3.03/3.27 ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26937, 121, 111, 910])).
% 3.03/3.27 tff(26939,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26938, 26931, 16771])).
% 3.03/3.27 tff(26940,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26941,plain,
% 3.03/3.27 (~r(s(s(s(s(z)))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26940, 26930, 26927, 26907, 412])).
% 3.03/3.27 tff(26942,plain,
% 3.03/3.27 (b(s(s(s(s(z)))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1095, 26941])).
% 3.03/3.27 tff(26943,plain,
% 3.03/3.27 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[22548, 26942, 19197, 220])).
% 3.03/3.27 tff(26944,plain,
% 3.03/3.27 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[932, 26943])).
% 3.03/3.27 tff(26945,plain,
% 3.03/3.27 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2562, 26920, 1242])).
% 3.03/3.27 tff(26946,plain,
% 3.03/3.27 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[760, 26945])).
% 3.03/3.27 tff(26947,plain,
% 3.03/3.27 ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26256, 121, 26946, 26944])).
% 3.03/3.27 tff(26948,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26947, 26928, 26912])).
% 3.03/3.27 tff(26949,plain,(b(s(elem!1), elem!1) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | b(s(z), elem!1) | r(elem!1, s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | b(z, elem!1) | (~r(z, elem!1)) | (elem!1 = z) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26950,plain,
% 3.03/3.27 (b(s(elem!1), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26949, 26893, 412, 19205, 220, 2344, 147, 2073, 307, 199, 10219, 9298, 2282, 1])).
% 3.03/3.27 tff(26951,plain,
% 3.03/3.27 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13128, 271, 307, 26950, 26896])).
% 3.03/3.27 tff(26952,plain,
% 3.03/3.27 (r(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1816, 26951, 26897])).
% 3.03/3.27 tff(26953,plain,
% 3.03/3.27 (~r(s(s(s(z))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3650, 26952, 412, 10219])).
% 3.03/3.27 tff(26954,plain,
% 3.03/3.27 (~b(s(s(s(z))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26513, 26952, 412, 26787, 220])).
% 3.03/3.27 tff(26955,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1155, 26954, 26953])).
% 3.03/3.27 tff(26956,plain,(b(z, elem!1) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26957,plain,
% 3.03/3.27 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26956, 71, 220, 25632, 907, 26196, 147, 26491, 2344, 1, 24230, 199])).
% 3.03/3.27 tff(26958,plain,
% 3.03/3.27 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19720, 26957, 257])).
% 3.03/3.27 tff(26959,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[486, 26958, 26587, 147])).
% 3.03/3.27 tff(26960,plain,(b(s(z), s(s(s(z)))) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26961,plain,
% 3.03/3.27 (b(s(z), s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26960, 5469, 147, 220, 5499, 907, 2344, 1, 199])).
% 3.03/3.27 tff(26962,plain,
% 3.03/3.27 (~b(s(s(s(z))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[21058, 26961, 19197, 220])).
% 3.03/3.27 tff(26963,plain,
% 3.03/3.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26566, 5469, 220, 1101, 26196, 19197, 26197, 230, 25632, 26442, 5499])).
% 3.03/3.27 tff(26964,plain,
% 3.03/3.27 (~(elem!1 = s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[7490, 26963])).
% 3.03/3.27 tff(26965,plain,
% 3.03/3.27 (~(elem!1 = s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13207, 3407, 199])).
% 3.03/3.27 tff(26966,plain,
% 3.03/3.27 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13222, 26965])).
% 3.03/3.27 tff(26967,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[486, 26966, 147])).
% 3.03/3.27 tff(26968,plain,
% 3.03/3.27 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[15649, 26967, 3407, 220])).
% 3.03/3.27 tff(26969,plain,
% 3.03/3.27 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[760, 26968])).
% 3.03/3.27 tff(26970,plain,
% 3.03/3.27 (~r(s(s(s(elem!1))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[22243, 26969, 19197, 412, 199, 68, 1, 147, 3407, 337, 259])).
% 3.03/3.27 tff(26971,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[16580, 26970])).
% 3.03/3.27 tff(26972,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(26973,plain,
% 3.03/3.27 (((~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))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(26974,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[26973])).
% 3.03/3.27 tff(26975,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[26974, 26972])).
% 3.03/3.27 tff(26976,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(26977,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[26976, 26975])).
% 3.03/3.27 tff(26978,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26977, 271, 19197, 220, 3407, 26971])).
% 3.03/3.27 tff(26979,plain,((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(elem!1), z)) | b(z, elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26980,plain,
% 3.03/3.27 (~b(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26979, 26964, 26196, 199, 220, 1, 147, 25634])).
% 3.03/3.27 tff(26981,plain,
% 3.03/3.27 (r(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19736, 26980])).
% 3.03/3.27 tff(26982,plain,
% 3.03/3.27 (~r(s(s(s(z))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26469, 26961, 25632, 221, 147, 5499, 26196, 26442, 19197, 26981, 907])).
% 3.03/3.27 tff(26983,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1155, 26982, 26962])).
% 3.03/3.27 tff(26984,plain,(r(s(s(s(z))), elem!1) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(26985,plain,
% 3.03/3.27 (r(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26984, 199, 5499, 907, 220, 2344, 1, 147])).
% 3.03/3.27 tff(26986,plain,
% 3.03/3.27 (~r(s(z), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26024, 26985, 26197, 220, 25634, 19197, 337, 26491])).
% 3.03/3.27 tff(26987,plain,
% 3.03/3.27 (b(s(z), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[236, 26986, 230])).
% 3.03/3.27 tff(26988,plain,
% 3.03/3.27 (~b(s(z), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3435, 26987, 25632, 26442])).
% 3.03/3.27 tff(26989,plain,
% 3.03/3.27 (r(s(z), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[444, 26988, 24230])).
% 3.03/3.27 tff(26990,plain,
% 3.03/3.27 (~b(s(elem!1), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3247, 271, 25632, 26442, 26987])).
% 3.03/3.27 tff(26991,plain,
% 3.03/3.27 (r(s(elem!1), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[429, 26990, 26198])).
% 3.03/3.27 tff(26992,plain,
% 3.03/3.27 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[23235, 26991, 26491, 26989])).
% 3.03/3.27 tff(26993,plain,
% 3.03/3.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[23458, 26992, 5499])).
% 3.03/3.27 tff(26994,plain,
% 3.03/3.27 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[24019, 26993, 26987, 26989, 25632, 26991, 26442])).
% 3.03/3.27 tff(26995,plain,
% 3.03/3.27 (s(s(s(elem!1))) = elem!1),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[486, 26994, 147])).
% 3.03/3.27 tff(26996,plain,
% 3.03/3.27 (~r(s(s(s(z))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3650, 3750, 412, 378])).
% 3.03/3.27 tff(26997,plain,
% 3.03/3.27 (b(s(s(s(z))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1155, 26996])).
% 3.03/3.27 tff(26998,plain,
% 3.03/3.27 (~r(s(s(s(z))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2640, 3750, 412, 431])).
% 3.03/3.27 tff(26999,plain,
% 3.03/3.27 (b(s(s(s(z))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2325, 26998])).
% 3.03/3.27 tff(27000,plain,
% 3.03/3.27 (~b(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[312, 26999, 260, 307])).
% 3.03/3.27 tff(27001,plain,
% 3.03/3.27 (r(s(s(s(z))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[255, 27000, 2612])).
% 3.03/3.27 tff(27002,plain,
% 3.03/3.27 (~r(s(elem!1), s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3865, 1140, 1500, 412])).
% 3.03/3.27 tff(27003,plain,
% 3.03/3.27 (b(s(elem!1), s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2044, 27002, 2037])).
% 3.03/3.27 tff(27004,plain,
% 3.03/3.27 (~r(elem!1, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[6723, 1140, 145, 378])).
% 3.03/3.27 tff(27005,plain,
% 3.03/3.27 (b(elem!1, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1192, 27004, 1102])).
% 3.03/3.27 tff(27006,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[10690, 27005, 27003, 307, 222])).
% 3.03/3.27 tff(27007,plain,((~r(z, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (s(elem!1) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(27008,plain,
% 3.03/3.27 (~r(z, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[27007, 26999, 307, 5676, 3841, 27001, 378, 3750, 412])).
% 3.03/3.27 tff(27009,plain,
% 3.03/3.27 (b(z, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1214, 27008])).
% 3.03/3.27 tff(27010,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26525, 271, 1281, 27009, 26999, 26997])).
% 3.03/3.27 tff(27011,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(elem!1))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(27012,plain,
% 3.03/3.27 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[27011, 26995, 26196, 26197, 26987, 25632, 26498, 19197, 26989])).
% 3.03/3.27 tff(27013,plain,
% 3.03/3.27 (~b(elem!1, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26482, 27012, 26442, 25632])).
% 3.03/3.27 tff(27014,plain,
% 3.03/3.27 (r(elem!1, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1192, 27013, 1101])).
% 3.03/3.27 tff(27015,plain,
% 3.03/3.27 (~r(z, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[6723, 27014, 26197, 26985])).
% 3.03/3.27 tff(27016,plain,
% 3.03/3.27 (b(z, s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1214, 27015])).
% 3.03/3.27 tff(27017,plain,
% 3.03/3.27 (~b(s(s(s(z))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[24799, 27016, 220, 26987])).
% 3.03/3.27 tff(27018,plain,
% 3.03/3.27 (r(s(s(s(z))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2325, 27017])).
% 3.03/3.27 tff(27019,plain,
% 3.03/3.27 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19692, 26995, 26987])).
% 3.03/3.27 tff(27020,plain,
% 3.03/3.27 (~(elem!1 = s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[7490, 26993])).
% 3.03/3.27 tff(27021,plain,
% 3.03/3.27 (~b(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26979, 27020, 26196, 199, 220, 1, 147, 25634])).
% 3.03/3.27 tff(27022,plain,
% 3.03/3.27 (r(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[19736, 27021])).
% 3.03/3.27 tff(27023,plain,
% 3.03/3.27 (~r(elem!1, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[24792, 27018, 26491, 27014])).
% 3.03/3.27 tff(27024,plain,
% 3.03/3.27 (b(elem!1, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[299, 27023, 337])).
% 3.03/3.27 tff(27025,plain,
% 3.03/3.27 (~b(elem!1, z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[8962, 27024, 220, 26987])).
% 3.03/3.27 tff(27026,plain,
% 3.03/3.27 (r(elem!1, z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[284, 27025, 25634])).
% 3.03/3.27 tff(27027,plain,
% 3.03/3.27 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[2505])).
% 3.03/3.27 tff(27028,plain,
% 3.03/3.27 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[27027])).
% 3.03/3.27 tff(27029,plain,
% 3.03/3.27 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[27028])).
% 3.03/3.27 tff(27030,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(27031,plain,
% 3.03/3.27 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(27032,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[27031])).
% 3.03/3.27 tff(27033,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[27032, 27030])).
% 3.03/3.27 tff(27034,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(27035,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[27034, 27033])).
% 3.03/3.27 tff(27036,plain,
% 3.03/3.27 (~r(elem!1, s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[27035, 121, 378, 1409, 24354])).
% 3.03/3.27 tff(27037,plain,
% 3.03/3.27 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[27036, 27029])).
% 3.03/3.27 tff(27038,plain,
% 3.03/3.27 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[26557, 937, 25009, 111, 750, 15942, 1281, 220])).
% 3.03/3.27 tff(27039,plain,
% 3.03/3.27 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1014, 27038, 1008])).
% 3.03/3.27 tff(27040,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[27039, 27037])).
% 3.03/3.27 tff(27041,plain,((~b(s(s(s(s(z)))), s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27042,plain,
% 3.03/3.28 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27041, 26995, 26197, 27026, 26788, 27022, 27019, 19197, 220])).
% 3.03/3.28 tff(27043,plain,
% 3.03/3.28 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[932, 27042])).
% 3.03/3.28 tff(27044,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~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))))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27045,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~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))))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(27046,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~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)))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27045, 27044])).
% 3.03/3.28 tff(27047,plain,
% 3.03/3.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27046, 121, 26989, 27043, 27018])).
% 3.03/3.28 tff(27048,plain,
% 3.03/3.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[10426, 27047])).
% 3.03/3.28 tff(27049,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27050,plain,
% 3.03/3.28 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27051,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27050])).
% 3.03/3.28 tff(27052,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.28 inference(transitivity,[status(thm)],[27051, 27049])).
% 3.03/3.28 tff(27053,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(27054,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27053, 27052])).
% 3.03/3.28 tff(27055,plain,
% 3.03/3.28 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27054, 121, 26989, 27043, 26991])).
% 3.03/3.28 tff(27056,plain,
% 3.03/3.28 (b(s(s(s(s(z)))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1559, 27055, 19204])).
% 3.03/3.28 tff(27057,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27058,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(27059,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27058, 27057])).
% 3.03/3.28 tff(27060,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27059, 271, 26442, 27012, 27056, 27048])).
% 3.03/3.28 tff(27061,plain,(b(z, elem!1) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27062,plain,
% 3.03/3.28 (b(z, elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27061, 147, 220, 1, 5499, 907, 2344])).
% 3.03/3.28 tff(27063,plain,
% 3.03/3.28 (~b(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[20398, 27062, 19197, 220])).
% 3.03/3.28 tff(27064,plain,
% 3.03/3.28 (~b(z, s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[4606, 271, 25632, 26442, 27062])).
% 3.03/3.28 tff(27065,plain,
% 3.03/3.28 (r(z, s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1439, 27064])).
% 3.03/3.28 tff(27066,plain,
% 3.03/3.28 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[23507, 82, 307, 412, 1326])).
% 3.03/3.28 tff(27067,plain,
% 3.03/3.28 (s(s(s(elem!1))) = elem!1),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[486, 27066, 147])).
% 3.03/3.28 tff(27068,plain,
% 3.03/3.28 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27067])).
% 3.03/3.28 tff(27069,plain,
% 3.03/3.28 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(symmetry,[status(thm)],[27068])).
% 3.03/3.28 tff(27070,plain,
% 3.03/3.28 (b(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[1326, 27069])).
% 3.03/3.28 tff(27071,plain,
% 3.03/3.28 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27067])).
% 3.03/3.28 tff(27072,plain,
% 3.03/3.28 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 3.03/3.28 inference(transitivity,[status(thm)],[27071, 1218])).
% 3.03/3.28 tff(27073,plain,
% 3.03/3.28 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27072])).
% 3.03/3.28 tff(27074,plain,
% 3.03/3.28 (~(elem!1 = s(z))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[61, 27073])).
% 3.03/3.28 tff(27075,plain,
% 3.03/3.28 (r(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[299, 27074, 294])).
% 3.03/3.28 tff(27076,plain,
% 3.03/3.28 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27067])).
% 3.03/3.28 tff(27077,plain,
% 3.03/3.28 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[2562, 27067, 23531])).
% 3.03/3.28 tff(27078,plain,
% 3.03/3.28 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[760, 27077])).
% 3.03/3.28 tff(27079,plain,
% 3.03/3.28 (r(s(z), elem!1)),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27078, 27076])).
% 3.03/3.28 tff(27080,plain,
% 3.03/3.28 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27067])).
% 3.03/3.28 tff(27081,plain,
% 3.03/3.28 (r(s(s(s(z))), elem!1)),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[5499, 27080])).
% 3.03/3.28 tff(27082,plain,
% 3.03/3.28 (~r(s(z), s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[4112, 27081, 27079, 27075])).
% 3.03/3.28 tff(27083,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[21665, 27082, 1, 19197, 27070, 27067, 1326])).
% 3.03/3.28 tff(27084,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[23119, 27083, 27082, 19197, 27070, 1, 10063])).
% 3.03/3.28 tff(27085,plain,((s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | b(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27086,plain,
% 3.03/3.28 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27085, 27062, 1, 27063, 5499, 147, 25632, 26196])).
% 3.03/3.28 tff(27087,plain,
% 3.03/3.28 (elem!1 = s(s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[78, 27086])).
% 3.03/3.28 tff(27088,plain,
% 3.03/3.28 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[2479, 27087, 25632])).
% 3.03/3.28 tff(27089,plain,
% 3.03/3.28 (b(s(elem!1), s(s(elem!1)))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3787, 27087, 26442])).
% 3.03/3.28 tff(27090,plain,
% 3.03/3.28 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[9038])).
% 3.03/3.28 tff(27091,plain,
% 3.03/3.28 (~r(s(s(s(s(z)))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1234, 147, 1222])).
% 3.03/3.28 tff(27092,plain,
% 3.03/3.28 (b(s(s(s(s(z)))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[932, 27091])).
% 3.03/3.28 tff(27093,plain,
% 3.03/3.28 (~b(s(s(s(s(z)))), z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[22548, 27092, 1281, 220])).
% 3.03/3.28 tff(27094,plain,
% 3.03/3.28 (~b(s(s(s(elem!1))), z)),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27093, 27090])).
% 3.03/3.28 tff(27095,plain,
% 3.03/3.28 (r(s(s(s(elem!1))), z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1904, 21, 30, 27094])).
% 3.03/3.28 tff(27096,plain,
% 3.03/3.28 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[1038])).
% 3.03/3.28 tff(27097,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[486, 147, 5087])).
% 3.03/3.28 tff(27098,plain,
% 3.03/3.28 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[10076, 27097, 543, 517])).
% 3.03/3.28 tff(27099,plain,
% 3.03/3.28 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[23654, 27098, 223])).
% 3.03/3.28 tff(27100,plain,
% 3.03/3.28 (r(s(elem!1), s(s(s(s(z)))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1995, 27099, 2603])).
% 3.03/3.28 tff(27101,plain,
% 3.03/3.28 (r(s(elem!1), s(s(s(elem!1))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27100, 27096])).
% 3.03/3.28 tff(27102,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27103,plain,
% 3.03/3.28 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27104,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27103])).
% 3.03/3.28 tff(27105,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 3.03/3.28 inference(transitivity,[status(thm)],[27104, 27102])).
% 3.03/3.28 tff(27106,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(27107,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27106, 27105])).
% 3.03/3.28 tff(27108,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27107, 121, 1441, 412, 27101, 27095])).
% 3.03/3.28 tff(27109,plain,(r(s(s(s(elem!1))), elem!1) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27110,plain,
% 3.03/3.28 (~(s(z) = elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27109, 27089, 26196, 147, 19205, 19197, 220, 27088, 27065])).
% 3.03/3.28 tff(27111,plain,
% 3.03/3.28 (~(elem!1 = s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[242, 27110])).
% 3.03/3.28 tff(27112,plain,
% 3.03/3.28 (r(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[299, 27111, 27063])).
% 3.03/3.28 tff(27113,plain,
% 3.03/3.28 (~b(s(z), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[20382, 27062, 19197, 25632])).
% 3.03/3.28 tff(27114,plain,
% 3.03/3.28 (r(s(z), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[236, 27110, 27113])).
% 3.03/3.28 tff(27115,plain,
% 3.03/3.28 (s(elem!1) = s(s(s(elem!1)))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27087])).
% 3.03/3.28 tff(27116,plain,
% 3.03/3.28 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27115])).
% 3.03/3.28 tff(27117,plain,
% 3.03/3.28 (r(s(s(s(elem!1))), z)),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[26196, 27116])).
% 3.03/3.28 tff(27118,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3790, 27087, 26442])).
% 3.03/3.28 tff(27119,plain,
% 3.03/3.28 (~b(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[15671, 27118, 25632, 27062])).
% 3.03/3.28 tff(27120,plain,
% 3.03/3.28 (r(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[19736, 27119])).
% 3.03/3.28 tff(27121,plain,
% 3.03/3.28 (~r(z, s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[7364, 121, 27120, 27117, 5499])).
% 3.03/3.28 tff(27122,plain,
% 3.03/3.28 (b(z, s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1214, 27121])).
% 3.03/3.28 tff(27123,plain,
% 3.03/3.28 (~b(s(s(s(z))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1978, 27122, 25632, 27062])).
% 3.03/3.28 tff(27124,plain,
% 3.03/3.28 (r(s(s(s(z))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[255, 27123, 907])).
% 3.03/3.28 tff(27125,plain,
% 3.03/3.28 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27087])).
% 3.03/3.28 tff(27126,plain,
% 3.03/3.28 (r(s(z), s(s(elem!1)))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27114, 27125])).
% 3.03/3.28 tff(27127,plain,
% 3.03/3.28 (~b(s(z), s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[25337, 27122, 19197, 907, 27126, 27112])).
% 3.03/3.28 tff(27128,plain,
% 3.03/3.28 (r(s(z), s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[105, 27127])).
% 3.03/3.28 tff(27129,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[4112, 27128, 27124, 27114, 27112])).
% 3.03/3.28 tff(27130,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27131,plain,
% 3.03/3.28 (r(s(s(s(elem!1))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27130, 907, 5499, 220, 1, 2344])).
% 3.03/3.28 tff(27132,plain,
% 3.03/3.28 (~r(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[26182, 357, 139, 378, 220])).
% 3.03/3.28 tff(27133,plain,
% 3.03/3.28 (b(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[299, 27132, 258])).
% 3.03/3.28 tff(27134,plain,
% 3.03/3.28 (~b(elem!1, z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[22281, 271, 1281, 27133, 220])).
% 3.03/3.28 tff(27135,plain,
% 3.03/3.28 (r(elem!1, z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[284, 27134, 259])).
% 3.03/3.28 tff(27136,plain,
% 3.03/3.28 (~r(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[6932, 121, 378, 27135, 139])).
% 3.03/3.28 tff(27137,plain,
% 3.03/3.28 (b(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[19736, 27136])).
% 3.03/3.28 tff(27138,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27139,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(27140,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27139, 27138])).
% 3.03/3.28 tff(27141,plain,
% 3.03/3.28 (~r(s(s(s(elem!1))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27140, 121, 357, 27135, 139])).
% 3.03/3.28 tff(27142,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[16580, 27141])).
% 3.03/3.28 tff(27143,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27144,plain,
% 3.03/3.28 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(27145,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27144])).
% 3.03/3.28 tff(27146,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 3.03/3.28 inference(transitivity,[status(thm)],[27145, 27143])).
% 3.03/3.28 tff(27147,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(27148,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27147, 27146])).
% 3.03/3.28 tff(27149,plain,
% 3.03/3.28 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27148, 121, 357, 27135, 139])).
% 3.03/3.28 tff(27150,plain,
% 3.03/3.28 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[760, 27149])).
% 3.03/3.28 tff(27151,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[17333, 27150, 27142, 220, 27137])).
% 3.03/3.28 tff(27152,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(z), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27153,plain,
% 3.03/3.28 (~r(s(z), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27152, 26197, 139, 220, 25634, 19197, 337])).
% 3.03/3.28 tff(27154,plain,
% 3.03/3.28 (b(s(z), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[236, 27153, 230])).
% 3.03/3.28 tff(27155,plain,
% 3.03/3.28 (~b(s(z), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3435, 27154, 25632, 2618])).
% 3.03/3.28 tff(27156,plain,
% 3.03/3.28 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13128, 271, 25632, 2618, 257])).
% 3.03/3.28 tff(27157,plain,
% 3.03/3.28 (~b(s(z), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3435, 20892, 307, 2618])).
% 3.03/3.28 tff(27158,plain,
% 3.03/3.28 (r(s(z), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[444, 27157, 348])).
% 3.03/3.28 tff(27159,plain,
% 3.03/3.28 (~b(z, elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[9079, 20892, 307, 220])).
% 3.03/3.28 tff(27160,plain,
% 3.03/3.28 (r(z, elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[355, 27159, 9297])).
% 3.03/3.28 tff(27161,plain,
% 3.03/3.28 (~(s(s(s(elem!1))) = elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27011, 27160, 412, 13129, 20892, 307, 9149, 19197, 27158])).
% 3.03/3.28 tff(27162,plain,
% 3.03/3.28 (~b(s(s(s(z))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[312, 20892, 307, 257])).
% 3.03/3.28 tff(27163,plain,
% 3.03/3.28 (r(s(s(s(z))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[2325, 27162])).
% 3.03/3.28 tff(27164,plain,
% 3.03/3.28 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[2640, 27158, 412, 27163])).
% 3.03/3.28 tff(27165,plain,
% 3.03/3.28 (s(s(s(z))) = s(elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1816, 27164, 13129])).
% 3.03/3.28 tff(27166,plain,
% 3.03/3.28 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27165])).
% 3.03/3.28 tff(27167,plain,
% 3.03/3.28 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27166])).
% 3.03/3.28 tff(27168,plain,
% 3.03/3.28 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27167])).
% 3.03/3.28 tff(27169,plain,
% 3.03/3.28 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[27168])).
% 3.03/3.28 tff(27170,plain,
% 3.03/3.28 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[17876, 27158, 412, 220])).
% 3.03/3.28 tff(27171,plain,
% 3.03/3.28 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[27170, 27169])).
% 3.03/3.28 tff(27172,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[681, 27171, 21302])).
% 3.03/3.28 tff(27173,plain,
% 3.03/3.28 (~b(elem!1, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[12887, 27172, 307, 2618])).
% 3.03/3.28 tff(27174,plain,
% 3.03/3.28 (~r(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[12884, 27173, 27160, 479, 27161])).
% 3.03/3.28 tff(27175,plain,
% 3.03/3.28 (b(z, s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[19736, 27174])).
% 3.03/3.28 tff(27176,plain,
% 3.03/3.28 (~b(s(s(s(elem!1))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[15639, 27175, 220, 20892])).
% 3.03/3.28 tff(27177,plain,
% 3.03/3.28 (r(s(s(s(elem!1))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[16580, 27176])).
% 3.03/3.28 tff(27178,plain,
% 3.03/3.28 (~b(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[21846, 27175, 19197, 27172])).
% 3.03/3.28 tff(27179,plain,
% 3.03/3.28 (r(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[760, 27178])).
% 3.03/3.28 tff(27180,plain,
% 3.03/3.28 (~r(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[22268, 27179, 139, 27177])).
% 3.03/3.28 tff(27181,plain,
% 3.03/3.28 (b(elem!1, s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[299, 27180, 258])).
% 3.03/3.28 tff(27182,plain,
% 3.03/3.28 (~(s(s(elem!1)) = elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[197, 21301])).
% 3.03/3.28 tff(27183,plain,
% 3.03/3.28 (~b(elem!1, z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[21030, 27175, 19197, 20892])).
% 3.03/3.28 tff(27184,plain,
% 3.03/3.28 (r(elem!1, z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[284, 27183, 9298])).
% 3.03/3.28 tff(27185,plain,
% 3.03/3.28 (~r(s(s(elem!1)), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[6958, 27184, 139, 1, 563, 27160])).
% 3.03/3.28 tff(27186,plain,
% 3.03/3.28 (b(s(s(elem!1)), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[862, 27185, 27182])).
% 3.03/3.28 tff(27187,plain,
% 3.03/3.28 (~b(s(s(elem!1)), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[5441, 27186, 20892, 27181])).
% 3.03/3.28 tff(27188,plain,
% 3.03/3.28 (~r(s(s(elem!1)), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[20012, 27181, 257, 20892, 19199, 27186])).
% 3.03/3.28 tff(27189,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[2143, 27188, 27187])).
% 3.03/3.28 tff(27190,plain,((elem!1 = s(z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | b(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27191,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27190, 232, 25632, 1, 220, 412, 139, 2618, 243, 24230, 257])).
% 3.03/3.28 tff(27192,plain,
% 3.03/3.28 (~b(s(z), s(s(s(z))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[24003, 237, 25632, 257])).
% 3.03/3.28 tff(27193,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[26586, 27192, 27191, 220, 82, 27156, 5499, 412, 25632, 2618])).
% 3.03/3.28 tff(27194,plain,(r(s(z), elem!1) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(27195,plain,
% 3.03/3.28 (~b(s(s(s(z))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[27194, 27153, 82, 5499, 412, 2618, 220, 1, 139, 230])).
% 3.03/3.28 tff(27196,plain,
% 3.03/3.28 (r(s(s(s(z))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[255, 27195, 907])).
% 3.03/3.28 tff(27197,plain,
% 3.03/3.28 (~b(s(elem!1), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3247, 271, 307, 2618, 20892])).
% 3.03/3.28 tff(27198,plain,
% 3.03/3.28 (r(s(elem!1), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[429, 27197, 2282])).
% 3.03/3.28 tff(27199,plain,
% 3.03/3.28 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[23235, 27198, 27158, 108])).
% 3.03/3.28 tff(27200,plain,
% 3.03/3.28 (~b(elem!1, z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[21030, 26180, 19197, 260])).
% 3.03/3.28 tff(27201,plain,
% 3.03/3.28 (r(elem!1, z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[284, 27200, 259])).
% 3.03/3.28 tff(27202,plain,
% 3.03/3.28 (~r(s(s(elem!1)), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[6958, 27201, 139, 1, 563, 378])).
% 3.03/3.28 tff(27203,plain,
% 3.03/3.28 (~b(s(s(s(elem!1))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[15639, 26180, 220, 260])).
% 3.03/3.28 tff(27204,plain,
% 3.03/3.28 (r(s(s(s(elem!1))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[16580, 27203])).
% 3.03/3.28 tff(27205,plain,
% 3.03/3.28 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[22268, 27204, 139, 3456])).
% 3.03/3.28 tff(27206,plain,
% 3.03/3.28 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[760, 27205])).
% 3.03/3.28 tff(27207,plain,
% 3.03/3.28 (~b(s(s(s(elem!1))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13752, 27206, 307, 260])).
% 3.03/3.28 tff(27208,plain,
% 3.03/3.28 (~(elem!1 = s(s(elem!1)))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3790, 27207, 2618])).
% 3.03/3.28 tff(27209,plain,
% 3.03/3.28 (~(s(s(elem!1)) = elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[197, 27208])).
% 3.03/3.28 tff(27210,plain,
% 3.03/3.28 (b(s(s(elem!1)), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[862, 27209, 27202])).
% 3.03/3.28 tff(27211,plain,
% 3.03/3.28 (~r(s(s(s(z))), z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[21430, 121, 378, 3456, 145])).
% 3.03/3.28 tff(27212,plain,
% 3.03/3.28 (b(s(s(s(z))), z)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1155, 27211])).
% 3.03/3.28 tff(27213,plain,
% 3.03/3.28 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[4006, 27211, 412])).
% 3.03/3.28 tff(27214,plain,
% 3.03/3.28 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1816, 27213, 1510])).
% 3.03/3.28 tff(27215,plain,
% 3.03/3.29 (~b(z, s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[23209, 27214, 2618, 27212])).
% 3.03/3.29 tff(27216,plain,
% 3.03/3.29 (r(z, s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1439, 27215])).
% 3.03/3.29 tff(27217,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(27218,plain,
% 3.03/3.29 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(27219,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27218])).
% 3.03/3.29 tff(27220,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[27219, 27217])).
% 3.03/3.29 tff(27221,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(27222,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27221, 27220])).
% 3.03/3.29 tff(27223,plain,
% 3.03/3.29 (~r(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27222, 121, 378, 3456, 145])).
% 3.03/3.29 tff(27224,plain,
% 3.03/3.29 (b(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1214, 27223])).
% 3.03/3.29 tff(27225,plain,
% 3.03/3.29 (~b(s(s(s(z))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[24799, 27224, 220, 260])).
% 3.03/3.29 tff(27226,plain,
% 3.03/3.29 (r(s(s(s(z))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2325, 27225])).
% 3.03/3.29 tff(27227,plain,
% 3.03/3.29 (~r(s(z), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[12518, 27226, 145, 3456])).
% 3.03/3.29 tff(27228,plain,
% 3.03/3.29 (b(s(z), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2167, 27227])).
% 3.03/3.29 tff(27229,plain,
% 3.03/3.29 (~b(s(s(elem!1)), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[17014, 27228, 19197, 220])).
% 3.03/3.29 tff(27230,plain,
% 3.03/3.29 (r(s(s(elem!1)), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2430, 27229])).
% 3.03/3.29 tff(27231,plain,
% 3.03/3.29 (~r(s(s(elem!1)), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[14657, 27230, 412, 27216])).
% 3.03/3.29 tff(27232,plain,
% 3.03/3.29 (b(s(s(elem!1)), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[701, 27231, 3313])).
% 3.03/3.29 tff(27233,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6807, 27232, 27210, 307, 2618])).
% 3.03/3.29 tff(27234,plain,((~r(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (elem!1 = z) | r(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27235,plain,
% 3.03/3.29 (~r(elem!1, s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27234, 20892, 2618, 412, 220, 307, 145, 139, 1, 27160, 9298, 27199])).
% 3.03/3.29 tff(27236,plain,
% 3.03/3.29 (b(elem!1, s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[299, 27235, 258])).
% 3.03/3.29 tff(27237,plain,
% 3.03/3.29 (~b(elem!1, z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[8962, 27236, 220, 20892])).
% 3.03/3.29 tff(27238,plain,
% 3.03/3.29 (r(elem!1, z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[284, 27237, 9298])).
% 3.03/3.29 tff(27239,plain,
% 3.03/3.29 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[16568, 121, 27238, 139, 145])).
% 3.03/3.29 tff(27240,plain,
% 3.03/3.29 (~r(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[10709, 121, 27160, 27238, 145])).
% 3.03/3.29 tff(27241,plain,
% 3.03/3.29 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4006, 27240, 412])).
% 3.03/3.29 tff(27242,plain,
% 3.03/3.29 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1816, 27241, 27199])).
% 3.03/3.29 tff(27243,plain,
% 3.03/3.29 (~r(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[19871, 27238, 145, 27160])).
% 3.03/3.29 tff(27244,plain,
% 3.03/3.29 (b(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1214, 27243])).
% 3.03/3.29 tff(27245,plain,
% 3.03/3.29 (~r(z, s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6932, 121, 27160, 27238, 139])).
% 3.03/3.29 tff(27246,plain,
% 3.03/3.29 (b(z, s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[19736, 27245])).
% 3.03/3.29 tff(27247,plain,
% 3.03/3.29 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[5687, 27246, 27244, 27242])).
% 3.03/3.29 tff(27248,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6237, 21, 27247, 27239, 15822])).
% 3.03/3.29 tff(27249,plain,((elem!1 = s(z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27250,plain,
% 3.03/3.29 (~r(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27249, 27196, 25632, 24230, 220, 412, 2618, 1, 139, 27153, 337])).
% 3.03/3.29 tff(27251,plain,
% 3.03/3.29 (b(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[105, 27250])).
% 3.03/3.29 tff(27252,plain,
% 3.03/3.29 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4929, 27251, 27155])).
% 3.03/3.29 tff(27253,plain,
% 3.03/3.29 (~b(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[21058, 27251, 19197, 220])).
% 3.03/3.29 tff(27254,plain,
% 3.03/3.29 (r(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1155, 27253])).
% 3.03/3.29 tff(27255,plain,
% 3.03/3.29 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[3650, 27254, 412, 26197])).
% 3.03/3.29 tff(27256,plain,
% 3.03/3.29 (b(s(s(s(z))), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1816, 27255, 27252])).
% 3.03/3.29 tff(27257,plain,
% 3.03/3.29 (~r(elem!1, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[26472, 27254, 26197, 27196])).
% 3.03/3.29 tff(27258,plain,
% 3.03/3.29 (b(elem!1, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1192, 27257, 1101])).
% 3.03/3.29 tff(27259,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[26482, 27258, 27256, 2618, 25632])).
% 3.03/3.29 tff(27260,plain,(b(z, elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(z))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27261,plain,
% 3.03/3.29 (b(z, elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27260, 82, 412, 220, 1, 139, 907, 2618, 5499])).
% 3.03/3.29 tff(27262,plain,
% 3.03/3.29 (r(elem!1, s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[299, 258, 24773])).
% 3.03/3.29 tff(27263,plain,
% 3.03/3.29 (~b(s(z), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[20382, 1326, 1281, 307])).
% 3.03/3.29 tff(27264,plain,
% 3.03/3.29 (r(s(z), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[236, 1257, 27263])).
% 3.03/3.29 tff(27265,plain,
% 3.03/3.29 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[18965, 258, 139, 27263, 24773])).
% 3.03/3.29 tff(27266,plain,
% 3.03/3.29 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[760, 27265])).
% 3.03/3.29 tff(27267,plain,
% 3.03/3.29 (~r(s(s(s(elem!1))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4618, 121, 27264, 139, 27262])).
% 3.03/3.29 tff(27268,plain,
% 3.03/3.29 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[16580, 27267])).
% 3.03/3.29 tff(27269,plain,
% 3.03/3.29 (~b(z, s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[17333, 27268, 220, 27266])).
% 3.03/3.29 tff(27270,plain,
% 3.03/3.29 (r(z, s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[19736, 27269])).
% 3.03/3.29 tff(27271,plain,
% 3.03/3.29 (~r(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[11698, 121, 27270, 139, 5499])).
% 3.03/3.29 tff(27272,plain,
% 3.03/3.29 (b(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1214, 27271])).
% 3.03/3.29 tff(27273,plain,
% 3.03/3.29 (~b(s(s(s(z))), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1978, 27272, 307, 1326])).
% 3.03/3.29 tff(27274,plain,
% 3.03/3.29 (r(s(s(s(z))), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[255, 27273, 907])).
% 3.03/3.29 tff(27275,plain,
% 3.03/3.29 (~r(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[11065, 121, 27270, 139, 5499])).
% 3.03/3.29 tff(27276,plain,
% 3.03/3.29 (b(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1155, 27275])).
% 3.03/3.29 tff(27277,plain,
% 3.03/3.29 (~b(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[21058, 27276, 1281, 220])).
% 3.03/3.29 tff(27278,plain,
% 3.03/3.29 (r(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[105, 27277])).
% 3.03/3.29 tff(27279,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4112, 27278, 27274, 27264, 27262])).
% 3.03/3.29 tff(27280,plain,((elem!1 = s(z)) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27281,plain,
% 3.03/3.29 (elem!1 = s(z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27280, 27261, 19197, 220, 25632, 907, 139, 5499])).
% 3.03/3.29 tff(27282,plain,
% 3.03/3.29 (s(elem!1) = s(s(z))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27281])).
% 3.03/3.29 tff(27283,plain,
% 3.03/3.29 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27282])).
% 3.03/3.29 tff(27284,plain,
% 3.03/3.29 (r(s(s(z)), z)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[412, 27283])).
% 3.03/3.29 tff(27285,plain,
% 3.03/3.29 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27282])).
% 3.03/3.29 tff(27286,plain,
% 3.03/3.29 (~b(z, s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4606, 271, 25632, 2618, 27261])).
% 3.03/3.29 tff(27287,plain,
% 3.03/3.29 (r(z, s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1439, 27286])).
% 3.03/3.29 tff(27288,plain,
% 3.03/3.29 (r(z, s(s(z)))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27287, 27285])).
% 3.03/3.29 tff(27289,plain,
% 3.03/3.29 (s(s(elem!1)) = s(s(s(z)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27282])).
% 3.03/3.29 tff(27290,plain,
% 3.03/3.29 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27289])).
% 3.03/3.29 tff(27291,plain,
% 3.03/3.29 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.29 inference(symmetry,[status(thm)],[27290])).
% 3.03/3.29 tff(27292,plain,
% 3.03/3.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[5499, 27291])).
% 3.03/3.29 tff(27293,plain,
% 3.03/3.29 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27281])).
% 3.03/3.29 tff(27294,plain,
% 3.03/3.29 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 3.03/3.29 inference(symmetry,[status(thm)],[27293])).
% 3.03/3.29 tff(27295,plain,
% 3.03/3.29 (s(z) = elem!1),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[242, 27281])).
% 3.03/3.29 tff(27296,plain,
% 3.03/3.29 (b(s(z), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1276, 27295, 25632])).
% 3.03/3.29 tff(27297,plain,
% 3.03/3.29 (~b(s(s(elem!1)), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[22224, 27296, 19197, 3313, 220, 412, 2618, 27287])).
% 3.03/3.29 tff(27298,plain,
% 3.03/3.29 (r(s(s(elem!1)), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2143, 27297])).
% 3.03/3.29 tff(27299,plain,
% 3.03/3.29 (r(s(s(elem!1)), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27298, 27294])).
% 3.03/3.29 tff(27300,plain,
% 3.03/3.29 (~r(elem!1, s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2670, 27299, 139, 27292])).
% 3.03/3.29 tff(27301,plain,
% 3.03/3.29 (b(elem!1, s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[599, 27300, 10063])).
% 3.03/3.29 tff(27302,plain,
% 3.03/3.29 (b(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6679, 27301, 27281])).
% 3.03/3.29 tff(27303,plain,
% 3.03/3.29 (~b(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[21058, 27302, 19197, 220])).
% 3.03/3.29 tff(27304,plain,
% 3.03/3.29 (r(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1155, 27303])).
% 3.03/3.29 tff(27305,plain,
% 3.03/3.29 (~r(s(s(s(z))), s(s(z)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[21564, 27304, 27288, 27284])).
% 3.03/3.29 tff(27306,plain,
% 3.03/3.29 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27282])).
% 3.03/3.29 tff(27307,plain,
% 3.03/3.29 ((s(s(s(z))) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[27306, 20097])).
% 3.03/3.29 tff(27308,plain,
% 3.03/3.29 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 3.03/3.29 inference(symmetry,[status(thm)],[27307])).
% 3.03/3.29 tff(27309,plain,
% 3.03/3.29 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27308])).
% 3.03/3.29 tff(27310,plain,
% 3.03/3.29 (~(s(s(s(z))) = s(elem!1))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[1136, 27309])).
% 3.03/3.29 tff(27311,plain,
% 3.03/3.29 (b(elem!1, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[11114, 27302, 27281])).
% 3.03/3.29 tff(27312,plain,
% 3.03/3.29 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[26482, 27311, 2618, 25632])).
% 3.03/3.29 tff(27313,plain,
% 3.03/3.29 (r(s(s(s(z))), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1816, 27312, 27310])).
% 3.03/3.29 tff(27314,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[10458, 27313, 27305, 27281])).
% 3.03/3.29 tff(27315,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (s(s(s(z))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27316,plain,
% 3.03/3.29 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27315, 26442, 220, 27131, 5499, 26196, 907, 1])).
% 3.03/3.29 tff(27317,plain,
% 3.03/3.29 (elem!1 = s(s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[78, 27316])).
% 3.03/3.29 tff(27318,plain,
% 3.03/3.29 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27317])).
% 3.03/3.29 tff(27319,plain,
% 3.03/3.29 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 3.03/3.29 inference(symmetry,[status(thm)],[27318])).
% 3.03/3.29 tff(27320,plain,
% 3.03/3.29 (s(elem!1) = s(s(s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27317])).
% 3.03/3.29 tff(27321,plain,
% 3.03/3.29 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27320])).
% 3.03/3.29 tff(27322,plain,
% 3.03/3.29 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(symmetry,[status(thm)],[27321])).
% 3.03/3.29 tff(27323,plain,
% 3.03/3.29 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 3.03/3.29 inference(transitivity,[status(thm)],[27322, 27319])).
% 3.03/3.29 tff(27324,plain,
% 3.03/3.29 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27317])).
% 3.03/3.29 tff(27325,plain,
% 3.03/3.29 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27131, 27324])).
% 3.03/3.29 tff(27326,plain,
% 3.03/3.29 (r(s(elem!1), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27325, 27323])).
% 3.03/3.29 tff(27327,plain,
% 3.03/3.29 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27317])).
% 3.03/3.29 tff(27328,plain,
% 3.03/3.29 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 3.03/3.29 inference(symmetry,[status(thm)],[27327])).
% 3.03/3.29 tff(27329,plain,
% 3.03/3.29 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 3.03/3.29 inference(transitivity,[status(thm)],[27328, 1218])).
% 3.03/3.29 tff(27330,plain,
% 3.03/3.29 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27329])).
% 3.03/3.29 tff(27331,plain,
% 3.03/3.29 (~(elem!1 = s(z))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[2137, 27330])).
% 3.03/3.29 tff(27332,plain,
% 3.03/3.29 (~b(z, elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27280, 27331, 19197, 220, 25632, 907, 27131, 5499])).
% 3.03/3.29 tff(27333,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[26284, 27332, 27326, 220, 25632, 26196, 19197, 19205, 5499])).
% 3.03/3.29 tff(27334,plain,((s(s(s(z))) = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27335,plain,
% 3.03/3.29 (s(s(s(z))) = elem!1),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27334, 2344, 5499, 1, 220])).
% 3.03/3.29 tff(27336,plain,
% 3.03/3.29 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27335])).
% 3.03/3.29 tff(27337,plain,
% 3.03/3.29 (r(elem!1, s(s(s(elem!1))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[5499, 27336])).
% 3.03/3.29 tff(27338,plain,
% 3.03/3.29 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[2606])).
% 3.03/3.29 tff(27339,plain,
% 3.03/3.29 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[27338, 935])).
% 3.03/3.29 tff(27340,plain,
% 3.03/3.29 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27339])).
% 3.03/3.29 tff(27341,plain,
% 3.03/3.29 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[17291, 27340])).
% 3.03/3.29 tff(27342,plain,
% 3.03/3.29 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[2606])).
% 3.03/3.29 tff(27343,plain,
% 3.03/3.29 (b(elem!1, s(s(s(s(z)))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[307, 27342])).
% 3.03/3.29 tff(27344,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(symmetry,[status(thm)],[15678])).
% 3.03/3.29 tff(27345,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(transitivity,[status(thm)],[15676, 27344])).
% 3.03/3.29 tff(27346,plain,
% 3.03/3.29 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27345])).
% 3.03/3.29 tff(27347,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 3.03/3.29 inference(symmetry,[status(thm)],[15686])).
% 3.03/3.29 tff(27348,plain,
% 3.03/3.29 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27347])).
% 3.03/3.29 tff(27349,plain,
% 3.03/3.29 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[4024])).
% 3.03/3.29 tff(27350,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 3.03/3.29 inference(symmetry,[status(thm)],[27349])).
% 3.03/3.29 tff(27351,plain,
% 3.03/3.29 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(elem!1), z))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27350])).
% 3.03/3.29 tff(27352,plain,
% 3.03/3.29 (~b(s(elem!1), z)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[1088, 27351])).
% 3.03/3.29 tff(27353,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[394, 27352])).
% 3.03/3.29 tff(27354,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(elem!1), z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27355,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27354, 394, 2606])).
% 3.03/3.29 tff(27356,plain,
% 3.03/3.29 (~b(s(s(s(s(z)))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[22548, 27355, 19197, 220])).
% 3.03/3.29 tff(27357,plain,
% 3.03/3.29 (~b(s(elem!1), s(z))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27356, 27348])).
% 3.03/3.29 tff(27358,plain,
% 3.03/3.29 (r(s(elem!1), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[429, 27357, 2282])).
% 3.03/3.29 tff(27359,plain,
% 3.03/3.29 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 3.03/3.29 inference(transitivity,[status(thm)],[9456, 1218])).
% 3.03/3.29 tff(27360,plain,
% 3.03/3.29 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27359])).
% 3.03/3.29 tff(27361,plain,
% 3.03/3.29 (~(elem!1 = s(z))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[97, 27360])).
% 3.03/3.29 tff(27362,plain,
% 3.03/3.29 (r(s(z), s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[444, 24242, 348])).
% 3.03/3.29 tff(27363,plain,
% 3.03/3.29 (r(elem!1, z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[284, 25639, 9298])).
% 3.03/3.29 tff(27364,plain,
% 3.03/3.29 (~b(z, elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[26193, 394, 19197, 307, 348, 219, 220])).
% 3.03/3.29 tff(27365,plain,
% 3.03/3.29 (b(s(elem!1), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[23984, 394, 307, 15680, 2344, 9297, 27364, 27363, 1, 27362, 9552, 27361, 27358, 147, 9458])).
% 3.03/3.29 tff(27366,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27365, 9466])).
% 3.03/3.29 tff(27367,plain,
% 3.03/3.29 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[244])).
% 3.03/3.29 tff(27368,plain,
% 3.03/3.29 ((~b(elem!1, z)) <=> (~b(s(s(s(z))), z))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[17270])).
% 3.03/3.29 tff(27369,plain,
% 3.03/3.29 (~b(s(s(s(z))), z)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[25639, 27368])).
% 3.03/3.29 tff(27370,plain,
% 3.03/3.29 (r(s(s(s(z))), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1155, 27369])).
% 3.03/3.29 tff(27371,plain,
% 3.03/3.29 (~b(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4210, 27364, 244])).
% 3.03/3.29 tff(27372,plain,
% 3.03/3.29 (r(z, s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1214, 27371])).
% 3.03/3.29 tff(27373,plain,
% 3.03/3.29 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[486, 147, 9552])).
% 3.03/3.29 tff(27374,plain,
% 3.03/3.29 (~b(s(z), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[24019, 27365, 17291, 27373, 307, 27362, 27358])).
% 3.03/3.29 tff(27375,plain,
% 3.03/3.29 (~b(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[10599, 27374, 244])).
% 3.03/3.29 tff(27376,plain,
% 3.03/3.29 (r(s(z), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[105, 27375])).
% 3.03/3.29 tff(27377,plain,
% 3.03/3.29 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[26349, 27376, 220, 27372, 27370, 19197])).
% 3.03/3.29 tff(27378,plain,
% 3.03/3.29 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1733, 27377])).
% 3.03/3.29 tff(27379,plain,
% 3.03/3.29 (b(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27378, 27367])).
% 3.03/3.29 tff(27380,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(27381,plain,
% 3.03/3.29 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(27382,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27381])).
% 3.03/3.29 tff(27383,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[27382, 27380])).
% 3.03/3.29 tff(27384,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(27385,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27384, 27383])).
% 3.03/3.29 tff(27386,plain,
% 3.03/3.29 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27385, 271, 27379, 27366, 27343])).
% 3.03/3.29 tff(27387,plain,
% 3.03/3.29 (~b(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27386, 27346])).
% 3.03/3.29 tff(27388,plain,
% 3.03/3.29 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[9439])).
% 3.03/3.29 tff(27389,plain,
% 3.03/3.29 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.03/3.29 inference(symmetry,[status(thm)],[27388])).
% 3.03/3.29 tff(27390,plain,
% 3.03/3.29 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 3.03/3.29 inference(transitivity,[status(thm)],[27367, 27389])).
% 3.03/3.29 tff(27391,plain,
% 3.03/3.29 (b(s(s(elem!1)), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27378, 27390])).
% 3.03/3.29 tff(27392,plain,
% 3.03/3.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[551, 27391, 307, 27373])).
% 3.03/3.29 tff(27393,plain,
% 3.03/3.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[556, 27392, 1])).
% 3.03/3.29 tff(27394,plain,
% 3.03/3.29 (~r(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[3192, 27393, 307, 27365, 27373, 17291])).
% 3.03/3.29 tff(27395,plain,
% 3.03/3.29 (b(s(elem!1), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[526, 27394, 211])).
% 3.03/3.29 tff(27396,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27395, 27387])).
% 3.03/3.29 tff(27397,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(s(s(s(z))) = elem!1)) | (~b(z, s(z))) | r(elem!1, s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(27398,plain,
% 3.03/3.29 (~b(s(elem!1), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[27397, 147, 1, 244, 220, 2344, 307, 348])).
% 3.03/3.29 tff(27399,plain,
% 3.03/3.29 (r(s(elem!1), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[409, 27398])).
% 3.03/3.29 tff(27400,plain,
% 3.03/3.29 (~b(z, elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[23507, 27399, 307, 17291, 27373])).
% 3.03/3.29 tff(27401,plain,
% 3.03/3.29 (r(z, elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[355, 27400, 9297])).
% 3.03/3.29 tff(27402,plain,
% 3.03/3.29 (~r(s(elem!1), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6817, 27401, 727, 27399])).
% 3.03/3.29 tff(27403,plain,
% 3.03/3.29 (b(s(elem!1), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2243, 27402, 2207])).
% 3.03/3.29 tff(27404,plain,
% 3.03/3.29 (b(s(s(s(s(z)))), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[27403, 9466])).
% 3.03/3.29 tff(27405,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(27406,plain,
% 3.03/3.29 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(27407,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[27406])).
% 3.03/3.29 tff(27408,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.30 inference(transitivity,[status(thm)],[27407, 27405])).
% 3.03/3.30 tff(27409,plain,
% 3.03/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.03/3.30 inference(quant_inst,[status(thm)],[])).
% 3.03/3.30 tff(27410,plain,
% 3.03/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.03/3.30 inference(modus_ponens,[status(thm)],[27409, 27408])).
% 3.03/3.30 tff(27411,plain,
% 3.03/3.30 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.03/3.30 inference(unit_resolution,[status(thm)],[27410, 271, 27373, 27404, 27343])).
% 3.03/3.30 tff(27412,plain,
% 3.03/3.30 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.03/3.30 inference(unit_resolution,[status(thm)],[1000, 21, 27411, 27341])).
% 3.03/3.30 tff(27413,plain,
% 3.03/3.30 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.03/3.30 inference(monotonicity,[status(thm)],[27338])).
% 3.03/3.30 tff(27414,plain,
% 3.03/3.30 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.03/3.30 inference(modus_ponens,[status(thm)],[17291, 27413])).
% 3.03/3.30 tff(27415,plain,
% 3.03/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.30 inference(rewrite,[status(thm)],[])).
% 3.03/3.30 tff(27416,plain,
% 3.03/3.30 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(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(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.30 inference(rewrite,[status(thm)],[])).
% 3.03/3.30 tff(27417,plain,
% 3.03/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.03/3.30 inference(monotonicity,[status(thm)],[27416])).
% 3.03/3.30 tff(27418,plain,
% 3.03/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.30 inference(transitivity,[status(thm)],[27417, 27415])).
% 3.03/3.30 tff(27419,plain,
% 3.03/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.30 inference(quant_inst,[status(thm)],[])).
% 3.03/3.30 tff(27420,plain,
% 3.03/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.03/3.30 inference(modus_ponens,[status(thm)],[27419, 27418])).
% 3.03/3.30 tff(27421,plain,
% 3.03/3.30 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.30 inference(unit_resolution,[status(thm)],[27420, 271, 27373, 27404, 27343])).
% 3.03/3.30 tff(27422,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[1014, 27421, 27414])).
% 3.12/3.30 tff(27423,plain,
% 3.12/3.30 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.12/3.30 inference(monotonicity,[status(thm)],[2606])).
% 3.12/3.30 tff(27424,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), z)),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27399, 27423])).
% 3.12/3.30 tff(27425,plain,
% 3.12/3.30 (~b(z, s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[26979, 27399, 147, 15680, 220, 1, 27400, 9298])).
% 3.12/3.30 tff(27426,plain,
% 3.12/3.30 (r(z, s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[19736, 27425])).
% 3.12/3.30 tff(27427,plain,
% 3.12/3.30 ($false),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[1021, 121, 27426, 27424, 27422, 27412])).
% 3.12/3.30 tff(27428,plain,(r(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~(s(s(s(z))) = elem!1)) | r(elem!1, s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.30 tff(27429,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27428, 27337, 220, 1, 25632, 27335, 2344, 24230])).
% 3.12/3.30 tff(27430,plain,
% 3.12/3.30 (~r(s(z), elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27152, 378, 139, 220, 259, 19197, 27361])).
% 3.12/3.30 tff(27431,plain,
% 3.12/3.30 (~r(z, s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[10623, 378, 727, 139])).
% 3.12/3.30 tff(27432,plain,
% 3.12/3.30 (r(s(z), s(s(s(z))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[23127, 27431, 1, 19197])).
% 3.12/3.30 tff(27433,plain,
% 3.12/3.30 ($false),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[250, 27432, 27430, 244])).
% 3.12/3.30 tff(27434,plain,((~r(z, elem!1)) | (~(s(s(s(z))) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.30 tff(27435,plain,
% 3.12/3.30 (~r(z, elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27434, 27335, 1, 27429, 220, 25634, 27337])).
% 3.12/3.30 tff(27436,plain,
% 3.12/3.30 (b(z, elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[355, 27435, 25633])).
% 3.12/3.30 tff(27437,plain,
% 3.12/3.30 (~b(elem!1, s(z))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[20398, 27436, 19197, 220])).
% 3.12/3.30 tff(27438,plain,
% 3.12/3.30 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27335])).
% 3.12/3.30 tff(27439,plain,
% 3.12/3.30 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 3.12/3.30 inference(transitivity,[status(thm)],[27438, 238])).
% 3.12/3.30 tff(27440,plain,
% 3.12/3.30 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 3.12/3.30 inference(transitivity,[status(thm)],[27439, 1218])).
% 3.12/3.30 tff(27441,plain,
% 3.12/3.30 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27440])).
% 3.12/3.30 tff(27442,plain,
% 3.12/3.30 (~(elem!1 = s(z))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[97, 27441])).
% 3.12/3.30 tff(27443,plain,
% 3.12/3.30 (~b(s(z), elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[20382, 27436, 19197, 25632])).
% 3.12/3.30 tff(27444,plain,
% 3.12/3.30 (~r(s(z), s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[18965, 27443, 27429, 27442, 27437])).
% 3.12/3.30 tff(27445,plain,
% 3.12/3.30 (b(s(z), s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[760, 27444])).
% 3.12/3.30 tff(27446,plain,
% 3.12/3.30 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27439])).
% 3.12/3.30 tff(27447,plain,
% 3.12/3.30 (~(s(z) = elem!1)),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[97, 27446])).
% 3.12/3.30 tff(27448,plain,
% 3.12/3.30 (r(s(z), elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[236, 27443, 27447])).
% 3.12/3.30 tff(27449,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27450,plain,
% 3.12/3.30 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27451,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27450])).
% 3.12/3.30 tff(27452,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)))),
% 3.12/3.30 inference(transitivity,[status(thm)],[27451, 27449])).
% 3.12/3.30 tff(27453,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 3.12/3.30 inference(quant_inst,[status(thm)],[])).
% 3.12/3.30 tff(27454,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27453, 27452])).
% 3.12/3.30 tff(27455,plain,
% 3.12/3.30 (~r(s(s(s(elem!1))), s(z))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27454, 121, 27448, 27429, 27337])).
% 3.12/3.30 tff(27456,plain,
% 3.12/3.30 (b(s(s(s(elem!1))), s(z))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[16580, 27455])).
% 3.12/3.30 tff(27457,plain,
% 3.12/3.30 (~b(z, s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[17333, 27456, 220, 27445])).
% 3.12/3.30 tff(27458,plain,
% 3.12/3.30 (r(z, s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[19736, 27457])).
% 3.12/3.30 tff(27459,plain,
% 3.12/3.30 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27335])).
% 3.12/3.30 tff(27460,plain,
% 3.12/3.30 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.12/3.30 inference(symmetry,[status(thm)],[27459])).
% 3.12/3.30 tff(27461,plain,
% 3.12/3.30 ((~r(elem!1, z)) <=> (~r(s(s(s(z))), z))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27460])).
% 3.12/3.30 tff(27462,plain,
% 3.12/3.30 (~r(elem!1, z)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[10989, 121, 27458, 27429, 27337])).
% 3.12/3.30 tff(27463,plain,
% 3.12/3.30 (~r(s(s(s(z))), z)),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27462, 27461])).
% 3.12/3.30 tff(27464,plain,
% 3.12/3.30 (b(s(s(s(z))), z)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[1155, 27463])).
% 3.12/3.30 tff(27465,plain,
% 3.12/3.30 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27335])).
% 3.12/3.30 tff(27466,plain,
% 3.12/3.30 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.12/3.30 inference(symmetry,[status(thm)],[27465])).
% 3.12/3.30 tff(27467,plain,
% 3.12/3.30 (~(elem!1 = s(s(elem!1)))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[3906, 27335])).
% 3.12/3.30 tff(27468,plain,
% 3.12/3.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[78, 27467])).
% 3.12/3.30 tff(27469,plain,
% 3.12/3.30 (s(elem!1) = s(s(s(s(z))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[2605, 27335])).
% 3.12/3.30 tff(27470,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27469])).
% 3.12/3.30 tff(27471,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.30 inference(symmetry,[status(thm)],[27470])).
% 3.12/3.30 tff(27472,plain,
% 3.12/3.30 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27471])).
% 3.12/3.30 tff(27473,plain,
% 3.12/3.30 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27469])).
% 3.12/3.30 tff(27474,plain,
% 3.12/3.30 (~b(s(elem!1), z)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[26193, 27436, 19197, 25632, 24230, 219, 220])).
% 3.12/3.30 tff(27475,plain,
% 3.12/3.30 (r(s(elem!1), z)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[409, 27474])).
% 3.12/3.30 tff(27476,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), z)),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27475, 27473])).
% 3.12/3.30 tff(27477,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27478,plain,
% 3.12/3.30 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27479,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27478])).
% 3.12/3.30 tff(27480,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.12/3.30 inference(transitivity,[status(thm)],[27479, 27477])).
% 3.12/3.30 tff(27481,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 3.12/3.30 inference(quant_inst,[status(thm)],[])).
% 3.12/3.30 tff(27482,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27481, 27480])).
% 3.12/3.30 tff(27483,plain,
% 3.12/3.30 (~b(s(s(s(elem!1))), z)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27482, 271, 27445, 220, 27456])).
% 3.12/3.30 tff(27484,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), z)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[8229, 27483])).
% 3.12/3.30 tff(27485,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27486,plain,
% 3.12/3.30 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27487,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27486])).
% 3.12/3.30 tff(27488,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.30 inference(transitivity,[status(thm)],[27487, 27485])).
% 3.12/3.30 tff(27489,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.30 inference(quant_inst,[status(thm)],[])).
% 3.12/3.30 tff(27490,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27489, 27488])).
% 3.12/3.30 tff(27491,plain,
% 3.12/3.30 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27490, 121, 27458, 27484, 27476])).
% 3.12/3.30 tff(27492,plain,
% 3.12/3.30 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27491, 27472])).
% 3.12/3.30 tff(27493,plain,
% 3.12/3.30 (b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[681, 27492, 27468])).
% 3.12/3.30 tff(27494,plain,
% 3.12/3.30 (r(elem!1, s(z))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[299, 27437, 27442])).
% 3.12/3.30 tff(27495,plain,
% 3.12/3.30 (~b(s(s(s(elem!1))), elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[23507, 27475, 25632, 27468, 27436])).
% 3.12/3.30 tff(27496,plain,
% 3.12/3.30 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[2611, 27335])).
% 3.12/3.30 tff(27497,plain,
% 3.12/3.30 (elem!1 = s(s(s(z)))),
% 3.12/3.30 inference(symmetry,[status(thm)],[244])).
% 3.12/3.30 tff(27498,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27497])).
% 3.12/3.30 tff(27499,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.12/3.30 inference(symmetry,[status(thm)],[27498])).
% 3.12/3.30 tff(27500,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 3.12/3.30 inference(monotonicity,[status(thm)],[2607, 244])).
% 3.12/3.30 tff(27501,plain,
% 3.12/3.30 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.30 inference(symmetry,[status(thm)],[27500])).
% 3.12/3.30 tff(27502,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[622, 27501])).
% 3.12/3.30 tff(27503,plain,
% 3.12/3.30 (r(s(s(s(s(z)))), elem!1)),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27502, 27499])).
% 3.12/3.30 tff(27504,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27505,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(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))))))),
% 3.12/3.30 inference(quant_inst,[status(thm)],[])).
% 3.12/3.30 tff(27506,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(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)))))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27505, 27504])).
% 3.12/3.30 tff(27507,plain,
% 3.12/3.30 ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27506, 121, 139, 727])).
% 3.12/3.30 tff(27508,plain,
% 3.12/3.30 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27507, 27503])).
% 3.12/3.30 tff(27509,plain,
% 3.12/3.30 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[1000, 21, 27508, 27341])).
% 3.12/3.30 tff(27510,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27511,plain,
% 3.12/3.30 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.12/3.30 inference(rewrite,[status(thm)],[])).
% 3.12/3.30 tff(27512,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27511])).
% 3.12/3.30 tff(27513,plain,
% 3.12/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.12/3.30 inference(transitivity,[status(thm)],[27512, 27510])).
% 3.12/3.30 tff(27514,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.30 inference(quant_inst,[status(thm)],[])).
% 3.12/3.30 tff(27515,plain,
% 3.12/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27514, 27513])).
% 3.12/3.30 tff(27516,plain,
% 3.12/3.30 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27515, 121, 139, 727])).
% 3.12/3.30 tff(27517,plain,
% 3.12/3.30 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[27516, 27503])).
% 3.12/3.30 tff(27518,plain,
% 3.12/3.30 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[1014, 27517, 27414])).
% 3.12/3.30 tff(27519,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[2606])).
% 3.12/3.30 tff(27520,plain,
% 3.12/3.30 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.30 inference(symmetry,[status(thm)],[27519])).
% 3.12/3.30 tff(27521,plain,
% 3.12/3.30 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.12/3.30 inference(monotonicity,[status(thm)],[27520])).
% 3.12/3.30 tff(27522,plain,
% 3.12/3.30 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.30 inference(modus_ponens,[status(thm)],[27517, 27521])).
% 3.12/3.30 tff(27523,plain,
% 3.12/3.30 (b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[681, 27522, 17291])).
% 3.12/3.30 tff(27524,plain,
% 3.12/3.30 (~b(z, elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[26193, 394, 1281, 307, 348, 377, 220])).
% 3.12/3.30 tff(27525,plain,
% 3.12/3.30 (r(z, elem!1)),
% 3.12/3.30 inference(unit_resolution,[status(thm)],[355, 27524, 9297])).
% 3.12/3.30 tff(27526,plain,
% 3.12/3.31 (~b(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3351, 394, 307, 9298, 139, 638])).
% 3.12/3.31 tff(27527,plain,
% 3.12/3.31 (r(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1439, 27526])).
% 3.12/3.31 tff(27528,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3387, 27527, 27525, 622, 27363])).
% 3.12/3.31 tff(27529,plain,((~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27530,plain,
% 3.12/3.31 (~b(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27529, 622, 307, 139, 27523, 1281, 348, 377, 220])).
% 3.12/3.31 tff(27531,plain,
% 3.12/3.31 (r(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[409, 27530])).
% 3.12/3.31 tff(27532,plain,
% 3.12/3.31 (~r(z, elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[6817, 27531, 727, 622])).
% 3.12/3.31 tff(27533,plain,
% 3.12/3.31 (b(z, elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[355, 27532, 9297])).
% 3.12/3.31 tff(27534,plain,
% 3.12/3.31 (~b(elem!1, s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20398, 27533, 1281, 220])).
% 3.12/3.31 tff(27535,plain,
% 3.12/3.31 (~b(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20382, 27533, 1281, 307])).
% 3.12/3.31 tff(27536,plain,
% 3.12/3.31 (~r(s(z), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[18965, 27535, 139, 27361, 27534])).
% 3.12/3.31 tff(27537,plain,
% 3.12/3.31 (b(s(z), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[760, 27536])).
% 3.12/3.31 tff(27538,plain,
% 3.12/3.31 (~b(s(s(s(s(z)))), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[12570, 27537, 27518, 27509])).
% 3.12/3.31 tff(27539,plain,
% 3.12/3.31 (r(s(s(s(s(z)))), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[932, 27538])).
% 3.12/3.31 tff(27540,plain,
% 3.12/3.31 (r(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[236, 27535, 9458])).
% 3.12/3.31 tff(27541,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27542,plain,
% 3.12/3.31 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27543,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27542])).
% 3.12/3.31 tff(27544,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.12/3.31 inference(transitivity,[status(thm)],[27543, 27541])).
% 3.12/3.31 tff(27545,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.12/3.31 inference(quant_inst,[status(thm)],[])).
% 3.12/3.31 tff(27546,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27545, 27544])).
% 3.12/3.31 tff(27547,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27546, 121, 27540, 727, 27539, 27503])).
% 3.12/3.31 tff(27548,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27549,plain,
% 3.12/3.31 (~r(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27548, 27337, 27429, 19197, 25632, 220, 24230, 219, 27335])).
% 3.12/3.31 tff(27550,plain,
% 3.12/3.31 (b(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2243, 27549, 2207])).
% 3.12/3.31 tff(27551,plain,
% 3.12/3.31 (~b(elem!1, s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[12887, 27493, 25632, 27550])).
% 3.12/3.31 tff(27552,plain,
% 3.12/3.31 (~r(elem!1, s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[21266, 27551, 27496, 1, 27445, 27495, 27494, 27493])).
% 3.12/3.31 tff(27553,plain,
% 3.12/3.31 (b(elem!1, s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[599, 27552, 27467])).
% 3.12/3.31 tff(27554,plain,
% 3.12/3.31 (b(s(s(s(z))), s(s(elem!1)))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27553, 27466])).
% 3.12/3.31 tff(27555,plain,
% 3.12/3.31 (~b(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[15101, 27436, 219, 2344, 27549])).
% 3.12/3.31 tff(27556,plain,
% 3.12/3.31 (r(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1439, 27555])).
% 3.12/3.31 tff(27557,plain,
% 3.12/3.31 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27469])).
% 3.12/3.31 tff(27558,plain,
% 3.12/3.31 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.31 inference(symmetry,[status(thm)],[27557])).
% 3.12/3.31 tff(27559,plain,
% 3.12/3.31 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27469])).
% 3.12/3.31 tff(27560,plain,
% 3.12/3.31 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.12/3.31 inference(transitivity,[status(thm)],[27559, 935])).
% 3.12/3.31 tff(27561,plain,
% 3.12/3.31 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27560])).
% 3.12/3.31 tff(27562,plain,
% 3.12/3.31 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27468, 27561])).
% 3.12/3.31 tff(27563,plain,
% 3.12/3.31 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[26553, 121, 27458, 27484, 27476])).
% 3.12/3.31 tff(27564,plain,
% 3.12/3.31 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1000, 21, 27563, 27562])).
% 3.12/3.31 tff(27565,plain,
% 3.12/3.31 (b(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27564, 27558])).
% 3.12/3.31 tff(27566,plain,
% 3.12/3.31 (~b(s(s(elem!1)), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[18873, 27565, 25632, 27553])).
% 3.12/3.31 tff(27567,plain,
% 3.12/3.31 (r(s(s(elem!1)), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[701, 27566, 3313])).
% 3.12/3.31 tff(27568,plain,
% 3.12/3.31 (~r(s(s(elem!1)), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[14657, 27567, 27475, 27556])).
% 3.12/3.31 tff(27569,plain,
% 3.12/3.31 (b(s(s(elem!1)), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2430, 27568])).
% 3.12/3.31 tff(27570,plain,
% 3.12/3.31 (~b(z, s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2454, 27569, 27554, 27464])).
% 3.12/3.31 tff(27571,plain,
% 3.12/3.31 (r(z, s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2106, 27570])).
% 3.12/3.31 tff(27572,plain,
% 3.12/3.31 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3425, 27571, 27429, 27458])).
% 3.12/3.31 tff(27573,plain,
% 3.12/3.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[17205, 27571, 25633, 27467, 220, 27442, 27569])).
% 3.12/3.31 tff(27574,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[556, 27573, 27572, 1])).
% 3.12/3.31 tff(27575,plain,(r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27576,plain,
% 3.12/3.31 (r(elem!1, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27575, 220, 1, 5499])).
% 3.12/3.31 tff(27577,plain,
% 3.12/3.31 (~r(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24738, 199, 2207, 27576, 220, 19197, 25633])).
% 3.12/3.31 tff(27578,plain,
% 3.12/3.31 (~b(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24701, 27577, 27576, 220, 25633, 147, 1, 5499])).
% 3.12/3.31 tff(27579,plain,
% 3.12/3.31 (b(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[409, 27577])).
% 3.12/3.31 tff(27580,plain,
% 3.12/3.31 (b(s(z), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24344, 27579, 27576, 220, 27578, 25633, 1, 5499])).
% 3.12/3.31 tff(27581,plain,
% 3.12/3.31 (~b(z, s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24348, 27580, 27577, 1])).
% 3.12/3.31 tff(27582,plain,
% 3.12/3.31 (r(z, s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[19736, 27581])).
% 3.12/3.31 tff(27583,plain,
% 3.12/3.31 (~b(elem!1, z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[402, 27579, 25632, 220])).
% 3.12/3.31 tff(27584,plain,
% 3.12/3.31 (r(elem!1, z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[284, 27583, 25634])).
% 3.12/3.31 tff(27585,plain,
% 3.12/3.31 (~b(s(s(s(elem!1))), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24421, 27582, 27576, 19197, 220, 27579, 24230])).
% 3.12/3.31 tff(27586,plain,
% 3.12/3.31 (r(s(s(s(elem!1))), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[8229, 27585])).
% 3.12/3.31 tff(27587,plain,
% 3.12/3.31 (r(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2243, 27578, 2207])).
% 3.12/3.31 tff(27588,plain,
% 3.12/3.31 (~b(s(z), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[9241, 27579, 19197, 220])).
% 3.12/3.31 tff(27589,plain,
% 3.12/3.31 (r(s(z), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[444, 27588, 24230])).
% 3.12/3.31 tff(27590,plain,
% 3.12/3.31 (~r(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[17391, 27589, 27576, 27587])).
% 3.12/3.31 tff(27591,plain,
% 3.12/3.31 (b(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[236, 27590, 230])).
% 3.12/3.31 tff(27592,plain,
% 3.12/3.31 (s(s(s(z))) = elem!1),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[25651, 27591, 25632, 27579, 220, 27580, 25634, 26197])).
% 3.12/3.31 tff(27593,plain,
% 3.12/3.31 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2611, 27592])).
% 3.12/3.31 tff(27594,plain,
% 3.12/3.31 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[486, 27593, 147])).
% 3.12/3.31 tff(27595,plain,
% 3.12/3.31 (~r(s(s(elem!1)), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20430, 27594, 25632, 1, 10064, 27586, 26197, 27584])).
% 3.12/3.31 tff(27596,plain,
% 3.12/3.31 (b(s(s(elem!1)), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2430, 27595])).
% 3.12/3.31 tff(27597,plain,
% 3.12/3.31 (~b(s(z), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[13752, 27594, 25632, 27591])).
% 3.12/3.31 tff(27598,plain,
% 3.12/3.31 (r(s(z), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[760, 27597])).
% 3.12/3.31 tff(27599,plain,
% 3.12/3.31 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[10857, 27598, 27596, 27582])).
% 3.12/3.31 tff(27600,plain,
% 3.12/3.31 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[586, 27599, 563])).
% 3.12/3.31 tff(27601,plain,
% 3.12/3.31 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[9617, 27598, 27587, 27589])).
% 3.12/3.31 tff(27602,plain,
% 3.12/3.31 (b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[681, 27601, 82])).
% 3.12/3.31 tff(27603,plain,
% 3.12/3.31 (~r(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3387, 27587, 26197, 27584])).
% 3.12/3.31 tff(27604,plain,
% 3.12/3.31 (b(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1439, 27603])).
% 3.12/3.31 tff(27605,plain,
% 3.12/3.31 (~b(s(s(elem!1)), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2853, 27596, 27579, 27604])).
% 3.12/3.31 tff(27606,plain,
% 3.12/3.31 (r(s(s(elem!1)), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[701, 27605, 3313])).
% 3.12/3.31 tff(27607,plain,
% 3.12/3.31 (~b(s(z), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[17014, 27596, 19197, 220])).
% 3.12/3.31 tff(27608,plain,
% 3.12/3.31 (r(s(z), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2167, 27607])).
% 3.12/3.31 tff(27609,plain,
% 3.12/3.31 (~r(s(elem!1), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3275, 27608, 27589, 27606])).
% 3.12/3.31 tff(27610,plain,
% 3.12/3.31 (b(s(elem!1), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[526, 27609, 211])).
% 3.12/3.31 tff(27611,plain,
% 3.12/3.31 (~b(s(s(elem!1)), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[16949, 27596, 19197, 220])).
% 3.12/3.31 tff(27612,plain,
% 3.12/3.31 (r(s(s(elem!1)), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2143, 27611])).
% 3.12/3.31 tff(27613,plain,
% 3.12/3.31 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2883, 27612, 25632, 27591, 27594])).
% 3.12/3.31 tff(27614,plain,
% 3.12/3.31 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[556, 27613, 1])).
% 3.12/3.31 tff(27615,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1459, 27614, 27610, 27602, 27600])).
% 3.12/3.31 tff(27616,plain,(b(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27617,plain,
% 3.12/3.31 (b(z, elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27616, 82, 1, 220, 147, 5499])).
% 3.12/3.31 tff(27618,plain,
% 3.12/3.31 (~b(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[26193, 27617, 19197, 25632, 24230, 219, 220])).
% 3.12/3.31 tff(27619,plain,
% 3.12/3.31 (~b(elem!1, s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20398, 27617, 19197, 220])).
% 3.12/3.31 tff(27620,plain,
% 3.12/3.31 (~r(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27085, 27619, 1, 147, 5499, 82, 25632, 27617])).
% 3.12/3.31 tff(27621,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[409, 27620, 27618])).
% 3.12/3.31 tff(27622,plain,((s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27623,plain,
% 3.12/3.31 (s(s(s(elem!1))) = s(elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27622, 147, 1, 5499, 220])).
% 3.12/3.31 tff(27624,plain,
% 3.12/3.31 (elem!1 = s(s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[78, 27623])).
% 3.12/3.31 tff(27625,plain,
% 3.12/3.31 (~(s(s(s(z))) = elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3906, 27624])).
% 3.12/3.31 tff(27626,plain,
% 3.12/3.31 (~(elem!1 = s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1100, 27625])).
% 3.12/3.31 tff(27627,plain,
% 3.12/3.31 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1516, 27626])).
% 3.12/3.31 tff(27628,plain,
% 3.12/3.31 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[17419, 27627])).
% 3.12/3.31 tff(27629,plain,
% 3.12/3.31 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2479, 27624, 25632])).
% 3.12/3.31 tff(27630,plain,
% 3.12/3.31 (b(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[12364, 27624, 1, 147])).
% 3.12/3.31 tff(27631,plain,
% 3.12/3.31 (b(s(elem!1), s(s(elem!1)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3787, 27624, 27630])).
% 3.12/3.31 tff(27632,plain,
% 3.12/3.31 (r(s(elem!1), z)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24701, 27630, 27576, 220, 25633, 147, 1, 5499])).
% 3.12/3.31 tff(27633,plain,
% 3.12/3.31 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3790, 27624, 27630])).
% 3.12/3.31 tff(27634,plain,
% 3.12/3.31 (b(z, elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24738, 27632, 2207, 27576, 220, 19197, 25633])).
% 3.12/3.31 tff(27635,plain,
% 3.12/3.31 (~b(z, s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[15671, 27634, 25632, 27633])).
% 3.12/3.31 tff(27636,plain,
% 3.12/3.31 (~b(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[6491, 27635, 27624])).
% 3.12/3.31 tff(27637,plain,
% 3.12/3.31 (r(z, s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1439, 27636])).
% 3.12/3.31 tff(27638,plain,
% 3.12/3.31 (~(s(z) = elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27109, 27637, 147, 27632, 27631, 19197, 220, 27629, 27628])).
% 3.12/3.31 tff(27639,plain,
% 3.12/3.31 (~(elem!1 = s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[242, 27638])).
% 3.12/3.31 tff(27640,plain,
% 3.12/3.31 (~b(elem!1, s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20398, 27634, 19197, 220])).
% 3.12/3.31 tff(27641,plain,
% 3.12/3.31 (~(s(s(s(z))) = s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3917, 27624, 24230])).
% 3.12/3.31 tff(27642,plain,
% 3.12/3.31 (r(s(s(s(z))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[23458, 27623, 5499])).
% 3.12/3.31 tff(27643,plain,
% 3.12/3.31 (~r(elem!1, s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[17626, 27632, 27576, 27642])).
% 3.12/3.31 tff(27644,plain,
% 3.12/3.31 (b(elem!1, s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1192, 27643, 27626])).
% 3.12/3.31 tff(27645,plain,
% 3.12/3.31 (~b(s(s(s(z))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[13144, 27644, 25632, 27632, 27630, 27634, 27641])).
% 3.12/3.31 tff(27646,plain,
% 3.12/3.31 (r(s(s(s(z))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[24754, 27632, 27576, 27642, 25634, 27634, 27625])).
% 3.12/3.31 tff(27647,plain,
% 3.12/3.31 (~r(s(elem!1), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[19641, 27646, 27576, 27642])).
% 3.12/3.31 tff(27648,plain,
% 3.12/3.31 (b(s(elem!1), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[429, 27647, 26198])).
% 3.12/3.31 tff(27649,plain,
% 3.12/3.31 (~b(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20382, 27634, 19197, 25632])).
% 3.12/3.31 tff(27650,plain,
% 3.12/3.31 (r(elem!1, s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[299, 27639, 27640])).
% 3.12/3.31 tff(27651,plain,
% 3.12/3.31 (r(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[236, 27638, 27649])).
% 3.12/3.31 tff(27652,plain,
% 3.12/3.31 (~r(s(z), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[4112, 27651, 27646, 27650])).
% 3.12/3.31 tff(27653,plain,
% 3.12/3.31 (b(s(z), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[105, 27652])).
% 3.12/3.31 tff(27654,plain,
% 3.12/3.31 (~r(s(z), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3709, 27650, 27576, 27632])).
% 3.12/3.31 tff(27655,plain,
% 3.12/3.31 (b(s(z), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[444, 27654, 24230])).
% 3.12/3.31 tff(27656,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[25416, 27655, 27653, 27632, 27630, 27649, 220, 27648, 27645, 27640, 27625, 27639])).
% 3.12/3.31 tff(27657,plain,(r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27658,plain,
% 3.12/3.31 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27657, 24223, 147, 1])).
% 3.12/3.31 tff(27659,plain,
% 3.12/3.31 (r(s(elem!1), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[429, 24240, 2282])).
% 3.12/3.31 tff(27660,plain,
% 3.12/3.31 (~r(s(z), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[20297, 121, 379, 27362, 27659])).
% 3.12/3.31 tff(27661,plain,
% 3.12/3.31 (~(s(s(s(z))) = elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[250, 27660, 108])).
% 3.12/3.31 tff(27662,plain,
% 3.12/3.31 (~(elem!1 = s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1100, 27661])).
% 3.12/3.31 tff(27663,plain,
% 3.12/3.31 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1516, 27662])).
% 3.12/3.31 tff(27664,plain,
% 3.12/3.31 (~r(elem!1, s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[19955, 121, 379, 27362, 27659])).
% 3.12/3.31 tff(27665,plain,
% 3.12/3.31 (r(s(s(z)), s(z))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[411, 10410])).
% 3.12/3.31 tff(27666,plain,
% 3.12/3.31 (~(s(s(s(z))) = elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[250, 20298, 108])).
% 3.12/3.31 tff(27667,plain,
% 3.12/3.31 (r(elem!1, s(s(elem!1)))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[108, 21519])).
% 3.12/3.31 tff(27668,plain,
% 3.12/3.31 (~b(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[11634, 24251, 394, 24252])).
% 3.12/3.31 tff(27669,plain,
% 3.12/3.31 (r(s(elem!1), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2243, 27668, 2564])).
% 3.12/3.31 tff(27670,plain,
% 3.12/3.31 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.31 inference(transitivity,[status(thm)],[10495, 10498])).
% 3.12/3.31 tff(27671,plain,
% 3.12/3.31 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27670])).
% 3.12/3.31 tff(27672,plain,
% 3.12/3.31 (~(elem!1 = s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1100, 27666])).
% 3.12/3.31 tff(27673,plain,
% 3.12/3.31 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1516, 27672])).
% 3.12/3.31 tff(27674,plain,
% 3.12/3.31 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[17419, 27673])).
% 3.12/3.31 tff(27675,plain,
% 3.12/3.31 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27674, 27671])).
% 3.12/3.31 tff(27676,plain,
% 3.12/3.31 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[239])).
% 3.12/3.31 tff(27677,plain,
% 3.12/3.31 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.12/3.31 inference(symmetry,[status(thm)],[27676])).
% 3.12/3.31 tff(27678,plain,
% 3.12/3.31 (r(elem!1, s(s(s(z))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[108, 27677])).
% 3.12/3.31 tff(27679,plain,
% 3.12/3.31 (~r(s(s(s(z))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[3849, 27678, 27669, 379])).
% 3.12/3.31 tff(27680,plain,
% 3.12/3.31 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1816, 23003, 27679])).
% 3.12/3.31 tff(27681,plain,
% 3.12/3.31 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[2114, 27680, 2073, 394])).
% 3.12/3.31 tff(27682,plain,
% 3.12/3.31 (r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[681, 27681, 27675])).
% 3.12/3.31 tff(27683,plain,
% 3.12/3.31 (~r(s(s(s(elem!1))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[720, 27682, 27669, 27667])).
% 3.12/3.31 tff(27684,plain,
% 3.12/3.31 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[486, 27683, 21570])).
% 3.12/3.31 tff(27685,plain,
% 3.12/3.31 (~b(s(s(s(z))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[11686, 27684, 24252, 24251, 11665])).
% 3.12/3.31 tff(27686,plain,
% 3.12/3.31 (r(s(s(s(z))), elem!1)),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[255, 27685, 27666])).
% 3.12/3.31 tff(27687,plain,
% 3.12/3.31 (r(s(s(s(z))), s(z))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27686, 11170])).
% 3.12/3.31 tff(27688,plain,
% 3.12/3.31 (r(s(z), s(s(z)))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[431, 21512])).
% 3.12/3.31 tff(27689,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27690,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.12/3.31 inference(quant_inst,[status(thm)],[])).
% 3.12/3.31 tff(27691,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27690, 27689])).
% 3.12/3.31 tff(27692,plain,
% 3.12/3.31 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27691, 121, 22781, 14778, 1660])).
% 3.12/3.31 tff(27693,plain,
% 3.12/3.31 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[10482, 21, 877, 27692])).
% 3.12/3.31 tff(27694,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27695,plain,
% 3.12/3.31 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27696,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27695])).
% 3.12/3.31 tff(27697,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.12/3.31 inference(transitivity,[status(thm)],[27696, 27694])).
% 3.12/3.31 tff(27698,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.12/3.31 inference(quant_inst,[status(thm)],[])).
% 3.12/3.31 tff(27699,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27698, 27697])).
% 3.12/3.31 tff(27700,plain,
% 3.12/3.31 (~r(s(s(z)), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27699, 121, 22781, 14778, 2327])).
% 3.12/3.31 tff(27701,plain,
% 3.12/3.31 (b(s(s(z)), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[10571, 21, 1136, 27700])).
% 3.12/3.31 tff(27702,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27703,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.31 inference(quant_inst,[status(thm)],[])).
% 3.12/3.31 tff(27704,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27703, 27702])).
% 3.12/3.31 tff(27705,plain,
% 3.12/3.31 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27704, 121, 22781, 1660, 2327])).
% 3.12/3.31 tff(27706,plain,
% 3.12/3.31 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1733, 27705])).
% 3.12/3.31 tff(27707,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27708,plain,
% 3.12/3.31 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27709,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27708])).
% 3.12/3.31 tff(27710,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.12/3.31 inference(transitivity,[status(thm)],[27709, 27707])).
% 3.12/3.31 tff(27711,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.12/3.31 inference(quant_inst,[status(thm)],[])).
% 3.12/3.31 tff(27712,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27711, 27710])).
% 3.12/3.31 tff(27713,plain,
% 3.12/3.31 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27712, 121, 22781, 1660, 2327])).
% 3.12/3.31 tff(27714,plain,
% 3.12/3.31 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1494, 27713])).
% 3.12/3.31 tff(27715,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27716,plain,
% 3.12/3.31 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.12/3.31 inference(rewrite,[status(thm)],[])).
% 3.12/3.31 tff(27717,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 3.12/3.31 inference(monotonicity,[status(thm)],[27716])).
% 3.12/3.31 tff(27718,plain,
% 3.12/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.12/3.31 inference(transitivity,[status(thm)],[27717, 27715])).
% 3.12/3.31 tff(27719,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.12/3.31 inference(quant_inst,[status(thm)],[])).
% 3.12/3.31 tff(27720,plain,
% 3.12/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.12/3.31 inference(modus_ponens,[status(thm)],[27719, 27718])).
% 3.12/3.31 tff(27721,plain,
% 3.12/3.31 ($false),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27720, 271, 27714, 27706, 27701, 27693])).
% 3.12/3.31 tff(27722,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.31 tff(27723,plain,
% 3.12/3.31 (~r(s(s(s(s(s(z))))), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[27722, 27688, 27687, 27665])).
% 3.12/3.31 tff(27724,plain,
% 3.12/3.31 (b(s(s(s(s(s(z))))), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1682, 27723])).
% 3.12/3.31 tff(27725,plain,
% 3.12/3.31 (~r(s(s(s(s(z)))), s(z))),
% 3.12/3.31 inference(unit_resolution,[status(thm)],[1234, 27683, 239])).
% 3.12/3.32 tff(27726,plain,
% 3.12/3.32 (b(s(s(s(s(z)))), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[932, 27725])).
% 3.12/3.32 tff(27727,plain,
% 3.12/3.32 (~r(s(z), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[9617, 27682, 431, 27669])).
% 3.12/3.32 tff(27728,plain,
% 3.12/3.32 (b(s(z), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[760, 27727])).
% 3.12/3.32 tff(27729,plain,
% 3.12/3.32 (b(s(z), s(s(s(s(z)))))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27728, 21607])).
% 3.12/3.32 tff(27730,plain,
% 3.12/3.32 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(s(z))))) = s(z))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[3029, 239])).
% 3.12/3.32 tff(27731,plain,
% 3.12/3.32 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.12/3.32 inference(symmetry,[status(thm)],[27730])).
% 3.12/3.32 tff(27732,plain,
% 3.12/3.32 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27731])).
% 3.12/3.32 tff(27733,plain,
% 3.12/3.32 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[1677, 27732])).
% 3.12/3.32 tff(27734,plain,
% 3.12/3.32 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[3029, 239])).
% 3.12/3.32 tff(27735,plain,
% 3.12/3.32 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 3.12/3.32 inference(symmetry,[status(thm)],[27734])).
% 3.12/3.32 tff(27736,plain,
% 3.12/3.32 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(elem!1)))), elem!1))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27735])).
% 3.12/3.32 tff(27737,plain,
% 3.12/3.32 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27723, 27736])).
% 3.12/3.32 tff(27738,plain,
% 3.12/3.32 (b(s(s(s(s(elem!1)))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[10196, 27737, 27733])).
% 3.12/3.32 tff(27739,plain,
% 3.12/3.32 (b(s(s(s(s(elem!1)))), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[14282, 27738, 2359])).
% 3.12/3.32 tff(27740,plain,
% 3.12/3.32 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[1226])).
% 3.12/3.32 tff(27741,plain,
% 3.12/3.32 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 3.12/3.32 inference(symmetry,[status(thm)],[27740])).
% 3.12/3.32 tff(27742,plain,
% 3.12/3.32 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27741])).
% 3.12/3.32 tff(27743,plain,
% 3.12/3.32 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.12/3.32 inference(symmetry,[status(thm)],[27742])).
% 3.12/3.32 tff(27744,plain,
% 3.12/3.32 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[1758, 27743])).
% 3.12/3.32 tff(27745,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27746,plain,
% 3.12/3.32 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27747,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27746])).
% 3.12/3.32 tff(27748,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 3.12/3.32 inference(transitivity,[status(thm)],[27747, 27745])).
% 3.12/3.32 tff(27749,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 3.12/3.32 inference(quant_inst,[status(thm)],[])).
% 3.12/3.32 tff(27750,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27749, 27748])).
% 3.12/3.32 tff(27751,plain,
% 3.12/3.32 (~b(s(s(s(s(z)))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27750, 271, 220, 937, 1067])).
% 3.12/3.32 tff(27752,plain,
% 3.12/3.32 (r(s(s(s(s(z)))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[1093, 21, 1090, 27751])).
% 3.12/3.32 tff(27753,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27754,plain,
% 3.12/3.32 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27755,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27754])).
% 3.12/3.32 tff(27756,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.12/3.32 inference(transitivity,[status(thm)],[27755, 27753])).
% 3.12/3.32 tff(27757,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.12/3.32 inference(quant_inst,[status(thm)],[])).
% 3.12/3.32 tff(27758,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27757, 27756])).
% 3.12/3.32 tff(27759,plain,
% 3.12/3.32 (~b(s(s(s(s(elem!1)))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27758, 271, 220, 1067, 14253])).
% 3.12/3.32 tff(27760,plain,
% 3.12/3.32 (r(s(s(s(s(elem!1)))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[3089, 21, 812, 27759])).
% 3.12/3.32 tff(27761,plain,
% 3.12/3.32 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 3.12/3.32 inference(symmetry,[status(thm)],[20516])).
% 3.12/3.32 tff(27762,plain,
% 3.12/3.32 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27761])).
% 3.12/3.32 tff(27763,plain,
% 3.12/3.32 (~(z = s(s(s(s(z)))))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[1090, 27762])).
% 3.12/3.32 tff(27764,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27765,plain,
% 3.12/3.32 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27766,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27765])).
% 3.12/3.32 tff(27767,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 3.12/3.32 inference(transitivity,[status(thm)],[27766, 27764])).
% 3.12/3.32 tff(27768,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 3.12/3.32 inference(quant_inst,[status(thm)],[])).
% 3.12/3.32 tff(27769,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27768, 27767])).
% 3.12/3.32 tff(27770,plain,
% 3.12/3.32 (~b(z, s(s(s(s(z)))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27769, 271, 220, 937, 1067])).
% 3.12/3.32 tff(27771,plain,
% 3.12/3.32 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[1119, 21, 27770])).
% 3.12/3.32 tff(27772,plain,
% 3.12/3.32 (r(z, s(s(s(s(z)))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27771, 27763])).
% 3.12/3.32 tff(27773,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27774,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 3.12/3.32 inference(quant_inst,[status(thm)],[])).
% 3.12/3.32 tff(27775,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27774, 27773])).
% 3.12/3.32 tff(27776,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27775, 121, 27772, 27760, 27752, 27744])).
% 3.12/3.32 tff(27777,plain,((~b(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27778,plain,
% 3.12/3.32 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27777, 27739, 220, 27726, 239, 27729])).
% 3.12/3.32 tff(27779,plain,
% 3.12/3.32 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[1777, 27778])).
% 3.12/3.32 tff(27780,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27781,plain,
% 3.12/3.32 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.12/3.32 inference(rewrite,[status(thm)],[])).
% 3.12/3.32 tff(27782,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.12/3.32 inference(monotonicity,[status(thm)],[27781])).
% 3.12/3.32 tff(27783,plain,
% 3.12/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.12/3.32 inference(transitivity,[status(thm)],[27782, 27780])).
% 3.12/3.32 tff(27784,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.12/3.32 inference(quant_inst,[status(thm)],[])).
% 3.12/3.32 tff(27785,plain,
% 3.12/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.12/3.32 inference(modus_ponens,[status(thm)],[27784, 27783])).
% 3.12/3.32 tff(27786,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27785, 271, 1281, 27779, 27726, 27724])).
% 3.12/3.32 tff(27787,plain,((~(elem!1 = s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27788,plain,
% 3.12/3.32 (~(elem!1 = s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27787, 27362, 220, 15822, 19197, 19776, 394, 379, 108, 27659, 2207])).
% 3.12/3.32 tff(27789,plain,
% 3.12/3.32 (b(elem!1, s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[299, 27788, 27664])).
% 3.12/3.32 tff(27790,plain,
% 3.12/3.32 (~(s(z) = elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[1221, 27788])).
% 3.12/3.32 tff(27791,plain,
% 3.12/3.32 (~b(z, elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[20894, 27788, 19197, 27664, 27660])).
% 3.12/3.32 tff(27792,plain,
% 3.12/3.32 (r(z, elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[355, 27791, 9297])).
% 3.12/3.32 tff(27793,plain,
% 3.12/3.32 (b(s(z), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[236, 231, 27660])).
% 3.12/3.32 tff(27794,plain,
% 3.12/3.32 (~r(s(z), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[20297, 121, 379, 24383, 24381])).
% 3.12/3.32 tff(27795,plain,
% 3.12/3.32 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[20307, 3407, 1281, 24384, 27794])).
% 3.12/3.32 tff(27796,plain,
% 3.12/3.32 (s(s(s(elem!1))) = s(elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[13625, 27795, 220, 394, 448, 260, 3407, 379, 24381, 378])).
% 3.12/3.32 tff(27797,plain,
% 3.12/3.32 (elem!1 = s(s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[78, 27796])).
% 3.12/3.32 tff(27798,plain,
% 3.12/3.32 (b(s(s(s(elem!1))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[12308, 27797, 394])).
% 3.12/3.32 tff(27799,plain,
% 3.12/3.32 (s(elem!1) = s(s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[22147, 27798, 1281, 2282, 394, 3407])).
% 3.12/3.32 tff(27800,plain,
% 3.12/3.32 (~(s(s(s(z))) = s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[3917, 27797, 348])).
% 3.12/3.32 tff(27801,plain,
% 3.12/3.32 (r(s(s(s(z))), s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[1816, 27800, 3506])).
% 3.12/3.32 tff(27802,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[13333, 27801, 27799, 906])).
% 3.12/3.32 tff(27803,plain,((~b(z, s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(s(z))), s(elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27804,plain,
% 3.12/3.32 (~b(z, s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27803, 3506, 906, 19197, 394, 348, 220, 448, 27793, 379, 378])).
% 3.12/3.32 tff(27805,plain,
% 3.12/3.32 (r(z, s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[36, 21, 27804, 32])).
% 3.12/3.32 tff(27806,plain,
% 3.12/3.32 (~r(s(s(s(elem!1))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[10227, 27805, 378, 379])).
% 3.12/3.32 tff(27807,plain,
% 3.12/3.32 (~b(s(s(s(elem!1))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[15649, 3407, 750, 220])).
% 3.12/3.32 tff(27808,plain,
% 3.12/3.32 (r(s(s(s(elem!1))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[486, 27807, 27795])).
% 3.12/3.32 tff(27809,plain,
% 3.12/3.32 (~r(s(s(s(elem!1))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[8972, 27808, 379, 378])).
% 3.12/3.32 tff(27810,plain,
% 3.12/3.32 (b(s(s(s(elem!1))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[8229, 27809])).
% 3.12/3.32 tff(27811,plain,
% 3.12/3.32 (s(elem!1) = s(s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[22147, 27810, 1281, 2282, 394, 3407])).
% 3.12/3.32 tff(27812,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[13333, 27801, 27811, 906])).
% 3.12/3.32 tff(27813,plain,((~b(z, s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(s(z))), s(elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27814,plain,
% 3.12/3.32 (~b(z, s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27813, 750, 3506, 1281, 394, 348, 379, 378, 220, 448, 260, 906])).
% 3.12/3.32 tff(27815,plain,
% 3.12/3.32 (r(z, s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[36, 21, 27814, 32])).
% 3.12/3.32 tff(27816,plain,
% 3.12/3.32 (~r(s(s(s(elem!1))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[10227, 27815, 378, 379])).
% 3.12/3.32 tff(27817,plain,
% 3.12/3.32 (~b(s(s(s(elem!1))), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[19985, 27816, 24381, 3506, 24383, 19776, 750, 448, 260])).
% 3.12/3.32 tff(27818,plain,
% 3.12/3.32 (r(s(s(s(elem!1))), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[16580, 27817])).
% 3.12/3.32 tff(27819,plain,
% 3.12/3.32 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[12809, 27818, 24384])).
% 3.12/3.32 tff(27820,plain,
% 3.12/3.32 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[486, 27819, 27816])).
% 3.12/3.32 tff(27821,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[12821, 271, 260, 750, 448, 27820])).
% 3.12/3.32 tff(27822,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | b(s(s(s(z))), s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27823,plain,
% 3.12/3.32 (~b(s(z), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27822, 3506, 448, 27793, 378, 379, 19197, 394, 348, 220, 906])).
% 3.12/3.32 tff(27824,plain,
% 3.12/3.32 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[19692, 27823, 27793])).
% 3.12/3.32 tff(27825,plain,
% 3.12/3.32 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[486, 27824, 27806])).
% 3.12/3.32 tff(27826,plain,
% 3.12/3.32 (~b(s(s(s(elem!1))), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[8132, 27825, 448, 27793])).
% 3.12/3.32 tff(27827,plain,
% 3.12/3.32 (r(s(s(s(elem!1))), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[16580, 27826])).
% 3.12/3.32 tff(27828,plain,
% 3.12/3.32 (~b(s(s(s(elem!1))), z)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[24421, 27805, 379, 19197, 220, 394, 348])).
% 3.12/3.32 tff(27829,plain,
% 3.12/3.32 (~(elem!1 = s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[12308, 27828, 394])).
% 3.12/3.32 tff(27830,plain,
% 3.12/3.32 (~(s(s(elem!1)) = elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[197, 27829])).
% 3.12/3.32 tff(27831,plain,
% 3.12/3.32 (~b(s(s(elem!1)), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[24281, 27830, 378, 379, 27793, 448, 19197, 220])).
% 3.12/3.32 tff(27832,plain,
% 3.12/3.32 (r(s(s(elem!1)), s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[2143, 27831])).
% 3.12/3.32 tff(27833,plain,
% 3.12/3.32 (r(s(z), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[760, 27823])).
% 3.12/3.32 tff(27834,plain,
% 3.12/3.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[78, 27829])).
% 3.12/3.32 tff(27835,plain,
% 3.12/3.32 (~b(s(elem!1), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[19657, 27825, 448, 27362, 27659, 27834, 27793])).
% 3.12/3.32 tff(27836,plain,
% 3.12/3.32 (r(s(elem!1), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[2243, 27835, 2207])).
% 3.12/3.32 tff(27837,plain,
% 3.12/3.32 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[9617, 27836, 27362, 27833])).
% 3.12/3.32 tff(27838,plain,
% 3.12/3.32 (b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[681, 27837, 27834])).
% 3.12/3.32 tff(27839,plain,
% 3.12/3.32 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[84, 27834])).
% 3.12/3.32 tff(27840,plain,
% 3.12/3.32 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[13276, 121, 27833, 27827, 27659])).
% 3.12/3.32 tff(27841,plain,
% 3.12/3.32 (b(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[2293, 21, 27840, 27839])).
% 3.12/3.32 tff(27842,plain,
% 3.12/3.32 (r(s(s(elem!1)), s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[701, 16223, 8423])).
% 3.12/3.32 tff(27843,plain,
% 3.12/3.32 (~b(s(z), s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[11755, 27842, 231, 543, 622, 431, 379, 68])).
% 3.12/3.32 tff(27844,plain,
% 3.12/3.32 (~b(s(elem!1), s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[10076, 543, 504, 739])).
% 3.12/3.32 tff(27845,plain,
% 3.12/3.32 (r(s(elem!1), s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[526, 27844, 216])).
% 3.12/3.32 tff(27846,plain,
% 3.12/3.32 (~r(s(z), s(s(elem!1)))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[3275, 27845, 431, 27842])).
% 3.12/3.32 tff(27847,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[2167, 27846, 27843])).
% 3.12/3.32 tff(27848,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27849,plain,
% 3.12/3.32 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27848, 27836, 231, 27362, 379, 27829, 211, 27825, 27841, 27838])).
% 3.12/3.32 tff(27850,plain,
% 3.12/3.32 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[556, 27849, 1])).
% 3.12/3.32 tff(27851,plain,
% 3.12/3.32 ($false),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[13294, 121, 27850, 27833, 27832, 27827])).
% 3.12/3.32 tff(27852,plain,(b(s(s(s(z))), s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.32 tff(27853,plain,
% 3.12/3.32 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[27852, 27792, 1, 379, 27790, 27789, 220, 394, 348, 906])).
% 3.12/3.32 tff(27854,plain,
% 3.12/3.32 (b(s(z), elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[236, 27790, 27660])).
% 3.12/3.32 tff(27855,plain,
% 3.12/3.32 (b(elem!1, s(z))),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[299, 258, 27664])).
% 3.12/3.32 tff(27856,plain,
% 3.12/3.32 (~b(z, elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[20894, 258, 19197, 27664, 27660])).
% 3.12/3.32 tff(27857,plain,
% 3.12/3.32 (r(z, elem!1)),
% 3.12/3.32 inference(unit_resolution,[status(thm)],[355, 27856, 9297])).
% 3.12/3.32 tff(27858,plain,
% 3.12/3.33 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27852, 1257, 1, 379, 27857, 27855, 220, 394, 348, 906])).
% 3.12/3.33 tff(27859,plain,
% 3.12/3.33 (~b(z, s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[19710, 27858, 394, 1307])).
% 3.12/3.33 tff(27860,plain,
% 3.12/3.33 (r(z, s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1439, 27859])).
% 3.12/3.33 tff(27861,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27862,plain,
% 3.12/3.33 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27863,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z)))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27862])).
% 3.12/3.33 tff(27864,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[27863, 27861])).
% 3.12/3.33 tff(27865,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 3.12/3.33 inference(quant_inst,[status(thm)],[])).
% 3.12/3.33 tff(27866,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), s(z)))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27865, 27864])).
% 3.12/3.33 tff(27867,plain,
% 3.12/3.33 ($false),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27866, 121, 379, 27857, 27860, 27659])).
% 3.12/3.33 tff(27868,plain,((elem!1 = s(z)) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.33 tff(27869,plain,
% 3.12/3.33 (elem!1 = s(z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27868, 1307, 394, 379, 1, 220, 348, 906])).
% 3.12/3.33 tff(27870,plain,
% 3.12/3.33 (s(elem!1) = s(s(z))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27869])).
% 3.12/3.33 tff(27871,plain,
% 3.12/3.33 (s(s(elem!1)) = s(s(s(z)))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27870])).
% 3.12/3.33 tff(27872,plain,
% 3.12/3.33 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27871])).
% 3.12/3.33 tff(27873,plain,
% 3.12/3.33 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27872])).
% 3.12/3.33 tff(27874,plain,
% 3.12/3.33 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(s(s(z))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27873])).
% 3.12/3.33 tff(27875,plain,
% 3.12/3.33 (s(z) = elem!1),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[242, 27869])).
% 3.12/3.33 tff(27876,plain,
% 3.12/3.33 (b(z, elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[229, 27875, 220])).
% 3.12/3.33 tff(27877,plain,
% 3.12/3.33 (b(elem!1, z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[20120, 27875, 19197])).
% 3.12/3.33 tff(27878,plain,
% 3.12/3.33 (~b(s(s(s(z))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1334, 27877, 1307, 27876])).
% 3.12/3.33 tff(27879,plain,
% 3.12/3.33 (r(s(s(s(z))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[255, 27878, 27661])).
% 3.12/3.33 tff(27880,plain,
% 3.12/3.33 (r(s(s(elem!1)), s(z))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[6824, 27879, 27875])).
% 3.12/3.33 tff(27881,plain,
% 3.12/3.33 (~(elem!1 = s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[12129, 27880, 27664])).
% 3.12/3.33 tff(27882,plain,
% 3.12/3.33 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[78, 27881])).
% 3.12/3.33 tff(27883,plain,
% 3.12/3.33 (~r(s(s(s(z))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[19641, 27879, 27659, 379])).
% 3.12/3.33 tff(27884,plain,
% 3.12/3.33 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27870])).
% 3.12/3.33 tff(27885,plain,
% 3.12/3.33 ((s(s(s(z))) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[27884, 20097])).
% 3.12/3.33 tff(27886,plain,
% 3.12/3.33 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 3.12/3.33 inference(symmetry,[status(thm)],[27885])).
% 3.12/3.33 tff(27887,plain,
% 3.12/3.33 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27886])).
% 3.12/3.33 tff(27888,plain,
% 3.12/3.33 (~(s(s(s(z))) = s(elem!1))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[1136, 27887])).
% 3.12/3.33 tff(27889,plain,
% 3.12/3.33 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1816, 27888, 27883])).
% 3.12/3.33 tff(27890,plain,
% 3.12/3.33 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[2114, 27889, 19776, 394])).
% 3.12/3.33 tff(27891,plain,
% 3.12/3.33 (r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[681, 27890, 27882])).
% 3.12/3.33 tff(27892,plain,
% 3.12/3.33 (~b(s(elem!1), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[11634, 27877, 394, 27876])).
% 3.12/3.33 tff(27893,plain,
% 3.12/3.33 (r(s(elem!1), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[2243, 27892, 2207])).
% 3.12/3.33 tff(27894,plain,
% 3.12/3.33 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27871])).
% 3.12/3.33 tff(27895,plain,
% 3.12/3.33 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.33 inference(symmetry,[status(thm)],[27894])).
% 3.12/3.33 tff(27896,plain,
% 3.12/3.33 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[19776, 27895])).
% 3.12/3.33 tff(27897,plain,
% 3.12/3.33 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27871])).
% 3.12/3.33 tff(27898,plain,
% 3.12/3.33 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.12/3.33 inference(symmetry,[status(thm)],[27897])).
% 3.12/3.33 tff(27899,plain,
% 3.12/3.33 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27898])).
% 3.12/3.33 tff(27900,plain,
% 3.12/3.33 (~r(s(elem!1), s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[3445, 27879, 108, 27362])).
% 3.12/3.33 tff(27901,plain,
% 3.12/3.33 (~r(s(elem!1), s(s(elem!1)))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27900, 27899])).
% 3.12/3.33 tff(27902,plain,
% 3.12/3.33 (b(s(elem!1), s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[526, 27901, 211])).
% 3.12/3.33 tff(27903,plain,
% 3.12/3.33 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27871])).
% 3.12/3.33 tff(27904,plain,
% 3.12/3.33 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 3.12/3.33 inference(symmetry,[status(thm)],[27903])).
% 3.12/3.33 tff(27905,plain,
% 3.12/3.33 (b(z, s(s(elem!1)))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[1307, 27904])).
% 3.12/3.33 tff(27906,plain,
% 3.12/3.33 (~b(z, s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[8781, 27905, 27902, 27896])).
% 3.12/3.33 tff(27907,plain,
% 3.12/3.33 (r(z, s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1439, 27906])).
% 3.12/3.33 tff(27908,plain,
% 3.12/3.33 (~r(z, s(s(s(elem!1))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[7694, 27907, 27893, 27891])).
% 3.12/3.33 tff(27909,plain,
% 3.12/3.33 (~r(z, s(s(s(s(z)))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27908, 27874])).
% 3.12/3.33 tff(27910,plain,
% 3.12/3.33 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27872])).
% 3.12/3.33 tff(27911,plain,
% 3.12/3.33 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, s(s(s(s(z))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27910])).
% 3.12/3.33 tff(27912,plain,
% 3.12/3.33 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27869])).
% 3.12/3.33 tff(27913,plain,
% 3.12/3.33 ((s(s(s(elem!1))) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[27912, 2858])).
% 3.12/3.33 tff(27914,plain,
% 3.12/3.33 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 3.12/3.33 inference(symmetry,[status(thm)],[27913])).
% 3.12/3.33 tff(27915,plain,
% 3.12/3.33 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27914])).
% 3.12/3.33 tff(27916,plain,
% 3.12/3.33 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[61, 27915])).
% 3.12/3.33 tff(27917,plain,
% 3.12/3.33 (~b(elem!1, s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[6679, 27869, 71])).
% 3.12/3.33 tff(27918,plain,
% 3.12/3.33 (r(elem!1, s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[599, 27881, 27917])).
% 3.12/3.33 tff(27919,plain,
% 3.12/3.33 (~r(s(s(s(elem!1))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[720, 27891, 27893, 27918])).
% 3.12/3.33 tff(27920,plain,
% 3.12/3.33 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[486, 27919, 27916])).
% 3.12/3.33 tff(27921,plain,
% 3.12/3.33 (~r(s(z), s(s(s(elem!1))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[9617, 27891, 27362, 27893])).
% 3.12/3.33 tff(27922,plain,
% 3.12/3.33 (b(s(z), s(s(s(elem!1))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[760, 27921])).
% 3.12/3.33 tff(27923,plain,
% 3.12/3.33 (~b(z, s(s(s(elem!1))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[15649, 27922, 27920, 220])).
% 3.12/3.33 tff(27924,plain,
% 3.12/3.33 (~b(z, s(s(s(s(z)))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27923, 27911])).
% 3.12/3.33 tff(27925,plain,
% 3.12/3.33 ($false),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1119, 21, 27924, 27909, 1114])).
% 3.12/3.33 tff(27926,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.33 tff(27927,plain,
% 3.12/3.33 (~b(z, s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27926, 394, 220, 108, 379, 71, 1, 348, 906])).
% 3.12/3.33 tff(27928,plain,
% 3.12/3.33 (r(z, s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1214, 27927])).
% 3.12/3.33 tff(27929,plain,
% 3.12/3.33 (~b(elem!1, z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[8962, 27854, 220, 27789])).
% 3.12/3.33 tff(27930,plain,
% 3.12/3.33 (r(elem!1, z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[284, 27929, 9298])).
% 3.12/3.33 tff(27931,plain,
% 3.12/3.33 (~r(s(s(s(z))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[19871, 27930, 27928, 27792])).
% 3.12/3.33 tff(27932,plain,
% 3.12/3.33 (b(s(s(s(z))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[255, 27931, 27661])).
% 3.12/3.33 tff(27933,plain,
% 3.12/3.33 (~(s(s(z)) = s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[960, 27790])).
% 3.12/3.33 tff(27934,plain,
% 3.12/3.33 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[953, 27933])).
% 3.12/3.33 tff(27935,plain,
% 3.12/3.33 (s(s(elem!1)) = elem!1),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[24295, 394, 3313, 379, 27792, 27659, 19197, 220, 27934, 27789, 27932, 27854])).
% 3.12/3.33 tff(27936,plain,
% 3.12/3.33 (s(s(s(elem!1))) = s(elem!1)),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27935])).
% 3.12/3.33 tff(27937,plain,
% 3.12/3.33 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27936])).
% 3.12/3.33 tff(27938,plain,
% 3.12/3.33 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(elem!1)))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27937])).
% 3.12/3.33 tff(27939,plain,
% 3.12/3.33 (elem!1 = s(s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[197, 27935])).
% 3.12/3.33 tff(27940,plain,
% 3.12/3.33 (b(s(s(s(elem!1))), z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[12308, 27939, 394])).
% 3.12/3.33 tff(27941,plain,
% 3.12/3.33 (~r(z, s(s(s(elem!1))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[24421, 27940, 379, 19197, 220, 394, 348])).
% 3.12/3.33 tff(27942,plain,
% 3.12/3.33 (~r(z, s(elem!1))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27941, 27938])).
% 3.12/3.33 tff(27943,plain,
% 3.12/3.33 (b(z, s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1437, 21, 27942, 1433])).
% 3.12/3.33 tff(27944,plain,
% 3.12/3.33 (r(s(s(s(z))), z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1427, 27943, 27853, 394])).
% 3.12/3.33 tff(27945,plain,
% 3.12/3.33 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 3.12/3.33 inference(commutativity,[status(thm)],[])).
% 3.12/3.33 tff(27946,plain,
% 3.12/3.33 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27935])).
% 3.12/3.33 tff(27947,plain,
% 3.12/3.33 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[27946, 27945])).
% 3.12/3.33 tff(27948,plain,
% 3.12/3.33 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27947])).
% 3.12/3.33 tff(27949,plain,
% 3.12/3.33 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[12235, 27939, 9149])).
% 3.12/3.33 tff(27950,plain,
% 3.12/3.33 (~(elem!1 = s(s(s(s(z)))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27949, 27948])).
% 3.12/3.33 tff(27951,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27952,plain,
% 3.12/3.33 (((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27953,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27952])).
% 3.12/3.33 tff(27954,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[27953, 27951])).
% 3.12/3.33 tff(27955,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 3.12/3.33 inference(quant_inst,[status(thm)],[])).
% 3.12/3.33 tff(27956,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27955, 27954])).
% 3.12/3.33 tff(27957,plain,
% 3.12/3.33 (~r(elem!1, s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27956, 121, 27792, 27930, 27944])).
% 3.12/3.33 tff(27958,plain,
% 3.12/3.33 (b(elem!1, s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1192, 27957, 27662])).
% 3.12/3.33 tff(27959,plain,
% 3.12/3.33 (~r(elem!1, s(s(s(s(z)))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27035, 121, 378, 1409, 910])).
% 3.12/3.33 tff(27960,plain,
% 3.12/3.33 (b(elem!1, s(s(s(s(z)))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[20539, 27959, 20532])).
% 3.12/3.33 tff(27961,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27962,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.12/3.33 inference(quant_inst,[status(thm)],[])).
% 3.12/3.33 tff(27963,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27962, 27961])).
% 3.12/3.33 tff(27964,plain,
% 3.12/3.33 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27963, 121, 378, 109, 910])).
% 3.12/3.33 tff(27965,plain,
% 3.12/3.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[10426, 27964])).
% 3.12/3.33 tff(27966,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27967,plain,
% 3.12/3.33 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27968,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[27967])).
% 3.12/3.33 tff(27969,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[27968, 27966])).
% 3.12/3.33 tff(27970,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.33 inference(quant_inst,[status(thm)],[])).
% 3.12/3.33 tff(27971,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27970, 27969])).
% 3.12/3.33 tff(27972,plain,
% 3.12/3.33 ($false),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27971, 271, 1195, 1422, 27965, 27960])).
% 3.12/3.33 tff(27973,plain,((~r(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.33 tff(27974,plain,
% 3.12/3.33 (~r(s(s(s(s(z)))), z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27973, 27958, 27853, 27950, 27792, 27930, 27944])).
% 3.12/3.33 tff(27975,plain,
% 3.12/3.33 (b(s(s(s(s(z)))), z)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1095, 27974])).
% 3.12/3.33 tff(27976,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(27977,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 3.12/3.33 inference(quant_inst,[status(thm)],[])).
% 3.12/3.33 tff(27978,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[27977, 27976])).
% 3.12/3.33 tff(27979,plain,
% 3.12/3.33 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27978, 271, 394, 220, 27975])).
% 3.12/3.33 tff(27980,plain,
% 3.12/3.33 (~b(s(s(s(s(z)))), s(z))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[22548, 27975, 19197, 220])).
% 3.12/3.33 tff(27981,plain,
% 3.12/3.33 (r(s(s(s(s(z)))), s(z))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[932, 27980])).
% 3.12/3.33 tff(27982,plain,
% 3.12/3.33 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27054, 121, 27362, 27981, 27659])).
% 3.12/3.33 tff(27983,plain,
% 3.12/3.33 ($false),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1559, 27982, 27979, 27663])).
% 3.12/3.33 tff(27984,plain,((~b(s(elem!1), z)) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.33 tff(27985,plain,
% 3.12/3.33 (~r(elem!1, s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27984, 348, 1, 106, 24223, 27658, 394, 71])).
% 3.12/3.33 tff(27986,plain,
% 3.12/3.33 (~r(s(s(s(z))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[23235, 27362, 27659, 108])).
% 3.12/3.33 tff(27987,plain,
% 3.12/3.33 (~b(s(s(s(z))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[3288, 257, 307, 394])).
% 3.12/3.33 tff(27988,plain,
% 3.12/3.33 (~(s(s(s(z))) = s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[26813, 257, 307, 2073, 147])).
% 3.12/3.33 tff(27989,plain,
% 3.12/3.33 ($false),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1816, 27988, 27987, 1510])).
% 3.12/3.33 tff(27990,plain,((~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.33 tff(27991,plain,
% 3.12/3.33 (~b(s(s(s(z))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[27990, 147, 307, 19776, 27986, 394])).
% 3.12/3.33 tff(27992,plain,
% 3.12/3.33 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[2114, 1422, 2073, 394])).
% 3.12/3.33 tff(27993,plain,
% 3.12/3.33 (r(s(z), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[250, 244, 108])).
% 3.12/3.33 tff(27994,plain,
% 3.12/3.33 (~(s(z) = elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1276, 24242, 307])).
% 3.12/3.33 tff(27995,plain,
% 3.12/3.33 (~(elem!1 = s(z))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[242, 27994])).
% 3.12/3.33 tff(27996,plain,
% 3.12/3.33 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[10635])).
% 3.12/3.33 tff(27997,plain,
% 3.12/3.33 (~r(elem!1, s(s(s(elem!1))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[906, 27996])).
% 3.12/3.33 tff(27998,plain,
% 3.12/3.33 (b(elem!1, s(s(s(elem!1))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[9580, 244, 2073])).
% 3.12/3.33 tff(27999,plain,
% 3.12/3.33 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 3.12/3.33 inference(symmetry,[status(thm)],[15711])).
% 3.12/3.33 tff(28000,plain,
% 3.12/3.33 (~b(elem!1, s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[11908, 543, 9552, 1043, 147])).
% 3.12/3.33 tff(28001,plain,
% 3.12/3.33 (r(elem!1, s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[599, 28000, 15680])).
% 3.12/3.33 tff(28002,plain,
% 3.12/3.33 (r(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[28001, 15691])).
% 3.12/3.33 tff(28003,plain,
% 3.12/3.33 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[244])).
% 3.12/3.33 tff(28004,plain,
% 3.12/3.33 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.12/3.33 inference(transitivity,[status(thm)],[28003, 1836])).
% 3.12/3.33 tff(28005,plain,
% 3.12/3.33 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[28004])).
% 3.12/3.33 tff(28006,plain,
% 3.12/3.33 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[1489, 28005])).
% 3.12/3.33 tff(28007,plain,
% 3.12/3.33 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[543, 15708])).
% 3.12/3.33 tff(28008,plain,
% 3.12/3.33 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[486, 9552, 147])).
% 3.12/3.33 tff(28009,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(28010,plain,
% 3.12/3.33 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.33 inference(rewrite,[status(thm)],[])).
% 3.12/3.33 tff(28011,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[28010])).
% 3.12/3.33 tff(28012,plain,
% 3.12/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[28011, 28009])).
% 3.12/3.33 tff(28013,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 3.12/3.33 inference(quant_inst,[status(thm)],[])).
% 3.12/3.33 tff(28014,plain,
% 3.12/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[28013, 28012])).
% 3.12/3.33 tff(28015,plain,
% 3.12/3.33 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[28014, 271, 28008, 738, 28007])).
% 3.12/3.33 tff(28016,plain,
% 3.12/3.33 (r(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[840, 28015, 28006])).
% 3.12/3.33 tff(28017,plain,
% 3.12/3.33 (~r(z, s(s(s(s(s(z))))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[5017, 28016, 28002, 378])).
% 3.12/3.33 tff(28018,plain,
% 3.12/3.33 (b(z, s(s(s(s(s(z))))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[1658, 28017])).
% 3.12/3.33 tff(28019,plain,
% 3.12/3.33 (b(z, s(s(elem!1)))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[28018, 27999])).
% 3.12/3.33 tff(28020,plain,
% 3.12/3.33 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.33 inference(monotonicity,[status(thm)],[244])).
% 3.12/3.33 tff(28021,plain,
% 3.12/3.33 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.33 inference(symmetry,[status(thm)],[28020])).
% 3.12/3.33 tff(28022,plain,
% 3.12/3.33 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.33 inference(transitivity,[status(thm)],[15691, 28021])).
% 3.12/3.33 tff(28023,plain,
% 3.12/3.33 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.33 inference(modus_ponens,[status(thm)],[28001, 28022])).
% 3.12/3.33 tff(28024,plain,
% 3.12/3.33 (~r(s(z), s(s(s(s(s(z))))))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[18909, 28016, 108, 28023])).
% 3.12/3.33 tff(28025,plain,
% 3.12/3.33 (~r(s(z), s(s(elem!1)))),
% 3.12/3.33 inference(unit_resolution,[status(thm)],[9700, 28024, 2606])).
% 3.12/3.33 tff(28026,plain,
% 3.12/3.34 (b(s(z), s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2167, 28025])).
% 3.12/3.34 tff(28027,plain,
% 3.12/3.34 (~b(z, s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[19354, 28026, 1281, 543])).
% 3.12/3.34 tff(28028,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28027, 28019])).
% 3.12/3.34 tff(28029,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(s(s(z))) = elem!1)) | r(elem!1, s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28030,plain,
% 3.12/3.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28029, 1243, 108, 19197, 738, 244, 1043, 147])).
% 3.12/3.34 tff(28031,plain,
% 3.12/3.34 (b(s(elem!1), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3326, 28030, 1, 2344, 394, 199, 675])).
% 3.12/3.34 tff(28032,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[14823, 28031, 28030, 307, 331, 394, 147, 675, 2344])).
% 3.12/3.34 tff(28033,plain,(b(z, elem!1) | (~b(elem!1, s(elem!1))) | (z = elem!1) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), s(elem!1)) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(s(s(z))) = elem!1)) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28034,plain,
% 3.12/3.34 (b(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28033, 27998, 331, 394, 147, 675, 2344, 1, 108, 307, 244, 27997])).
% 3.12/3.34 tff(28035,plain,
% 3.12/3.34 (~b(elem!1, s(z))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[20398, 28034, 19197, 220])).
% 3.12/3.34 tff(28036,plain,
% 3.12/3.34 (r(elem!1, s(z))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[299, 28035, 27995])).
% 3.12/3.34 tff(28037,plain,
% 3.12/3.34 (~b(s(elem!1), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[4598, 28034, 307, 394])).
% 3.12/3.34 tff(28038,plain,
% 3.12/3.34 (r(s(elem!1), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2243, 28037, 2207])).
% 3.12/3.34 tff(28039,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[6525, 28038, 28036, 431, 27993])).
% 3.12/3.34 tff(28040,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (z = elem!1) | r(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), s(elem!1)) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28041,plain,
% 3.12/3.34 (~(s(s(s(z))) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28040, 27992, 307, 394, 220, 331, 147, 431, 2344, 1, 108, 906, 2073])).
% 3.12/3.34 tff(28042,plain,
% 3.12/3.34 (r(s(s(s(z))), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[255, 28041, 2346])).
% 3.12/3.34 tff(28043,plain,
% 3.12/3.34 (r(elem!1, z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[284, 25639, 358])).
% 3.12/3.34 tff(28044,plain,
% 3.12/3.34 (~(elem!1 = s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1100, 28041])).
% 3.12/3.34 tff(28045,plain,
% 3.12/3.34 (r(elem!1, s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1192, 28044, 23994])).
% 3.12/3.34 tff(28046,plain,
% 3.12/3.34 (~r(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[9831, 28045, 108, 28042])).
% 3.12/3.34 tff(28047,plain,
% 3.12/3.34 (b(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[236, 28046, 27994])).
% 3.12/3.34 tff(28048,plain,
% 3.12/3.34 (~b(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[9079, 28047, 307, 220])).
% 3.12/3.34 tff(28049,plain,
% 3.12/3.34 (r(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[355, 28048, 331])).
% 3.12/3.34 tff(28050,plain,
% 3.12/3.34 (~r(z, s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[19871, 28049, 28043, 28042])).
% 3.12/3.34 tff(28051,plain,
% 3.12/3.34 (b(z, s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1214, 28050])).
% 3.12/3.34 tff(28052,plain,
% 3.12/3.34 (~b(s(s(s(z))), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[8279, 28051, 394, 1422])).
% 3.12/3.34 tff(28053,plain,
% 3.12/3.34 (r(s(s(s(z))), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1155, 28052])).
% 3.12/3.34 tff(28054,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[10776, 121, 28049, 28045, 28042, 28053])).
% 3.12/3.34 tff(28055,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (z = elem!1) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(z))), elem!1) | r(s(s(s(elem!1))), elem!1) | (~r(s(z), s(elem!1))) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28056,plain,
% 3.12/3.34 (~b(s(s(s(z))), s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28055, 27991, 9297, 307, 220, 108, 394, 147, 27362, 2344, 1, 906, 19776])).
% 3.12/3.34 tff(28057,plain,
% 3.12/3.34 (s(s(s(z))) = s(elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1816, 28056, 27986])).
% 3.12/3.34 tff(28058,plain,
% 3.12/3.34 (~(s(s(s(z))) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[4909, 28056, 307])).
% 3.12/3.34 tff(28059,plain,
% 3.12/3.34 (r(s(s(s(z))), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[255, 28058, 27991])).
% 3.12/3.34 tff(28060,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2596, 28057])).
% 3.12/3.34 tff(28061,plain,
% 3.12/3.34 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[486, 28060, 147])).
% 3.12/3.34 tff(28062,plain,
% 3.12/3.34 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28057])).
% 3.12/3.34 tff(28063,plain,
% 3.12/3.34 (r(s(elem!1), elem!1)),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28059, 28062])).
% 3.12/3.34 tff(28064,plain,
% 3.12/3.34 (~(elem!1 = s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3917, 28057, 348])).
% 3.12/3.34 tff(28065,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[78, 28064])).
% 3.12/3.34 tff(28066,plain,
% 3.12/3.34 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28057])).
% 3.12/3.34 tff(28067,plain,
% 3.12/3.34 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28066])).
% 3.12/3.34 tff(28068,plain,
% 3.12/3.34 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[906, 28067])).
% 3.12/3.34 tff(28069,plain,
% 3.12/3.34 (r(s(s(s(elem!1))), s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[11152, 28068, 307, 28061, 28065])).
% 3.12/3.34 tff(28070,plain,
% 3.12/3.34 (~r(s(z), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[9617, 28069, 27362, 28063])).
% 3.12/3.34 tff(28071,plain,
% 3.12/3.34 (b(s(z), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[760, 28070])).
% 3.12/3.34 tff(28072,plain,
% 3.12/3.34 (~b(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[13752, 28071, 307, 28061])).
% 3.12/3.34 tff(28073,plain,
% 3.12/3.34 (r(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[236, 28072, 27994])).
% 3.12/3.34 tff(28074,plain,
% 3.12/3.34 (~b(z, s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[15964, 28073, 27363, 220, 28059])).
% 3.12/3.34 tff(28075,plain,
% 3.12/3.34 (~b(z, s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[15649, 28071, 28061, 220])).
% 3.12/3.34 tff(28076,plain,
% 3.12/3.34 (r(z, s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[19736, 28075])).
% 3.12/3.34 tff(28077,plain,
% 3.12/3.34 (~r(z, s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[7694, 28076, 28063, 28069])).
% 3.12/3.34 tff(28078,plain,
% 3.12/3.34 (b(z, s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1439, 28077])).
% 3.12/3.34 tff(28079,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[16218, 28078, 28074, 28057])).
% 3.12/3.34 tff(28080,plain,(r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28081,plain,
% 3.12/3.34 (r(s(s(s(elem!1))), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28080, 394, 307, 906, 348, 108, 220, 2344, 1])).
% 3.12/3.34 tff(28082,plain,
% 3.12/3.34 (~b(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[26193, 394, 19197, 348, 307, 219, 220])).
% 3.12/3.34 tff(28083,plain,
% 3.12/3.34 (r(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[355, 28082, 9297])).
% 3.12/3.34 tff(28084,plain,
% 3.12/3.34 (s(s(s(z))) = elem!1),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[25677, 28083, 394, 307, 27986, 348, 19197, 27363, 28081])).
% 3.12/3.34 tff(28085,plain,
% 3.12/3.34 (~(elem!1 = s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3906, 28084])).
% 3.12/3.34 tff(28086,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[78, 28085])).
% 3.12/3.34 tff(28087,plain,
% 3.12/3.34 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[84, 28086])).
% 3.12/3.34 tff(28088,plain,
% 3.12/3.34 (~r(z, s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[6932, 121, 28083, 27363, 28081])).
% 3.12/3.34 tff(28089,plain,
% 3.12/3.34 (b(z, s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[19736, 28088])).
% 3.12/3.34 tff(28090,plain,
% 3.12/3.34 (~r(s(s(s(elem!1))), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[13798, 121, 28083, 27363, 28081])).
% 3.12/3.34 tff(28091,plain,
% 3.12/3.34 (b(s(s(s(elem!1))), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[8229, 28090])).
% 3.12/3.34 tff(28092,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[22147, 28091, 28089, 19197, 2282, 394, 28087])).
% 3.12/3.34 tff(28093,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (~b(z, s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28094,plain,
% 3.12/3.34 (~b(s(elem!1), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28093, 2344, 348, 220, 906, 108, 307, 1])).
% 3.12/3.34 tff(28095,plain,
% 3.12/3.34 (r(s(elem!1), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[409, 28094])).
% 3.12/3.34 tff(28096,plain,
% 3.12/3.34 (b(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[26956, 907, 220, 307, 2073, 147, 412, 108, 2344, 1, 348, 71])).
% 3.12/3.34 tff(28097,plain,
% 3.12/3.34 (~b(elem!1, s(z))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[20398, 28096, 19197, 220])).
% 3.12/3.34 tff(28098,plain,
% 3.12/3.34 (b(s(elem!1), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[23545, 28097, 412, 2282, 307, 28096, 2073, 147, 1])).
% 3.12/3.34 tff(28099,plain,
% 3.12/3.34 (s(s(s(elem!1))) = s(elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[23507, 26697, 307, 412, 1326])).
% 3.12/3.34 tff(28100,plain,
% 3.12/3.34 (elem!1 = s(s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[78, 28099])).
% 3.12/3.34 tff(28101,plain,
% 3.12/3.34 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2479, 28100, 307])).
% 3.12/3.34 tff(28102,plain,
% 3.12/3.34 (r(z, s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1439, 4607])).
% 3.12/3.34 tff(28103,plain,
% 3.12/3.34 (b(s(elem!1), s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3787, 28100, 2618])).
% 3.12/3.34 tff(28104,plain,
% 3.12/3.34 (~(s(z) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[27109, 28103, 412, 28102, 19205, 1281, 220, 28101, 147])).
% 3.12/3.34 tff(28105,plain,
% 3.12/3.34 (r(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[236, 28104, 27263])).
% 3.12/3.34 tff(28106,plain,
% 3.12/3.34 (~(elem!1 = s(z))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[242, 28104])).
% 3.12/3.34 tff(28107,plain,
% 3.12/3.34 (r(elem!1, s(z))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[299, 28106, 24773])).
% 3.12/3.34 tff(28108,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[4112, 28107, 28105, 108, 17770])).
% 3.12/3.34 tff(28109,plain,(b(s(s(s(z))), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28110,plain,
% 3.12/3.34 (b(s(s(s(z))), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28109, 28098, 412, 19197, 220, 147, 108, 307, 28096, 2073, 907])).
% 3.12/3.34 tff(28111,plain,
% 3.12/3.34 (~b(z, s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1978, 28110, 307, 28096])).
% 3.12/3.34 tff(28112,plain,
% 3.12/3.34 (~(s(s(s(z))) = s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[26813, 28110, 307, 2073, 147])).
% 3.12/3.34 tff(28113,plain,
% 3.12/3.34 (~r(z, s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[13140, 28110, 307, 412, 28098, 28112])).
% 3.12/3.34 tff(28114,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1214, 28113, 28111])).
% 3.12/3.34 tff(28115,plain,((s(s(s(z))) = elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(elem!1, s(elem!1)) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28116,plain,
% 3.12/3.34 (s(s(s(z))) = elem!1),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28115, 147, 28095, 19776, 307, 220, 108, 1, 2344, 348, 71])).
% 3.12/3.34 tff(28117,plain,
% 3.12/3.34 (s(elem!1) = s(s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2605, 28116])).
% 3.12/3.34 tff(28118,plain,
% 3.12/3.34 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28117])).
% 3.12/3.34 tff(28119,plain,
% 3.12/3.34 (b(elem!1, s(s(s(s(z)))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[307, 28118])).
% 3.12/3.34 tff(28120,plain,
% 3.12/3.34 (~(elem!1 = s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3906, 28116])).
% 3.12/3.34 tff(28121,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[78, 28120])).
% 3.12/3.34 tff(28122,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2611, 28116])).
% 3.12/3.34 tff(28123,plain,
% 3.12/3.34 (b(s(s(s(elem!1))), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[486, 28122, 147])).
% 3.12/3.34 tff(28124,plain,
% 3.12/3.34 (~b(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[23507, 28123, 307, 28095, 28121])).
% 3.12/3.34 tff(28125,plain,
% 3.12/3.34 (~(s(z) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[229, 28124, 220])).
% 3.12/3.34 tff(28126,plain,
% 3.12/3.34 (~(s(s(z)) = s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[960, 28125])).
% 3.12/3.34 tff(28127,plain,
% 3.12/3.34 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[953, 28126])).
% 3.12/3.34 tff(28128,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[946, 28127])).
% 3.12/3.34 tff(28129,plain,
% 3.12/3.34 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[25008, 28128])).
% 3.12/3.34 tff(28130,plain,
% 3.12/3.34 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28117])).
% 3.12/3.34 tff(28131,plain,
% 3.12/3.34 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28130])).
% 3.12/3.34 tff(28132,plain,
% 3.12/3.34 (b(elem!1, s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[9580, 28116, 19776])).
% 3.12/3.34 tff(28133,plain,
% 3.12/3.34 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[747, 28132, 307, 28123])).
% 3.12/3.34 tff(28134,plain,
% 3.12/3.34 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28133, 28131])).
% 3.12/3.34 tff(28135,plain,
% 3.12/3.34 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1000, 21, 28134, 28129])).
% 3.12/3.34 tff(28136,plain,
% 3.12/3.34 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28117])).
% 3.12/3.34 tff(28137,plain,
% 3.12/3.34 (~(elem!1 = s(z))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[242, 28125])).
% 3.12/3.34 tff(28138,plain,
% 3.12/3.34 (r(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[250, 28116, 108])).
% 3.12/3.34 tff(28139,plain,
% 3.12/3.34 (r(z, elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[355, 28124, 9297])).
% 3.12/3.34 tff(28140,plain,
% 3.12/3.34 (~r(s(elem!1), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[26272, 28132, 28095, 307, 28121, 28139, 19197, 9298, 28138, 2282, 28137])).
% 3.12/3.34 tff(28141,plain,
% 3.12/3.34 (b(s(elem!1), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2243, 28140, 2207])).
% 3.12/3.34 tff(28142,plain,
% 3.12/3.34 (b(s(s(s(s(z)))), elem!1)),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28141, 28136])).
% 3.12/3.34 tff(28143,plain,
% 3.12/3.34 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28117])).
% 3.12/3.34 tff(28144,plain,
% 3.12/3.34 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28143])).
% 3.12/3.34 tff(28145,plain,
% 3.12/3.34 (~(s(s(elem!1)) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[197, 28120])).
% 3.12/3.34 tff(28146,plain,
% 3.12/3.34 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28116])).
% 3.12/3.34 tff(28147,plain,
% 3.12/3.34 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28146])).
% 3.12/3.34 tff(28148,plain,
% 3.12/3.34 (~r(elem!1, s(s(s(elem!1))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[906, 28147])).
% 3.12/3.34 tff(28149,plain,
% 3.12/3.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28029, 28148, 108, 19197, 147, 28116, 28132, 28139])).
% 3.12/3.34 tff(28150,plain,
% 3.12/3.34 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[556, 28149, 1])).
% 3.12/3.34 tff(28151,plain,
% 3.12/3.34 (~r(elem!1, s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3310, 28150, 9297, 2344, 28124, 28145, 28121])).
% 3.12/3.34 tff(28152,plain,
% 3.12/3.34 (b(elem!1, s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[599, 28151, 28120])).
% 3.12/3.34 tff(28153,plain,
% 3.12/3.34 (b(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28152, 28144])).
% 3.12/3.34 tff(28154,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.34 inference(rewrite,[status(thm)],[])).
% 3.12/3.34 tff(28155,plain,
% 3.12/3.34 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.34 inference(rewrite,[status(thm)],[])).
% 3.12/3.34 tff(28156,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28155])).
% 3.12/3.34 tff(28157,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.34 inference(transitivity,[status(thm)],[28156, 28154])).
% 3.12/3.34 tff(28158,plain,
% 3.12/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.34 inference(quant_inst,[status(thm)],[])).
% 3.12/3.34 tff(28159,plain,
% 3.12/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28158, 28157])).
% 3.12/3.34 tff(28160,plain,
% 3.12/3.34 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28159, 271, 28153, 28123, 28142])).
% 3.12/3.34 tff(28161,plain,
% 3.12/3.34 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1014, 28160, 28128])).
% 3.12/3.34 tff(28162,plain,
% 3.12/3.34 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28143])).
% 3.12/3.34 tff(28163,plain,
% 3.12/3.34 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28150, 28162])).
% 3.12/3.34 tff(28164,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.12/3.34 inference(rewrite,[status(thm)],[])).
% 3.12/3.34 tff(28165,plain,
% 3.12/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.12/3.34 inference(quant_inst,[status(thm)],[])).
% 3.12/3.34 tff(28166,plain,
% 3.12/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28165, 28164])).
% 3.12/3.34 tff(28167,plain,
% 3.12/3.34 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28166, 121, 28163, 28161, 28135])).
% 3.12/3.34 tff(28168,plain,
% 3.12/3.34 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[9512, 28167])).
% 3.12/3.34 tff(28169,plain,
% 3.12/3.34 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 3.12/3.34 inference(symmetry,[status(thm)],[28143])).
% 3.12/3.34 tff(28170,plain,
% 3.12/3.34 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28169])).
% 3.12/3.34 tff(28171,plain,
% 3.12/3.34 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.34 inference(symmetry,[status(thm)],[28170])).
% 3.12/3.34 tff(28172,plain,
% 3.12/3.34 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28117])).
% 3.12/3.34 tff(28173,plain,
% 3.12/3.34 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.34 inference(transitivity,[status(thm)],[28172, 28171])).
% 3.12/3.34 tff(28174,plain,
% 3.12/3.34 (~r(s(elem!1), s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3192, 28141, 307, 28150, 28123, 28121])).
% 3.12/3.34 tff(28175,plain,
% 3.12/3.34 (b(s(elem!1), s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[526, 28174, 211])).
% 3.12/3.34 tff(28176,plain,
% 3.12/3.34 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28175, 28173])).
% 3.12/3.34 tff(28177,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.34 inference(rewrite,[status(thm)],[])).
% 3.12/3.34 tff(28178,plain,
% 3.12/3.34 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(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))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.34 inference(rewrite,[status(thm)],[])).
% 3.12/3.34 tff(28179,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28178])).
% 3.12/3.34 tff(28180,plain,
% 3.12/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.12/3.34 inference(transitivity,[status(thm)],[28179, 28177])).
% 3.12/3.34 tff(28181,plain,
% 3.12/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.12/3.34 inference(quant_inst,[status(thm)],[])).
% 3.12/3.34 tff(28182,plain,
% 3.12/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28181, 28180])).
% 3.12/3.34 tff(28183,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28182, 271, 28176, 28153, 28168, 28119])).
% 3.12/3.34 tff(28184,plain,(r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(elem!1))) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28185,plain,
% 3.12/3.34 (~b(elem!1, s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28184, 27985, 1, 24223, 348, 106, 27658, 71, 147])).
% 3.12/3.34 tff(28186,plain,
% 3.12/3.34 ($false),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[392, 28185, 27985, 219])).
% 3.12/3.34 tff(28187,plain,((s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z)))) | r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.34 tff(28188,plain,
% 3.12/3.34 (~b(s(elem!1), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[28187, 348, 71, 147, 1])).
% 3.12/3.34 tff(28189,plain,
% 3.12/3.34 (r(s(elem!1), z)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[409, 28188])).
% 3.12/3.34 tff(28190,plain,
% 3.12/3.34 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[19196, 2])).
% 3.12/3.34 tff(28191,plain,
% 3.12/3.34 (s(s(s(elem!1))) = elem!1),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[3895, 28190])).
% 3.12/3.34 tff(28192,plain,
% 3.12/3.34 (~(s(s(s(z))) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2611, 28191])).
% 3.12/3.34 tff(28193,plain,
% 3.12/3.34 (~(elem!1 = s(s(s(z))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1100, 28192])).
% 3.12/3.34 tff(28194,plain,
% 3.12/3.34 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[1516, 28193])).
% 3.12/3.34 tff(28195,plain,
% 3.12/3.34 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.34 tff(28196,plain,
% 3.12/3.34 (elem!1 = s(s(s(elem!1)))),
% 3.12/3.34 inference(symmetry,[status(thm)],[25718])).
% 3.12/3.34 tff(28197,plain,
% 3.12/3.34 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.34 tff(28198,plain,
% 3.12/3.34 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.34 tff(28199,plain,
% 3.12/3.34 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 3.12/3.34 inference(symmetry,[status(thm)],[28198])).
% 3.12/3.34 tff(28200,plain,
% 3.12/3.34 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28199])).
% 3.12/3.34 tff(28201,plain,
% 3.12/3.34 (~(s(z) = elem!1)),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[61, 28200])).
% 3.12/3.34 tff(28202,plain,
% 3.12/3.34 (r(s(z), elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[236, 1242, 28201])).
% 3.12/3.34 tff(28203,plain,
% 3.12/3.34 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.34 tff(28204,plain,
% 3.12/3.34 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 3.12/3.34 inference(symmetry,[status(thm)],[28203])).
% 3.12/3.34 tff(28205,plain,
% 3.12/3.34 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28204])).
% 3.12/3.34 tff(28206,plain,
% 3.12/3.34 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[601])).
% 3.12/3.34 tff(28207,plain,
% 3.12/3.34 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.12/3.34 inference(transitivity,[status(thm)],[28206, 934])).
% 3.12/3.34 tff(28208,plain,
% 3.12/3.34 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28207])).
% 3.12/3.34 tff(28209,plain,
% 3.12/3.34 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[12235, 3891, 2065])).
% 3.12/3.34 tff(28210,plain,
% 3.12/3.34 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28209, 28208])).
% 3.12/3.34 tff(28211,plain,
% 3.12/3.34 (~(elem!1 = s(s(s(s(z)))))),
% 3.12/3.34 inference(modus_ponens,[status(thm)],[28210, 28205])).
% 3.12/3.34 tff(28212,plain,
% 3.12/3.34 (~b(s(z), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[2562, 1242, 25718])).
% 3.12/3.34 tff(28213,plain,
% 3.12/3.34 (r(s(z), s(s(s(elem!1))))),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[760, 28212])).
% 3.12/3.34 tff(28214,plain,
% 3.12/3.34 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.34 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.34 tff(28215,plain,
% 3.12/3.34 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.12/3.34 inference(unit_resolution,[status(thm)],[25867, 601, 25718])).
% 3.12/3.34 tff(28216,plain,
% 3.12/3.34 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.35 tff(28217,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28216])).
% 3.12/3.35 tff(28218,plain,
% 3.12/3.35 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.35 tff(28219,plain,
% 3.12/3.35 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28218, 28217])).
% 3.12/3.35 tff(28220,plain,
% 3.12/3.35 (~(s(s(s(z))) = elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2611, 25718])).
% 3.12/3.35 tff(28221,plain,
% 3.12/3.35 (~(elem!1 = s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1100, 28220])).
% 3.12/3.35 tff(28222,plain,
% 3.12/3.35 (~r(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1797, 1243, 110, 357])).
% 3.12/3.35 tff(28223,plain,
% 3.12/3.35 (b(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1192, 28222, 28221])).
% 3.12/3.35 tff(28224,plain,
% 3.12/3.35 (b(s(elem!1), s(s(s(z))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28223, 28219])).
% 3.12/3.35 tff(28225,plain,
% 3.12/3.35 (elem!1 = s(s(s(elem!1)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[13222, 25718])).
% 3.12/3.35 tff(28226,plain,
% 3.12/3.35 (~b(z, s(s(s(elem!1))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[13207, 199, 28225])).
% 3.12/3.35 tff(28227,plain,
% 3.12/3.35 (r(z, s(s(s(elem!1))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[19736, 28226])).
% 3.12/3.35 tff(28228,plain,
% 3.12/3.35 (~r(s(s(s(elem!1))), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[12769, 28227, 110, 572])).
% 3.12/3.35 tff(28229,plain,
% 3.12/3.35 (r(s(s(elem!1)), s(z)) <=> r(s(elem!1), s(z))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[202])).
% 3.12/3.35 tff(28230,plain,
% 3.12/3.35 (r(s(elem!1), s(z)) <=> r(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28229])).
% 3.12/3.35 tff(28231,plain,
% 3.12/3.35 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[210, 201])).
% 3.12/3.35 tff(28232,plain,
% 3.12/3.35 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28231])).
% 3.12/3.35 tff(28233,plain,
% 3.12/3.35 (s(s(s(elem!1))) = s(elem!1)),
% 3.12/3.35 inference(transitivity,[status(thm)],[28232, 202])).
% 3.12/3.35 tff(28234,plain,
% 3.12/3.35 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28233])).
% 3.12/3.35 tff(28235,plain,
% 3.12/3.35 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28234, 28230])).
% 3.12/3.35 tff(28236,plain,
% 3.12/3.35 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28235])).
% 3.12/3.35 tff(28237,plain,
% 3.12/3.35 (~r(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[38, 28236])).
% 3.12/3.35 tff(28238,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2117, 28237])).
% 3.12/3.35 tff(28239,plain,(r(s(s(s(elem!1))), s(z)) | (~r(s(s(elem!1)), s(z))) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28240,plain,
% 3.12/3.35 (~r(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28239, 28228, 609])).
% 3.12/3.35 tff(28241,plain,
% 3.12/3.35 (b(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2143, 28240])).
% 3.12/3.35 tff(28242,plain,
% 3.12/3.35 (b(s(s(elem!1)), s(z)) <=> b(s(elem!1), s(z))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[202])).
% 3.12/3.35 tff(28243,plain,
% 3.12/3.35 (b(s(elem!1), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28242])).
% 3.12/3.35 tff(28244,plain,
% 3.12/3.35 ((~b(s(elem!1), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28243])).
% 3.12/3.35 tff(28245,plain,
% 3.12/3.35 (~b(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[424, 28244])).
% 3.12/3.35 tff(28246,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[981, 28245])).
% 3.12/3.35 tff(28247,plain,(b(s(elem!1), s(z)) | (~b(s(s(elem!1)), s(z))) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28248,plain,
% 3.12/3.35 (b(s(elem!1), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28247, 28241, 609])).
% 3.12/3.35 tff(28249,plain,
% 3.12/3.35 (r(s(z), s(elem!1)) <=> r(s(z), s(s(elem!1)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[201])).
% 3.12/3.35 tff(28250,plain,
% 3.12/3.35 (r(s(z), s(s(elem!1))) <=> r(s(z), s(elem!1))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28249])).
% 3.12/3.35 tff(28251,plain,
% 3.12/3.35 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28232])).
% 3.12/3.35 tff(28252,plain,
% 3.12/3.35 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28251, 28250])).
% 3.12/3.35 tff(28253,plain,
% 3.12/3.35 (r(s(z), s(elem!1))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[572, 28252])).
% 3.12/3.35 tff(28254,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[438, 28253])).
% 3.12/3.35 tff(28255,plain,((~r(s(z), s(s(s(elem!1))))) | r(s(z), s(elem!1)) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28256,plain,
% 3.12/3.35 (r(s(z), s(elem!1))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28255, 572, 609])).
% 3.12/3.35 tff(28257,plain,
% 3.12/3.35 (~r(s(elem!1), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[436, 1243, 110, 28256])).
% 3.12/3.35 tff(28258,plain,
% 3.12/3.35 (b(s(elem!1), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[409, 28257])).
% 3.12/3.35 tff(28259,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[12308, 394, 3891])).
% 3.12/3.35 tff(28260,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 3.12/3.35 tff(28261,plain,
% 3.12/3.35 (s(s(z)) = s(s(s(elem!1)))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28260])).
% 3.12/3.35 tff(28262,plain,
% 3.12/3.35 (s(s(z)) = s(elem!1)),
% 3.12/3.35 inference(transitivity,[status(thm)],[28261, 611, 610])).
% 3.12/3.35 tff(28263,plain,
% 3.12/3.35 (s(elem!1) = elem!1),
% 3.12/3.35 inference(transitivity,[status(thm)],[609, 3892])).
% 3.12/3.35 tff(28264,plain,
% 3.12/3.35 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = elem!1)),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28263])).
% 3.12/3.35 tff(28265,plain,
% 3.12/3.35 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(elem!1))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28264])).
% 3.12/3.35 tff(28266,plain,
% 3.12/3.35 ((~(s(s(z)) = elem!1)) <=> (~(s(s(z)) = s(elem!1)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28265])).
% 3.12/3.35 tff(28267,plain,
% 3.12/3.35 (s(s(s(elem!1))) = s(elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[614, 28231])).
% 3.12/3.35 tff(28268,plain,
% 3.12/3.35 (elem!1 = s(s(elem!1))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[78, 28267])).
% 3.12/3.35 tff(28269,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 3.12/3.35 tff(28270,plain,
% 3.12/3.35 (s(s(z)) = s(s(elem!1))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28269, 28268])).
% 3.12/3.35 tff(28271,plain,
% 3.12/3.35 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28270])).
% 3.12/3.35 tff(28272,plain,
% 3.12/3.35 (s(z) = s(s(elem!1))),
% 3.12/3.35 inference(transitivity,[status(thm)],[957, 28271, 604, 201])).
% 3.12/3.35 tff(28273,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2137, 28272])).
% 3.12/3.35 tff(28274,plain,((~(s(s(z)) = elem!1)) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28275,plain,
% 3.12/3.35 (~(s(s(z)) = elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28274, 609])).
% 3.12/3.35 tff(28276,plain,
% 3.12/3.35 (~(s(s(z)) = s(elem!1))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28275, 28266])).
% 3.12/3.35 tff(28277,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28276, 28262])).
% 3.12/3.35 tff(28278,plain,((~(s(s(s(elem!1))) = s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28279,plain,
% 3.12/3.35 (~(s(s(s(elem!1))) = s(s(z)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28278, 601])).
% 3.12/3.35 tff(28280,plain,
% 3.12/3.35 (~r(s(s(s(z))), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[9421, 1140, 110, 108])).
% 3.12/3.35 tff(28281,plain,
% 3.12/3.35 (b(s(s(s(z))), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2325, 28280])).
% 3.12/3.35 tff(28282,plain,
% 3.12/3.35 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25696])).
% 3.12/3.35 tff(28283,plain,
% 3.12/3.35 (~r(s(s(s(z))), elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[3375, 1140, 108, 110])).
% 3.12/3.35 tff(28284,plain,
% 3.12/3.35 (b(s(s(s(z))), elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[255, 28283, 28220])).
% 3.12/3.35 tff(28285,plain,
% 3.12/3.35 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28284, 28282])).
% 3.12/3.35 tff(28286,plain,
% 3.12/3.35 (~b(s(z), s(s(s(elem!1))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[14970, 28285, 28281, 1638])).
% 3.12/3.35 tff(28287,plain,
% 3.12/3.35 (r(s(z), s(s(s(elem!1))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[760, 28286])).
% 3.12/3.35 tff(28288,plain,
% 3.12/3.35 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1471, 28287, 111, 110])).
% 3.12/3.35 tff(28289,plain,
% 3.12/3.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28290,plain,
% 3.12/3.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 3.12/3.35 inference(quant_inst,[status(thm)],[])).
% 3.12/3.35 tff(28291,plain,
% 3.12/3.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28290, 28289])).
% 3.12/3.35 tff(28292,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), s(s(z)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28291, 21, 28288, 28279])).
% 3.12/3.35 tff(28293,plain,
% 3.12/3.35 (~r(s(s(s(z))), s(s(z)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1356, 1140, 110, 108])).
% 3.12/3.35 tff(28294,plain,
% 3.12/3.35 (b(s(s(s(z))), s(s(z)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1366, 21, 1362, 28293])).
% 3.12/3.35 tff(28295,plain,
% 3.12/3.35 (elem!1 = s(elem!1)),
% 3.12/3.35 inference(transitivity,[status(thm)],[3891, 610])).
% 3.12/3.35 tff(28296,plain,
% 3.12/3.35 (b(elem!1, s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28295])).
% 3.12/3.35 tff(28297,plain,
% 3.12/3.35 (b(s(elem!1), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28296])).
% 3.12/3.35 tff(28298,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[612])).
% 3.12/3.35 tff(28299,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28298, 28297])).
% 3.12/3.35 tff(28300,plain,
% 3.12/3.35 (b(elem!1, s(s(z)))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28292, 28299])).
% 3.12/3.35 tff(28301,plain,
% 3.12/3.35 (~b(s(s(z)), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[6740, 28300, 28284, 28294])).
% 3.12/3.35 tff(28302,plain,
% 3.12/3.35 (r(s(s(z)), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[4670, 28301])).
% 3.12/3.35 tff(28303,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28304,plain,
% 3.12/3.35 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28305,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28304])).
% 3.12/3.35 tff(28306,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28305, 28303])).
% 3.12/3.35 tff(28307,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 3.12/3.35 inference(quant_inst,[status(thm)],[])).
% 3.12/3.35 tff(28308,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28307, 28306])).
% 3.12/3.35 tff(28309,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28308, 121, 111, 110, 3599, 14778])).
% 3.12/3.35 tff(28310,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28311,plain,
% 3.12/3.35 (~r(s(s(z)), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28310, 28302, 110, 111])).
% 3.12/3.35 tff(28312,plain,
% 3.12/3.35 (((~![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))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28313,plain,
% 3.12/3.35 ((~![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))),
% 3.12/3.35 inference(quant_inst,[status(thm)],[])).
% 3.12/3.35 tff(28314,plain,
% 3.12/3.35 ((~![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)),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28313, 28312])).
% 3.12/3.35 tff(28315,plain,
% 3.12/3.35 (b(s(s(z)), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28314, 21, 95, 28311])).
% 3.12/3.35 tff(28316,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28317,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.12/3.35 inference(quant_inst,[status(thm)],[])).
% 3.12/3.35 tff(28318,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28317, 28316])).
% 3.12/3.35 tff(28319,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28318, 271, 28285, 28315, 28294, 28292])).
% 3.12/3.35 tff(28320,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28321,plain,
% 3.12/3.35 (~r(z, s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28320, 108, 110, 601, 111, 28259])).
% 3.12/3.35 tff(28322,plain,
% 3.12/3.35 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.35 tff(28323,plain,
% 3.12/3.35 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = elem!1)),
% 3.12/3.35 inference(transitivity,[status(thm)],[28322, 653])).
% 3.12/3.35 tff(28324,plain,
% 3.12/3.35 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28323])).
% 3.12/3.35 tff(28325,plain,
% 3.12/3.35 ((s(s(s(elem!1))) = elem!1) <=> (s(elem!1) = elem!1)),
% 3.12/3.35 inference(transitivity,[status(thm)],[28324, 11206])).
% 3.12/3.35 tff(28326,plain,
% 3.12/3.35 (s(elem!1) = elem!1),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[25718, 28325])).
% 3.12/3.35 tff(28327,plain,
% 3.12/3.35 (r(z, s(s(elem!1))) <=> r(z, s(s(s(elem!1))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[601])).
% 3.12/3.35 tff(28328,plain,
% 3.12/3.35 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(elem!1)))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28327])).
% 3.12/3.35 tff(28329,plain,
% 3.12/3.35 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 3.12/3.35 inference(transitivity,[status(thm)],[25745, 28328])).
% 3.12/3.35 tff(28330,plain,
% 3.12/3.35 (r(z, s(s(elem!1)))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[378, 28329])).
% 3.12/3.35 tff(28331,plain,
% 3.12/3.35 (~r(s(s(s(z))), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2096, 28330, 108, 110])).
% 3.12/3.35 tff(28332,plain,
% 3.12/3.35 (b(s(s(s(z))), z)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1155, 28331])).
% 3.12/3.35 tff(28333,plain,
% 3.12/3.35 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25696])).
% 3.12/3.35 tff(28334,plain,
% 3.12/3.35 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25696])).
% 3.12/3.35 tff(28335,plain,
% 3.12/3.35 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 3.12/3.35 inference(symmetry,[status(thm)],[28334])).
% 3.12/3.35 tff(28336,plain,
% 3.12/3.35 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28335])).
% 3.12/3.35 tff(28337,plain,
% 3.12/3.35 (~(s(z) = elem!1)),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[61, 28336])).
% 3.12/3.35 tff(28338,plain,
% 3.12/3.35 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25696])).
% 3.12/3.35 tff(28339,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 3.12/3.35 inference(symmetry,[status(thm)],[28338])).
% 3.12/3.35 tff(28340,plain,
% 3.12/3.35 (b(elem!1, z)),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[25703, 28339])).
% 3.12/3.35 tff(28341,plain,
% 3.12/3.35 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.35 tff(28342,plain,
% 3.12/3.35 (~(s(s(s(z))) = s(elem!1))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2596, 25718])).
% 3.12/3.35 tff(28343,plain,
% 3.12/3.35 (~b(s(s(s(z))), s(elem!1))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[8279, 1307, 394, 28332])).
% 3.12/3.35 tff(28344,plain,
% 3.12/3.35 (r(s(s(s(z))), s(elem!1))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1816, 28343, 28342])).
% 3.12/3.35 tff(28345,plain,
% 3.12/3.35 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28344, 28341])).
% 3.12/3.35 tff(28346,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28333])).
% 3.12/3.35 tff(28347,plain,
% 3.12/3.35 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28346])).
% 3.12/3.35 tff(28348,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28349,plain,
% 3.12/3.35 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28350,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28349])).
% 3.12/3.35 tff(28351,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28350, 28348])).
% 3.12/3.35 tff(28352,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.12/3.35 inference(quant_inst,[status(thm)],[])).
% 3.12/3.35 tff(28353,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28352, 28351])).
% 3.12/3.35 tff(28354,plain,
% 3.12/3.35 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28353, 271, 1307, 1638, 1935])).
% 3.12/3.35 tff(28355,plain,
% 3.12/3.35 (~b(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28354, 28347])).
% 3.12/3.35 tff(28356,plain,
% 3.12/3.35 (r(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1192, 28355, 28221])).
% 3.12/3.35 tff(28357,plain,
% 3.12/3.35 (elem!1 = s(elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2206, 2203])).
% 3.12/3.35 tff(28358,plain,
% 3.12/3.35 (s(elem!1) = s(s(elem!1))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[218, 28357])).
% 3.12/3.35 tff(28359,plain,
% 3.12/3.35 (s(s(elem!1)) = s(elem!1)),
% 3.12/3.35 inference(symmetry,[status(thm)],[28358])).
% 3.12/3.35 tff(28360,plain,
% 3.12/3.35 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[210, 28358])).
% 3.12/3.35 tff(28361,plain,
% 3.12/3.35 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28360])).
% 3.12/3.35 tff(28362,plain,
% 3.12/3.35 (s(s(s(elem!1))) = elem!1),
% 3.12/3.35 inference(transitivity,[status(thm)],[28361, 28359, 2203])).
% 3.12/3.35 tff(28363,plain,
% 3.12/3.35 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28362])).
% 3.12/3.35 tff(28364,plain,
% 3.12/3.35 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28363])).
% 3.12/3.35 tff(28365,plain,
% 3.12/3.35 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[1184, 28364])).
% 3.12/3.35 tff(28366,assumption,(~r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 3.12/3.35 tff(28367,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28366, 28365])).
% 3.12/3.35 tff(28368,plain,((~r(elem!1, s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(z)))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28369,plain,
% 3.12/3.35 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28368, 28356, 2203])).
% 3.12/3.35 tff(28370,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28371,plain,
% 3.12/3.35 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28372,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28371])).
% 3.12/3.35 tff(28373,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.12/3.35 inference(transitivity,[status(thm)],[28372, 28370])).
% 3.12/3.35 tff(28374,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~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))))),
% 3.12/3.35 inference(quant_inst,[status(thm)],[])).
% 3.12/3.35 tff(28375,plain,
% 3.12/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28374, 28373])).
% 3.12/3.35 tff(28376,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28375, 121, 12761, 108, 5499, 28369])).
% 3.12/3.35 tff(28377,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~(s(elem!1) = elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28378,plain,
% 3.12/3.35 (~r(s(s(s(elem!1))), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28377, 28345, 108, 2203, 601, 1307, 25703, 28332])).
% 3.12/3.35 tff(28379,plain,
% 3.12/3.35 (~r(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28239, 28378, 609])).
% 3.12/3.35 tff(28380,plain,
% 3.12/3.35 (b(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[2143, 28379])).
% 3.12/3.35 tff(28381,plain,
% 3.12/3.35 (s(s(elem!1)) = elem!1),
% 3.12/3.35 inference(transitivity,[status(thm)],[601, 2505])).
% 3.12/3.35 tff(28382,plain,
% 3.12/3.35 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28381])).
% 3.12/3.35 tff(28383,plain,
% 3.12/3.35 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(symmetry,[status(thm)],[28382])).
% 3.12/3.35 tff(28384,plain,
% 3.12/3.35 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 3.12/3.35 inference(monotonicity,[status(thm)],[28383])).
% 3.12/3.35 tff(28385,plain,
% 3.12/3.35 (~b(s(s(elem!1)), s(z))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[294, 28384])).
% 3.12/3.35 tff(28386,plain,
% 3.12/3.35 ($false),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[981, 28385])).
% 3.12/3.35 tff(28387,plain,(b(elem!1, s(z)) | (~b(s(s(elem!1)), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.35 tff(28388,plain,
% 3.12/3.35 (b(elem!1, s(z))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[28387, 28380, 601, 25718])).
% 3.12/3.35 tff(28389,plain,
% 3.12/3.35 (~b(s(z), elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[8962, 28388, 28340, 220])).
% 3.12/3.35 tff(28390,plain,
% 3.12/3.35 (r(s(z), elem!1)),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[236, 28389, 28337])).
% 3.12/3.35 tff(28391,plain,
% 3.12/3.35 (~r(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1797, 28390, 378, 110])).
% 3.12/3.35 tff(28392,plain,
% 3.12/3.35 (b(elem!1, s(s(s(z))))),
% 3.12/3.35 inference(unit_resolution,[status(thm)],[1192, 28391, 28221])).
% 3.12/3.35 tff(28393,plain,
% 3.12/3.35 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.35 inference(modus_ponens,[status(thm)],[28392, 28333])).
% 3.12/3.35 tff(28394,plain,
% 3.12/3.35 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.12/3.35 inference(rewrite,[status(thm)],[])).
% 3.12/3.35 tff(28395,plain,
% 3.12/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28394])).
% 3.12/3.36 tff(28396,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.12/3.36 inference(transitivity,[status(thm)],[28395, 28348])).
% 3.12/3.36 tff(28397,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 3.12/3.36 inference(quant_inst,[status(thm)],[])).
% 3.12/3.36 tff(28398,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28397, 28396])).
% 3.12/3.36 tff(28399,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28398, 271, 1307, 28393, 25703, 28332])).
% 3.12/3.36 tff(28400,plain,((~b(z, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~(s(elem!1) = elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28401,plain,
% 3.12/3.36 (~b(z, s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28400, 108, 110, 601, 220, 378, 28326, 394])).
% 3.12/3.36 tff(28402,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1214, 28401, 28321])).
% 3.12/3.36 tff(28403,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28404,plain,
% 3.12/3.36 (~r(s(z), s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28403, 1243, 601, 220, 110, 28258, 28227])).
% 3.12/3.36 tff(28405,plain,
% 3.12/3.36 (b(s(z), s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[105, 28404])).
% 3.12/3.36 tff(28406,plain,
% 3.12/3.36 (~b(s(s(s(z))), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[3622, 28405, 28248, 28224])).
% 3.12/3.36 tff(28407,plain,
% 3.12/3.36 (r(s(s(s(z))), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[2325, 28406])).
% 3.12/3.36 tff(28408,plain,
% 3.12/3.36 (b(elem!1, s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28387, 28241, 601, 25718])).
% 3.12/3.36 tff(28409,plain,
% 3.12/3.36 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[20703, 28405, 28223, 28408])).
% 3.12/3.36 tff(28410,plain,
% 3.12/3.36 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1494, 28409])).
% 3.12/3.36 tff(28411,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28412,plain,
% 3.12/3.36 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28413,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28412])).
% 3.12/3.36 tff(28414,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.12/3.36 inference(transitivity,[status(thm)],[28413, 28411])).
% 3.12/3.36 tff(28415,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 3.12/3.36 inference(quant_inst,[status(thm)],[])).
% 3.12/3.36 tff(28416,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28415, 28414])).
% 3.12/3.36 tff(28417,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28416, 121, 378, 357, 110, 16461])).
% 3.12/3.36 tff(28418,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28419,plain,
% 3.12/3.36 (~r(elem!1, s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28418, 1243, 110, 357])).
% 3.12/3.36 tff(28420,plain,
% 3.12/3.36 (b(elem!1, s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[20539, 28419, 20532])).
% 3.12/3.36 tff(28421,plain,
% 3.12/3.36 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28295])).
% 3.12/3.36 tff(28422,plain,
% 3.12/3.36 (b(s(elem!1), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.12/3.36 inference(symmetry,[status(thm)],[28421])).
% 3.12/3.36 tff(28423,plain,
% 3.12/3.36 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.12/3.36 inference(transitivity,[status(thm)],[25694, 28422])).
% 3.12/3.36 tff(28424,plain,
% 3.12/3.36 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28423])).
% 3.12/3.36 tff(28425,plain,
% 3.12/3.36 (~b(elem!1, s(s(s(s(z)))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[1009, 28424])).
% 3.12/3.36 tff(28426,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 3.12/3.36 tff(28427,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28426, 28425])).
% 3.12/3.36 tff(28428,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28429,plain,
% 3.12/3.36 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28428, 28420, 601])).
% 3.12/3.36 tff(28430,plain,
% 3.12/3.36 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28223, 28218])).
% 3.12/3.36 tff(28431,plain,
% 3.12/3.36 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[21371, 121, 572, 911, 2327])).
% 3.12/3.36 tff(28432,plain,
% 3.12/3.36 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1167, 21, 28431, 20146])).
% 3.12/3.36 tff(28433,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28434,plain,
% 3.12/3.36 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28435,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(z))))))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28434])).
% 3.12/3.36 tff(28436,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(transitivity,[status(thm)],[28435, 28433])).
% 3.12/3.36 tff(28437,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(quant_inst,[status(thm)],[])).
% 3.12/3.36 tff(28438,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28437, 28436])).
% 3.12/3.36 tff(28439,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28438, 271, 6202, 26854, 28432, 1066])).
% 3.12/3.36 tff(28440,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28441,plain,
% 3.12/3.36 (~r(s(s(s(s(z)))), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28440, 28430, 28429, 572, 28407])).
% 3.12/3.36 tff(28442,plain,
% 3.12/3.36 (b(s(s(s(s(z)))), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[932, 28441])).
% 3.12/3.36 tff(28443,plain,
% 3.12/3.36 (b(s(s(s(elem!1))), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[16580, 28228])).
% 3.12/3.36 tff(28444,plain,
% 3.12/3.36 (~b(s(z), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1075, 28442, 28429, 28443])).
% 3.12/3.36 tff(28445,plain,
% 3.12/3.36 (r(s(z), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[16482, 28444])).
% 3.12/3.36 tff(28446,plain,
% 3.12/3.36 (~r(s(s(s(s(z)))), z)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1034, 28445, 110, 28227])).
% 3.12/3.36 tff(28447,plain,
% 3.12/3.36 (b(s(s(s(s(z)))), z)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1095, 28446])).
% 3.12/3.36 tff(28448,plain,
% 3.12/3.36 (~b(s(z), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[15749, 28447, 220, 28442])).
% 3.12/3.36 tff(28449,plain,
% 3.12/3.36 (r(s(z), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1756, 28448])).
% 3.12/3.36 tff(28450,plain,
% 3.12/3.36 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[21250, 28449, 28410, 28407])).
% 3.12/3.36 tff(28451,plain,
% 3.12/3.36 (b(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[840, 28450, 28215])).
% 3.12/3.36 tff(28452,plain,
% 3.12/3.36 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28451, 28214])).
% 3.12/3.36 tff(28453,plain,
% 3.12/3.36 (~b(s(s(s(z))), z)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[11038, 28405, 28223, 28408])).
% 3.12/3.36 tff(28454,plain,
% 3.12/3.36 (r(s(s(s(z))), z)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1155, 28453])).
% 3.12/3.36 tff(28455,plain,
% 3.12/3.36 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[15185, 25718, 28342])).
% 3.12/3.36 tff(28456,plain,
% 3.12/3.36 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1834, 1243, 110, 357])).
% 3.12/3.36 tff(28457,plain,
% 3.12/3.36 (b(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1847, 28456, 28455])).
% 3.12/3.36 tff(28458,plain,
% 3.12/3.36 (elem!1 = s(elem!1)),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[25718, 28324])).
% 3.12/3.36 tff(28459,plain,
% 3.12/3.36 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[25909, 28451, 28458])).
% 3.12/3.36 tff(28460,plain,
% 3.12/3.36 (~b(z, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[25946, 28459, 28458, 28258, 28457])).
% 3.12/3.36 tff(28461,plain,
% 3.12/3.36 (r(z, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1658, 28460])).
% 3.12/3.36 tff(28462,plain,
% 3.12/3.36 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[19088, 28461, 28454, 28410])).
% 3.12/3.36 tff(28463,plain,
% 3.12/3.36 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[9512, 28462])).
% 3.12/3.36 tff(28464,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28465,plain,
% 3.12/3.36 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(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(s(elem!1)))))) <=> ((~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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28466,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28465])).
% 3.12/3.36 tff(28467,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.36 inference(transitivity,[status(thm)],[28466, 28464])).
% 3.12/3.36 tff(28468,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.36 inference(quant_inst,[status(thm)],[])).
% 3.12/3.36 tff(28469,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28468, 28467])).
% 3.12/3.36 tff(28470,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28469, 271, 28463, 28442, 28429, 28452])).
% 3.12/3.36 tff(28471,plain,(b(z, elem!1) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28472,plain,
% 3.12/3.36 (b(z, elem!1)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28471, 28213, 110, 220, 601, 28211, 28202, 331])).
% 3.12/3.36 tff(28473,plain,
% 3.12/3.36 (b(z, s(s(s(elem!1))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28472, 28197])).
% 3.12/3.36 tff(28474,plain,
% 3.12/3.36 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.36 tff(28475,plain,
% 3.12/3.36 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 3.12/3.36 inference(symmetry,[status(thm)],[28474])).
% 3.12/3.36 tff(28476,plain,
% 3.12/3.36 (b(z, elem!1) <=> b(z, s(elem!1))),
% 3.12/3.36 inference(transitivity,[status(thm)],[28197, 28475])).
% 3.12/3.36 tff(28477,plain,
% 3.12/3.36 (b(z, s(elem!1))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28472, 28476])).
% 3.12/3.36 tff(28478,plain,
% 3.12/3.36 (r(s(elem!1), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[429, 424, 422])).
% 3.12/3.36 tff(28479,plain,
% 3.12/3.36 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.36 tff(28480,plain,
% 3.12/3.36 (~r(z, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[4785, 412, 110, 431])).
% 3.12/3.36 tff(28481,plain,
% 3.12/3.36 (b(z, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1658, 28480])).
% 3.12/3.36 tff(28482,plain,
% 3.12/3.36 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[6358, 3891, 28342])).
% 3.12/3.36 tff(28483,plain,
% 3.12/3.36 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[17876, 412, 220, 431])).
% 3.12/3.36 tff(28484,plain,
% 3.12/3.36 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[4138, 28483, 28482])).
% 3.12/3.36 tff(28485,plain,
% 3.12/3.36 (~b(s(elem!1), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[15001, 28484, 1421, 28481])).
% 3.12/3.36 tff(28486,plain,
% 3.12/3.36 (r(s(elem!1), s(z))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[429, 28485, 422])).
% 3.12/3.36 tff(28487,plain,
% 3.12/3.36 (~r(z, s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[13090, 28486, 110, 412])).
% 3.12/3.36 tff(28488,plain,
% 3.12/3.36 (b(z, s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1121, 28487])).
% 3.12/3.36 tff(28489,plain,
% 3.12/3.36 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1516, 28221])).
% 3.12/3.36 tff(28490,plain,
% 3.12/3.36 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[17419, 28489])).
% 3.12/3.36 tff(28491,plain,
% 3.12/3.36 (r(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[611])).
% 3.12/3.36 tff(28492,plain,
% 3.12/3.36 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(symmetry,[status(thm)],[28491])).
% 3.12/3.36 tff(28493,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28494,plain,
% 3.12/3.36 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28495,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28494])).
% 3.12/3.36 tff(28496,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 3.12/3.36 inference(transitivity,[status(thm)],[28495, 28493])).
% 3.12/3.36 tff(28497,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(elem!1))))),
% 3.12/3.36 inference(quant_inst,[status(thm)],[])).
% 3.12/3.36 tff(28498,plain,
% 3.12/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28497, 28496])).
% 3.12/3.36 tff(28499,plain,
% 3.12/3.36 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28498, 271, 1421, 1639, 9894])).
% 3.12/3.36 tff(28500,plain,
% 3.12/3.36 ($false),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28499, 25937])).
% 3.12/3.36 tff(28501,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~(elem!1 = s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.36 tff(28502,plain,
% 3.12/3.36 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[28501, 28484, 28458, 1421, 28481])).
% 3.12/3.36 tff(28503,plain,
% 3.12/3.36 (r(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1847, 28502, 28455])).
% 3.12/3.36 tff(28504,plain,
% 3.12/3.36 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[16341, 28503, 3891])).
% 3.12/3.36 tff(28505,plain,
% 3.12/3.36 (r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[28504, 28492])).
% 3.12/3.36 tff(28506,plain,
% 3.12/3.36 (~r(z, s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[15256, 28486, 110, 412])).
% 3.12/3.36 tff(28507,plain,
% 3.12/3.36 (b(z, s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1214, 28506])).
% 3.12/3.36 tff(28508,plain,
% 3.12/3.36 (s(elem!1) = s(s(s(elem!1)))),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[3890, 2839])).
% 3.12/3.36 tff(28509,plain,
% 3.12/3.36 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 3.12/3.36 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.36 tff(28510,plain,
% 3.12/3.36 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 3.12/3.36 inference(symmetry,[status(thm)],[28509])).
% 3.12/3.36 tff(28511,plain,
% 3.12/3.36 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 3.12/3.36 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.36 tff(28512,plain,
% 3.12/3.36 (r(s(elem!1), z) <=> r(elem!1, z)),
% 3.12/3.36 inference(transitivity,[status(thm)],[28511, 28510])).
% 3.12/3.36 tff(28513,plain,
% 3.12/3.36 (r(elem!1, z)),
% 3.12/3.36 inference(modus_ponens,[status(thm)],[412, 28512])).
% 3.12/3.36 tff(28514,plain,
% 3.12/3.36 (~r(s(s(s(z))), elem!1)),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[15964, 28513, 220, 28507, 357])).
% 3.12/3.36 tff(28515,plain,
% 3.12/3.36 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[19994, 28514, 25718])).
% 3.12/3.36 tff(28516,plain,
% 3.12/3.36 (~r(s(s(s(z))), s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[13333, 28515, 28508])).
% 3.12/3.36 tff(28517,plain,
% 3.12/3.36 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1816, 28516, 28342])).
% 3.12/3.36 tff(28518,plain,
% 3.12/3.36 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[6049, 28517, 28481, 28507])).
% 3.12/3.36 tff(28519,plain,
% 3.12/3.36 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1733, 28518])).
% 3.12/3.36 tff(28520,plain,
% 3.12/3.36 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[14589, 28488, 28484, 28481])).
% 3.12/3.36 tff(28521,plain,
% 3.12/3.36 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.36 inference(unit_resolution,[status(thm)],[1777, 28520])).
% 3.12/3.36 tff(28522,plain,
% 3.12/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.36 inference(rewrite,[status(thm)],[])).
% 3.12/3.36 tff(28523,plain,
% 3.12/3.36 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28524,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28523])).
% 3.12/3.37 tff(28525,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(transitivity,[status(thm)],[28524, 28522])).
% 3.12/3.37 tff(28526,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28527,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28526, 28525])).
% 3.12/3.37 tff(28528,plain,
% 3.12/3.37 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28527, 121, 28521, 28519])).
% 3.12/3.37 tff(28529,plain,
% 3.12/3.37 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28528, 28505])).
% 3.12/3.37 tff(28530,plain,
% 3.12/3.37 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[1551, 25731])).
% 3.12/3.37 tff(28531,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[25010, 28530])).
% 3.12/3.37 tff(28532,plain,(r(s(s(s(s(z)))), s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28533,plain,
% 3.12/3.37 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28532, 28529, 601])).
% 3.12/3.37 tff(28534,plain,
% 3.12/3.37 (r(s(elem!1), s(s(s(s(z)))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[14020, 28533, 28490, 1421, 28488])).
% 3.12/3.37 tff(28535,plain,
% 3.12/3.37 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28534, 28479])).
% 3.12/3.37 tff(28536,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28537,plain,
% 3.12/3.37 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28538,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28537])).
% 3.12/3.37 tff(28539,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(transitivity,[status(thm)],[28538, 28536])).
% 3.12/3.37 tff(28540,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28541,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28540, 28539])).
% 3.12/3.37 tff(28542,plain,
% 3.12/3.37 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28541, 121, 28521, 28519])).
% 3.12/3.37 tff(28543,plain,
% 3.12/3.37 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28542, 28505])).
% 3.12/3.37 tff(28544,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28543, 28535])).
% 3.12/3.37 tff(28545,plain,((~r(s(elem!1), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28546,plain,
% 3.12/3.37 (~r(s(elem!1), z)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28545, 1421, 601, 220, 357, 110, 422, 28256])).
% 3.12/3.37 tff(28547,plain,
% 3.12/3.37 (b(s(elem!1), z)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[409, 28546])).
% 3.12/3.37 tff(28548,plain,
% 3.12/3.37 (~b(s(s(elem!1)), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28247, 424, 609])).
% 3.12/3.37 tff(28549,plain,
% 3.12/3.37 (r(s(s(elem!1)), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[2143, 28548])).
% 3.12/3.37 tff(28550,plain,
% 3.12/3.37 (r(elem!1, s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[12129, 28549, 3891])).
% 3.12/3.37 tff(28551,plain,
% 3.12/3.37 (r(s(s(s(elem!1))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28239, 28549, 609])).
% 3.12/3.37 tff(28552,plain,
% 3.12/3.37 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[601])).
% 3.12/3.37 tff(28553,plain,
% 3.12/3.37 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 3.12/3.37 inference(symmetry,[status(thm)],[28552])).
% 3.12/3.37 tff(28554,plain,
% 3.12/3.37 (r(s(z), s(s(elem!1)))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[572, 28553])).
% 3.12/3.37 tff(28555,plain,
% 3.12/3.37 (~r(s(s(s(z))), s(elem!1))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[23235, 108, 431, 411])).
% 3.12/3.37 tff(28556,plain,
% 3.12/3.37 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1816, 28555, 2033])).
% 3.12/3.37 tff(28557,plain,
% 3.12/3.37 (~b(z, s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[19710, 28556, 1421, 394])).
% 3.12/3.37 tff(28558,plain,
% 3.12/3.37 (r(z, s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1214, 28557])).
% 3.12/3.37 tff(28559,plain,
% 3.12/3.37 (r(s(s(s(z))), z)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1427, 28556, 1421, 394])).
% 3.12/3.37 tff(28560,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[15478, 121, 110, 28559, 28558, 108])).
% 3.12/3.37 tff(28561,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(z))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28562,plain,
% 3.12/3.37 (~r(s(z), s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28561, 411, 1421, 394, 28342, 28256, 110])).
% 3.12/3.37 tff(28563,plain,
% 3.12/3.37 (b(s(z), s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[105, 28562])).
% 3.12/3.37 tff(28564,plain,
% 3.12/3.37 (~r(s(s(s(z))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[24825, 1500, 357, 411])).
% 3.12/3.37 tff(28565,plain,
% 3.12/3.37 (b(s(s(s(z))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[2325, 28564])).
% 3.12/3.37 tff(28566,plain,
% 3.12/3.37 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[13333, 1500, 28508])).
% 3.12/3.37 tff(28567,plain,
% 3.12/3.37 (r(s(s(s(z))), elem!1)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[19994, 28566, 25718])).
% 3.12/3.37 tff(28568,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.37 tff(28569,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.37 inference(symmetry,[status(thm)],[28568])).
% 3.12/3.37 tff(28570,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.37 tff(28571,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.37 inference(transitivity,[status(thm)],[28570, 28569])).
% 3.12/3.37 tff(28572,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[3061, 28571])).
% 3.12/3.37 tff(28573,plain,
% 3.12/3.37 (~r(s(s(s(s(s(z))))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[25896, 3061, 1625, 3456])).
% 3.12/3.37 tff(28574,plain,
% 3.12/3.37 (b(s(s(s(s(s(z))))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1682, 28573])).
% 3.12/3.37 tff(28575,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[18460, 271, 3871, 222, 1723, 5393])).
% 3.12/3.37 tff(28576,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28577,plain,
% 3.12/3.37 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28576, 28574, 3871, 222])).
% 3.12/3.37 tff(28578,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1733, 28577])).
% 3.12/3.37 tff(28579,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28580,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28581,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28580, 28579])).
% 3.12/3.37 tff(28582,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28581, 121, 12761, 1736, 5499, 7793])).
% 3.12/3.37 tff(28583,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28584,plain,
% 3.12/3.37 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28583, 28578, 12761, 5499])).
% 3.12/3.37 tff(28585,plain,
% 3.12/3.37 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[17429, 28584, 3891])).
% 3.12/3.37 tff(28586,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28585, 28572])).
% 3.12/3.37 tff(28587,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28588,plain,
% 3.12/3.37 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28587, 28566, 12761, 601, 3871, 28565, 1625, 3456])).
% 3.12/3.37 tff(28589,plain,
% 3.12/3.37 (b(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[840, 28588, 28215])).
% 3.12/3.37 tff(28590,plain,
% 3.12/3.37 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28589, 28214])).
% 3.12/3.37 tff(28591,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28592,plain,
% 3.12/3.37 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28593,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28592])).
% 3.12/3.37 tff(28594,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(transitivity,[status(thm)],[28593, 28591])).
% 3.12/3.37 tff(28595,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28596,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28595, 28594])).
% 3.12/3.37 tff(28597,plain,
% 3.12/3.37 (~b(z, s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28596, 271, 3407, 1638, 28590])).
% 3.12/3.37 tff(28598,plain,
% 3.12/3.37 (r(z, s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1658, 28597])).
% 3.12/3.37 tff(28599,plain,
% 3.12/3.37 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[16283, 28598, 1140, 28567])).
% 3.12/3.37 tff(28600,plain,
% 3.12/3.37 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1733, 28599])).
% 3.12/3.37 tff(28601,plain,
% 3.12/3.37 (~b(s(z), s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[23326, 28600, 3871, 28565])).
% 3.12/3.37 tff(28602,plain,
% 3.12/3.37 (r(s(z), s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1756, 28601])).
% 3.12/3.37 tff(28603,plain,
% 3.12/3.37 (~b(s(s(s(s(s(z))))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28576, 28600, 3871, 28565])).
% 3.12/3.37 tff(28604,plain,
% 3.12/3.37 (r(s(s(s(s(s(z))))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1682, 28603])).
% 3.12/3.37 tff(28605,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28606,plain,
% 3.12/3.37 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28607,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28606])).
% 3.12/3.37 tff(28608,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.12/3.37 inference(transitivity,[status(thm)],[28607, 28605])).
% 3.12/3.37 tff(28609,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28610,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28609, 28608])).
% 3.12/3.37 tff(28611,plain,
% 3.12/3.37 ($false),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28610, 121, 110, 28598, 28604, 28602])).
% 3.12/3.37 tff(28612,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.37 tff(28613,plain,
% 3.12/3.37 (~r(s(s(s(z))), s(elem!1))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28612, 1140, 28563, 110, 3407, 28259, 12761, 601, 28554, 3456, 357, 411])).
% 3.12/3.37 tff(28614,plain,
% 3.12/3.37 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[23458, 28613, 3890])).
% 3.12/3.37 tff(28615,plain,
% 3.12/3.37 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[2071, 28614, 2065])).
% 3.12/3.37 tff(28616,plain,
% 3.12/3.37 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1816, 28613, 28342])).
% 3.12/3.37 tff(28617,plain,
% 3.12/3.37 (r(s(s(s(z))), z)),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1427, 28616, 1421, 394])).
% 3.12/3.37 tff(28618,plain,
% 3.12/3.37 (~r(s(s(s(z))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[15445, 121, 110, 28617, 1140])).
% 3.12/3.37 tff(28619,plain,
% 3.12/3.37 (b(s(s(s(z))), s(z))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[2325, 28618])).
% 3.12/3.37 tff(28620,plain,
% 3.12/3.37 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.37 inference(symmetry,[status(thm)],[28214])).
% 3.12/3.37 tff(28621,plain,
% 3.12/3.37 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28620])).
% 3.12/3.37 tff(28622,plain,
% 3.12/3.37 (~b(z, s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28596, 271, 3407, 1638, 15718])).
% 3.12/3.37 tff(28623,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28624,plain,
% 3.12/3.37 (((~b(s(s(s(elem!1))), z)) | (~b(s(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(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28625,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.12/3.37 inference(monotonicity,[status(thm)],[28624])).
% 3.12/3.37 tff(28626,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.37 inference(transitivity,[status(thm)],[28625, 28623])).
% 3.12/3.37 tff(28627,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(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(s(z))))))))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28628,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.12/3.37 inference(modus_ponens,[status(thm)],[28627, 28626])).
% 3.12/3.37 tff(28629,plain,
% 3.12/3.37 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[28628, 271, 2073, 1638, 15718])).
% 3.12/3.37 tff(28630,plain,
% 3.12/3.37 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.12/3.37 inference(unit_resolution,[status(thm)],[1494, 28629])).
% 3.12/3.37 tff(28631,plain,
% 3.12/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.37 inference(rewrite,[status(thm)],[])).
% 3.12/3.37 tff(28632,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.37 inference(quant_inst,[status(thm)],[])).
% 3.12/3.37 tff(28633,plain,
% 3.12/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28632, 28631])).
% 3.12/3.38 tff(28634,plain,
% 3.12/3.38 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28633, 271, 2073, 1638, 15718])).
% 3.12/3.38 tff(28635,plain,
% 3.12/3.38 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1733, 28634])).
% 3.12/3.38 tff(28636,plain,
% 3.12/3.38 ($false),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[5135, 28635, 28630, 109, 1661])).
% 3.12/3.38 tff(28637,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.38 tff(28638,plain,
% 3.12/3.38 (~r(z, s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28637, 15718, 1638, 2073, 109])).
% 3.12/3.38 tff(28639,plain,
% 3.12/3.38 ($false),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1658, 28638, 28622])).
% 3.12/3.38 tff(28640,plain,((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.38 tff(28641,plain,
% 3.12/3.38 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28640, 28615, 28259, 28617, 3407])).
% 3.12/3.38 tff(28642,plain,
% 3.12/3.38 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28641, 28621])).
% 3.12/3.38 tff(28643,plain,
% 3.12/3.38 (r(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[840, 28642, 28215])).
% 3.12/3.38 tff(28644,plain,
% 3.12/3.38 (~r(s(s(s(s(s(z))))), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[25896, 28643, 28554, 3456])).
% 3.12/3.38 tff(28645,plain,
% 3.12/3.38 (b(s(s(s(s(s(z))))), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1682, 28644])).
% 3.12/3.38 tff(28646,plain,
% 3.12/3.38 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28576, 222, 3871, 5393])).
% 3.12/3.38 tff(28647,plain,
% 3.12/3.38 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1733, 28646])).
% 3.12/3.38 tff(28648,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28649,plain,
% 3.12/3.38 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28650,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.12/3.38 inference(monotonicity,[status(thm)],[28649])).
% 3.12/3.38 tff(28651,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.38 inference(transitivity,[status(thm)],[28650, 28648])).
% 3.12/3.38 tff(28652,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28653,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28652, 28651])).
% 3.12/3.38 tff(28654,plain,
% 3.12/3.38 (~r(z, s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28653, 121, 28647, 109, 1140])).
% 3.12/3.38 tff(28655,plain,
% 3.12/3.38 (b(z, s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1658, 28654])).
% 3.12/3.38 tff(28656,plain,
% 3.12/3.38 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[10418, 271, 3871, 222, 937])).
% 3.12/3.38 tff(28657,plain,
% 3.12/3.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[10426, 28656])).
% 3.12/3.38 tff(28658,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28659,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28660,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28659, 28658])).
% 3.12/3.38 tff(28661,plain,
% 3.12/3.38 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28660, 121, 28647, 109, 28657])).
% 3.12/3.38 tff(28662,plain,
% 3.12/3.38 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1777, 28661])).
% 3.12/3.38 tff(28663,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28664,plain,
% 3.12/3.38 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28665,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 3.12/3.38 inference(monotonicity,[status(thm)],[28664])).
% 3.12/3.38 tff(28666,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 3.12/3.38 inference(transitivity,[status(thm)],[28665, 28663])).
% 3.12/3.38 tff(28667,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28668,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28667, 28666])).
% 3.12/3.38 tff(28669,plain,
% 3.12/3.38 (~r(z, s(s(s(s(z)))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28668, 121, 109, 1140, 28657])).
% 3.12/3.38 tff(28670,plain,
% 3.12/3.38 (b(z, s(s(s(s(z)))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1121, 28669])).
% 3.12/3.38 tff(28671,plain,
% 3.12/3.38 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[14589, 28670, 28662, 28655])).
% 3.12/3.38 tff(28672,plain,
% 3.12/3.38 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[4138, 28671, 4132])).
% 3.12/3.38 tff(28673,plain,
% 3.12/3.38 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[17429, 28672, 2470])).
% 3.12/3.38 tff(28674,plain,
% 3.12/3.38 (~b(s(z), s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1785, 28662, 937, 5393])).
% 3.12/3.38 tff(28675,plain,
% 3.12/3.38 (r(s(z), s(s(s(s(s(z))))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1756, 28674])).
% 3.12/3.38 tff(28676,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28677,plain,
% 3.12/3.38 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(z)))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28678,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.12/3.38 inference(monotonicity,[status(thm)],[28677])).
% 3.12/3.38 tff(28679,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(transitivity,[status(thm)],[28678, 28676])).
% 3.12/3.38 tff(28680,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(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(s(z))))))))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28681,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28680, 28679])).
% 3.12/3.38 tff(28682,plain,
% 3.12/3.38 ($false),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28681, 121, 572, 12761, 28675, 28673])).
% 3.12/3.38 tff(28683,plain,((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.38 tff(28684,plain,
% 3.12/3.38 (~b(s(s(s(s(z)))), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28683, 28645, 3891, 12761, 28482, 28563, 572, 1140, 28617, 28619])).
% 3.12/3.38 tff(28685,plain,
% 3.12/3.38 (r(s(s(s(s(z)))), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[932, 28684])).
% 3.12/3.38 tff(28686,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28687,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28688,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28687, 28686])).
% 3.12/3.38 tff(28689,plain,
% 3.12/3.38 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28688, 121, 572, 12761, 28685])).
% 3.12/3.38 tff(28690,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28691,plain,
% 3.12/3.38 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28692,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.12/3.38 inference(monotonicity,[status(thm)],[28691])).
% 3.12/3.38 tff(28693,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.38 inference(transitivity,[status(thm)],[28692, 28690])).
% 3.12/3.38 tff(28694,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28695,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28694, 28693])).
% 3.12/3.38 tff(28696,plain,
% 3.12/3.38 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28695, 121, 572, 12761, 28685])).
% 3.12/3.38 tff(28697,plain,
% 3.12/3.38 ($false),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[25036, 28696, 28689, 220, 28210, 28615, 1140, 28259])).
% 3.12/3.38 tff(28698,plain,((~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.38 tff(28699,plain,
% 3.12/3.38 (~r(z, s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28698, 28551, 572, 220, 28550, 3407, 110, 1421, 28547, 2065, 601, 357, 28478])).
% 3.12/3.38 tff(28700,plain,
% 3.12/3.38 (b(z, s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1214, 28699])).
% 3.12/3.38 tff(28701,plain,
% 3.12/3.38 (~b(s(s(s(z))), s(elem!1))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[19710, 28700, 1421, 28547])).
% 3.12/3.38 tff(28702,plain,
% 3.12/3.38 (r(s(s(s(z))), s(elem!1))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[1816, 28701, 28342])).
% 3.12/3.38 tff(28703,plain,
% 3.12/3.38 (~r(s(z), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28561, 28478, 1421, 28547, 28342, 28256, 110])).
% 3.12/3.38 tff(28704,plain,
% 3.12/3.38 (b(s(z), s(s(s(z))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[105, 28703])).
% 3.12/3.38 tff(28705,plain,
% 3.12/3.38 (~b(s(s(s(z))), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[15813, 28700, 220, 28704])).
% 3.12/3.38 tff(28706,plain,
% 3.12/3.38 (r(s(s(s(z))), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[2325, 28705])).
% 3.12/3.38 tff(28707,plain,
% 3.12/3.38 ($false),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[24825, 28706, 28702, 357, 28478])).
% 3.12/3.38 tff(28708,plain,(b(s(elem!1), s(z)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.38 tff(28709,plain,
% 3.12/3.38 (b(s(elem!1), s(z))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28708, 28202, 220, 28477, 28213, 28473, 110, 2065, 601, 422])).
% 3.12/3.38 tff(28710,plain,
% 3.12/3.38 (b(s(s(s(elem!1))), s(z))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28709, 28195])).
% 3.12/3.38 tff(28711,plain,
% 3.12/3.38 (r(s(z), s(elem!1))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28255, 28213, 609])).
% 3.12/3.38 tff(28712,plain,
% 3.12/3.38 (~r(s(elem!1), z)),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28545, 28477, 601, 220, 28202, 110, 422, 28711])).
% 3.12/3.38 tff(28713,plain,
% 3.12/3.38 (b(s(elem!1), z)),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[409, 28712])).
% 3.12/3.38 tff(28714,plain,
% 3.12/3.38 (b(s(s(s(elem!1))), z)),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[12308, 28713, 3891])).
% 3.12/3.38 tff(28715,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28716,plain,
% 3.12/3.38 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28717,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 3.12/3.38 inference(monotonicity,[status(thm)],[28716])).
% 3.12/3.38 tff(28718,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.12/3.38 inference(transitivity,[status(thm)],[28717, 28715])).
% 3.12/3.38 tff(28719,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28720,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 3.12/3.38 inference(modus_ponens,[status(thm)],[28719, 28718])).
% 3.12/3.38 tff(28721,plain,
% 3.12/3.38 ($false),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28720, 271, 220, 1638, 503, 1067])).
% 3.12/3.38 tff(28722,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.38 tff(28723,plain,
% 3.12/3.38 (~b(s(z), s(s(s(s(z)))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[28722, 28714, 220, 28710])).
% 3.12/3.38 tff(28724,plain,
% 3.12/3.38 (r(s(z), s(s(s(s(z)))))),
% 3.12/3.38 inference(unit_resolution,[status(thm)],[16482, 28723])).
% 3.12/3.38 tff(28725,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28726,plain,
% 3.12/3.38 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(rewrite,[status(thm)],[])).
% 3.12/3.38 tff(28727,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.12/3.38 inference(monotonicity,[status(thm)],[28726])).
% 3.12/3.38 tff(28728,plain,
% 3.12/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.12/3.38 inference(transitivity,[status(thm)],[28727, 28725])).
% 3.12/3.38 tff(28729,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 3.12/3.38 inference(quant_inst,[status(thm)],[])).
% 3.12/3.38 tff(28730,plain,
% 3.12/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28729, 28728])).
% 3.12/3.39 tff(28731,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28730, 271, 3407, 1638, 1103, 12562])).
% 3.12/3.39 tff(28732,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28733,plain,
% 3.12/3.39 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28732, 1103, 3407, 1638])).
% 3.12/3.39 tff(28734,plain,
% 3.12/3.39 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.39 tff(28735,plain,
% 3.12/3.39 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[1562, 28734])).
% 3.12/3.39 tff(28736,assumption,(~b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 3.12/3.39 tff(28737,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28736, 28735])).
% 3.12/3.39 tff(28738,plain,((~b(s(s(s(s(z)))), s(elem!1))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28739,plain,
% 3.12/3.39 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28738, 28733, 601])).
% 3.12/3.39 tff(28740,plain,
% 3.12/3.39 (r(s(s(s(s(z)))), s(elem!1))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1559, 28739, 28489])).
% 3.12/3.39 tff(28741,plain,
% 3.12/3.39 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28532, 28740, 601])).
% 3.12/3.39 tff(28742,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28743,plain,
% 3.12/3.39 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28744,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28743])).
% 3.12/3.39 tff(28745,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.39 inference(transitivity,[status(thm)],[28744, 28742])).
% 3.12/3.39 tff(28746,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.12/3.39 inference(quant_inst,[status(thm)],[])).
% 3.12/3.39 tff(28747,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28746, 28745])).
% 3.12/3.39 tff(28748,plain,
% 3.12/3.39 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28747, 271, 220, 1638, 1103])).
% 3.12/3.39 tff(28749,plain,
% 3.12/3.39 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1014, 28748, 1008])).
% 3.12/3.39 tff(28750,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28751,plain,
% 3.12/3.39 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28752,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28751])).
% 3.12/3.39 tff(28753,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(transitivity,[status(thm)],[28752, 28750])).
% 3.12/3.39 tff(28754,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.12/3.39 inference(quant_inst,[status(thm)],[])).
% 3.12/3.39 tff(28755,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28754, 28753])).
% 3.12/3.39 tff(28756,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28755, 121, 572, 1026, 28749, 28741])).
% 3.12/3.39 tff(28757,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28758,plain,
% 3.12/3.39 (~b(s(s(s(s(z)))), z)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28757, 28213, 28724, 28210, 220, 28714, 601, 28473])).
% 3.12/3.39 tff(28759,plain,
% 3.12/3.39 (r(s(s(s(s(z)))), z)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1095, 28758])).
% 3.12/3.39 tff(28760,plain,
% 3.12/3.39 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28196])).
% 3.12/3.39 tff(28761,plain,
% 3.12/3.39 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 3.12/3.39 inference(symmetry,[status(thm)],[28760])).
% 3.12/3.39 tff(28762,plain,
% 3.12/3.39 (b(elem!1, z)),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28714, 28761])).
% 3.12/3.39 tff(28763,plain,
% 3.12/3.39 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[2203])).
% 3.12/3.39 tff(28764,plain,
% 3.12/3.39 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 3.12/3.39 inference(symmetry,[status(thm)],[28763])).
% 3.12/3.39 tff(28765,plain,
% 3.12/3.39 ((~b(elem!1, s(z))) <=> (~b(s(elem!1), s(z)))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28764])).
% 3.12/3.39 tff(28766,plain,
% 3.12/3.39 (~b(s(elem!1), s(z))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[294, 28765])).
% 3.12/3.39 tff(28767,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[447, 28766])).
% 3.12/3.39 tff(28768,plain,(b(elem!1, s(z)) | (~b(s(elem!1), s(z))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28769,plain,
% 3.12/3.39 (b(elem!1, s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28768, 28709, 28326])).
% 3.12/3.39 tff(28770,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28771,plain,
% 3.12/3.39 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28772,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28771])).
% 3.12/3.39 tff(28773,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(transitivity,[status(thm)],[28772, 28770])).
% 3.12/3.39 tff(28774,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(quant_inst,[status(thm)],[])).
% 3.12/3.39 tff(28775,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28774, 28773])).
% 3.12/3.39 tff(28776,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28775, 121, 110, 1661, 910, 1026])).
% 3.12/3.39 tff(28777,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28778,plain,
% 3.12/3.39 (~r(z, s(s(s(s(s(z))))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28777, 28759, 110, 28724])).
% 3.12/3.39 tff(28779,plain,
% 3.12/3.39 (b(z, s(s(s(s(s(z))))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1658, 28778])).
% 3.12/3.39 tff(28780,plain,
% 3.12/3.39 (~b(s(z), s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[11002, 28769, 220, 28472])).
% 3.12/3.39 tff(28781,plain,
% 3.12/3.39 (r(s(z), s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[105, 28780])).
% 3.12/3.39 tff(28782,plain,
% 3.12/3.39 (~r(z, s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[9421, 2327, 110, 108])).
% 3.12/3.39 tff(28783,plain,
% 3.12/3.39 (b(z, s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1214, 28782])).
% 3.12/3.39 tff(28784,plain,
% 3.12/3.39 (~b(s(s(s(z))), s(elem!1))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[19710, 28783, 1421, 394])).
% 3.12/3.39 tff(28785,plain,
% 3.12/3.39 (r(s(s(s(z))), s(elem!1))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1816, 28784, 28342])).
% 3.12/3.39 tff(28786,plain,
% 3.12/3.39 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[13333, 28785, 28508])).
% 3.12/3.39 tff(28787,plain,
% 3.12/3.39 (r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[16344, 28492])).
% 3.12/3.39 tff(28788,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28789,plain,
% 3.12/3.39 (((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28790,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28789])).
% 3.12/3.39 tff(28791,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.12/3.39 inference(transitivity,[status(thm)],[28790, 28788])).
% 3.12/3.39 tff(28792,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~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))))),
% 3.12/3.39 inference(quant_inst,[status(thm)],[])).
% 3.12/3.39 tff(28793,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28792, 28791])).
% 3.12/3.39 tff(28794,plain,
% 3.12/3.39 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28793, 121, 572, 2327, 5499])).
% 3.12/3.39 tff(28795,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28794, 28787])).
% 3.12/3.39 tff(28796,plain,((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28797,plain,
% 3.12/3.39 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28796, 28786, 572, 601, 2327])).
% 3.12/3.39 tff(28798,plain,
% 3.12/3.39 (b(elem!1, z)),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28259, 28761])).
% 3.12/3.39 tff(28799,plain,
% 3.12/3.39 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[15227, 28785, 108, 1639, 448, 28798])).
% 3.12/3.39 tff(28800,plain,
% 3.12/3.39 (r(elem!1, s(s(s(s(s(z))))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1847, 28799, 28455])).
% 3.12/3.39 tff(28801,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[16341, 28800, 28797, 3891])).
% 3.12/3.39 tff(28802,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28803,plain,
% 3.12/3.39 (~r(s(s(s(z))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28802, 28213, 601, 28781, 28779, 28769, 28477, 28713, 110])).
% 3.12/3.39 tff(28804,plain,
% 3.12/3.39 (b(s(s(s(z))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2325, 28803])).
% 3.12/3.39 tff(28805,plain,
% 3.12/3.39 (~(s(elem!1) = s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2035, 28342])).
% 3.12/3.39 tff(28806,plain,
% 3.12/3.39 (~b(s(s(s(z))), elem!1)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1334, 1307, 1326, 261])).
% 3.12/3.39 tff(28807,plain,
% 3.12/3.39 (r(s(s(s(z))), elem!1)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[255, 28806, 907])).
% 3.12/3.39 tff(28808,plain,
% 3.12/3.39 (~b(s(elem!1), s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2029, 1307, 394, 222])).
% 3.12/3.39 tff(28809,plain,
% 3.12/3.39 (r(s(elem!1), s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2044, 28808, 2037])).
% 3.12/3.39 tff(28810,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[3445, 28809, 28807, 431, 108])).
% 3.12/3.39 tff(28811,plain,((~b(z, s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28812,plain,
% 3.12/3.39 (~b(z, s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28811, 28711, 28781, 28805, 28220, 28713, 28804, 28472, 28762])).
% 3.12/3.39 tff(28813,plain,
% 3.12/3.39 (r(z, s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1214, 28812])).
% 3.12/3.39 tff(28814,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28815,plain,
% 3.12/3.39 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(rewrite,[status(thm)],[])).
% 3.12/3.39 tff(28816,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28815])).
% 3.12/3.39 tff(28817,plain,
% 3.12/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(transitivity,[status(thm)],[28816, 28814])).
% 3.12/3.39 tff(28818,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.12/3.39 inference(quant_inst,[status(thm)],[])).
% 3.12/3.39 tff(28819,plain,
% 3.12/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28818, 28817])).
% 3.12/3.39 tff(28820,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28819, 121, 110, 28813, 28759, 28724])).
% 3.12/3.39 tff(28821,plain,(b(s(z), elem!1) | (~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (s(elem!1) = s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28822,plain,
% 3.12/3.39 (b(s(z), elem!1)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28821, 220, 601, 110, 2065, 422, 331])).
% 3.12/3.39 tff(28823,plain,
% 3.12/3.39 (b(s(z), s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[19692, 260, 25718])).
% 3.12/3.39 tff(28824,plain,
% 3.12/3.39 (r(s(s(s(elem!1))), z)),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[412, 28511])).
% 3.12/3.39 tff(28825,plain,
% 3.12/3.39 (~r(elem!1, s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[15784, 1140, 110, 1409])).
% 3.12/3.39 tff(28826,plain,
% 3.12/3.39 (~r(s(s(s(elem!1))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[12809, 28825, 25718])).
% 3.12/3.39 tff(28827,plain,
% 3.12/3.39 (b(s(s(s(elem!1))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[16580, 28826])).
% 3.12/3.39 tff(28828,plain,
% 3.12/3.39 (~r(s(s(s(z))), elem!1)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[3375, 1140, 110, 108])).
% 3.12/3.39 tff(28829,plain,
% 3.12/3.39 (b(s(s(s(z))), elem!1)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[255, 28828, 28220])).
% 3.12/3.39 tff(28830,plain,
% 3.12/3.39 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[257, 28282])).
% 3.12/3.39 tff(28831,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2066, 28830])).
% 3.12/3.39 tff(28832,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28833,plain,
% 3.12/3.39 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28832, 28829, 601])).
% 3.12/3.39 tff(28834,plain,
% 3.12/3.39 ($false),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2081, 28833, 28827, 750, 28281])).
% 3.12/3.39 tff(28835,plain,((~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.39 tff(28836,plain,
% 3.12/3.39 (~r(z, s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[28835, 108, 601, 110, 28823, 1409])).
% 3.12/3.39 tff(28837,plain,
% 3.12/3.39 (b(z, s(s(s(z))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1214, 28836])).
% 3.12/3.39 tff(28838,plain,
% 3.12/3.39 (~b(s(s(s(z))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[24799, 28837, 220, 260])).
% 3.12/3.39 tff(28839,plain,
% 3.12/3.39 (r(s(s(s(z))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2325, 28838])).
% 3.12/3.39 tff(28840,plain,
% 3.12/3.39 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[601])).
% 3.12/3.39 tff(28841,plain,
% 3.12/3.39 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 3.12/3.39 inference(symmetry,[status(thm)],[28840])).
% 3.12/3.39 tff(28842,plain,
% 3.12/3.39 (b(s(z), s(s(elem!1)))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[28823, 28841])).
% 3.12/3.39 tff(28843,plain,
% 3.12/3.39 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[25701])).
% 3.12/3.39 tff(28844,plain,
% 3.12/3.39 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 3.12/3.39 inference(symmetry,[status(thm)],[28843])).
% 3.12/3.39 tff(28845,plain,
% 3.12/3.39 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28844])).
% 3.12/3.39 tff(28846,plain,
% 3.12/3.39 (~r(s(s(s(elem!1))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[12809, 293, 25718])).
% 3.12/3.39 tff(28847,plain,
% 3.12/3.39 (b(s(s(s(elem!1))), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[16580, 28846])).
% 3.12/3.39 tff(28848,plain,
% 3.12/3.39 (b(s(z), s(s(elem!1)))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[750, 28841])).
% 3.12/3.39 tff(28849,plain,
% 3.12/3.39 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 3.12/3.39 inference(transitivity,[status(thm)],[28199, 1218])).
% 3.12/3.39 tff(28850,plain,
% 3.12/3.39 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[28849])).
% 3.12/3.39 tff(28851,plain,
% 3.12/3.39 (~(elem!1 = s(z))),
% 3.12/3.39 inference(modus_ponens,[status(thm)],[61, 28850])).
% 3.12/3.39 tff(28852,plain,
% 3.12/3.39 (b(elem!1, s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[299, 293, 28851])).
% 3.12/3.39 tff(28853,plain,
% 3.12/3.39 (~b(z, elem!1)),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[16645, 28852, 220, 28848])).
% 3.12/3.39 tff(28854,plain,
% 3.12/3.39 (~b(z, s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[13207, 28853, 28225])).
% 3.12/3.39 tff(28855,plain,
% 3.12/3.39 (r(z, s(s(s(elem!1))))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[19736, 28854])).
% 3.12/3.39 tff(28856,plain,
% 3.12/3.39 (~r(s(s(elem!1)), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[12129, 293, 3891])).
% 3.12/3.39 tff(28857,plain,
% 3.12/3.39 (b(s(s(elem!1)), s(z))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[2143, 28856])).
% 3.12/3.39 tff(28858,plain,
% 3.12/3.39 (b(s(s(s(z))), s(elem!1))),
% 3.12/3.39 inference(unit_resolution,[status(thm)],[1816, 1510, 28342])).
% 3.12/3.39 tff(28859,plain,
% 3.12/3.39 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.39 inference(monotonicity,[status(thm)],[601])).
% 3.12/3.39 tff(28860,plain,
% 3.12/3.40 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.12/3.40 inference(symmetry,[status(thm)],[28859])).
% 3.12/3.40 tff(28861,plain,
% 3.12/3.40 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[23458, 1510, 3890])).
% 3.12/3.40 tff(28862,plain,
% 3.12/3.40 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[2071, 28861, 2065])).
% 3.12/3.40 tff(28863,plain,
% 3.12/3.40 (b(s(s(s(z))), s(s(elem!1)))),
% 3.12/3.40 inference(modus_ponens,[status(thm)],[28862, 28860])).
% 3.12/3.40 tff(28864,plain,
% 3.12/3.40 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.40 inference(monotonicity,[status(thm)],[2590])).
% 3.12/3.40 tff(28865,plain,
% 3.12/3.40 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.40 inference(monotonicity,[status(thm)],[2590])).
% 3.12/3.40 tff(28866,plain,
% 3.12/3.40 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.12/3.40 inference(modus_ponens,[status(thm)],[831, 28865])).
% 3.12/3.40 tff(28867,plain,
% 3.12/3.40 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.12/3.40 inference(monotonicity,[status(thm)],[5456])).
% 3.12/3.40 tff(28868,plain,
% 3.12/3.40 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.12/3.40 inference(symmetry,[status(thm)],[28867])).
% 3.12/3.40 tff(28869,plain,
% 3.12/3.40 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.12/3.40 inference(modus_ponens,[status(thm)],[831, 28868])).
% 3.12/3.40 tff(28870,plain,
% 3.12/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.40 inference(rewrite,[status(thm)],[])).
% 3.12/3.40 tff(28871,plain,
% 3.12/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.12/3.40 inference(quant_inst,[status(thm)],[])).
% 3.12/3.40 tff(28872,plain,
% 3.12/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.12/3.40 inference(modus_ponens,[status(thm)],[28871, 28870])).
% 3.12/3.40 tff(28873,plain,
% 3.12/3.40 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[28872, 271, 1723, 2448, 981])).
% 3.12/3.40 tff(28874,plain,
% 3.12/3.40 ($false),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[28873, 28869])).
% 3.12/3.40 tff(28875,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.12/3.40 tff(28876,plain,
% 3.12/3.40 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[28875, 831, 2470, 981, 2448])).
% 3.12/3.40 tff(28877,plain,
% 3.12/3.40 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[1733, 28876])).
% 3.12/3.40 tff(28878,plain,
% 3.12/3.40 (~r(s(z), s(s(s(s(s(z))))))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[1744, 28877, 110, 1661])).
% 3.12/3.40 tff(28879,plain,
% 3.12/3.40 (b(s(z), s(s(s(s(s(z))))))),
% 3.12/3.40 inference(unit_resolution,[status(thm)],[1756, 28878])).
% 3.12/3.40 tff(28880,plain,
% 3.12/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.12/3.40 inference(rewrite,[status(thm)],[])).
% 3.12/3.40 tff(28881,plain,
% 3.12/3.40 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28882,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.40 inference(monotonicity,[status(thm)],[28881])).
% 3.22/3.40 tff(28883,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.40 inference(transitivity,[status(thm)],[28882, 28880])).
% 3.22/3.40 tff(28884,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28885,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28884, 28883])).
% 3.22/3.40 tff(28886,plain,
% 3.22/3.40 ($false),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28885, 271, 750, 503, 28879, 28866])).
% 3.22/3.40 tff(28887,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.40 tff(28888,plain,
% 3.22/3.40 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28887, 1661, 503, 2505, 110, 750, 2470, 981, 2448])).
% 3.22/3.40 tff(28889,plain,
% 3.22/3.40 (r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[840, 28888, 4997])).
% 3.22/3.40 tff(28890,plain,
% 3.22/3.40 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28889, 28864])).
% 3.22/3.40 tff(28891,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28892,plain,
% 3.22/3.40 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28893,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.40 inference(monotonicity,[status(thm)],[28892])).
% 3.22/3.40 tff(28894,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.40 inference(transitivity,[status(thm)],[28893, 28891])).
% 3.22/3.40 tff(28895,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28896,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28895, 28894])).
% 3.22/3.40 tff(28897,plain,
% 3.22/3.40 ($false),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28896, 121, 111, 1661, 6842, 28890])).
% 3.22/3.40 tff(28898,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.40 tff(28899,plain,
% 3.22/3.40 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28898, 28863, 6842, 25718, 28215, 503, 110, 750, 3891, 981, 111])).
% 3.22/3.40 tff(28900,plain,
% 3.22/3.40 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1658, 28899])).
% 3.22/3.40 tff(28901,plain,
% 3.22/3.40 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[6049, 28900, 1307, 28858])).
% 3.22/3.40 tff(28902,plain,
% 3.22/3.40 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1733, 28901])).
% 3.22/3.40 tff(28903,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28904,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28905,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~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)))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28904, 28903])).
% 3.22/3.40 tff(28906,plain,
% 3.22/3.40 (~r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28905, 121, 28902, 2327, 108])).
% 3.22/3.40 tff(28907,plain,
% 3.22/3.40 (b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1682, 28906])).
% 3.22/3.40 tff(28908,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28909,plain,
% 3.22/3.40 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28910,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.22/3.40 inference(monotonicity,[status(thm)],[28909])).
% 3.22/3.40 tff(28911,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(transitivity,[status(thm)],[28910, 28908])).
% 3.22/3.40 tff(28912,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28913,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28912, 28911])).
% 3.22/3.40 tff(28914,plain,
% 3.22/3.40 ($false),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28913, 271, 750, 220, 28900, 28907])).
% 3.22/3.40 tff(28915,plain,(r(s(s(s(z))), s(elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.40 tff(28916,plain,
% 3.22/3.40 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28915, 28847, 220, 2327, 108, 1307, 6842, 750, 110, 28857, 28855, 601, 2065])).
% 3.22/3.40 tff(28917,plain,
% 3.22/3.40 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[13333, 28916, 28508])).
% 3.22/3.40 tff(28918,plain,
% 3.22/3.40 (r(s(s(s(z))), elem!1)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[19994, 28917, 25718])).
% 3.22/3.40 tff(28919,plain,
% 3.22/3.40 (~r(s(s(s(z))), z)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[129, 28855, 110, 108])).
% 3.22/3.40 tff(28920,plain,
% 3.22/3.40 (b(s(s(s(z))), z)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1155, 28919])).
% 3.22/3.40 tff(28921,plain,
% 3.22/3.40 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[4072, 1723, 1935, 1639])).
% 3.22/3.40 tff(28922,plain,
% 3.22/3.40 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1494, 28921])).
% 3.22/3.40 tff(28923,plain,
% 3.22/3.40 (~r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[18909, 28922, 3061, 108])).
% 3.22/3.40 tff(28924,plain,
% 3.22/3.40 (b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1754, 21, 28923, 1749])).
% 3.22/3.40 tff(28925,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28926,plain,
% 3.22/3.40 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28927,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.22/3.40 inference(monotonicity,[status(thm)],[28926])).
% 3.22/3.40 tff(28928,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(transitivity,[status(thm)],[28927, 28925])).
% 3.22/3.40 tff(28929,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28930,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28929, 28928])).
% 3.22/3.40 tff(28931,plain,
% 3.22/3.40 ($false),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28930, 271, 220, 1639, 1723, 28924])).
% 3.22/3.40 tff(28932,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.40 tff(28933,plain,
% 3.22/3.40 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28932, 108, 1639, 3061, 220, 1935])).
% 3.22/3.40 tff(28934,plain,
% 3.22/3.40 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1733, 28933])).
% 3.22/3.40 tff(28935,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28936,plain,
% 3.22/3.40 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28937,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.22/3.40 inference(monotonicity,[status(thm)],[28936])).
% 3.22/3.40 tff(28938,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(transitivity,[status(thm)],[28937, 28935])).
% 3.22/3.40 tff(28939,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28940,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28939, 28938])).
% 3.22/3.40 tff(28941,plain,
% 3.22/3.40 (~r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28940, 121, 145, 28934, 108])).
% 3.22/3.40 tff(28942,plain,
% 3.22/3.40 (b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1754, 21, 28941, 1749])).
% 3.22/3.40 tff(28943,plain,
% 3.22/3.40 (~r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[23750, 28934, 145, 108])).
% 3.22/3.40 tff(28944,plain,
% 3.22/3.40 (b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[1682, 28943])).
% 3.22/3.40 tff(28945,plain,
% 3.22/3.40 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(rewrite,[status(thm)],[])).
% 3.22/3.40 tff(28946,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.22/3.40 inference(monotonicity,[status(thm)],[28945])).
% 3.22/3.40 tff(28947,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(transitivity,[status(thm)],[28946, 17852])).
% 3.22/3.40 tff(28948,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.40 inference(quant_inst,[status(thm)],[])).
% 3.22/3.40 tff(28949,plain,
% 3.22/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28948, 28947])).
% 3.22/3.40 tff(28950,plain,
% 3.22/3.40 ($false),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28949, 271, 220, 1639, 28944, 28942])).
% 3.22/3.40 tff(28951,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.40 tff(28952,plain,
% 3.22/3.40 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[28951, 1639, 220, 1935, 145, 108])).
% 3.22/3.40 tff(28953,plain,
% 3.22/3.40 (b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.40 inference(unit_resolution,[status(thm)],[840, 28952, 4997])).
% 3.22/3.40 tff(28954,plain,
% 3.22/3.40 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.40 inference(modus_ponens,[status(thm)],[28953, 28865])).
% 3.22/3.40 tff(28955,plain,
% 3.22/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(28956,plain,
% 3.22/3.41 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(28957,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[28956])).
% 3.22/3.41 tff(28958,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(transitivity,[status(thm)],[28957, 28955])).
% 3.22/3.41 tff(28959,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.22/3.41 inference(quant_inst,[status(thm)],[])).
% 3.22/3.41 tff(28960,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[28959, 28958])).
% 3.22/3.41 tff(28961,plain,
% 3.22/3.41 (~b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28960, 271, 750, 503, 28954])).
% 3.22/3.41 tff(28962,plain,
% 3.22/3.41 (r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1682, 28961])).
% 3.22/3.41 tff(28963,plain,
% 3.22/3.41 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[23750, 28962, 108, 145])).
% 3.22/3.41 tff(28964,plain,
% 3.22/3.41 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1733, 28963])).
% 3.22/3.41 tff(28965,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z))))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(28966,plain,
% 3.22/3.41 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(28967,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z)))))))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[28966])).
% 3.22/3.41 tff(28968,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z))))))))),
% 3.22/3.41 inference(transitivity,[status(thm)],[28967, 28965])).
% 3.22/3.41 tff(28969,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.41 inference(quant_inst,[status(thm)],[])).
% 3.22/3.41 tff(28970,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[28969, 28968])).
% 3.22/3.41 tff(28971,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28970, 271, 1307, 1639, 28964, 1935])).
% 3.22/3.41 tff(28972,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(28973,plain,
% 3.22/3.41 (~b(z, s(s(s(s(s(z))))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28972, 28920, 1307, 108, 28918, 750, 28847, 25718, 28215, 220])).
% 3.22/3.41 tff(28974,plain,
% 3.22/3.41 (r(z, s(s(s(s(s(z))))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1658, 28973])).
% 3.22/3.41 tff(28975,plain,
% 3.22/3.41 (~b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28885, 271, 750, 503, 15718])).
% 3.22/3.41 tff(28976,plain,
% 3.22/3.41 (r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1756, 28975])).
% 3.22/3.41 tff(28977,plain,
% 3.22/3.41 (~b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28960, 271, 750, 503, 15718])).
% 3.22/3.41 tff(28978,plain,
% 3.22/3.41 (r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1682, 28977])).
% 3.22/3.41 tff(28979,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28610, 121, 110, 1661, 28978, 28976])).
% 3.22/3.41 tff(28980,plain,((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(28981,plain,
% 3.22/3.41 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28980, 28974, 110, 750, 28847])).
% 3.22/3.41 tff(28982,plain,
% 3.22/3.41 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[28981, 28845])).
% 3.22/3.41 tff(28983,plain,
% 3.22/3.41 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[4138, 28982, 28482])).
% 3.22/3.41 tff(28984,plain,
% 3.22/3.41 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[17429, 28983, 3891])).
% 3.22/3.41 tff(28985,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28896, 121, 28855, 28974, 6842, 28984])).
% 3.22/3.41 tff(28986,plain,(r(elem!1, s(z)) | (~r(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(28987,plain,
% 3.22/3.41 (r(elem!1, s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28986, 28837, 601, 110, 28823, 6842, 108, 220, 28839, 2065])).
% 3.22/3.41 tff(28988,plain,
% 3.22/3.41 (~r(z, s(s(elem!1)))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[15629, 28987, 110, 1409])).
% 3.22/3.41 tff(28989,plain,
% 3.22/3.41 (b(z, s(s(elem!1)))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2106, 28988])).
% 3.22/3.41 tff(28990,plain,
% 3.22/3.41 (~b(s(s(elem!1)), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12176, 28989, 220, 28842])).
% 3.22/3.41 tff(28991,plain,
% 3.22/3.41 (r(s(s(elem!1)), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2143, 28990])).
% 3.22/3.41 tff(28992,plain,
% 3.22/3.41 (r(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28239, 28991, 609])).
% 3.22/3.41 tff(28993,plain,
% 3.22/3.41 (~r(elem!1, s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[24792, 28987, 28839, 108])).
% 3.22/3.41 tff(28994,plain,
% 3.22/3.41 (b(elem!1, s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1192, 28993, 28221])).
% 3.22/3.41 tff(28995,plain,
% 3.22/3.41 (~r(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[8902, 28987, 110, 1409])).
% 3.22/3.41 tff(28996,plain,
% 3.22/3.41 (b(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[355, 28995, 331])).
% 3.22/3.41 tff(28997,plain,
% 3.22/3.41 (~b(s(s(s(z))), elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2020, 28996, 28837, 28994])).
% 3.22/3.41 tff(28998,plain,
% 3.22/3.41 (r(s(s(s(z))), elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[255, 28997, 28220])).
% 3.22/3.41 tff(28999,plain,
% 3.22/3.41 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.41 tff(29000,plain,
% 3.22/3.41 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[145, 28999])).
% 3.22/3.41 tff(29001,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[906, 29000])).
% 3.22/3.41 tff(29002,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29003,plain,
% 3.22/3.41 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29002, 28998, 601])).
% 3.22/3.41 tff(29004,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(29005,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(quant_inst,[status(thm)],[])).
% 3.22/3.41 tff(29006,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[29005, 29004])).
% 3.22/3.41 tff(29007,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29006, 121, 110, 12761, 2327, 5499])).
% 3.22/3.41 tff(29008,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29009,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29008, 29003, 28992, 110, 28839])).
% 3.22/3.41 tff(29010,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (z = elem!1) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29011,plain,
% 3.22/3.41 (~r(s(z), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29010, 28513, 601, 220, 331, 110, 28824, 2065, 260])).
% 3.22/3.41 tff(29012,plain,
% 3.22/3.41 (b(s(z), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[105, 29011])).
% 3.22/3.41 tff(29013,plain,
% 3.22/3.41 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[2590])).
% 3.22/3.41 tff(29014,plain,
% 3.22/3.41 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 3.22/3.41 inference(symmetry,[status(thm)],[29013])).
% 3.22/3.41 tff(29015,plain,
% 3.22/3.41 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 3.22/3.41 inference(transitivity,[status(thm)],[29014, 1218])).
% 3.22/3.41 tff(29016,plain,
% 3.22/3.41 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29015])).
% 3.22/3.41 tff(29017,plain,
% 3.22/3.41 (~(elem!1 = s(z))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[61, 29016])).
% 3.22/3.41 tff(29018,plain,
% 3.22/3.41 (b(elem!1, s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[299, 28825, 29017])).
% 3.22/3.41 tff(29019,plain,
% 3.22/3.41 (~b(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[11002, 29018, 220, 3871])).
% 3.22/3.41 tff(29020,plain,
% 3.22/3.41 (r(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[355, 29019, 331])).
% 3.22/3.41 tff(29021,plain,
% 3.22/3.41 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12809, 28825, 2505])).
% 3.22/3.41 tff(29022,plain,
% 3.22/3.41 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[16580, 29021])).
% 3.22/3.41 tff(29023,plain,
% 3.22/3.41 (r(s(s(s(z))), elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[10250, 29022, 147, 3871, 260, 29018])).
% 3.22/3.41 tff(29024,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[19871, 29023, 29020, 1409, 1140])).
% 3.22/3.41 tff(29025,plain,((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (z = elem!1) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29026,plain,
% 3.22/3.41 (~r(z, s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29025, 28513, 147, 29012, 260, 331, 220, 25718, 110])).
% 3.22/3.41 tff(29027,plain,
% 3.22/3.41 (b(z, s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1214, 29026])).
% 3.22/3.41 tff(29028,plain,
% 3.22/3.41 (~b(s(s(s(z))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[15813, 29027, 220, 29012])).
% 3.22/3.41 tff(29029,plain,
% 3.22/3.41 (r(s(s(s(z))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2325, 29028])).
% 3.22/3.41 tff(29030,plain,
% 3.22/3.41 (r(elem!1, s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12809, 12761, 25718])).
% 3.22/3.41 tff(29031,plain,
% 3.22/3.41 (~r(elem!1, s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[16082, 29030, 110, 2327])).
% 3.22/3.41 tff(29032,plain,
% 3.22/3.41 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29008, 12761, 110, 2327])).
% 3.22/3.41 tff(29033,plain,
% 3.22/3.41 (~r(s(s(s(z))), elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29002, 29032, 601])).
% 3.22/3.41 tff(29034,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[10306, 29033, 29031, 25718, 260, 2065, 3871])).
% 3.22/3.41 tff(29035,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29036,plain,
% 3.22/3.41 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29035, 29012, 2065, 260, 601, 110, 29029])).
% 3.22/3.41 tff(29037,plain,
% 3.22/3.41 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[16580, 29036])).
% 3.22/3.41 tff(29038,plain,
% 3.22/3.41 (~b(z, s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[17333, 29037, 220, 28823])).
% 3.22/3.41 tff(29039,plain,
% 3.22/3.41 (r(z, s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[19736, 29038])).
% 3.22/3.41 tff(29040,plain,
% 3.22/3.41 (r(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[11073, 29039, 25718])).
% 3.22/3.41 tff(29041,plain,
% 3.22/3.41 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12484, 29037, 28823, 29012])).
% 3.22/3.41 tff(29042,plain,
% 3.22/3.41 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2071, 29041, 2065])).
% 3.22/3.41 tff(29043,plain,
% 3.22/3.41 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[23458, 29042, 3890])).
% 3.22/3.41 tff(29044,plain,
% 3.22/3.41 (~r(s(s(s(z))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[3650, 29043, 412, 29040])).
% 3.22/3.41 tff(29045,plain,
% 3.22/3.41 (b(s(s(s(z))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1155, 29044])).
% 3.22/3.41 tff(29046,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[10270, 271, 220, 29027, 29012, 29045])).
% 3.22/3.41 tff(29047,plain,((~r(s(elem!1), z)) | (~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | r(s(s(s(elem!1))), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29048,plain,
% 3.22/3.41 (~r(s(elem!1), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29047, 220, 2065, 28822, 601, 110, 147, 331])).
% 3.22/3.41 tff(29049,plain,
% 3.22/3.41 (b(s(elem!1), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[409, 29048])).
% 3.22/3.41 tff(29050,plain,
% 3.22/3.41 (b(s(s(s(elem!1))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12308, 29049, 3891])).
% 3.22/3.41 tff(29051,plain,
% 3.22/3.41 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[19692, 28822, 25718])).
% 3.22/3.41 tff(29052,plain,
% 3.22/3.41 (~b(s(elem!1), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[8926, 29049, 220, 28822])).
% 3.22/3.41 tff(29053,plain,
% 3.22/3.41 (~b(s(s(elem!1)), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28247, 29052, 609])).
% 3.22/3.41 tff(29054,plain,
% 3.22/3.41 (r(s(s(elem!1)), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2143, 29053])).
% 3.22/3.41 tff(29055,plain,
% 3.22/3.41 (r(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28239, 29054, 609])).
% 3.22/3.41 tff(29056,plain,
% 3.22/3.41 (b(elem!1, z)),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[29050, 28761])).
% 3.22/3.41 tff(29057,plain,
% 3.22/3.41 (~b(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12145, 29056, 220, 28822])).
% 3.22/3.41 tff(29058,plain,
% 3.22/3.41 (r(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[355, 29057, 331])).
% 3.22/3.41 tff(29059,plain,
% 3.22/3.41 (~b(z, s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[13207, 29057, 28225])).
% 3.22/3.41 tff(29060,plain,
% 3.22/3.41 (r(z, s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[19736, 29059])).
% 3.22/3.41 tff(29061,plain,
% 3.22/3.41 (~r(s(z), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28403, 29060, 601, 220, 110, 29049, 29058])).
% 3.22/3.41 tff(29062,plain,
% 3.22/3.41 (b(s(z), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[105, 29061])).
% 3.22/3.41 tff(29063,plain,
% 3.22/3.41 (~r(s(s(s(z))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29035, 29062, 2065, 28822, 601, 110, 29055])).
% 3.22/3.41 tff(29064,plain,
% 3.22/3.41 (b(s(s(s(z))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2325, 29063])).
% 3.22/3.41 tff(29065,plain,
% 3.22/3.41 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[14970, 29064, 29051, 29050])).
% 3.22/3.41 tff(29066,plain,
% 3.22/3.41 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2071, 29065, 2065])).
% 3.22/3.41 tff(29067,plain,
% 3.22/3.41 (b(s(z), s(s(elem!1)))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[29051, 28841])).
% 3.22/3.41 tff(29068,plain,
% 3.22/3.41 (~b(s(s(s(z))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[17276, 29064, 220, 29067])).
% 3.22/3.41 tff(29069,plain,
% 3.22/3.41 (r(s(s(s(z))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1155, 29068])).
% 3.22/3.41 tff(29070,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(29071,plain,
% 3.22/3.41 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(29072,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29071])).
% 3.22/3.41 tff(29073,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.22/3.41 inference(transitivity,[status(thm)],[29072, 29070])).
% 3.22/3.41 tff(29074,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 3.22/3.41 inference(quant_inst,[status(thm)],[])).
% 3.22/3.41 tff(29075,plain,
% 3.22/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[29074, 29073])).
% 3.22/3.41 tff(29076,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29075, 121, 29060, 29055, 29069, 29066])).
% 3.22/3.41 tff(29077,plain,((~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (z = elem!1) | r(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29078,plain,
% 3.22/3.41 (~b(z, s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29077, 28190, 2065, 26, 331, 147, 422])).
% 3.22/3.41 tff(29079,plain,
% 3.22/3.41 (r(z, s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[904, 29078])).
% 3.22/3.41 tff(29080,plain,
% 3.22/3.41 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.22/3.41 inference(transitivity,[status(thm)],[28333, 28217])).
% 3.22/3.41 tff(29081,plain,
% 3.22/3.41 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[601])).
% 3.22/3.41 tff(29082,plain,
% 3.22/3.41 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(elem!1)))),
% 3.22/3.41 inference(symmetry,[status(thm)],[29081])).
% 3.22/3.41 tff(29083,plain,
% 3.22/3.41 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.41 tff(29084,plain,
% 3.22/3.41 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 3.22/3.41 inference(transitivity,[status(thm)],[29083, 3136])).
% 3.22/3.41 tff(29085,plain,
% 3.22/3.41 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 3.22/3.41 inference(symmetry,[status(thm)],[29084])).
% 3.22/3.41 tff(29086,plain,
% 3.22/3.41 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29085])).
% 3.22/3.41 tff(29087,plain,
% 3.22/3.41 (~(z = elem!1)),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[30, 29086])).
% 3.22/3.41 tff(29088,plain,
% 3.22/3.41 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.41 tff(29089,plain,
% 3.22/3.41 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.22/3.41 inference(symmetry,[status(thm)],[29088])).
% 3.22/3.41 tff(29090,plain,
% 3.22/3.41 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, elem!1))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29089])).
% 3.22/3.41 tff(29091,plain,
% 3.22/3.41 (~b(z, elem!1)),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[33, 29090])).
% 3.22/3.41 tff(29092,plain,
% 3.22/3.41 (r(z, elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[355, 29091, 29087])).
% 3.22/3.41 tff(29093,plain,
% 3.22/3.41 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.41 tff(29094,plain,
% 3.22/3.41 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 3.22/3.41 inference(symmetry,[status(thm)],[29093])).
% 3.22/3.41 tff(29095,plain,
% 3.22/3.41 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29082])).
% 3.22/3.41 tff(29096,plain,
% 3.22/3.41 (~b(z, s(s(elem!1)))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[33, 29095])).
% 3.22/3.41 tff(29097,plain,
% 3.22/3.41 (r(z, s(s(elem!1)))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2106, 29096])).
% 3.22/3.41 tff(29098,plain,
% 3.22/3.41 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 3.22/3.41 inference(transitivity,[status(thm)],[28335, 1218])).
% 3.22/3.41 tff(29099,plain,
% 3.22/3.41 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29098])).
% 3.22/3.41 tff(29100,plain,
% 3.22/3.41 (~(elem!1 = s(z))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[61, 29099])).
% 3.22/3.41 tff(29101,plain,
% 3.22/3.41 (b(elem!1, s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[299, 8335, 29100])).
% 3.22/3.41 tff(29102,plain,
% 3.22/3.41 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[12779, 111, 110, 909])).
% 3.22/3.41 tff(29103,plain,
% 3.22/3.41 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[16580, 29102])).
% 3.22/3.41 tff(29104,plain,
% 3.22/3.41 (b(s(z), elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[2562, 750, 25718])).
% 3.22/3.41 tff(29105,plain,
% 3.22/3.41 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.41 tff(29106,plain,
% 3.22/3.41 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.22/3.41 inference(symmetry,[status(thm)],[29105])).
% 3.22/3.41 tff(29107,plain,
% 3.22/3.41 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29106])).
% 3.22/3.41 tff(29108,plain,
% 3.22/3.41 (~r(s(s(s(elem!1))), elem!1)),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[179, 29107])).
% 3.22/3.41 tff(29109,plain,
% 3.22/3.41 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.41 tff(29110,plain,
% 3.22/3.41 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 3.22/3.41 inference(symmetry,[status(thm)],[29109])).
% 3.22/3.41 tff(29111,plain,
% 3.22/3.41 (r(s(elem!1), z) <=> r(elem!1, z)),
% 3.22/3.41 inference(transitivity,[status(thm)],[28511, 29110])).
% 3.22/3.41 tff(29112,plain,
% 3.22/3.41 (r(elem!1, z)),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[412, 29111])).
% 3.22/3.41 tff(29113,plain,
% 3.22/3.41 (~r(s(z), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[129, 109, 110, 111])).
% 3.22/3.41 tff(29114,plain,
% 3.22/3.41 (~r(s(s(s(z))), elem!1)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[15900, 109, 909, 1409])).
% 3.22/3.41 tff(29115,plain,
% 3.22/3.41 (~b(s(z), s(s(s(z))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[10250, 29114, 147, 29103, 448, 260])).
% 3.22/3.41 tff(29116,plain,
% 3.22/3.41 ($false),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[105, 29115, 29113])).
% 3.22/3.41 tff(29117,plain,((~r(s(s(s(z))), z)) | r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.41 tff(29118,plain,
% 3.22/3.41 (~r(s(s(s(z))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[29117, 29112, 29101, 29104, 110, 111, 909, 29108])).
% 3.22/3.41 tff(29119,plain,
% 3.22/3.41 (b(s(s(s(z))), z)),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1155, 29118])).
% 3.22/3.41 tff(29120,plain,
% 3.22/3.41 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[996, 271, 750, 29103, 937])).
% 3.22/3.41 tff(29121,plain,
% 3.22/3.41 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[28738, 29120, 601])).
% 3.22/3.41 tff(29122,plain,
% 3.22/3.41 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[1559, 29121, 28489])).
% 3.22/3.41 tff(29123,plain,
% 3.22/3.41 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[29122, 25731])).
% 3.22/3.41 tff(29124,plain,
% 3.22/3.41 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.41 tff(29125,plain,
% 3.22/3.41 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29124])).
% 3.22/3.41 tff(29126,plain,
% 3.22/3.41 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.22/3.41 inference(modus_ponens,[status(thm)],[28490, 29125])).
% 3.22/3.41 tff(29127,plain,
% 3.22/3.41 (b(s(z), s(s(s(s(z)))))),
% 3.22/3.41 inference(unit_resolution,[status(thm)],[16482, 1035])).
% 3.22/3.41 tff(29128,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(29129,plain,
% 3.22/3.41 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.41 inference(rewrite,[status(thm)],[])).
% 3.22/3.41 tff(29130,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.22/3.41 inference(monotonicity,[status(thm)],[29129])).
% 3.22/3.41 tff(29131,plain,
% 3.22/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.42 inference(transitivity,[status(thm)],[29130, 29128])).
% 3.22/3.42 tff(29132,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.42 inference(quant_inst,[status(thm)],[])).
% 3.22/3.42 tff(29133,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29132, 29131])).
% 3.22/3.42 tff(29134,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29133, 121, 909, 6842, 910, 13550])).
% 3.22/3.42 tff(29135,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29136,plain,
% 3.22/3.42 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29135, 910, 6842, 909])).
% 3.22/3.42 tff(29137,plain,
% 3.22/3.42 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1014, 29136, 1008])).
% 3.22/3.42 tff(29138,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1075, 29137, 29127, 29103, 937])).
% 3.22/3.42 tff(29139,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29140,plain,
% 3.22/3.42 (~r(s(s(s(s(z)))), z)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29139, 937, 29126, 6842, 909, 110, 111])).
% 3.22/3.42 tff(29141,plain,
% 3.22/3.42 (b(s(s(s(s(z)))), z)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1095, 29140])).
% 3.22/3.42 tff(29142,plain,
% 3.22/3.42 (r(s(s(s(z))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[11090, 3871, 110, 231, 378, 147, 2505, 503])).
% 3.22/3.42 tff(29143,plain,
% 3.22/3.42 (~b(elem!1, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[11038, 3871, 1935, 448])).
% 3.22/3.42 tff(29144,plain,
% 3.22/3.42 (r(elem!1, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1192, 29143, 11082])).
% 3.22/3.42 tff(29145,plain,
% 3.22/3.42 (~r(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[6723, 29144, 378, 29142])).
% 3.22/3.42 tff(29146,plain,
% 3.22/3.42 (b(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1214, 29145])).
% 3.22/3.42 tff(29147,plain,
% 3.22/3.42 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28368, 29144, 2203])).
% 3.22/3.42 tff(29148,plain,
% 3.22/3.42 (r(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[13482, 29142, 2470])).
% 3.22/3.42 tff(29149,plain,
% 3.22/3.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[12573, 29148, 2470, 750, 937, 29147])).
% 3.22/3.42 tff(29150,plain,
% 3.22/3.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[10426, 29149])).
% 3.22/3.42 tff(29151,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[13513, 29150, 29146, 1103, 1935])).
% 3.22/3.42 tff(29152,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (s(z) = elem!1) | r(s(s(s(elem!1))), elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29153,plain,
% 3.22/3.42 (~b(s(z), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29152, 29141, 1935, 3891, 750, 937, 28326, 378, 110, 28337, 29108, 25718, 29103, 29101])).
% 3.22/3.42 tff(29154,plain,
% 3.22/3.42 (r(s(z), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[105, 29153])).
% 3.22/3.42 tff(29155,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.42 tff(29156,plain,
% 3.22/3.42 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.42 inference(transitivity,[status(thm)],[28282, 28860])).
% 3.22/3.42 tff(29157,plain,
% 3.22/3.42 (b(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[257, 29156])).
% 3.22/3.42 tff(29158,plain,
% 3.22/3.42 (~r(s(s(elem!1)), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28239, 29102, 609])).
% 3.22/3.42 tff(29159,plain,
% 3.22/3.42 (b(s(s(elem!1)), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[2143, 29158])).
% 3.22/3.42 tff(29160,plain,
% 3.22/3.42 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 3.22/3.42 inference(transitivity,[status(thm)],[29085, 361])).
% 3.22/3.42 tff(29161,plain,
% 3.22/3.42 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[29160])).
% 3.22/3.42 tff(29162,plain,
% 3.22/3.42 (~(elem!1 = z)),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[30, 29161])).
% 3.22/3.42 tff(29163,plain,
% 3.22/3.42 (~b(s(s(s(z))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[305, 257, 29162, 29104, 111, 110, 29100])).
% 3.22/3.42 tff(29164,plain,
% 3.22/3.42 (r(s(s(s(z))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[2325, 29163])).
% 3.22/3.42 tff(29165,plain,
% 3.22/3.42 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.42 inference(symmetry,[status(thm)],[28734])).
% 3.22/3.42 tff(29166,plain,
% 3.22/3.42 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.42 tff(29167,plain,
% 3.22/3.42 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.42 inference(transitivity,[status(thm)],[29166, 29165])).
% 3.22/3.42 tff(29168,plain,
% 3.22/3.42 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[29167])).
% 3.22/3.42 tff(29169,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29170,plain,
% 3.22/3.42 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29171,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[29170])).
% 3.22/3.42 tff(29172,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(transitivity,[status(thm)],[29171, 29169])).
% 3.22/3.42 tff(29173,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(quant_inst,[status(thm)],[])).
% 3.22/3.42 tff(29174,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29173, 29172])).
% 3.22/3.42 tff(29175,plain,
% 3.22/3.42 (~r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29174, 121, 1736, 2327, 108])).
% 3.22/3.42 tff(29176,plain,
% 3.22/3.42 (b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1756, 29175])).
% 3.22/3.42 tff(29177,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[18131, 29176, 448, 937])).
% 3.22/3.42 tff(29178,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29177, 29168])).
% 3.22/3.42 tff(29179,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1559, 29178, 28489])).
% 3.22/3.42 tff(29180,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29179, 25731])).
% 3.22/3.42 tff(29181,plain,
% 3.22/3.42 (~r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28905, 121, 1736, 2327, 108])).
% 3.22/3.42 tff(29182,plain,
% 3.22/3.42 (b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1682, 29181])).
% 3.22/3.42 tff(29183,plain,
% 3.22/3.42 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[7039, 271, 750, 503, 29182])).
% 3.22/3.42 tff(29184,plain,
% 3.22/3.42 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29183, 28845])).
% 3.22/3.42 tff(29185,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[4138, 29184, 28482])).
% 3.22/3.42 tff(29186,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[17429, 29185, 3891])).
% 3.22/3.42 tff(29187,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1785, 29182, 937, 29176])).
% 3.22/3.42 tff(29188,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1777, 29187])).
% 3.22/3.42 tff(29189,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29190,plain,
% 3.22/3.42 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29191,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[29190])).
% 3.22/3.42 tff(29192,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.42 inference(transitivity,[status(thm)],[29191, 29189])).
% 3.22/3.42 tff(29193,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(quant_inst,[status(thm)],[])).
% 3.22/3.42 tff(29194,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29193, 29192])).
% 3.22/3.42 tff(29195,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29194, 121, 29188, 6842, 29186, 29180])).
% 3.22/3.42 tff(29196,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~(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(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29197,plain,
% 3.22/3.42 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29196, 29164, 601, 750, 29103, 448, 937, 6842, 108])).
% 3.22/3.42 tff(29198,plain,
% 3.22/3.42 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1733, 29197])).
% 3.22/3.42 tff(29199,plain,
% 3.22/3.42 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28875, 29198, 3891, 29159, 29157])).
% 3.22/3.42 tff(29200,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[840, 29199, 28215])).
% 3.22/3.42 tff(29201,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29200, 29155])).
% 3.22/3.42 tff(29202,plain,
% 3.22/3.42 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.42 tff(29203,plain,
% 3.22/3.42 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 3.22/3.42 inference(symmetry,[status(thm)],[29202])).
% 3.22/3.42 tff(29204,plain,
% 3.22/3.42 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 3.22/3.42 inference(transitivity,[status(thm)],[28282, 29203])).
% 3.22/3.42 tff(29205,plain,
% 3.22/3.42 (b(s(s(s(z))), s(elem!1))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[257, 29204])).
% 3.22/3.42 tff(29206,plain,
% 3.22/3.42 (~r(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[11100, 29164, 909, 110])).
% 3.22/3.42 tff(29207,plain,
% 3.22/3.42 (b(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1214, 29206])).
% 3.22/3.42 tff(29208,plain,
% 3.22/3.42 (~b(z, s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[6049, 29198, 29207, 29205])).
% 3.22/3.42 tff(29209,plain,
% 3.22/3.42 (r(z, s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1658, 29208])).
% 3.22/3.42 tff(29210,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28896, 121, 111, 29209, 6842, 29201])).
% 3.22/3.42 tff(29211,plain,((~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29212,plain,
% 3.22/3.42 (~b(s(s(s(z))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29211, 937, 6842, 601, 750, 29101, 111, 29154, 909, 110])).
% 3.22/3.42 tff(29213,plain,
% 3.22/3.42 (r(s(s(s(z))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[255, 29212, 28220])).
% 3.22/3.42 tff(29214,plain,
% 3.22/3.42 (~r(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[3375, 29213, 29154, 110])).
% 3.22/3.42 tff(29215,plain,
% 3.22/3.42 (b(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1214, 29214])).
% 3.22/3.42 tff(29216,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[13513, 29215, 29141, 1935])).
% 3.22/3.42 tff(29217,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[10426, 29216])).
% 3.22/3.42 tff(29218,plain,
% 3.22/3.42 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29002, 29213, 601])).
% 3.22/3.42 tff(29219,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29220,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.42 inference(quant_inst,[status(thm)],[])).
% 3.22/3.42 tff(29221,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29220, 29219])).
% 3.22/3.42 tff(29222,plain,
% 3.22/3.42 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29221, 121, 6842, 29218, 29217])).
% 3.22/3.42 tff(29223,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29222, 29123])).
% 3.22/3.42 tff(29224,plain,((~b(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29225,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29224, 28824, 601, 750, 29119, 110, 111, 909, 378])).
% 3.22/3.42 tff(29226,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[932, 29225])).
% 3.22/3.42 tff(29227,plain,
% 3.22/3.42 (~r(s(s(s(s(z)))), z)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[919, 29226, 909, 110])).
% 3.22/3.42 tff(29228,plain,
% 3.22/3.42 (b(s(s(s(s(z)))), z)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1095, 29227])).
% 3.22/3.42 tff(29229,plain,
% 3.22/3.42 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.42 tff(29230,plain,
% 3.22/3.42 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[831, 29229])).
% 3.22/3.42 tff(29231,plain,
% 3.22/3.42 (~b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28960, 271, 750, 503, 29230])).
% 3.22/3.42 tff(29232,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1682, 29231])).
% 3.22/3.42 tff(29233,plain,
% 3.22/3.42 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[25909, 831, 28458])).
% 3.22/3.42 tff(29234,plain,
% 3.22/3.42 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1669, 29232, 110, 909])).
% 3.22/3.42 tff(29235,plain,
% 3.22/3.42 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1658, 29234])).
% 3.22/3.42 tff(29236,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[14589, 29235, 1122, 29233])).
% 3.22/3.42 tff(29237,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1777, 29236])).
% 3.22/3.42 tff(29238,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29239,plain,
% 3.22/3.42 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(rewrite,[status(thm)],[])).
% 3.22/3.42 tff(29240,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.22/3.42 inference(monotonicity,[status(thm)],[29239])).
% 3.22/3.42 tff(29241,plain,
% 3.22/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(transitivity,[status(thm)],[29240, 29238])).
% 3.22/3.42 tff(29242,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.42 inference(quant_inst,[status(thm)],[])).
% 3.22/3.42 tff(29243,plain,
% 3.22/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[29242, 29241])).
% 3.22/3.42 tff(29244,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29243, 121, 110, 29237, 911, 29232])).
% 3.22/3.42 tff(29245,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29246,plain,
% 3.22/3.42 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29245, 29226, 110, 909, 750, 29103, 601])).
% 3.22/3.42 tff(29247,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[840, 29246, 28215])).
% 3.22/3.42 tff(29248,plain,
% 3.22/3.42 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.42 inference(modus_ponens,[status(thm)],[3061, 29155])).
% 3.22/3.42 tff(29249,plain,
% 3.22/3.42 (~b(s(s(s(z))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[305, 5469, 259, 260, 111, 110, 258])).
% 3.22/3.42 tff(29250,plain,
% 3.22/3.42 (r(s(s(s(z))), s(z))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[2325, 29249])).
% 3.22/3.42 tff(29251,plain,
% 3.22/3.42 (~b(s(z), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[10250, 221, 147, 503, 448, 260])).
% 3.22/3.42 tff(29252,plain,
% 3.22/3.42 (r(s(z), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[105, 29251])).
% 3.22/3.42 tff(29253,plain,
% 3.22/3.42 (~r(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[9421, 29252, 110, 29250])).
% 3.22/3.42 tff(29254,plain,
% 3.22/3.42 (b(z, s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1214, 29253])).
% 3.22/3.42 tff(29255,plain,
% 3.22/3.42 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[13513, 29254, 1103, 1935])).
% 3.22/3.42 tff(29256,plain,
% 3.22/3.42 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[10426, 29255])).
% 3.22/3.42 tff(29257,plain,
% 3.22/3.42 ($false),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[12199, 121, 110, 911, 29250, 29256])).
% 3.22/3.42 tff(29258,plain,(r(s(s(s(z))), elem!1) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~b(s(z), elem!1)) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.22/3.42 tff(29259,plain,
% 3.22/3.42 (r(s(s(s(z))), elem!1)),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29258, 1935, 911, 1103, 110, 29162, 260, 111, 29100, 29108, 503, 448, 28220])).
% 3.22/3.42 tff(29260,plain,
% 3.22/3.42 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[29002, 29259, 601])).
% 3.22/3.42 tff(29261,plain,
% 3.22/3.42 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[28896, 121, 111, 6842, 29248])).
% 3.22/3.42 tff(29262,plain,
% 3.22/3.42 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1658, 29261])).
% 3.22/3.42 tff(29263,plain,
% 3.22/3.42 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[3066, 29259, 1409, 3061])).
% 3.22/3.42 tff(29264,plain,
% 3.22/3.42 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1733, 29263])).
% 3.22/3.42 tff(29265,plain,
% 3.22/3.42 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[4072, 29264, 1935, 29262])).
% 3.22/3.42 tff(29266,plain,
% 3.22/3.42 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.42 inference(unit_resolution,[status(thm)],[1494, 29265])).
% 3.22/3.42 tff(29267,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29268,plain,
% 3.22/3.43 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29269,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29268])).
% 3.22/3.43 tff(29270,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29269, 29267])).
% 3.22/3.43 tff(29271,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29272,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29271, 29270])).
% 3.22/3.43 tff(29273,plain,
% 3.22/3.43 ($false),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29272, 121, 29266, 6842, 29260, 29248])).
% 3.22/3.43 tff(29274,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.43 tff(29275,plain,
% 3.22/3.43 ($false),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29274, 29247, 29228, 29112, 28824, 601, 29119, 29226, 110, 29104, 111, 29103, 29101])).
% 3.22/3.43 tff(29276,plain,((~r(s(elem!1), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.43 tff(29277,plain,
% 3.22/3.43 (~r(s(elem!1), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29276, 750, 110, 111, 909, 601, 378])).
% 3.22/3.43 tff(29278,plain,
% 3.22/3.43 (b(s(elem!1), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[409, 29277])).
% 3.22/3.43 tff(29279,plain,
% 3.22/3.43 (b(s(s(s(elem!1))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[12308, 29278, 3891])).
% 3.22/3.43 tff(29280,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29281,plain,
% 3.22/3.43 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29282,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29281])).
% 3.22/3.43 tff(29283,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29282, 29280])).
% 3.22/3.43 tff(29284,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29285,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29284, 29283])).
% 3.22/3.43 tff(29286,plain,
% 3.22/3.43 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29285, 271, 1638, 1122, 12196])).
% 3.22/3.43 tff(29287,plain,
% 3.22/3.43 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1014, 29286, 29126])).
% 3.22/3.43 tff(29288,plain,
% 3.22/3.43 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29245, 911, 110, 909, 750, 29103, 601])).
% 3.22/3.43 tff(29289,plain,
% 3.22/3.43 (r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[840, 29288, 28215])).
% 3.22/3.43 tff(29290,plain,
% 3.22/3.43 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29289, 29155])).
% 3.22/3.43 tff(29291,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29292,plain,
% 3.22/3.43 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29293,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29292])).
% 3.22/3.43 tff(29294,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29293, 29291])).
% 3.22/3.43 tff(29295,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29296,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29295, 29294])).
% 3.22/3.43 tff(29297,plain,
% 3.22/3.43 (~r(s(s(s(s(s(z))))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29296, 121, 111, 29290, 29287])).
% 3.22/3.43 tff(29298,plain,
% 3.22/3.43 (b(s(s(s(s(s(z))))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[6593, 21, 711, 29297])).
% 3.22/3.43 tff(29299,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29300,plain,
% 3.22/3.43 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29301,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(elem!1)))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29300])).
% 3.22/3.43 tff(29302,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(s(s(elem!1))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29301, 29299])).
% 3.22/3.43 tff(29303,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29304,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(s(s(elem!1)))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29303, 29302])).
% 3.22/3.43 tff(29305,plain,
% 3.22/3.43 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29304, 271, 1638, 1122, 12196])).
% 3.22/3.43 tff(29306,plain,
% 3.22/3.43 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[28738, 29305, 601])).
% 3.22/3.43 tff(29307,plain,
% 3.22/3.43 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1559, 29306, 28489])).
% 3.22/3.43 tff(29308,plain,
% 3.22/3.43 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29307, 25731])).
% 3.22/3.43 tff(29309,plain,
% 3.22/3.43 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[28166, 121, 29290, 29287])).
% 3.22/3.43 tff(29310,plain,
% 3.22/3.43 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29309, 29308])).
% 3.22/3.43 tff(29311,plain,
% 3.22/3.43 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[9512, 29310])).
% 3.22/3.43 tff(29312,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29313,plain,
% 3.22/3.43 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29314,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29313])).
% 3.22/3.43 tff(29315,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29314, 29312])).
% 3.22/3.43 tff(29316,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29317,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29316, 29315])).
% 3.22/3.43 tff(29318,plain,
% 3.22/3.43 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29317, 121, 111, 29290, 29287])).
% 3.22/3.43 tff(29319,plain,
% 3.22/3.43 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1658, 29318])).
% 3.22/3.43 tff(29320,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29321,plain,
% 3.22/3.43 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29322,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29321])).
% 3.22/3.43 tff(29323,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29322, 29320])).
% 3.22/3.43 tff(29324,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29325,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29324, 29323])).
% 3.22/3.43 tff(29326,plain,
% 3.22/3.43 ($false),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29325, 271, 29319, 29311, 12196, 29298])).
% 3.22/3.43 tff(29327,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.43 tff(29328,plain,
% 3.22/3.43 (~r(s(s(s(s(z)))), s(z))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29327, 29279, 111, 601, 110, 909, 750])).
% 3.22/3.43 tff(29329,plain,
% 3.22/3.43 (b(s(s(s(s(z)))), s(z))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[932, 29328])).
% 3.22/3.43 tff(29330,plain,
% 3.22/3.43 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[996, 271, 750, 29103, 29329])).
% 3.22/3.43 tff(29331,plain,
% 3.22/3.43 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[28738, 29330, 601])).
% 3.22/3.43 tff(29332,plain,
% 3.22/3.43 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1559, 29331, 28489])).
% 3.22/3.43 tff(29333,plain,
% 3.22/3.43 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29332, 25731])).
% 3.22/3.43 tff(29334,plain,
% 3.22/3.43 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1005, 271, 750, 29103, 29329])).
% 3.22/3.43 tff(29335,plain,
% 3.22/3.43 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1014, 29334, 29126])).
% 3.22/3.43 tff(29336,plain,
% 3.22/3.43 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1021, 121, 111, 29335])).
% 3.22/3.43 tff(29337,plain,
% 3.22/3.43 (~r(s(s(s(s(z)))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29336, 29333])).
% 3.22/3.43 tff(29338,plain,
% 3.22/3.43 (b(s(s(s(s(z)))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1095, 29337])).
% 3.22/3.43 tff(29339,plain,
% 3.22/3.43 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.43 tff(29340,plain,
% 3.22/3.43 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29339])).
% 3.22/3.43 tff(29341,plain,
% 3.22/3.43 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[28342, 29340])).
% 3.22/3.43 tff(29342,plain,
% 3.22/3.43 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[12484, 3871, 503, 750])).
% 3.22/3.43 tff(29343,plain,
% 3.22/3.43 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[2071, 29342, 2065])).
% 3.22/3.43 tff(29344,plain,
% 3.22/3.43 (~b(s(s(s(z))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29152, 3871, 937, 2470, 750, 1103, 2203, 378, 110, 231, 147, 2505, 503, 448])).
% 3.22/3.43 tff(29345,plain,
% 3.22/3.43 (r(s(s(s(z))), z)),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[1155, 29344])).
% 3.22/3.43 tff(29346,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29347,plain,
% 3.22/3.43 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(rewrite,[status(thm)],[])).
% 3.22/3.43 tff(29348,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.22/3.43 inference(monotonicity,[status(thm)],[29347])).
% 3.22/3.43 tff(29349,plain,
% 3.22/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.43 inference(transitivity,[status(thm)],[29348, 29346])).
% 3.22/3.43 tff(29350,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 3.22/3.43 inference(quant_inst,[status(thm)],[])).
% 3.22/3.43 tff(29351,plain,
% 3.22/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.22/3.43 inference(modus_ponens,[status(thm)],[29350, 29349])).
% 3.22/3.43 tff(29352,plain,
% 3.22/3.43 ($false),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29351, 121, 111, 29345, 29343, 13550])).
% 3.22/3.43 tff(29353,plain,((~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~(s(elem!1) = elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (s(z) = elem!1) | r(s(s(s(elem!1))), elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.43 tff(29354,plain,
% 3.22/3.43 (~b(s(z), s(s(s(z))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[29353, 29335, 111, 29341, 29329, 3891, 750, 29338, 28326, 378, 110, 28337, 29108, 25718, 29103, 29101])).
% 3.22/3.43 tff(29355,plain,
% 3.22/3.43 (r(s(z), s(s(s(z))))),
% 3.22/3.43 inference(unit_resolution,[status(thm)],[105, 29354])).
% 3.22/3.44 tff(29356,plain,
% 3.22/3.44 (~r(s(s(s(z))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[2096, 29355, 2088, 110])).
% 3.22/3.44 tff(29357,plain,
% 3.22/3.44 (b(s(s(s(z))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1155, 29356])).
% 3.22/3.44 tff(29358,plain,
% 3.22/3.44 (~r(z, s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28320, 29355, 110, 601, 111, 29279])).
% 3.22/3.44 tff(29359,plain,
% 3.22/3.44 (b(z, s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1214, 29358])).
% 3.22/3.44 tff(29360,plain,
% 3.22/3.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[13513, 29359, 29338, 29357])).
% 3.22/3.44 tff(29361,plain,
% 3.22/3.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[10426, 29360])).
% 3.22/3.44 tff(29362,plain,
% 3.22/3.44 (~b(s(s(s(z))), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[8279, 29357, 29278, 29359])).
% 3.22/3.44 tff(29363,plain,
% 3.22/3.44 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1816, 29362, 28342])).
% 3.22/3.44 tff(29364,plain,
% 3.22/3.44 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[13333, 29363, 28508])).
% 3.22/3.44 tff(29365,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29366,plain,
% 3.22/3.44 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29367,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[29366])).
% 3.22/3.44 tff(29368,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.44 inference(transitivity,[status(thm)],[29367, 29365])).
% 3.22/3.44 tff(29369,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.44 inference(quant_inst,[status(thm)],[])).
% 3.22/3.44 tff(29370,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29369, 29368])).
% 3.22/3.44 tff(29371,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29370, 121, 29364, 29361, 29335, 29333])).
% 3.22/3.44 tff(29372,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29373,plain,
% 3.22/3.44 (~b(s(z), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29372, 37, 601, 110, 29097, 29092, 909])).
% 3.22/3.44 tff(29374,plain,
% 3.22/3.44 (r(s(z), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[760, 29373])).
% 3.22/3.44 tff(29375,plain,
% 3.22/3.44 (r(s(z), elem!1)),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29374, 29094])).
% 3.22/3.44 tff(29376,plain,
% 3.22/3.44 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1834, 29375, 110, 29092])).
% 3.22/3.44 tff(29377,plain,
% 3.22/3.44 (b(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1847, 29376, 28455])).
% 3.22/3.44 tff(29378,plain,
% 3.22/3.44 (~r(elem!1, s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1797, 29375, 110, 29092])).
% 3.22/3.44 tff(29379,plain,
% 3.22/3.44 (b(elem!1, s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1192, 29378, 28221])).
% 3.22/3.44 tff(29380,plain,
% 3.22/3.44 (~r(elem!1, s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[4202, 29092, 110, 909])).
% 3.22/3.44 tff(29381,plain,
% 3.22/3.44 (b(elem!1, s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[299, 29380, 29100])).
% 3.22/3.44 tff(29382,plain,
% 3.22/3.44 (r(s(z), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28255, 29374, 609])).
% 3.22/3.44 tff(29383,plain,
% 3.22/3.44 (b(s(elem!1), s(s(s(z))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29379, 29080])).
% 3.22/3.44 tff(29384,plain,
% 3.22/3.44 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[12779, 37, 110, 909])).
% 3.22/3.44 tff(29385,plain,
% 3.22/3.44 (~r(s(s(elem!1)), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28239, 29384, 609])).
% 3.22/3.44 tff(29386,plain,
% 3.22/3.44 (b(s(s(elem!1)), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[2143, 29385])).
% 3.22/3.44 tff(29387,plain,
% 3.22/3.44 (b(s(elem!1), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28247, 29386, 609])).
% 3.22/3.44 tff(29388,plain,
% 3.22/3.44 (b(s(z), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[105, 29113])).
% 3.22/3.44 tff(29389,plain,
% 3.22/3.44 (~r(s(s(s(z))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[10317, 109, 909, 431])).
% 3.22/3.44 tff(29390,plain,
% 3.22/3.44 (b(s(s(s(z))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[2325, 29389])).
% 3.22/3.44 tff(29391,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[3622, 29390, 29388, 447, 3870])).
% 3.22/3.44 tff(29392,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29393,plain,
% 3.22/3.44 (~r(s(s(s(z))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29392, 29387, 29383, 909, 29382, 110, 37])).
% 3.22/3.44 tff(29394,plain,
% 3.22/3.44 (b(s(s(s(z))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1155, 29393])).
% 3.22/3.44 tff(29395,plain,
% 3.22/3.44 (~b(s(z), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[11038, 29394, 29379, 29381])).
% 3.22/3.44 tff(29396,plain,
% 3.22/3.44 (r(s(z), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[105, 29395])).
% 3.22/3.44 tff(29397,plain,
% 3.22/3.44 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[25696])).
% 3.22/3.44 tff(29398,plain,
% 3.22/3.44 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 3.22/3.44 inference(symmetry,[status(thm)],[29397])).
% 3.22/3.44 tff(29399,plain,
% 3.22/3.44 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[29398])).
% 3.22/3.44 tff(29400,plain,
% 3.22/3.44 (~(elem!1 = s(s(s(s(z)))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29126, 29399])).
% 3.22/3.44 tff(29401,plain,
% 3.22/3.44 (~r(elem!1, s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28418, 29375, 110, 29092])).
% 3.22/3.44 tff(29402,plain,
% 3.22/3.44 (b(elem!1, s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[20539, 29401, 29400])).
% 3.22/3.44 tff(29403,plain,
% 3.22/3.44 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28428, 29402, 601])).
% 3.22/3.44 tff(29404,plain,
% 3.22/3.44 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[16580, 29384])).
% 3.22/3.44 tff(29405,plain,
% 3.22/3.44 (~r(s(elem!1), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1300, 29382, 110, 909])).
% 3.22/3.44 tff(29406,plain,
% 3.22/3.44 (b(s(elem!1), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[409, 29405])).
% 3.22/3.44 tff(29407,plain,
% 3.22/3.44 (b(s(s(s(elem!1))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[12308, 29406, 3891])).
% 3.22/3.44 tff(29408,plain,
% 3.22/3.44 (~r(z, s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[9490, 911, 909, 572])).
% 3.22/3.44 tff(29409,plain,
% 3.22/3.44 (b(z, s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1121, 29408])).
% 3.22/3.44 tff(29410,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29285, 271, 1638, 29409, 12196, 1066])).
% 3.22/3.44 tff(29411,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29412,plain,
% 3.22/3.44 (~r(s(s(s(s(z)))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29411, 29407, 29403, 909, 29374, 110])).
% 3.22/3.44 tff(29413,plain,
% 3.22/3.44 (b(s(s(s(s(z)))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[932, 29412])).
% 3.22/3.44 tff(29414,plain,
% 3.22/3.44 (~b(s(z), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1075, 29413, 29404, 29403])).
% 3.22/3.44 tff(29415,plain,
% 3.22/3.44 (r(s(z), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[16482, 29414])).
% 3.22/3.44 tff(29416,plain,
% 3.22/3.44 (~r(s(s(s(s(z)))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1034, 29415, 110, 37])).
% 3.22/3.44 tff(29417,plain,
% 3.22/3.44 (b(s(s(s(s(z)))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1095, 29416])).
% 3.22/3.44 tff(29418,plain,
% 3.22/3.44 (~r(z, s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28320, 29396, 110, 601, 37, 29407])).
% 3.22/3.44 tff(29419,plain,
% 3.22/3.44 (b(z, s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1214, 29418])).
% 3.22/3.44 tff(29420,plain,
% 3.22/3.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[13513, 29419, 29417, 29394])).
% 3.22/3.44 tff(29421,plain,
% 3.22/3.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[10426, 29420])).
% 3.22/3.44 tff(29422,plain,
% 3.22/3.44 (~r(s(s(s(z))), elem!1)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[17603, 29421, 29415, 29396])).
% 3.22/3.44 tff(29423,plain,
% 3.22/3.44 (b(s(s(s(z))), elem!1)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[255, 29422, 28220])).
% 3.22/3.44 tff(29424,plain,
% 3.22/3.44 (~b(s(s(s(z))), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[8279, 29419, 29406, 29394])).
% 3.22/3.44 tff(29425,plain,
% 3.22/3.44 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1816, 29424, 28342])).
% 3.22/3.44 tff(29426,plain,
% 3.22/3.44 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[15217, 29425, 29377, 29381, 29396])).
% 3.22/3.44 tff(29427,plain,
% 3.22/3.44 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1733, 29426])).
% 3.22/3.44 tff(29428,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1857, 29427, 29423, 29379, 29377])).
% 3.22/3.44 tff(29429,plain,(b(z, s(s(s(elem!1)))) | (~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29430,plain,
% 3.22/3.44 (b(z, s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29429, 909, 601, 110])).
% 3.22/3.44 tff(29431,plain,
% 3.22/3.44 (b(z, s(s(elem!1)))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29430, 29082])).
% 3.22/3.44 tff(29432,plain,
% 3.22/3.44 (r(s(z), elem!1)),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[572, 29094])).
% 3.22/3.44 tff(29433,plain,
% 3.22/3.44 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[25896, 1660, 3456, 1625])).
% 3.22/3.44 tff(29434,plain,
% 3.22/3.44 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[16014, 1660, 357, 3456])).
% 3.22/3.44 tff(29435,plain,
% 3.22/3.44 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1669, 1660, 110, 909])).
% 3.22/3.44 tff(29436,plain,
% 3.22/3.44 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1658, 29435])).
% 3.22/3.44 tff(29437,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[16299, 29436, 29434, 2470, 4997, 1894, 29433])).
% 3.22/3.44 tff(29438,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(s(s(z))))) = elem!1) | (~b(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29439,plain,
% 3.22/3.44 (~r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29438, 29432, 28215, 29431, 3891, 29030, 110, 909, 28554])).
% 3.22/3.44 tff(29440,plain,
% 3.22/3.44 (b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1682, 29439])).
% 3.22/3.44 tff(29441,plain,
% 3.22/3.44 (b(z, elem!1)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[13207, 29430, 28225])).
% 3.22/3.44 tff(29442,plain,
% 3.22/3.44 (~r(s(elem!1), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1300, 28256, 110, 909])).
% 3.22/3.44 tff(29443,plain,
% 3.22/3.44 (b(s(elem!1), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[409, 29442])).
% 3.22/3.44 tff(29444,plain,
% 3.22/3.44 (b(s(s(s(elem!1))), z)),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[12308, 29443, 3891])).
% 3.22/3.44 tff(29445,plain,
% 3.22/3.44 (b(elem!1, z)),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29444, 28339])).
% 3.22/3.44 tff(29446,plain,
% 3.22/3.44 (~r(s(z), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[23313, 29445, 29441, 909, 28220, 29030, 29432])).
% 3.22/3.44 tff(29447,plain,
% 3.22/3.44 (b(s(z), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[105, 29446])).
% 3.22/3.44 tff(29448,plain,
% 3.22/3.44 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29411, 911, 29444, 909, 572, 110])).
% 3.22/3.44 tff(29449,plain,
% 3.22/3.44 (~r(elem!1, s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[21233, 911, 3456, 572])).
% 3.22/3.44 tff(29450,plain,
% 3.22/3.44 (b(elem!1, s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[20539, 29449, 29400])).
% 3.22/3.44 tff(29451,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28428, 29450, 29448, 601])).
% 3.22/3.44 tff(29452,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29453,plain,
% 3.22/3.44 (~r(s(s(s(s(z)))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29452, 572, 909, 601, 110, 29030])).
% 3.22/3.44 tff(29454,plain,
% 3.22/3.44 (b(s(s(s(s(z)))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[932, 29453])).
% 3.22/3.44 tff(29455,plain,
% 3.22/3.44 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.44 tff(29456,plain,
% 3.22/3.44 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 3.22/3.44 inference(symmetry,[status(thm)],[29455])).
% 3.22/3.44 tff(29457,plain,
% 3.22/3.44 (r(s(elem!1), s(z))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[12761, 29456])).
% 3.22/3.44 tff(29458,plain,
% 3.22/3.44 (b(z, s(elem!1))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[3407, 28475])).
% 3.22/3.44 tff(29459,plain,
% 3.22/3.44 (~r(s(s(s(z))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[10317, 109, 909, 28256])).
% 3.22/3.44 tff(29460,plain,
% 3.22/3.44 (b(s(s(s(z))), s(z))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[2325, 29459])).
% 3.22/3.44 tff(29461,plain,
% 3.22/3.44 (r(z, s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1658, 28622])).
% 3.22/3.44 tff(29462,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29463,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.44 inference(quant_inst,[status(thm)],[])).
% 3.22/3.44 tff(29464,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29463, 29462])).
% 3.22/3.44 tff(29465,plain,
% 3.22/3.44 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29464, 271, 1638, 12562, 15718])).
% 3.22/3.44 tff(29466,plain,
% 3.22/3.44 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[9512, 29465])).
% 3.22/3.44 tff(29467,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29468,plain,
% 3.22/3.44 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29469,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[29468])).
% 3.22/3.44 tff(29470,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.44 inference(transitivity,[status(thm)],[29469, 29467])).
% 3.22/3.44 tff(29471,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.44 inference(quant_inst,[status(thm)],[])).
% 3.22/3.44 tff(29472,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29471, 29470])).
% 3.22/3.44 tff(29473,plain,
% 3.22/3.44 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29472, 271, 1638, 12562, 15718])).
% 3.22/3.44 tff(29474,plain,
% 3.22/3.44 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1777, 29473])).
% 3.22/3.44 tff(29475,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29476,plain,
% 3.22/3.44 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29477,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[29476])).
% 3.22/3.44 tff(29478,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.44 inference(transitivity,[status(thm)],[29477, 29475])).
% 3.22/3.44 tff(29479,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 3.22/3.44 inference(quant_inst,[status(thm)],[])).
% 3.22/3.44 tff(29480,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29479, 29478])).
% 3.22/3.44 tff(29481,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29480, 121, 29474, 1661, 29466, 910])).
% 3.22/3.44 tff(29482,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29483,plain,
% 3.22/3.44 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29482, 29461, 1638, 910, 15718])).
% 3.22/3.44 tff(29484,plain,
% 3.22/3.44 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28738, 29483, 601])).
% 3.22/3.44 tff(29485,plain,
% 3.22/3.44 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1559, 29484, 28489])).
% 3.22/3.44 tff(29486,plain,
% 3.22/3.44 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29485, 25731])).
% 3.22/3.44 tff(29487,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29488,plain,
% 3.22/3.44 (((~r(s(s(s(elem!1))), s(z))) | (~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(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29489,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.22/3.44 inference(monotonicity,[status(thm)],[29488])).
% 3.22/3.44 tff(29490,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.44 inference(transitivity,[status(thm)],[29489, 29487])).
% 3.22/3.44 tff(29491,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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)))))))),
% 3.22/3.44 inference(quant_inst,[status(thm)],[])).
% 3.22/3.44 tff(29492,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29491, 29490])).
% 3.22/3.44 tff(29493,plain,
% 3.22/3.44 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29492, 121, 572, 12761])).
% 3.22/3.44 tff(29494,plain,
% 3.22/3.44 (~r(s(z), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29493, 29486])).
% 3.22/3.44 tff(29495,plain,
% 3.22/3.44 (b(s(z), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[16482, 29494])).
% 3.22/3.44 tff(29496,plain,
% 3.22/3.44 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[28637, 29461, 109, 1638, 15718])).
% 3.22/3.44 tff(29497,plain,
% 3.22/3.44 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[2071, 29496, 29341])).
% 3.22/3.44 tff(29498,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.44 inference(rewrite,[status(thm)],[])).
% 3.22/3.44 tff(29499,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.44 inference(quant_inst,[status(thm)],[])).
% 3.22/3.44 tff(29500,plain,
% 3.22/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.22/3.44 inference(modus_ponens,[status(thm)],[29499, 29498])).
% 3.22/3.44 tff(29501,plain,
% 3.22/3.44 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29500, 121, 12761, 5499, 12542])).
% 3.22/3.44 tff(29502,plain,
% 3.22/3.44 ($false),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29501, 28530])).
% 3.22/3.44 tff(29503,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.44 tff(29504,plain,
% 3.22/3.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[29503, 29497, 601, 12761, 29485])).
% 3.22/3.44 tff(29505,plain,
% 3.22/3.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[10426, 29504])).
% 3.22/3.44 tff(29506,plain,
% 3.22/3.44 (~b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[9499, 29505, 937, 29460])).
% 3.22/3.44 tff(29507,plain,
% 3.22/3.44 (r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[1756, 29506])).
% 3.22/3.44 tff(29508,plain,
% 3.22/3.44 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[9510, 29507, 909, 29461])).
% 3.22/3.44 tff(29509,plain,
% 3.22/3.44 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.44 inference(unit_resolution,[status(thm)],[9512, 29508])).
% 3.22/3.44 tff(29510,plain,
% 3.22/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29511,plain,
% 3.22/3.45 (((~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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29512,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.22/3.45 inference(monotonicity,[status(thm)],[29511])).
% 3.22/3.45 tff(29513,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(transitivity,[status(thm)],[29512, 29510])).
% 3.22/3.45 tff(29514,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.22/3.45 inference(quant_inst,[status(thm)],[])).
% 3.22/3.45 tff(29515,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29514, 29513])).
% 3.22/3.45 tff(29516,plain,
% 3.22/3.45 ($false),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29515, 271, 29509, 937, 29495, 5393])).
% 3.22/3.45 tff(29517,plain,((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.45 tff(29518,plain,
% 3.22/3.45 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29517, 109, 5393, 909, 601, 12761, 937, 1638, 572, 910, 3407])).
% 3.22/3.45 tff(29519,plain,
% 3.22/3.45 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29518, 28845])).
% 3.22/3.45 tff(29520,plain,
% 3.22/3.45 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[4138, 29519, 28482])).
% 3.22/3.45 tff(29521,plain,
% 3.22/3.45 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[17429, 29520, 3891])).
% 3.22/3.45 tff(29522,plain,
% 3.22/3.45 (~r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[28681, 121, 572, 12761, 29521])).
% 3.22/3.45 tff(29523,plain,
% 3.22/3.45 (b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1756, 29522])).
% 3.22/3.45 tff(29524,plain,
% 3.22/3.45 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[9499, 29523, 937, 29460])).
% 3.22/3.45 tff(29525,plain,
% 3.22/3.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[10426, 29524])).
% 3.22/3.45 tff(29526,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29527,plain,
% 3.22/3.45 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29528,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.22/3.45 inference(monotonicity,[status(thm)],[29527])).
% 3.22/3.45 tff(29529,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(transitivity,[status(thm)],[29528, 29526])).
% 3.22/3.45 tff(29530,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(quant_inst,[status(thm)],[])).
% 3.22/3.45 tff(29531,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29530, 29529])).
% 3.22/3.45 tff(29532,plain,
% 3.22/3.45 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29531, 271, 937, 5393, 29523])).
% 3.22/3.45 tff(29533,plain,
% 3.22/3.45 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[9512, 29532])).
% 3.22/3.45 tff(29534,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29535,plain,
% 3.22/3.45 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29536,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.22/3.45 inference(monotonicity,[status(thm)],[29535])).
% 3.22/3.45 tff(29537,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(transitivity,[status(thm)],[29536, 29534])).
% 3.22/3.45 tff(29538,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(quant_inst,[status(thm)],[])).
% 3.22/3.45 tff(29539,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29538, 29537])).
% 3.22/3.45 tff(29540,plain,
% 3.22/3.45 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29539, 271, 3871, 29460, 5393])).
% 3.22/3.45 tff(29541,plain,
% 3.22/3.45 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1494, 29540])).
% 3.22/3.45 tff(29542,plain,
% 3.22/3.45 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1785, 29523, 937, 5393])).
% 3.22/3.45 tff(29543,plain,
% 3.22/3.45 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1777, 29542])).
% 3.22/3.45 tff(29544,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29545,plain,
% 3.22/3.45 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29546,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.22/3.45 inference(monotonicity,[status(thm)],[29545])).
% 3.22/3.45 tff(29547,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(transitivity,[status(thm)],[29546, 29544])).
% 3.22/3.45 tff(29548,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.45 inference(quant_inst,[status(thm)],[])).
% 3.22/3.45 tff(29549,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29548, 29547])).
% 3.22/3.45 tff(29550,plain,
% 3.22/3.45 ($false),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29549, 121, 29543, 29541, 29533, 29525])).
% 3.22/3.45 tff(29551,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.45 tff(29552,plain,
% 3.22/3.45 (~r(s(s(s(z))), z)),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29551, 3871, 5393, 937, 572, 12761, 601, 909, 28259, 910, 3407])).
% 3.22/3.45 tff(29553,plain,
% 3.22/3.45 (~b(s(s(s(z))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1427, 29552, 29458, 394])).
% 3.22/3.45 tff(29554,plain,
% 3.22/3.45 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1816, 29553, 28342])).
% 3.22/3.45 tff(29555,plain,
% 3.22/3.45 (~r(s(s(s(z))), s(z))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[24825, 29554, 29432, 29457])).
% 3.22/3.45 tff(29556,plain,
% 3.22/3.45 (b(s(s(s(z))), s(z))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[2325, 29555])).
% 3.22/3.45 tff(29557,plain,
% 3.22/3.45 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[10418, 271, 3871, 29556, 937])).
% 3.22/3.45 tff(29558,plain,
% 3.22/3.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[10426, 29557])).
% 3.22/3.45 tff(29559,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29560,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.45 inference(quant_inst,[status(thm)],[])).
% 3.22/3.45 tff(29561,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29560, 29559])).
% 3.22/3.45 tff(29562,plain,
% 3.22/3.45 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29561, 271, 3871, 937, 5393])).
% 3.22/3.45 tff(29563,plain,
% 3.22/3.45 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[9512, 29562])).
% 3.22/3.45 tff(29564,plain,
% 3.22/3.45 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29539, 271, 3871, 29556, 5393])).
% 3.22/3.45 tff(29565,plain,
% 3.22/3.45 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1494, 29564])).
% 3.22/3.45 tff(29566,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29567,plain,
% 3.22/3.45 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29568,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.22/3.45 inference(monotonicity,[status(thm)],[29567])).
% 3.22/3.45 tff(29569,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(transitivity,[status(thm)],[29568, 29566])).
% 3.22/3.45 tff(29570,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(quant_inst,[status(thm)],[])).
% 3.22/3.45 tff(29571,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[29570, 29569])).
% 3.22/3.45 tff(29572,plain,
% 3.22/3.45 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29571, 271, 3871, 937, 5393])).
% 3.22/3.45 tff(29573,plain,
% 3.22/3.45 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1777, 29572])).
% 3.22/3.45 tff(29574,plain,
% 3.22/3.45 ($false),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29549, 121, 29573, 29565, 29563, 29558])).
% 3.22/3.45 tff(29575,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.45 tff(29576,plain,
% 3.22/3.45 (~r(s(s(s(s(z)))), z)),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29575, 29447, 29440, 29443, 572, 12761, 601, 909, 29454, 29430])).
% 3.22/3.45 tff(29577,plain,
% 3.22/3.45 (b(s(s(s(s(z)))), z)),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1095, 29576])).
% 3.22/3.45 tff(29578,plain,
% 3.22/3.45 (~b(s(s(s(z))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1427, 141, 29458, 394])).
% 3.22/3.45 tff(29579,plain,
% 3.22/3.45 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1816, 29578, 28342])).
% 3.22/3.45 tff(29580,plain,
% 3.22/3.45 (~r(s(s(s(z))), s(z))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[24825, 29579, 357, 29457])).
% 3.22/3.45 tff(29581,plain,
% 3.22/3.45 (b(s(s(s(z))), s(z))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[2325, 29580])).
% 3.22/3.45 tff(29582,plain,
% 3.22/3.45 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[13333, 29579, 28508])).
% 3.22/3.45 tff(29583,plain,
% 3.22/3.45 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[28732, 28259, 3407, 1103])).
% 3.22/3.45 tff(29584,plain,
% 3.22/3.45 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[28738, 29583, 601])).
% 3.22/3.45 tff(29585,plain,
% 3.22/3.45 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1559, 29584, 28489])).
% 3.22/3.45 tff(29586,plain,
% 3.22/3.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[29503, 29582, 601, 12761, 29585])).
% 3.22/3.45 tff(29587,plain,
% 3.22/3.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[10426, 29586])).
% 3.22/3.45 tff(29588,plain,
% 3.22/3.45 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[28576, 29581, 3871, 5393])).
% 3.22/3.45 tff(29589,plain,
% 3.22/3.45 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1733, 29588])).
% 3.22/3.45 tff(29590,plain,
% 3.22/3.45 (~b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[9499, 13508, 937, 222])).
% 3.22/3.45 tff(29591,plain,
% 3.22/3.45 (r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1756, 29590])).
% 3.22/3.45 tff(29592,plain,
% 3.22/3.45 (b(elem!1, z)),
% 3.22/3.45 inference(modus_ponens,[status(thm)],[28259, 28339])).
% 3.22/3.45 tff(29593,plain,
% 3.22/3.45 (b(z, elem!1)),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[13207, 3407, 28225])).
% 3.22/3.45 tff(29594,plain,
% 3.22/3.45 (~b(s(s(s(z))), elem!1)),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1947, 1935, 29593, 29592])).
% 3.22/3.45 tff(29595,plain,
% 3.22/3.45 (r(s(s(s(z))), elem!1)),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[255, 29594, 28220])).
% 3.22/3.45 tff(29596,plain,
% 3.22/3.45 (~b(z, s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[13513, 13508, 1103, 1935])).
% 3.22/3.45 tff(29597,plain,
% 3.22/3.45 (r(z, s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1214, 29596])).
% 3.22/3.45 tff(29598,plain,
% 3.22/3.45 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[16283, 29597, 29595, 1736])).
% 3.22/3.45 tff(29599,plain,
% 3.22/3.45 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1658, 29598])).
% 3.22/3.45 tff(29600,plain,
% 3.22/3.45 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[4072, 1639, 1935, 1519])).
% 3.22/3.45 tff(29601,plain,
% 3.22/3.45 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1733, 29600])).
% 3.22/3.45 tff(29602,plain,
% 3.22/3.45 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[28583, 29601, 12761, 5499])).
% 3.22/3.45 tff(29603,plain,
% 3.22/3.45 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[17429, 29602, 3891])).
% 3.22/3.45 tff(29604,plain,
% 3.22/3.45 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[4138, 29603, 28482])).
% 3.22/3.45 tff(29605,plain,
% 3.22/3.45 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[25946, 29604, 28458, 394, 1639])).
% 3.22/3.45 tff(29606,plain,
% 3.22/3.45 (r(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[1847, 29605, 28455])).
% 3.22/3.45 tff(29607,plain,
% 3.22/3.45 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.22/3.45 inference(unit_resolution,[status(thm)],[16341, 29606, 3891])).
% 3.22/3.45 tff(29608,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29609,plain,
% 3.22/3.45 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(rewrite,[status(thm)],[])).
% 3.22/3.45 tff(29610,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.22/3.45 inference(monotonicity,[status(thm)],[29609])).
% 3.22/3.45 tff(29611,plain,
% 3.22/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.22/3.45 inference(transitivity,[status(thm)],[29610, 29608])).
% 3.22/3.45 tff(29612,plain,
% 3.22/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.22/3.46 inference(quant_inst,[status(thm)],[])).
% 3.22/3.46 tff(29613,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29612, 29611])).
% 3.22/3.46 tff(29614,plain,
% 3.22/3.46 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29613, 121, 12761, 9502, 1735])).
% 3.22/3.46 tff(29615,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29614, 28787])).
% 3.22/3.46 tff(29616,plain,((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29617,plain,
% 3.22/3.46 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29616, 29607, 12761, 601, 1735])).
% 3.22/3.46 tff(29618,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[9512, 29617])).
% 3.22/3.46 tff(29619,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29620,plain,
% 3.22/3.46 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29621,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[29620])).
% 3.22/3.46 tff(29622,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.22/3.46 inference(transitivity,[status(thm)],[29621, 29619])).
% 3.22/3.46 tff(29623,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 3.22/3.46 inference(quant_inst,[status(thm)],[])).
% 3.22/3.46 tff(29624,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29623, 29622])).
% 3.22/3.46 tff(29625,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29624, 271, 1639, 1519, 29618, 1935])).
% 3.22/3.46 tff(29626,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29627,plain,
% 3.22/3.46 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29626, 29599, 1935, 12761, 601, 29591, 394, 5499])).
% 3.22/3.46 tff(29628,plain,
% 3.22/3.46 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28583, 1736, 12761, 5499])).
% 3.22/3.46 tff(29629,plain,
% 3.22/3.46 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[17429, 29628, 3891])).
% 3.22/3.46 tff(29630,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[4138, 29629, 28482])).
% 3.22/3.46 tff(29631,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[601])).
% 3.22/3.46 tff(29632,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.22/3.46 inference(symmetry,[status(thm)],[29631])).
% 3.22/3.46 tff(29633,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.22/3.46 inference(transitivity,[status(thm)],[29229, 29632])).
% 3.22/3.46 tff(29634,plain,
% 3.22/3.46 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[25946, 1639, 28458, 394, 9894])).
% 3.22/3.46 tff(29635,plain,
% 3.22/3.46 (r(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1847, 29634, 28455])).
% 3.22/3.46 tff(29636,plain,
% 3.22/3.46 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[23759, 29635, 145, 1477])).
% 3.22/3.46 tff(29637,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[840, 29636, 28215])).
% 3.22/3.46 tff(29638,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29637, 29633])).
% 3.22/3.46 tff(29639,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[611])).
% 3.22/3.46 tff(29640,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.46 inference(symmetry,[status(thm)],[29639])).
% 3.22/3.46 tff(29641,assumption,(b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 3.22/3.46 tff(29642,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29641, 29640])).
% 3.22/3.46 tff(29643,plain,
% 3.22/3.46 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28596, 271, 3407, 1639, 1638])).
% 3.22/3.46 tff(29644,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29643, 29642])).
% 3.22/3.46 tff(29645,plain,((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29646,plain,
% 3.22/3.46 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29645, 1639, 601, 3407, 28259])).
% 3.22/3.46 tff(29647,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29646, 29638])).
% 3.22/3.46 tff(29648,plain,((~b(z, s(s(s(s(s(z))))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29649,plain,
% 3.22/3.46 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29648, 29599, 29595, 601, 394, 29630, 3407])).
% 3.22/3.46 tff(29650,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1494, 29649, 29627])).
% 3.22/3.46 tff(29651,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29652,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29651, 29589, 29587, 394, 3407, 601, 12761, 4010, 29582, 937, 29581, 1103])).
% 3.22/3.46 tff(29653,plain,(r(s(s(s(z))), z) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29654,plain,
% 3.22/3.46 (r(s(s(s(z))), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29653, 29443, 29430, 601, 12761, 29454, 29577, 29447, 29440, 29432])).
% 3.22/3.46 tff(29655,plain,
% 3.22/3.46 (~r(s(s(s(z))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[10317, 29654, 909, 28256])).
% 3.22/3.46 tff(29656,plain,
% 3.22/3.46 (b(s(s(s(z))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2325, 29655])).
% 3.22/3.46 tff(29657,plain,
% 3.22/3.46 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28576, 29656, 29447, 29440])).
% 3.22/3.46 tff(29658,plain,
% 3.22/3.46 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1733, 29657])).
% 3.22/3.46 tff(29659,plain,
% 3.22/3.46 (~r(z, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28683, 572, 12761, 3891, 28482, 29454, 29440, 29654, 29447, 29656])).
% 3.22/3.46 tff(29660,plain,
% 3.22/3.46 (b(z, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1214, 29659])).
% 3.22/3.46 tff(29661,plain,
% 3.22/3.46 (~b(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1334, 29660, 29441, 29445])).
% 3.22/3.46 tff(29662,plain,
% 3.22/3.46 (r(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[255, 29661, 28220])).
% 3.22/3.46 tff(29663,plain,
% 3.22/3.46 (r(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[13482, 29662, 3891])).
% 3.22/3.46 tff(29664,plain,
% 3.22/3.46 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29002, 29662, 601])).
% 3.22/3.46 tff(29665,plain,
% 3.22/3.46 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28583, 29664, 12761, 29658])).
% 3.22/3.46 tff(29666,plain,
% 3.22/3.46 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[17429, 29665, 3891])).
% 3.22/3.46 tff(29667,plain,
% 3.22/3.46 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[4138, 29666, 28482])).
% 3.22/3.46 tff(29668,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28732, 29444, 29430, 29577])).
% 3.22/3.46 tff(29669,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28738, 29668, 601])).
% 3.22/3.46 tff(29670,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1559, 29669, 28489])).
% 3.22/3.46 tff(29671,plain,
% 3.22/3.46 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29503, 29664, 601, 12761, 29670])).
% 3.22/3.46 tff(29672,plain,
% 3.22/3.46 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[10426, 29671])).
% 3.22/3.46 tff(29673,plain,
% 3.22/3.46 (~b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[9499, 29672, 29454, 29656])).
% 3.22/3.46 tff(29674,plain,
% 3.22/3.46 (r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1756, 29673])).
% 3.22/3.46 tff(29675,plain,
% 3.22/3.46 (~r(z, s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1744, 29674, 110, 29658])).
% 3.22/3.46 tff(29676,plain,
% 3.22/3.46 (b(z, s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1658, 29675])).
% 3.22/3.46 tff(29677,plain,
% 3.22/3.46 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[25946, 29676, 28458, 29443, 29667])).
% 3.22/3.46 tff(29678,plain,
% 3.22/3.46 (r(elem!1, s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1847, 29677, 28455])).
% 3.22/3.46 tff(29679,plain,
% 3.22/3.46 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[16341, 29678, 3891])).
% 3.22/3.46 tff(29680,plain,
% 3.22/3.46 (~r(s(s(elem!1)), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[16352, 29679, 29663, 29658])).
% 3.22/3.46 tff(29681,plain,
% 3.22/3.46 (~r(elem!1, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[12242, 29680, 3891])).
% 3.22/3.46 tff(29682,plain,
% 3.22/3.46 (b(elem!1, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1192, 29681, 28221])).
% 3.22/3.46 tff(29683,plain,
% 3.22/3.46 (b(s(elem!1), s(s(s(z))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29682, 29080])).
% 3.22/3.46 tff(29684,plain,
% 3.22/3.46 (~b(s(elem!1), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2029, 29660, 29443, 29656])).
% 3.22/3.46 tff(29685,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29684, 29683])).
% 3.22/3.46 tff(29686,plain,((~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29687,plain,
% 3.22/3.46 (~r(s(z), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29686, 12761, 110, 601, 909])).
% 3.22/3.46 tff(29688,plain,
% 3.22/3.46 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[760, 29687])).
% 3.22/3.46 tff(29689,plain,
% 3.22/3.46 (b(s(z), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2562, 29688, 25718])).
% 3.22/3.46 tff(29690,plain,
% 3.22/3.46 ((~r(s(s(s(elem!1))), z)) <=> (~r(elem!1, z))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[29110])).
% 3.22/3.46 tff(29691,plain,
% 3.22/3.46 (~r(s(s(s(elem!1))), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[11808, 121, 110, 909, 12761])).
% 3.22/3.46 tff(29692,plain,
% 3.22/3.46 (~r(elem!1, z)),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29691, 29690])).
% 3.22/3.46 tff(29693,plain,
% 3.22/3.46 (b(elem!1, z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[284, 29692, 29162])).
% 3.22/3.46 tff(29694,plain,
% 3.22/3.46 (~b(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[16591, 29693, 110, 909, 29441, 29689])).
% 3.22/3.46 tff(29695,plain,
% 3.22/3.46 (r(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[255, 29694, 28220])).
% 3.22/3.46 tff(29696,plain,
% 3.22/3.46 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29002, 29695, 601])).
% 3.22/3.46 tff(29697,plain,
% 3.22/3.46 (b(s(s(s(elem!1))), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[8229, 29691])).
% 3.22/3.46 tff(29698,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28732, 12196, 29430, 29697])).
% 3.22/3.46 tff(29699,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28738, 29698, 601])).
% 3.22/3.46 tff(29700,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1559, 29699, 28489])).
% 3.22/3.46 tff(29701,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29700, 25731])).
% 3.22/3.46 tff(29702,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29703,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.46 inference(quant_inst,[status(thm)],[])).
% 3.22/3.46 tff(29704,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29703, 29702])).
% 3.22/3.46 tff(29705,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29704, 121, 110, 12761, 911, 29701])).
% 3.22/3.46 tff(29706,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29707,plain,
% 3.22/3.46 (~r(s(s(s(s(z)))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29706, 12761, 110, 601, 909])).
% 3.22/3.46 tff(29708,plain,
% 3.22/3.46 (b(s(s(s(s(z)))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[932, 29707])).
% 3.22/3.46 tff(29709,plain,
% 3.22/3.46 (~r(s(s(s(z))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29008, 12761, 110, 29696])).
% 3.22/3.46 tff(29710,plain,
% 3.22/3.46 (b(s(s(s(z))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2325, 29709])).
% 3.22/3.46 tff(29711,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29712,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.46 inference(quant_inst,[status(thm)],[])).
% 3.22/3.46 tff(29713,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29712, 29711])).
% 3.22/3.46 tff(29714,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29713, 271, 29688, 29710, 29708])).
% 3.22/3.46 tff(29715,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[10426, 29714])).
% 3.22/3.46 tff(29716,plain,
% 3.22/3.46 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29503, 29715, 601, 12761, 29696])).
% 3.22/3.46 tff(29717,plain,
% 3.22/3.46 (b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1559, 29716, 28489])).
% 3.22/3.46 tff(29718,plain,
% 3.22/3.46 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28738, 29717, 601])).
% 3.22/3.46 tff(29719,plain,
% 3.22/3.46 (r(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[13482, 29695, 3891])).
% 3.22/3.46 tff(29720,plain,
% 3.22/3.46 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[12573, 29715, 3891, 29688, 29719, 29708])).
% 3.22/3.46 tff(29721,plain,
% 3.22/3.46 (~r(elem!1, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28368, 29720, 28326])).
% 3.22/3.46 tff(29722,plain,
% 3.22/3.46 (b(elem!1, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1192, 29721, 28221])).
% 3.22/3.46 tff(29723,plain,
% 3.22/3.46 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29722, 28333])).
% 3.22/3.46 tff(29724,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29725,plain,
% 3.22/3.46 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29726,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[29725])).
% 3.22/3.46 tff(29727,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.46 inference(transitivity,[status(thm)],[29726, 29724])).
% 3.22/3.46 tff(29728,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.22/3.46 inference(quant_inst,[status(thm)],[])).
% 3.22/3.46 tff(29729,plain,
% 3.22/3.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29728, 29727])).
% 3.22/3.46 tff(29730,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29729, 271, 29688, 29723, 29708, 29718])).
% 3.22/3.46 tff(29731,plain,((~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29732,plain,
% 3.22/3.46 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29731, 29079, 26, 28190])).
% 3.22/3.46 tff(29733,plain,
% 3.22/3.46 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[16580, 29732])).
% 3.22/3.46 tff(29734,plain,
% 3.22/3.46 (b(z, s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29429, 29079, 28190, 26])).
% 3.22/3.46 tff(29735,plain,
% 3.22/3.46 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29731, 909, 110, 601])).
% 3.22/3.46 tff(29736,plain,
% 3.22/3.46 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[16580, 29735])).
% 3.22/3.46 tff(29737,plain,
% 3.22/3.46 ($false),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[16613, 271, 3407, 503, 1103, 12562])).
% 3.22/3.46 tff(29738,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.46 tff(29739,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29738, 12196, 29736, 29430])).
% 3.22/3.46 tff(29740,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28738, 29739, 601])).
% 3.22/3.46 tff(29741,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1559, 29740, 28489])).
% 3.22/3.46 tff(29742,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29741, 25731])).
% 3.22/3.46 tff(29743,plain,
% 3.22/3.46 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 3.22/3.46 inference(transitivity,[status(thm)],[29339, 6198])).
% 3.22/3.46 tff(29744,plain,
% 3.22/3.46 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[29743])).
% 3.22/3.46 tff(29745,plain,
% 3.22/3.46 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[28342, 29744])).
% 3.22/3.46 tff(29746,plain,
% 3.22/3.46 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[28216])).
% 3.22/3.46 tff(29747,plain,
% 3.22/3.46 (~r(s(s(elem!1)), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28239, 29735, 609])).
% 3.22/3.46 tff(29748,plain,
% 3.22/3.46 (b(s(s(elem!1)), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2143, 29747])).
% 3.22/3.46 tff(29749,plain,
% 3.22/3.46 (b(elem!1, s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28387, 29748, 601, 25718])).
% 3.22/3.46 tff(29750,plain,
% 3.22/3.46 (~b(s(elem!1), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[12308, 8226, 3891])).
% 3.22/3.46 tff(29751,plain,
% 3.22/3.46 (r(s(elem!1), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[409, 29750])).
% 3.22/3.46 tff(29752,plain,
% 3.22/3.46 (~r(s(z), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1300, 29751, 110, 909])).
% 3.22/3.46 tff(29753,plain,
% 3.22/3.46 (~r(s(z), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28255, 29752, 609])).
% 3.22/3.46 tff(29754,plain,
% 3.22/3.46 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[760, 29753])).
% 3.22/3.46 tff(29755,plain,
% 3.22/3.46 (b(s(z), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2562, 29754, 25718])).
% 3.22/3.46 tff(29756,plain,
% 3.22/3.46 (~b(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[4827, 29755, 29441, 29749])).
% 3.22/3.46 tff(29757,plain,
% 3.22/3.46 (r(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[255, 29756, 28220])).
% 3.22/3.46 tff(29758,plain,
% 3.22/3.46 (r(elem!1, z)),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[20245, 29110])).
% 3.22/3.46 tff(29759,plain,
% 3.22/3.46 (~r(s(s(s(z))), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[15900, 29758, 909, 29757])).
% 3.22/3.46 tff(29760,plain,
% 3.22/3.46 (b(s(s(s(z))), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1155, 29759])).
% 3.22/3.46 tff(29761,plain,
% 3.22/3.46 (~r(s(s(s(z))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[12206, 29760, 909, 110, 29431, 911])).
% 3.22/3.46 tff(29762,plain,
% 3.22/3.46 (b(s(s(s(z))), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2325, 29761])).
% 3.22/3.46 tff(29763,plain,
% 3.22/3.46 (b(s(elem!1), s(z))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28247, 29748, 609])).
% 3.22/3.46 tff(29764,plain,
% 3.22/3.46 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.46 tff(29765,plain,
% 3.22/3.46 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(elem!1))),
% 3.22/3.46 inference(symmetry,[status(thm)],[29764])).
% 3.22/3.46 tff(29766,plain,
% 3.22/3.46 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = s(elem!1)))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[29765])).
% 3.22/3.46 tff(29767,plain,
% 3.22/3.46 (~(s(z) = s(elem!1))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[61, 29766])).
% 3.22/3.46 tff(29768,plain,
% 3.22/3.46 (~r(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[29002, 906, 601])).
% 3.22/3.46 tff(29769,plain,
% 3.22/3.46 (b(s(s(s(z))), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[255, 29768, 28220])).
% 3.22/3.46 tff(29770,plain,
% 3.22/3.46 (~b(s(z), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[4827, 29769, 29441, 29749])).
% 3.22/3.46 tff(29771,plain,
% 3.22/3.46 (r(s(z), elem!1)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[236, 29770, 28337])).
% 3.22/3.46 tff(29772,plain,
% 3.22/3.46 (~b(z, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[15974, 29769, 29441, 29749])).
% 3.22/3.46 tff(29773,plain,
% 3.22/3.46 (r(z, s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1214, 29772])).
% 3.22/3.46 tff(29774,plain,
% 3.22/3.46 (~r(elem!1, z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[15950, 29773, 110, 29771])).
% 3.22/3.46 tff(29775,plain,
% 3.22/3.46 (b(elem!1, z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[284, 29774, 29162])).
% 3.22/3.46 tff(29776,plain,
% 3.22/3.46 (~r(s(elem!1), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[15490, 29775, 29769, 110, 29767, 29441, 28805])).
% 3.22/3.46 tff(29777,plain,
% 3.22/3.46 (b(s(elem!1), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[409, 29776])).
% 3.22/3.46 tff(29778,plain,
% 3.22/3.46 (b(s(s(s(elem!1))), z)),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[12308, 29777, 3891])).
% 3.22/3.46 tff(29779,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28732, 29778, 29430, 12196])).
% 3.22/3.46 tff(29780,plain,
% 3.22/3.46 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[28738, 29779, 601])).
% 3.22/3.46 tff(29781,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1559, 29780, 28489])).
% 3.22/3.46 tff(29782,plain,
% 3.22/3.46 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29781, 25731])).
% 3.22/3.46 tff(29783,plain,
% 3.22/3.46 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2071, 906, 29341])).
% 3.22/3.46 tff(29784,plain,
% 3.22/3.46 (~r(s(z), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[1177, 29773, 909, 110, 1122, 12196])).
% 3.22/3.46 tff(29785,plain,
% 3.22/3.46 (b(s(z), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[105, 29784])).
% 3.22/3.46 tff(29786,plain,
% 3.22/3.46 (~b(s(elem!1), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[7781, 29785, 29763, 29783])).
% 3.22/3.46 tff(29787,plain,
% 3.22/3.46 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.46 inference(modus_ponens,[status(thm)],[29786, 29746])).
% 3.22/3.46 tff(29788,plain,
% 3.22/3.46 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[6237, 21, 29787, 29745])).
% 3.22/3.46 tff(29789,plain,
% 3.22/3.46 (~b(s(z), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[2562, 29770, 25718])).
% 3.22/3.46 tff(29790,plain,
% 3.22/3.46 (r(s(z), s(s(s(elem!1))))),
% 3.22/3.46 inference(unit_resolution,[status(thm)],[760, 29789])).
% 3.22/3.46 tff(29791,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29792,plain,
% 3.22/3.46 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.46 inference(rewrite,[status(thm)],[])).
% 3.22/3.46 tff(29793,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.22/3.46 inference(monotonicity,[status(thm)],[29792])).
% 3.22/3.46 tff(29794,plain,
% 3.22/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.47 inference(transitivity,[status(thm)],[29793, 29791])).
% 3.22/3.47 tff(29795,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29796,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29795, 29794])).
% 3.22/3.47 tff(29797,plain,
% 3.22/3.47 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29796, 121, 29790, 911, 29788])).
% 3.22/3.47 tff(29798,plain,
% 3.22/3.47 ($false),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29797, 29782])).
% 3.22/3.47 tff(29799,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.47 tff(29800,plain,
% 3.22/3.47 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29799, 911, 601, 110, 909])).
% 3.22/3.47 tff(29801,plain,
% 3.22/3.47 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29221, 121, 6842, 5499, 12542])).
% 3.22/3.47 tff(29802,plain,
% 3.22/3.47 ($false),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29801, 28530])).
% 3.22/3.47 tff(29803,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.47 tff(29804,plain,
% 3.22/3.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29803, 20245, 601, 29800, 29741])).
% 3.22/3.47 tff(29805,plain,
% 3.22/3.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[10426, 29804])).
% 3.22/3.47 tff(29806,plain,
% 3.22/3.47 (~b(z, s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[13513, 29760, 12196, 29805])).
% 3.22/3.47 tff(29807,plain,
% 3.22/3.47 (~r(s(z), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[17261, 29806, 29441, 110, 29756])).
% 3.22/3.47 tff(29808,plain,
% 3.22/3.47 (b(s(z), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[105, 29807])).
% 3.22/3.47 tff(29809,plain,
% 3.22/3.47 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(elem!1))),
% 3.22/3.47 inference(symmetry,[status(thm)],[28341])).
% 3.22/3.47 tff(29810,plain,
% 3.22/3.47 (r(s(s(s(z))), s(elem!1))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29800, 29809])).
% 3.22/3.47 tff(29811,plain,
% 3.22/3.47 (r(z, s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[1214, 29806])).
% 3.22/3.47 tff(29812,plain,
% 3.22/3.47 (~r(s(elem!1), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[3865, 29811, 29751, 29810])).
% 3.22/3.47 tff(29813,plain,
% 3.22/3.47 (b(s(elem!1), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[2044, 29812, 28805])).
% 3.22/3.47 tff(29814,plain,
% 3.22/3.47 ($false),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[3622, 29813, 29808, 29763, 29762])).
% 3.22/3.47 tff(29815,plain,(b(s(s(s(elem!1))), z) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.47 tff(29816,plain,
% 3.22/3.47 (b(s(s(s(elem!1))), z)),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29815, 911, 909, 110, 601])).
% 3.22/3.47 tff(29817,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29818,plain,
% 3.22/3.47 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29819,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.22/3.47 inference(monotonicity,[status(thm)],[29818])).
% 3.22/3.47 tff(29820,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.47 inference(transitivity,[status(thm)],[29819, 29817])).
% 3.22/3.47 tff(29821,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29822,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29821, 29820])).
% 3.22/3.47 tff(29823,plain,
% 3.22/3.47 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29822, 271, 29430, 29816, 12196])).
% 3.22/3.47 tff(29824,plain,
% 3.22/3.47 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[1014, 29823, 29126])).
% 3.22/3.47 tff(29825,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29826,plain,
% 3.22/3.47 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29827,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(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(s(z)))), s(s(s(elem!1)))))))),
% 3.22/3.47 inference(monotonicity,[status(thm)],[29826])).
% 3.22/3.47 tff(29828,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(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(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.47 inference(transitivity,[status(thm)],[29827, 29825])).
% 3.22/3.47 tff(29829,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29830,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29829, 29828])).
% 3.22/3.47 tff(29831,plain,
% 3.22/3.47 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29830, 121, 5499, 13550])).
% 3.22/3.47 tff(29832,plain,
% 3.22/3.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29831, 28530])).
% 3.22/3.47 tff(29833,plain,
% 3.22/3.47 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[1167, 21, 29832])).
% 3.22/3.47 tff(29834,plain,
% 3.22/3.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29833, 1139])).
% 3.22/3.47 tff(29835,plain,
% 3.22/3.47 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29370, 121, 5499, 13550])).
% 3.22/3.47 tff(29836,plain,
% 3.22/3.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29835, 28530])).
% 3.22/3.47 tff(29837,plain,
% 3.22/3.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[10426, 29836])).
% 3.22/3.47 tff(29838,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~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))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29839,plain,
% 3.22/3.47 (((~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)))))) | (~b(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29840,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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)))))))),
% 3.22/3.47 inference(monotonicity,[status(thm)],[29839])).
% 3.22/3.47 tff(29841,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~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))))))),
% 3.22/3.47 inference(transitivity,[status(thm)],[29840, 29838])).
% 3.22/3.47 tff(29842,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29843,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29842, 29841])).
% 3.22/3.47 tff(29844,plain,
% 3.22/3.47 ($false),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29843, 271, 1307, 1157, 29837, 29834])).
% 3.22/3.47 tff(29845,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.47 tff(29846,plain,
% 3.22/3.47 (~b(z, s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29845, 1122, 29800, 29824, 29741, 601])).
% 3.22/3.47 tff(29847,plain,
% 3.22/3.47 (r(z, s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[1214, 29846])).
% 3.22/3.47 tff(29848,plain,
% 3.22/3.47 (~r(s(s(s(z))), s(z))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[11100, 29847, 909, 110])).
% 3.22/3.47 tff(29849,plain,
% 3.22/3.47 (b(s(s(s(z))), s(z))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[2325, 29848])).
% 3.22/3.47 tff(29850,plain,
% 3.22/3.47 (~r(s(z), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[1177, 29847, 909, 110, 1122, 12196])).
% 3.22/3.47 tff(29851,plain,
% 3.22/3.47 (b(s(z), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[105, 29850])).
% 3.22/3.47 tff(29852,plain,
% 3.22/3.47 (~b(s(elem!1), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[3622, 29851, 29763, 29849])).
% 3.22/3.47 tff(29853,plain,
% 3.22/3.47 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29852, 29746])).
% 3.22/3.47 tff(29854,plain,
% 3.22/3.47 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[6237, 21, 29853, 29745])).
% 3.22/3.47 tff(29855,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29856,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29857,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29856, 29855])).
% 3.22/3.47 tff(29858,plain,
% 3.22/3.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29857, 121, 29800, 29854, 29742])).
% 3.22/3.47 tff(29859,plain,
% 3.22/3.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[10426, 29858])).
% 3.22/3.47 tff(29860,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29861,plain,
% 3.22/3.47 (((~b(s(s(s(z))), 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29862,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.22/3.47 inference(monotonicity,[status(thm)],[29861])).
% 3.22/3.47 tff(29863,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.22/3.47 inference(transitivity,[status(thm)],[29862, 29860])).
% 3.22/3.47 tff(29864,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29865,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29864, 29863])).
% 3.22/3.47 tff(29866,plain,
% 3.22/3.47 (~b(s(z), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29865, 271, 29851, 29849, 29859])).
% 3.22/3.47 tff(29867,plain,
% 3.22/3.47 (r(s(z), s(s(s(s(z)))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[16482, 29866])).
% 3.22/3.47 tff(29868,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29869,plain,
% 3.22/3.47 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29870,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.22/3.47 inference(monotonicity,[status(thm)],[29869])).
% 3.22/3.47 tff(29871,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.47 inference(transitivity,[status(thm)],[29870, 29868])).
% 3.22/3.47 tff(29872,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29873,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29872, 29871])).
% 3.22/3.47 tff(29874,plain,
% 3.22/3.47 (~r(s(z), s(s(s(elem!1))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29873, 121, 911, 29867, 29824])).
% 3.22/3.47 tff(29875,plain,
% 3.22/3.47 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[760, 29874])).
% 3.22/3.47 tff(29876,plain,
% 3.22/3.47 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29245, 29875, 110, 909, 29736, 911, 601])).
% 3.22/3.47 tff(29877,plain,
% 3.22/3.47 (r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[840, 29876, 28215])).
% 3.22/3.47 tff(29878,plain,
% 3.22/3.47 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29877, 29155])).
% 3.22/3.47 tff(29879,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29880,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.22/3.47 inference(quant_inst,[status(thm)],[])).
% 3.22/3.47 tff(29881,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.22/3.47 inference(modus_ponens,[status(thm)],[29880, 29879])).
% 3.22/3.47 tff(29882,plain,
% 3.22/3.47 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[29881, 121, 29800, 29854, 29878])).
% 3.22/3.47 tff(29883,plain,
% 3.22/3.47 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.47 inference(unit_resolution,[status(thm)],[1733, 29882])).
% 3.22/3.47 tff(29884,plain,
% 3.22/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.47 inference(rewrite,[status(thm)],[])).
% 3.22/3.47 tff(29885,plain,
% 3.22/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(29886,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29885, 29884])).
% 3.22/3.48 tff(29887,plain,
% 3.22/3.48 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29886, 121, 29854, 29878, 29742])).
% 3.22/3.48 tff(29888,plain,
% 3.22/3.48 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[9512, 29887])).
% 3.22/3.48 tff(29889,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29890,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(29891,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29890, 29889])).
% 3.22/3.48 tff(29892,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29891, 271, 29849, 29888, 29883, 29859])).
% 3.22/3.48 tff(29893,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29894,plain,
% 3.22/3.48 (~r(s(s(s(s(z)))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29893, 29079, 26, 28190])).
% 3.22/3.48 tff(29895,plain,
% 3.22/3.48 (b(s(s(s(s(z)))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[932, 29894])).
% 3.22/3.48 tff(29896,plain,
% 3.22/3.48 (~r(s(s(s(s(z)))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29893, 909, 110, 601])).
% 3.22/3.48 tff(29897,plain,
% 3.22/3.48 (b(s(s(s(s(z)))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[932, 29896])).
% 3.22/3.48 tff(29898,plain,
% 3.22/3.48 (~r(s(s(s(z))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[11100, 29773, 909, 110])).
% 3.22/3.48 tff(29899,plain,
% 3.22/3.48 (b(s(s(s(z))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[2325, 29898])).
% 3.22/3.48 tff(29900,plain,
% 3.22/3.48 (~r(elem!1, z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[15739, 29771, 110, 909])).
% 3.22/3.48 tff(29901,plain,
% 3.22/3.48 (b(elem!1, z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[284, 29900, 29162])).
% 3.22/3.48 tff(29902,plain,
% 3.22/3.48 (~b(s(s(s(z))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1947, 29901, 29441, 29769])).
% 3.22/3.48 tff(29903,plain,
% 3.22/3.48 (r(s(s(s(z))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1155, 29902])).
% 3.22/3.48 tff(29904,plain,
% 3.22/3.48 (~r(s(z), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1148, 29903, 29773, 909])).
% 3.22/3.48 tff(29905,plain,
% 3.22/3.48 (b(s(z), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[105, 29904])).
% 3.22/3.48 tff(29906,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[12641, 271, 29783, 29905, 29899, 29736])).
% 3.22/3.48 tff(29907,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29908,plain,
% 3.22/3.48 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29907, 909, 110, 601])).
% 3.22/3.48 tff(29909,plain,
% 3.22/3.48 (b(z, s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[17261, 29756, 29441, 110, 108])).
% 3.22/3.48 tff(29910,plain,
% 3.22/3.48 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1005, 271, 29754, 29736, 29897])).
% 3.22/3.48 tff(29911,plain,
% 3.22/3.48 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1014, 29910, 29126])).
% 3.22/3.48 tff(29912,plain,
% 3.22/3.48 (~r(s(s(s(s(z)))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29135, 29911, 20245, 909])).
% 3.22/3.48 tff(29913,plain,
% 3.22/3.48 (b(s(s(s(s(z)))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1095, 29912])).
% 3.22/3.48 tff(29914,plain,
% 3.22/3.48 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[996, 271, 29754, 29736, 29897])).
% 3.22/3.48 tff(29915,plain,
% 3.22/3.48 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[28738, 29914, 601])).
% 3.22/3.48 tff(29916,plain,
% 3.22/3.48 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1559, 29915, 28489])).
% 3.22/3.48 tff(29917,plain,
% 3.22/3.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29803, 29916, 601, 29908, 20245])).
% 3.22/3.48 tff(29918,plain,
% 3.22/3.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[10426, 29917])).
% 3.22/3.48 tff(29919,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[13513, 29918, 29913, 29909, 29760])).
% 3.22/3.48 tff(29920,plain,(b(s(s(s(elem!1))), z) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29921,plain,
% 3.22/3.48 (b(s(s(s(elem!1))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29920, 108, 909, 110, 601])).
% 3.22/3.48 tff(29922,plain,
% 3.22/3.48 (~b(s(s(s(s(z)))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[28732, 12562, 3407, 1638])).
% 3.22/3.48 tff(29923,plain,
% 3.22/3.48 (r(s(s(s(s(z)))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1095, 29922])).
% 3.22/3.48 tff(29924,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29925,plain,
% 3.22/3.48 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29926,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 3.22/3.48 inference(monotonicity,[status(thm)],[29925])).
% 3.22/3.48 tff(29927,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.48 inference(transitivity,[status(thm)],[29926, 29924])).
% 3.22/3.48 tff(29928,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(29929,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29928, 29927])).
% 3.22/3.48 tff(29930,plain,
% 3.22/3.48 (~r(s(z), s(s(s(s(z)))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29929, 121, 110, 909, 29923])).
% 3.22/3.48 tff(29931,plain,
% 3.22/3.48 (b(s(z), s(s(s(s(z)))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[16482, 29930])).
% 3.22/3.48 tff(29932,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29933,plain,
% 3.22/3.48 (((~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(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29934,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.22/3.48 inference(monotonicity,[status(thm)],[29933])).
% 3.22/3.48 tff(29935,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.22/3.48 inference(transitivity,[status(thm)],[29934, 29932])).
% 3.22/3.48 tff(29936,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(29937,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29936, 29935])).
% 3.22/3.48 tff(29938,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29937, 271, 503, 937, 29931, 12562])).
% 3.22/3.48 tff(29939,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29940,plain,
% 3.22/3.48 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29939, 29921, 29897, 110, 909, 29430, 29736])).
% 3.22/3.48 tff(29941,plain,
% 3.22/3.48 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[28738, 29940, 601])).
% 3.22/3.48 tff(29942,plain,
% 3.22/3.48 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1559, 29941, 28489])).
% 3.22/3.48 tff(29943,plain,
% 3.22/3.48 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[28532, 29942, 601])).
% 3.22/3.48 tff(29944,plain,
% 3.22/3.48 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 3.22/3.48 inference(symmetry,[status(thm)],[25702])).
% 3.22/3.48 tff(29945,plain,
% 3.22/3.48 (b(s(elem!1), z)),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29921, 29944])).
% 3.22/3.48 tff(29946,plain,
% 3.22/3.48 (b(z, s(elem!1))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29430, 28475])).
% 3.22/3.48 tff(29947,plain,
% 3.22/3.48 (b(elem!1, z)),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29921, 28339])).
% 3.22/3.48 tff(29948,plain,
% 3.22/3.48 (~r(s(s(s(z))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1148, 6533, 108, 909])).
% 3.22/3.48 tff(29949,plain,
% 3.22/3.48 (b(s(s(s(z))), elem!1)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[17261, 1209, 1326, 110, 108])).
% 3.22/3.48 tff(29950,plain,
% 3.22/3.48 (~b(s(s(s(z))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1947, 29949, 1326, 261])).
% 3.22/3.48 tff(29951,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1155, 29950, 29948])).
% 3.22/3.48 tff(29952,plain,(b(z, s(s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29953,plain,
% 3.22/3.48 (b(z, s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29952, 29947, 29441, 108, 909, 110])).
% 3.22/3.48 tff(29954,plain,
% 3.22/3.48 (~b(s(s(s(z))), elem!1)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1334, 29953, 29441, 29947])).
% 3.22/3.48 tff(29955,plain,
% 3.22/3.48 (r(s(s(s(z))), elem!1)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[255, 29954, 28220])).
% 3.22/3.48 tff(29956,plain,
% 3.22/3.48 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.22/3.48 inference(monotonicity,[status(thm)],[28217])).
% 3.22/3.48 tff(29957,plain,
% 3.22/3.48 (~b(s(elem!1), s(s(s(z))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[13108, 29956])).
% 3.22/3.48 tff(29958,plain,
% 3.22/3.48 (r(s(elem!1), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[2044, 29957, 28805])).
% 3.22/3.48 tff(29959,plain,
% 3.22/3.48 (~r(s(z), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[3445, 29958, 108, 29955])).
% 3.22/3.48 tff(29960,plain,
% 3.22/3.48 (b(s(z), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[444, 29959, 29767])).
% 3.22/3.48 tff(29961,plain,
% 3.22/3.48 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[17479, 29960, 29946, 29763, 29945, 909])).
% 3.22/3.48 tff(29962,plain,
% 3.22/3.48 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[4138, 29961, 28482])).
% 3.22/3.48 tff(29963,plain,
% 3.22/3.48 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[17429, 29962, 3891])).
% 3.22/3.48 tff(29964,plain,
% 3.22/3.48 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[6237, 21, 13108, 29745])).
% 3.22/3.48 tff(29965,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29966,plain,
% 3.22/3.48 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29967,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.22/3.48 inference(monotonicity,[status(thm)],[29966])).
% 3.22/3.48 tff(29968,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.22/3.48 inference(transitivity,[status(thm)],[29967, 29965])).
% 3.22/3.48 tff(29969,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(29970,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29969, 29968])).
% 3.22/3.48 tff(29971,plain,
% 3.22/3.48 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29970, 121, 29964, 29963, 29943])).
% 3.22/3.48 tff(29972,plain,
% 3.22/3.48 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1777, 29971])).
% 3.22/3.48 tff(29973,plain,
% 3.22/3.48 (r(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[13482, 29955, 3891])).
% 3.22/3.48 tff(29974,plain,
% 3.22/3.48 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[7802, 29963, 29973, 29964])).
% 3.22/3.48 tff(29975,plain,
% 3.22/3.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1733, 29974])).
% 3.22/3.48 tff(29976,plain,
% 3.22/3.48 (~b(z, s(s(s(s(s(z))))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[28970, 271, 29953, 29975, 1935])).
% 3.22/3.48 tff(29977,plain,
% 3.22/3.48 (r(z, s(s(s(s(s(z))))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1658, 29976])).
% 3.22/3.48 tff(29978,plain,
% 3.22/3.48 (~r(s(s(s(s(s(z))))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1669, 29977, 110, 909])).
% 3.22/3.48 tff(29979,plain,
% 3.22/3.48 (b(s(s(s(s(s(z))))), s(z))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1682, 29978])).
% 3.22/3.48 tff(29980,plain,
% 3.22/3.48 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[25909, 29961, 28458])).
% 3.22/3.48 tff(29981,plain,
% 3.22/3.48 (r(s(s(s(s(s(z))))), elem!1)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[840, 29980, 28215])).
% 3.22/3.48 tff(29982,plain,
% 3.22/3.48 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[5462, 29981, 3891])).
% 3.22/3.48 tff(29983,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29984,plain,
% 3.22/3.48 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29985,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.22/3.48 inference(monotonicity,[status(thm)],[29984])).
% 3.22/3.48 tff(29986,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.22/3.48 inference(transitivity,[status(thm)],[29985, 29983])).
% 3.22/3.48 tff(29987,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(29988,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[29987, 29986])).
% 3.22/3.48 tff(29989,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29988, 121, 909, 1661, 1735, 5523])).
% 3.22/3.48 tff(29990,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29991,plain,
% 3.22/3.48 (~r(s(z), s(s(s(s(s(z))))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29990, 29977, 909, 29982])).
% 3.22/3.48 tff(29992,plain,
% 3.22/3.48 (b(s(z), s(s(s(s(s(z))))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1756, 29991])).
% 3.22/3.48 tff(29993,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1785, 29992, 29979, 29897, 29972])).
% 3.22/3.48 tff(29994,plain,(b(s(s(s(elem!1))), s(s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(29995,plain,
% 3.22/3.48 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[29994, 1935, 110, 909, 108, 601])).
% 3.22/3.48 tff(29996,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29997,plain,
% 3.22/3.48 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.22/3.48 inference(rewrite,[status(thm)],[])).
% 3.22/3.48 tff(29998,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z))))),
% 3.22/3.48 inference(monotonicity,[status(thm)],[29997])).
% 3.22/3.48 tff(29999,plain,
% 3.22/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)))),
% 3.22/3.48 inference(transitivity,[status(thm)],[29998, 29996])).
% 3.22/3.48 tff(30000,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.48 inference(quant_inst,[status(thm)],[])).
% 3.22/3.48 tff(30001,plain,
% 3.22/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z))),
% 3.22/3.48 inference(modus_ponens,[status(thm)],[30000, 29999])).
% 3.22/3.48 tff(30002,plain,
% 3.22/3.48 ($false),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[30001, 271, 29430, 29995, 29921, 1935])).
% 3.22/3.48 tff(30003,plain,((~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.48 tff(30004,plain,
% 3.22/3.48 (~b(s(s(s(z))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[30003, 108, 909, 110, 601])).
% 3.22/3.48 tff(30005,plain,
% 3.22/3.48 (r(s(s(s(z))), z)),
% 3.22/3.48 inference(unit_resolution,[status(thm)],[1155, 30004])).
% 3.22/3.48 tff(30006,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30007,plain,
% 3.22/3.49 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30008,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30007])).
% 3.22/3.49 tff(30009,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30008, 30006])).
% 3.22/3.49 tff(30010,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(quant_inst,[status(thm)],[])).
% 3.22/3.49 tff(30011,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30010, 30009])).
% 3.22/3.49 tff(30012,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30011, 121, 110, 909, 30005, 108])).
% 3.22/3.49 tff(30013,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30014,plain,
% 3.22/3.49 (~r(s(z), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30013, 909, 110, 601])).
% 3.22/3.49 tff(30015,plain,
% 3.22/3.49 (b(s(z), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[105, 30014])).
% 3.22/3.49 tff(30016,plain,
% 3.22/3.49 (~b(s(elem!1), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[3622, 222, 447, 3871])).
% 3.22/3.49 tff(30017,plain,
% 3.22/3.49 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30016, 29746])).
% 3.22/3.49 tff(30018,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[6237, 21, 30017, 29745])).
% 3.22/3.49 tff(30019,plain,
% 3.22/3.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29857, 121, 5499, 30018, 26839])).
% 3.22/3.49 tff(30020,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[10426, 30019, 28656])).
% 3.22/3.49 tff(30021,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30022,plain,
% 3.22/3.49 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30021, 222, 30015, 29763, 29897, 601, 29908])).
% 3.22/3.49 tff(30023,plain,
% 3.22/3.49 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28532, 30022, 601])).
% 3.22/3.49 tff(30024,plain,
% 3.22/3.49 (b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1559, 30023, 28489])).
% 3.22/3.49 tff(30025,plain,
% 3.22/3.49 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28738, 30024, 601])).
% 3.22/3.49 tff(30026,plain,
% 3.22/3.49 (~b(s(s(s(elem!1))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29939, 30025, 110, 909, 29897, 29430, 29736])).
% 3.22/3.49 tff(30027,plain,
% 3.22/3.49 (r(s(s(s(z))), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19994, 29908, 25718])).
% 3.22/3.49 tff(30028,plain,
% 3.22/3.49 (r(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[13482, 30027, 3891])).
% 3.22/3.49 tff(30029,plain,
% 3.22/3.49 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29939, 29444, 110, 909, 29897, 29430, 29736])).
% 3.22/3.49 tff(30030,plain,
% 3.22/3.49 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28738, 30029, 601])).
% 3.22/3.49 tff(30031,plain,
% 3.22/3.49 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1559, 30030, 28489])).
% 3.22/3.49 tff(30032,plain,
% 3.22/3.49 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28532, 30031, 601])).
% 3.22/3.49 tff(30033,plain,
% 3.22/3.49 (~b(s(s(s(z))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30021, 30032, 30015, 29763, 29897, 601, 29908])).
% 3.22/3.49 tff(30034,plain,
% 3.22/3.49 (r(s(s(s(z))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2325, 30033])).
% 3.22/3.49 tff(30035,plain,
% 3.22/3.49 (~r(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[10317, 30034, 909, 28256])).
% 3.22/3.49 tff(30036,plain,
% 3.22/3.49 (b(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1155, 30035])).
% 3.22/3.49 tff(30037,plain,
% 3.22/3.49 (~b(elem!1, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[11038, 30036, 30015, 29749])).
% 3.22/3.49 tff(30038,plain,
% 3.22/3.49 (r(elem!1, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1192, 30037, 28221])).
% 3.22/3.49 tff(30039,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28368, 30038, 28326])).
% 3.22/3.49 tff(30040,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30041,plain,
% 3.22/3.49 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30042,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30041])).
% 3.22/3.49 tff(30043,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30042, 30040])).
% 3.22/3.49 tff(30044,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~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))))),
% 3.22/3.49 inference(quant_inst,[status(thm)],[])).
% 3.22/3.49 tff(30045,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30044, 30043])).
% 3.22/3.49 tff(30046,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30045, 121, 572, 30034, 29908, 30039])).
% 3.22/3.49 tff(30047,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30048,plain,
% 3.22/3.49 (~r(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30047, 909, 601, 110])).
% 3.22/3.49 tff(30049,plain,
% 3.22/3.49 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[760, 30048])).
% 3.22/3.49 tff(30050,plain,
% 3.22/3.49 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[12583, 222, 3891, 29897, 30015, 30049, 30028])).
% 3.22/3.49 tff(30051,plain,
% 3.22/3.49 (~r(elem!1, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28368, 30050, 28326])).
% 3.22/3.49 tff(30052,plain,
% 3.22/3.49 (b(elem!1, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1192, 30051, 28221])).
% 3.22/3.49 tff(30053,plain,
% 3.22/3.49 (~b(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[11038, 30052, 30015, 29749])).
% 3.22/3.49 tff(30054,plain,
% 3.22/3.49 (r(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1155, 30053])).
% 3.22/3.49 tff(30055,plain,
% 3.22/3.49 (r(s(s(s(z))), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[10250, 29755, 29108, 29736, 29749, 30015])).
% 3.22/3.49 tff(30056,plain,
% 3.22/3.49 (~r(elem!1, z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[15900, 30055, 909, 109])).
% 3.22/3.49 tff(30057,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30056, 29758])).
% 3.22/3.49 tff(30058,plain,(b(s(s(s(elem!1))), z) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30059,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30058, 30054, 30026, 601, 909, 110])).
% 3.22/3.49 tff(30060,plain,((~b(s(s(s(z))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30061,plain,
% 3.22/3.49 (~b(s(s(s(z))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30060, 28190, 29079, 26])).
% 3.22/3.49 tff(30062,plain,
% 3.22/3.49 (r(s(s(s(z))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2325, 30061])).
% 3.22/3.49 tff(30063,plain,
% 3.22/3.49 (~r(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[10548, 121, 26, 29079, 30062])).
% 3.22/3.49 tff(30064,plain,
% 3.22/3.49 (b(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1155, 30063])).
% 3.22/3.49 tff(30065,plain,
% 3.22/3.49 (~r(z, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[11100, 30062, 26, 29079])).
% 3.22/3.49 tff(30066,plain,
% 3.22/3.49 (b(z, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1214, 30065])).
% 3.22/3.49 tff(30067,plain,
% 3.22/3.49 (~r(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30047, 29079, 28190, 26])).
% 3.22/3.49 tff(30068,plain,
% 3.22/3.49 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[760, 30067])).
% 3.22/3.49 tff(30069,plain,
% 3.22/3.49 (s(s(s(elem!1))) = s(elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[614, 28190])).
% 3.22/3.49 tff(30070,plain,
% 3.22/3.49 (elem!1 = s(s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[78, 30069])).
% 3.22/3.49 tff(30071,plain,
% 3.22/3.49 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29907, 29079, 26, 28190])).
% 3.22/3.49 tff(30072,plain,
% 3.22/3.49 (r(s(s(s(z))), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19994, 30071, 28191])).
% 3.22/3.49 tff(30073,plain,
% 3.22/3.49 (r(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[13482, 30072, 30070])).
% 3.22/3.49 tff(30074,plain,
% 3.22/3.49 (s(elem!1) = s(s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[608, 28190])).
% 3.22/3.49 tff(30075,plain,
% 3.22/3.49 (s(elem!1) = s(s(s(elem!1)))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30074, 28190])).
% 3.22/3.49 tff(30076,plain,
% 3.22/3.49 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30075])).
% 3.22/3.49 tff(30077,plain,
% 3.22/3.49 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = elem!1)),
% 3.22/3.49 inference(transitivity,[status(thm)],[30076, 653])).
% 3.22/3.49 tff(30078,plain,
% 3.22/3.49 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(elem!1))),
% 3.22/3.49 inference(symmetry,[status(thm)],[30077])).
% 3.22/3.49 tff(30079,plain,
% 3.22/3.49 ((s(s(s(elem!1))) = elem!1) <=> (s(elem!1) = elem!1)),
% 3.22/3.49 inference(transitivity,[status(thm)],[30078, 11206])).
% 3.22/3.49 tff(30080,plain,
% 3.22/3.49 (s(elem!1) = elem!1),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[28191, 30079])).
% 3.22/3.49 tff(30081,plain,
% 3.22/3.49 (~r(s(s(elem!1)), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28239, 29732, 30074])).
% 3.22/3.49 tff(30082,plain,
% 3.22/3.49 (b(s(s(elem!1)), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2143, 30081])).
% 3.22/3.49 tff(30083,plain,
% 3.22/3.49 (b(elem!1, s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28387, 30082, 28190, 28191])).
% 3.22/3.49 tff(30084,plain,
% 3.22/3.49 (~r(s(z), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30013, 29079, 26, 28190])).
% 3.22/3.49 tff(30085,plain,
% 3.22/3.49 (b(s(z), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[105, 30084])).
% 3.22/3.49 tff(30086,plain,
% 3.22/3.49 (~b(elem!1, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[11038, 30064, 30085, 30083])).
% 3.22/3.49 tff(30087,plain,
% 3.22/3.49 (r(elem!1, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1192, 30086, 28193])).
% 3.22/3.49 tff(30088,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28368, 30087, 30080])).
% 3.22/3.49 tff(30089,plain,
% 3.22/3.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[12573, 30088, 30070, 29895, 30073, 30068])).
% 3.22/3.49 tff(30090,plain,
% 3.22/3.49 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[10426, 30089])).
% 3.22/3.49 tff(30091,plain,
% 3.22/3.49 (~b(s(s(s(s(z)))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[13513, 30090, 30066, 30064])).
% 3.22/3.49 tff(30092,plain,
% 3.22/3.49 (r(s(s(s(s(z)))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1095, 30091])).
% 3.22/3.49 tff(30093,plain,
% 3.22/3.49 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[28190])).
% 3.22/3.49 tff(30094,plain,
% 3.22/3.49 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30093, 934])).
% 3.22/3.49 tff(30095,plain,
% 3.22/3.49 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30094])).
% 3.22/3.49 tff(30096,plain,
% 3.22/3.49 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[12235, 30070, 2065])).
% 3.22/3.49 tff(30097,plain,
% 3.22/3.49 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30096, 30095])).
% 3.22/3.49 tff(30098,plain,
% 3.22/3.49 (~r(s(z), s(s(s(s(z)))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29929, 121, 26, 29079, 30092])).
% 3.22/3.49 tff(30099,plain,
% 3.22/3.49 (b(s(z), s(s(s(s(z)))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[16482, 30098])).
% 3.22/3.49 tff(30100,plain,
% 3.22/3.49 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1075, 30099, 29895, 29733])).
% 3.22/3.49 tff(30101,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1014, 30100, 30097])).
% 3.22/3.49 tff(30102,plain,
% 3.22/3.49 (~r(s(s(s(elem!1))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29135, 30101, 29079, 30092])).
% 3.22/3.49 tff(30103,plain,
% 3.22/3.49 (b(s(s(s(elem!1))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[8229, 30102])).
% 3.22/3.49 tff(30104,plain,
% 3.22/3.49 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[29939, 30103, 26, 29079, 29895, 29734, 29733])).
% 3.22/3.49 tff(30105,plain,
% 3.22/3.49 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28738, 30104, 28190])).
% 3.22/3.49 tff(30106,plain,
% 3.22/3.49 (r(s(s(s(s(z)))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1559, 30105, 28194])).
% 3.22/3.49 tff(30107,plain,
% 3.22/3.49 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28532, 30106, 28190])).
% 3.22/3.49 tff(30108,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30109,plain,
% 3.22/3.49 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30110,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30109])).
% 3.22/3.49 tff(30111,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30110, 30108])).
% 3.22/3.49 tff(30112,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.22/3.49 inference(quant_inst,[status(thm)],[])).
% 3.22/3.49 tff(30113,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30112, 30111])).
% 3.22/3.49 tff(30114,plain,
% 3.22/3.49 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30113, 121, 30071, 30088, 30107])).
% 3.22/3.49 tff(30115,plain,
% 3.22/3.49 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[14911, 30090, 30085, 29895])).
% 3.22/3.49 tff(30116,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1167, 21, 30115, 30114, 20146])).
% 3.22/3.49 tff(30117,plain,(b(s(z), z) | (s(s(s(z))) = s(s(s(elem!1)))) | (z = elem!1) | r(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30118,plain,
% 3.22/3.49 (b(s(z), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30117, 9149, 9297, 147, 2282])).
% 3.22/3.49 tff(30119,plain,
% 3.22/3.49 (~r(s(s(s(z))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[13333, 906, 28508])).
% 3.22/3.49 tff(30120,plain,
% 3.22/3.49 (b(s(s(s(z))), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1816, 30119, 28342])).
% 3.22/3.49 tff(30121,plain,
% 3.22/3.49 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2071, 906, 2065])).
% 3.22/3.49 tff(30122,plain,
% 3.22/3.49 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.49 tff(30123,plain,
% 3.22/3.49 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 3.22/3.49 inference(symmetry,[status(thm)],[30122])).
% 3.22/3.49 tff(30124,plain,
% 3.22/3.49 (b(s(s(s(z))), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19808, 2073, 28225])).
% 3.22/3.49 tff(30125,plain,
% 3.22/3.49 (~r(z, elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[3464, 29030, 909, 108])).
% 3.22/3.49 tff(30126,plain,
% 3.22/3.49 (~r(z, s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[11073, 30125, 25718])).
% 3.22/3.49 tff(30127,plain,
% 3.22/3.49 (b(z, s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19736, 30126])).
% 3.22/3.49 tff(30128,plain,
% 3.22/3.49 (b(z, s(s(elem!1)))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30127, 29082])).
% 3.22/3.49 tff(30129,plain,
% 3.22/3.49 (b(z, elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[355, 30125, 331])).
% 3.22/3.49 tff(30130,plain,
% 3.22/3.49 (b(z, s(elem!1))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30127, 28475])).
% 3.22/3.49 tff(30131,plain,
% 3.22/3.49 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[29014])).
% 3.22/3.49 tff(30132,plain,
% 3.22/3.49 (~(s(z) = elem!1)),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[61, 30131])).
% 3.22/3.49 tff(30133,plain,
% 3.22/3.49 (~b(s(z), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19692, 9874, 2505])).
% 3.22/3.49 tff(30134,plain,
% 3.22/3.49 (r(s(z), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[236, 30133, 30132])).
% 3.22/3.49 tff(30135,plain,
% 3.22/3.49 (r(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[760, 9874])).
% 3.22/3.49 tff(30136,plain,
% 3.22/3.49 (r(s(z), s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28255, 30135, 201])).
% 3.22/3.49 tff(30137,plain,
% 3.22/3.49 (s(s(s(elem!1))) = elem!1),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[3895, 28231])).
% 3.22/3.49 tff(30138,plain,
% 3.22/3.49 (~(s(s(s(z))) = s(elem!1))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2596, 30137])).
% 3.22/3.49 tff(30139,plain,
% 3.22/3.49 (~(s(elem!1) = s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2035, 30138])).
% 3.22/3.49 tff(30140,plain,
% 3.22/3.49 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[28233])).
% 3.22/3.49 tff(30141,plain,
% 3.22/3.49 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30140])).
% 3.22/3.49 tff(30142,plain,
% 3.22/3.49 (~b(s(s(s(z))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2650, 1935, 1281, 1894])).
% 3.22/3.49 tff(30143,plain,
% 3.22/3.49 (r(s(s(s(z))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2325, 30142])).
% 3.22/3.49 tff(30144,plain,
% 3.22/3.49 (~r(z, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[6541, 30143, 909, 357])).
% 3.22/3.49 tff(30145,plain,
% 3.22/3.49 (b(z, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1214, 30144])).
% 3.22/3.49 tff(30146,plain,
% 3.22/3.49 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[5687, 30145, 3407, 1422])).
% 3.22/3.49 tff(30147,plain,
% 3.22/3.49 (~b(s(elem!1), s(s(s(z))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30146, 30141])).
% 3.22/3.49 tff(30148,plain,
% 3.22/3.49 (r(s(elem!1), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2042, 21, 30147, 30139])).
% 3.22/3.49 tff(30149,plain,
% 3.22/3.49 (~b(s(z), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[5539, 271, 1281, 30145, 1935])).
% 3.22/3.49 tff(30150,plain,
% 3.22/3.49 (r(s(z), s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[105, 30149])).
% 3.22/3.49 tff(30151,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[8512, 121, 431, 30143, 30150, 30148])).
% 3.22/3.49 tff(30152,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(elem!1))) | (~b(s(z), z)) | (~(s(elem!1) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30153,plain,
% 3.22/3.49 (~b(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30152, 30136, 1281, 201, 1422, 3407, 909, 30134, 1894])).
% 3.22/3.49 tff(30154,plain,
% 3.22/3.49 (r(s(s(s(z))), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1155, 30153])).
% 3.22/3.49 tff(30155,plain,
% 3.22/3.49 (~r(z, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1148, 30154, 909, 108])).
% 3.22/3.49 tff(30156,plain,
% 3.22/3.49 (b(z, s(s(s(z))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1214, 30155])).
% 3.22/3.49 tff(30157,plain,
% 3.22/3.49 (~b(s(elem!1), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19710, 30156, 1422, 1421])).
% 3.22/3.49 tff(30158,plain,
% 3.22/3.49 (r(s(elem!1), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[409, 30157])).
% 3.22/3.49 tff(30159,plain,
% 3.22/3.49 (~b(elem!1, s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[15974, 30156, 257, 1326])).
% 3.22/3.49 tff(30160,plain,
% 3.22/3.49 (~b(s(elem!1), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28768, 30159, 2203])).
% 3.22/3.49 tff(30161,plain,
% 3.22/3.49 (r(s(elem!1), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[429, 30160, 422])).
% 3.22/3.49 tff(30162,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[1254, 30161, 30158, 909, 30134])).
% 3.22/3.49 tff(30163,plain,(b(s(z), s(s(s(elem!1)))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~(s(elem!1) = elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~(s(elem!1) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30164,plain,
% 3.22/3.49 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30163, 30130, 422, 28326, 1422, 909, 257, 30129, 108, 1281, 609, 30127, 30128, 25718])).
% 3.22/3.49 tff(30165,plain,
% 3.22/3.49 (b(s(z), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2562, 30164, 25718])).
% 3.22/3.49 tff(30166,plain,
% 3.22/3.49 (~b(s(elem!1), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[25803, 30165, 1281, 28458, 108])).
% 3.22/3.49 tff(30167,plain,
% 3.22/3.49 (r(s(elem!1), z)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[409, 30166])).
% 3.22/3.49 tff(30168,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), z)),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30167, 28511])).
% 3.22/3.49 tff(30169,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30170,plain,
% 3.22/3.49 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(rewrite,[status(thm)],[])).
% 3.22/3.49 tff(30171,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(z)))))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30170])).
% 3.22/3.49 tff(30172,plain,
% 3.22/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30171, 30169])).
% 3.22/3.49 tff(30173,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 3.22/3.49 inference(quant_inst,[status(thm)],[])).
% 3.22/3.49 tff(30174,plain,
% 3.22/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(z)))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30173, 30172])).
% 3.22/3.49 tff(30175,plain,
% 3.22/3.49 ($false),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30174, 121, 909, 12761, 30168, 108])).
% 3.22/3.49 tff(30176,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.22/3.49 tff(30177,plain,
% 3.22/3.49 (~r(s(s(s(elem!1))), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[30176, 108, 909, 601, 1281, 422, 1422, 30124, 331])).
% 3.22/3.49 tff(30178,plain,
% 3.22/3.49 (~r(s(s(elem!1)), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28239, 30177, 609])).
% 3.22/3.49 tff(30179,plain,
% 3.22/3.49 (b(s(s(elem!1)), s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[2143, 30178])).
% 3.22/3.49 tff(30180,plain,
% 3.22/3.49 (b(s(s(s(z))), s(s(elem!1)))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[2073, 28860])).
% 3.22/3.49 tff(30181,plain,
% 3.22/3.49 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[28196])).
% 3.22/3.49 tff(30182,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 3.22/3.49 inference(symmetry,[status(thm)],[30181])).
% 3.22/3.49 tff(30183,plain,
% 3.22/3.49 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(elem!1, s(z)))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30182])).
% 3.22/3.49 tff(30184,plain,
% 3.22/3.49 (~r(elem!1, s(z))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[30177, 30183])).
% 3.22/3.49 tff(30185,plain,
% 3.22/3.49 (b(elem!1, s(z))),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[28387, 30179, 601, 25718])).
% 3.22/3.49 tff(30186,plain,
% 3.22/3.49 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[28328])).
% 3.22/3.49 tff(30187,plain,
% 3.22/3.49 (~b(s(z), elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[19692, 9874, 25718])).
% 3.22/3.49 tff(30188,plain,
% 3.22/3.49 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[601])).
% 3.22/3.49 tff(30189,plain,
% 3.22/3.49 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.22/3.49 inference(symmetry,[status(thm)],[30188])).
% 3.22/3.49 tff(30190,plain,
% 3.22/3.49 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30189])).
% 3.22/3.49 tff(30191,plain,
% 3.22/3.49 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[12265, 30190])).
% 3.22/3.49 tff(30192,plain,
% 3.22/3.49 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[25701])).
% 3.22/3.49 tff(30193,plain,
% 3.22/3.49 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 3.22/3.49 inference(symmetry,[status(thm)],[30192])).
% 3.22/3.49 tff(30194,plain,
% 3.22/3.49 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[28196])).
% 3.22/3.49 tff(30195,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.22/3.49 inference(symmetry,[status(thm)],[30194])).
% 3.22/3.49 tff(30196,plain,
% 3.22/3.49 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 3.22/3.49 inference(transitivity,[status(thm)],[30195, 30193])).
% 3.22/3.49 tff(30197,plain,
% 3.22/3.49 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(elem!1, s(elem!1)))),
% 3.22/3.49 inference(monotonicity,[status(thm)],[30196])).
% 3.22/3.49 tff(30198,plain,
% 3.22/3.49 (~r(elem!1, s(elem!1))),
% 3.22/3.49 inference(modus_ponens,[status(thm)],[179, 30197])).
% 3.22/3.49 tff(30199,plain,
% 3.22/3.49 (r(z, elem!1)),
% 3.22/3.49 inference(unit_resolution,[status(thm)],[11073, 111, 25718])).
% 3.22/3.50 tff(30200,plain,
% 3.22/3.50 (~b(s(elem!1), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[25755, 30199, 1281, 601, 293, 30198, 30191, 1242])).
% 3.22/3.50 tff(30201,plain,
% 3.22/3.50 (r(s(elem!1), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[409, 30200])).
% 3.22/3.50 tff(30202,plain,
% 3.22/3.50 (r(s(s(s(elem!1))), z)),
% 3.22/3.50 inference(modus_ponens,[status(thm)],[30201, 28511])).
% 3.22/3.50 tff(30203,plain,
% 3.22/3.50 ($false),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[23351, 121, 111, 572, 909, 30202])).
% 3.22/3.50 tff(30204,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | r(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.22/3.50 tff(30205,plain,
% 3.22/3.50 (~r(z, s(s(s(elem!1))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[30204, 30135, 909, 601, 1281, 293, 30187])).
% 3.22/3.50 tff(30206,plain,
% 3.22/3.50 (~r(z, s(s(elem!1)))),
% 3.22/3.50 inference(modus_ponens,[status(thm)],[30205, 30186])).
% 3.22/3.50 tff(30207,plain,
% 3.22/3.50 (b(z, s(s(s(elem!1))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[19736, 30205])).
% 3.22/3.50 tff(30208,plain,
% 3.22/3.50 (r(s(z), elem!1)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[236, 30187, 28201])).
% 3.22/3.50 tff(30209,plain,
% 3.22/3.50 (r(s(z), s(elem!1))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[28255, 30135, 609])).
% 3.22/3.50 tff(30210,plain,
% 3.22/3.50 (b(z, elem!1)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[13207, 30207, 28225])).
% 3.22/3.50 tff(30211,plain,
% 3.22/3.50 (~b(z, s(s(s(z))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[15974, 30210, 257, 448])).
% 3.22/3.50 tff(30212,plain,
% 3.22/3.50 (r(z, s(s(s(z))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[1214, 30211])).
% 3.22/3.50 tff(30213,plain,
% 3.22/3.50 (~r(s(s(s(z))), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[1148, 30212, 909, 108])).
% 3.22/3.50 tff(30214,plain,
% 3.22/3.50 (b(s(s(s(z))), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[1155, 30213])).
% 3.22/3.50 tff(30215,plain,
% 3.22/3.50 (~b(z, s(s(elem!1)))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[30152, 30214, 1281, 609, 1422, 30209, 909, 30208, 30207])).
% 3.22/3.50 tff(30216,plain,
% 3.22/3.50 (r(z, s(s(elem!1)))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[2106, 30215])).
% 3.22/3.50 tff(30217,plain,
% 3.22/3.50 ($false),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[30216, 30206])).
% 3.22/3.50 tff(30218,plain,(b(s(z), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.22/3.50 tff(30219,plain,
% 3.22/3.50 (b(s(z), s(s(s(elem!1))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[30218, 108, 1281, 1422, 909, 601, 30124, 30185, 30184])).
% 3.22/3.50 tff(30220,plain,
% 3.22/3.50 (b(s(s(s(elem!1))), s(z))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[16580, 30177])).
% 3.22/3.50 tff(30221,plain,
% 3.22/3.50 (b(s(z), elem!1)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[2562, 30219, 25718])).
% 3.22/3.50 tff(30222,plain,
% 3.22/3.50 (~b(s(elem!1), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[25803, 30221, 1281, 28458, 108])).
% 3.22/3.50 tff(30223,plain,
% 3.22/3.50 (r(s(elem!1), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[409, 30222])).
% 3.22/3.50 tff(30224,plain,
% 3.22/3.50 (r(s(s(s(elem!1))), z)),
% 3.22/3.50 inference(modus_ponens,[status(thm)],[30223, 28511])).
% 3.22/3.50 tff(30225,plain,
% 3.22/3.50 (~b(s(s(s(z))), s(z))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[2081, 30219, 2073, 30220])).
% 3.22/3.50 tff(30226,plain,
% 3.22/3.50 (r(s(s(s(z))), s(z))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[2325, 30225])).
% 3.22/3.50 tff(30227,plain,
% 3.22/3.50 (~r(s(s(s(z))), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[6186, 121, 909, 2327, 108])).
% 3.22/3.50 tff(30228,plain,
% 3.22/3.50 (b(s(s(s(z))), z)),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[1155, 30227])).
% 3.22/3.50 tff(30229,plain,
% 3.22/3.50 (~r(z, s(s(s(z))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[2335, 2327, 909, 108])).
% 3.22/3.50 tff(30230,plain,
% 3.22/3.50 (b(z, s(s(s(z))))),
% 3.22/3.50 inference(unit_resolution,[status(thm)],[1214, 30229])).
% 3.22/3.50 tff(30231,plain,
% 3.22/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30232,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.50 inference(quant_inst,[status(thm)],[])).
% 3.32/3.50 tff(30233,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30232, 30231])).
% 3.32/3.50 tff(30234,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30233, 121, 911, 2327, 108, 12542])).
% 3.32/3.50 tff(30235,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30236,plain,
% 3.32/3.50 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30235, 911, 108, 2327])).
% 3.32/3.50 tff(30237,plain,
% 3.32/3.50 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[10426, 30236])).
% 3.32/3.50 tff(30238,plain,
% 3.32/3.50 (~b(s(s(s(s(z)))), z)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[13513, 30237, 30230, 30228])).
% 3.32/3.50 tff(30239,plain,
% 3.32/3.50 (r(s(s(s(s(z)))), z)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1095, 30238])).
% 3.32/3.50 tff(30240,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[6690, 121, 909, 911, 108, 30239])).
% 3.32/3.50 tff(30241,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30242,plain,
% 3.32/3.50 (~r(s(s(s(s(z)))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30241, 108, 909, 30226])).
% 3.32/3.50 tff(30243,plain,
% 3.32/3.50 (b(s(s(s(s(z)))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[932, 30242])).
% 3.32/3.50 tff(30244,plain,
% 3.32/3.50 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[29196, 30243, 601, 30226, 30224, 30185, 30220, 30219, 108])).
% 3.32/3.50 tff(30245,plain,
% 3.32/3.50 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1733, 30244])).
% 3.32/3.50 tff(30246,plain,
% 3.32/3.50 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28875, 30245, 3891, 30180, 30179])).
% 3.32/3.50 tff(30247,plain,
% 3.32/3.50 (r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[840, 30246, 28215])).
% 3.32/3.50 tff(30248,plain,
% 3.32/3.50 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30247, 28570])).
% 3.32/3.50 tff(30249,plain,
% 3.32/3.50 (~r(z, s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2335, 30226, 909, 108])).
% 3.32/3.50 tff(30250,plain,
% 3.32/3.50 (b(z, s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1214, 30249])).
% 3.32/3.50 tff(30251,plain,
% 3.32/3.50 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[6049, 30245, 1422, 30250])).
% 3.32/3.50 tff(30252,plain,
% 3.32/3.50 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1658, 30251])).
% 3.32/3.50 tff(30253,plain,
% 3.32/3.50 (~b(z, elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[4827, 30221, 30124, 30185])).
% 3.32/3.50 tff(30254,plain,
% 3.32/3.50 (~b(z, s(s(s(elem!1))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[13207, 30253, 28225])).
% 3.32/3.50 tff(30255,plain,
% 3.32/3.50 (r(z, s(s(s(elem!1))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[19736, 30254])).
% 3.32/3.50 tff(30256,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28896, 121, 30255, 30252, 30224, 30248])).
% 3.32/3.50 tff(30257,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30258,plain,
% 3.32/3.50 (~r(s(z), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30257, 909, 601, 1422, 1281, 2073, 422, 331])).
% 3.32/3.50 tff(30259,plain,
% 3.32/3.50 (b(s(z), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[105, 30258])).
% 3.32/3.50 tff(30260,plain,
% 3.32/3.50 (r(s(z), s(s(elem!1)))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30135, 28553])).
% 3.32/3.50 tff(30261,plain,
% 3.32/3.50 (~b(z, s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[19817, 3871, 1281, 2073])).
% 3.32/3.50 tff(30262,plain,
% 3.32/3.50 (r(z, s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1214, 30261])).
% 3.32/3.50 tff(30263,plain,
% 3.32/3.50 (~r(s(s(s(z))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[6541, 30208, 909, 30262])).
% 3.32/3.50 tff(30264,plain,
% 3.32/3.50 (b(s(s(s(z))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2325, 30263])).
% 3.32/3.50 tff(30265,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[12641, 271, 2073, 3871, 222, 503])).
% 3.32/3.50 tff(30266,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30267,plain,
% 3.32/3.50 (~b(s(s(s(elem!1))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30266, 30264, 2073, 3871])).
% 3.32/3.50 tff(30268,plain,
% 3.32/3.50 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[16580, 30267])).
% 3.32/3.50 tff(30269,plain,
% 3.32/3.50 (r(elem!1, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[12809, 30268, 25718])).
% 3.32/3.50 tff(30270,plain,
% 3.32/3.50 (~r(z, elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[19790, 30269, 909, 30135])).
% 3.32/3.50 tff(30271,plain,
% 3.32/3.50 (b(z, elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[355, 30270, 331])).
% 3.32/3.50 tff(30272,plain,
% 3.32/3.50 (~r(z, s(s(s(elem!1))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[11073, 30270, 25718])).
% 3.32/3.50 tff(30273,plain,
% 3.32/3.50 (b(z, s(s(s(elem!1))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[19736, 30272])).
% 3.32/3.50 tff(30274,plain,
% 3.32/3.50 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[3891])).
% 3.32/3.50 tff(30275,plain,
% 3.32/3.50 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.50 inference(transitivity,[status(thm)],[30274, 29640])).
% 3.32/3.50 tff(30276,plain,
% 3.32/3.50 (~b(s(z), s(s(s(elem!1))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[22129, 271, 1281, 3407, 28259])).
% 3.32/3.50 tff(30277,plain,
% 3.32/3.50 (r(s(z), s(s(s(elem!1))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[760, 30276])).
% 3.32/3.50 tff(30278,plain,
% 3.32/3.50 (r(s(z), s(s(elem!1)))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30277, 28553])).
% 3.32/3.50 tff(30279,plain,
% 3.32/3.50 (b(z, elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[13207, 28225, 3407])).
% 3.32/3.50 tff(30280,plain,
% 3.32/3.50 (~b(elem!1, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[4775, 29592, 30279, 1281])).
% 3.32/3.50 tff(30281,plain,
% 3.32/3.50 (r(elem!1, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[299, 30280, 29100])).
% 3.32/3.50 tff(30282,plain,
% 3.32/3.50 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.50 inference(symmetry,[status(thm)],[30274])).
% 3.32/3.50 tff(30283,plain,
% 3.32/3.50 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[30282])).
% 3.32/3.50 tff(30284,plain,
% 3.32/3.50 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[29645, 1639, 3407, 601, 1638])).
% 3.32/3.50 tff(30285,plain,
% 3.32/3.50 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30284, 30283])).
% 3.32/3.50 tff(30286,plain,
% 3.32/3.50 (r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[840, 30285, 28215])).
% 3.32/3.50 tff(30287,plain,
% 3.32/3.50 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30286, 29155])).
% 3.32/3.50 tff(30288,plain,
% 3.32/3.50 (b(elem!1, z)),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[1638, 28339])).
% 3.32/3.50 tff(30289,plain,
% 3.32/3.50 (~b(elem!1, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[4775, 30288, 30279, 1281])).
% 3.32/3.50 tff(30290,plain,
% 3.32/3.50 (~b(s(s(elem!1)), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28387, 30289, 601, 25718])).
% 3.32/3.50 tff(30291,plain,
% 3.32/3.50 (r(s(s(elem!1)), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2143, 30290])).
% 3.32/3.50 tff(30292,plain,
% 3.32/3.50 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28239, 30291, 609])).
% 3.32/3.50 tff(30293,plain,
% 3.32/3.50 (~r(s(z), s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28681, 121, 22145, 30292, 30287])).
% 3.32/3.50 tff(30294,plain,
% 3.32/3.50 (b(s(z), s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1756, 30293])).
% 3.32/3.50 tff(30295,plain,
% 3.32/3.50 (r(s(z), s(s(elem!1)))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[22145, 28553])).
% 3.32/3.50 tff(30296,plain,
% 3.32/3.50 (r(elem!1, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[299, 30289, 29100])).
% 3.32/3.50 tff(30297,plain,
% 3.32/3.50 (~r(s(s(s(s(s(z))))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[25896, 30286, 30296, 30295])).
% 3.32/3.50 tff(30298,plain,
% 3.32/3.50 (b(s(s(s(s(s(z))))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1682, 30297])).
% 3.32/3.50 tff(30299,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30300,plain,
% 3.32/3.50 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30301,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[30300])).
% 3.32/3.50 tff(30302,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(transitivity,[status(thm)],[30301, 30299])).
% 3.32/3.50 tff(30303,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 3.32/3.50 inference(quant_inst,[status(thm)],[])).
% 3.32/3.50 tff(30304,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30303, 30302])).
% 3.32/3.50 tff(30305,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30304, 271, 1281, 1639, 30298, 30294])).
% 3.32/3.50 tff(30306,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30307,plain,
% 3.32/3.50 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30306, 28259, 601, 3407, 1281])).
% 3.32/3.50 tff(30308,plain,
% 3.32/3.50 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1658, 30307])).
% 3.32/3.50 tff(30309,plain,
% 3.32/3.50 (~b(z, s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[25337, 30281, 30278, 28220, 1281, 3871])).
% 3.32/3.50 tff(30310,plain,
% 3.32/3.50 (r(z, s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1214, 30309])).
% 3.32/3.50 tff(30311,plain,
% 3.32/3.50 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 3.32/3.50 inference(symmetry,[status(thm)],[28282])).
% 3.32/3.50 tff(30312,plain,
% 3.32/3.50 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), elem!1))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[30311])).
% 3.32/3.50 tff(30313,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 3.32/3.50 tff(30314,plain,
% 3.32/3.50 (s(elem!1) = s(s(s(s(z))))),
% 3.32/3.50 inference(transitivity,[status(thm)],[2203, 30313])).
% 3.32/3.50 tff(30315,plain,
% 3.32/3.50 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[25692, 28357])).
% 3.32/3.50 tff(30316,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30315, 30314])).
% 3.32/3.50 tff(30317,plain,((~(elem!1 = s(s(s(s(z)))))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30318,plain,
% 3.32/3.50 (~(elem!1 = s(s(s(s(z)))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30317, 28326])).
% 3.32/3.50 tff(30319,plain,
% 3.32/3.50 (~b(s(z), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[21030, 29592, 1281, 3407])).
% 3.32/3.50 tff(30320,plain,
% 3.32/3.50 (r(s(z), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[236, 30319, 28337])).
% 3.32/3.50 tff(30321,plain,
% 3.32/3.50 (~b(s(z), s(elem!1))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[23220, 394, 30279, 1281])).
% 3.32/3.50 tff(30322,plain,
% 3.32/3.50 (r(s(z), s(elem!1))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[444, 30321, 29767])).
% 3.32/3.50 tff(30323,plain,
% 3.32/3.50 (b(z, s(s(elem!1)))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[3407, 29082])).
% 3.32/3.50 tff(30324,plain,
% 3.32/3.50 (~r(s(s(s(z))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[6541, 909, 357, 1140])).
% 3.32/3.50 tff(30325,plain,
% 3.32/3.50 (b(s(s(s(z))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2325, 30324])).
% 3.32/3.50 tff(30326,plain,
% 3.32/3.50 (~r(s(s(s(z))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[10317, 109, 431, 909])).
% 3.32/3.50 tff(30327,plain,
% 3.32/3.50 (b(s(s(s(z))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2325, 30326])).
% 3.32/3.50 tff(30328,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30329,plain,
% 3.32/3.50 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30330,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[30329])).
% 3.32/3.50 tff(30331,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(transitivity,[status(thm)],[30330, 30328])).
% 3.32/3.50 tff(30332,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(quant_inst,[status(thm)],[])).
% 3.32/3.50 tff(30333,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30332, 30331])).
% 3.32/3.50 tff(30334,plain,
% 3.32/3.50 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30333, 271, 1281, 30327, 5393])).
% 3.32/3.50 tff(30335,plain,
% 3.32/3.50 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1494, 30334])).
% 3.32/3.50 tff(30336,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30337,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.32/3.50 inference(quant_inst,[status(thm)],[])).
% 3.32/3.50 tff(30338,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30337, 30336])).
% 3.32/3.50 tff(30339,plain,
% 3.32/3.50 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30338, 271, 1281, 30327, 5393])).
% 3.32/3.50 tff(30340,plain,
% 3.32/3.50 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1733, 30339])).
% 3.32/3.50 tff(30341,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[5135, 30340, 30335, 1661, 109])).
% 3.32/3.50 tff(30342,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30343,plain,
% 3.32/3.50 (~b(s(s(s(s(s(z))))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30342, 1661, 109, 909, 431, 1281])).
% 3.32/3.50 tff(30344,plain,
% 3.32/3.50 (r(s(s(s(s(s(z))))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1682, 30343])).
% 3.32/3.50 tff(30345,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30346,plain,
% 3.32/3.50 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.32/3.50 inference(rewrite,[status(thm)],[])).
% 3.32/3.50 tff(30347,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[30346])).
% 3.32/3.50 tff(30348,plain,
% 3.32/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.32/3.50 inference(transitivity,[status(thm)],[30347, 30345])).
% 3.32/3.50 tff(30349,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.32/3.50 inference(quant_inst,[status(thm)],[])).
% 3.32/3.50 tff(30350,plain,
% 3.32/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 3.32/3.50 inference(modus_ponens,[status(thm)],[30349, 30348])).
% 3.32/3.50 tff(30351,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30350, 121, 572, 909, 1661, 30344])).
% 3.32/3.50 tff(30352,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(elem!1))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30353,plain,
% 3.32/3.50 (~r(s(s(s(z))), z)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30352, 909, 572, 1661, 431, 1281])).
% 3.32/3.50 tff(30354,plain,
% 3.32/3.50 (b(s(s(s(z))), z)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[1155, 30353])).
% 3.32/3.50 tff(30355,plain,
% 3.32/3.50 ($false),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2650, 30354, 30325, 1281, 1894])).
% 3.32/3.50 tff(30356,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.50 tff(30357,plain,
% 3.32/3.50 (~r(z, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[30356, 30277, 30323, 1281, 30308, 30322, 30320, 30310])).
% 3.32/3.50 tff(30358,plain,
% 3.32/3.50 (b(z, s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[904, 30357])).
% 3.32/3.50 tff(30359,plain,
% 3.32/3.50 (~b(s(s(elem!1)), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28387, 30280, 601, 25718])).
% 3.32/3.50 tff(30360,plain,
% 3.32/3.50 (r(s(s(elem!1)), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[2143, 30359])).
% 3.32/3.50 tff(30361,plain,
% 3.32/3.50 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[28239, 30360, 609])).
% 3.32/3.50 tff(30362,plain,
% 3.32/3.50 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[25692, 28458])).
% 3.32/3.50 tff(30363,plain,
% 3.32/3.50 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[14008, 30362])).
% 3.32/3.50 tff(30364,plain,
% 3.32/3.50 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 3.32/3.50 inference(monotonicity,[status(thm)],[25730])).
% 3.32/3.50 tff(30365,plain,
% 3.32/3.50 (~r(s(s(s(z))), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[12518, 2327, 3456, 28554])).
% 3.32/3.50 tff(30366,plain,
% 3.32/3.50 (b(s(s(s(z))), elem!1)),
% 3.32/3.50 inference(unit_resolution,[status(thm)],[255, 30365, 28220])).
% 3.32/3.50 tff(30367,plain,
% 3.32/3.51 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30366, 28282])).
% 3.32/3.51 tff(30368,plain,
% 3.32/3.51 (~b(s(s(s(s(z)))), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[22548, 937, 220, 1281])).
% 3.32/3.51 tff(30369,plain,
% 3.32/3.51 (r(s(s(s(s(z)))), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1095, 30368])).
% 3.32/3.51 tff(30370,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30371,plain,
% 3.32/3.51 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30372,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30371])).
% 3.32/3.51 tff(30373,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.51 inference(transitivity,[status(thm)],[30372, 30370])).
% 3.32/3.51 tff(30374,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.51 inference(quant_inst,[status(thm)],[])).
% 3.32/3.51 tff(30375,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30374, 30373])).
% 3.32/3.51 tff(30376,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30375, 121, 1661, 21200, 30369])).
% 3.32/3.51 tff(30377,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[10424, 21, 1138, 30376])).
% 3.32/3.51 tff(30378,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30379,plain,
% 3.32/3.51 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30380,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30379])).
% 3.32/3.51 tff(30381,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.51 inference(transitivity,[status(thm)],[30380, 30378])).
% 3.32/3.51 tff(30382,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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))))),
% 3.32/3.51 inference(quant_inst,[status(thm)],[])).
% 3.32/3.51 tff(30383,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30382, 30381])).
% 3.32/3.51 tff(30384,plain,
% 3.32/3.51 ($false),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30383, 271, 2073, 3871, 937, 30377])).
% 3.32/3.51 tff(30385,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.51 tff(30386,plain,
% 3.32/3.51 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30385, 30367, 3871, 1661, 220, 1281])).
% 3.32/3.51 tff(30387,plain,
% 3.32/3.51 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[932, 30386])).
% 3.32/3.51 tff(30388,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[28688, 121, 572, 12761, 30387])).
% 3.32/3.51 tff(30389,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30388, 30364])).
% 3.32/3.51 tff(30390,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1559, 30389, 30363])).
% 3.32/3.51 tff(30391,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30390, 28734])).
% 3.32/3.51 tff(30392,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[26852, 121, 572, 30387, 2327])).
% 3.32/3.51 tff(30393,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[10424, 21, 1138, 30392])).
% 3.32/3.51 tff(30394,plain,
% 3.32/3.51 (~r(elem!1, s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[11254, 2327, 3456, 357])).
% 3.32/3.51 tff(30395,plain,
% 3.32/3.51 (b(elem!1, s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1192, 30394, 28221])).
% 3.32/3.51 tff(30396,plain,
% 3.32/3.51 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30395, 28333])).
% 3.32/3.51 tff(30397,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30398,plain,
% 3.32/3.51 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30399,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30398])).
% 3.32/3.51 tff(30400,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.51 inference(transitivity,[status(thm)],[30399, 30397])).
% 3.32/3.51 tff(30401,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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))))))),
% 3.32/3.51 inference(quant_inst,[status(thm)],[])).
% 3.32/3.51 tff(30402,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30401, 30400])).
% 3.32/3.51 tff(30403,plain,
% 3.32/3.51 ($false),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30402, 271, 30396, 30367, 30393, 30391])).
% 3.32/3.51 tff(30404,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.51 tff(30405,plain,
% 3.32/3.51 (~r(s(s(s(z))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30404, 30277, 601, 30361, 3871, 30308, 30358, 1281, 30281, 30320])).
% 3.32/3.51 tff(30406,plain,
% 3.32/3.51 (b(s(s(s(z))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[2325, 30405])).
% 3.32/3.51 tff(30407,plain,
% 3.32/3.51 ($false),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[12581, 271, 3871, 222, 937, 30377])).
% 3.32/3.51 tff(30408,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.51 tff(30409,plain,
% 3.32/3.51 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30408, 30406, 3871, 30308, 30358, 1281])).
% 3.32/3.51 tff(30410,plain,
% 3.32/3.51 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[932, 30409])).
% 3.32/3.51 tff(30411,plain,
% 3.32/3.51 (~r(elem!1, s(s(s(s(z)))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[21233, 30410, 30281, 30277])).
% 3.32/3.51 tff(30412,plain,
% 3.32/3.51 (b(elem!1, s(s(s(s(z)))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[20539, 30411, 30318])).
% 3.32/3.51 tff(30413,plain,
% 3.32/3.51 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[28428, 30412, 601])).
% 3.32/3.51 tff(30414,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[28688, 121, 30277, 30361, 30410])).
% 3.32/3.51 tff(30415,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30414, 30364])).
% 3.32/3.51 tff(30416,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1559, 30415, 30363])).
% 3.32/3.51 tff(30417,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30416, 28734])).
% 3.32/3.51 tff(30418,plain,
% 3.32/3.51 (~b(s(s(s(s(z)))), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[28730, 271, 3407, 28259, 30417])).
% 3.32/3.51 tff(30419,plain,
% 3.32/3.51 (r(s(s(s(s(z)))), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1095, 30418])).
% 3.32/3.51 tff(30420,plain,
% 3.32/3.51 (~b(s(s(s(z))), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[21058, 30358, 1281, 3871])).
% 3.32/3.51 tff(30421,plain,
% 3.32/3.51 (r(s(s(s(z))), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1155, 30420])).
% 3.32/3.51 tff(30422,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30423,plain,
% 3.32/3.51 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30424,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30423])).
% 3.32/3.51 tff(30425,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.51 inference(transitivity,[status(thm)],[30424, 30422])).
% 3.32/3.51 tff(30426,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.32/3.51 inference(quant_inst,[status(thm)],[])).
% 3.32/3.51 tff(30427,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30426, 30425])).
% 3.32/3.51 tff(30428,plain,
% 3.32/3.51 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30427, 121, 30308, 30421, 30419])).
% 3.32/3.51 tff(30429,plain,
% 3.32/3.51 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1167, 21, 30428])).
% 3.32/3.51 tff(30430,plain,
% 3.32/3.51 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30429, 1139])).
% 3.32/3.51 tff(30431,plain,
% 3.32/3.51 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30375, 121, 30308, 30421, 30419])).
% 3.32/3.51 tff(30432,plain,
% 3.32/3.51 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[10424, 21, 1138, 30431])).
% 3.32/3.51 tff(30433,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30434,plain,
% 3.32/3.51 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30435,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30434])).
% 3.32/3.51 tff(30436,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.51 inference(transitivity,[status(thm)],[30435, 30433])).
% 3.32/3.51 tff(30437,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.32/3.51 inference(quant_inst,[status(thm)],[])).
% 3.32/3.51 tff(30438,plain,
% 3.32/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30437, 30436])).
% 3.32/3.51 tff(30439,plain,
% 3.32/3.51 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30438, 271, 30432, 30430, 30413])).
% 3.32/3.51 tff(30440,plain,
% 3.32/3.51 (~b(s(s(s(z))), elem!1)),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30439, 30312])).
% 3.32/3.51 tff(30441,plain,
% 3.32/3.51 (r(s(s(s(z))), elem!1)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[255, 30440, 28220])).
% 3.32/3.51 tff(30442,plain,
% 3.32/3.51 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[16283, 30441, 30310, 30308])).
% 3.32/3.51 tff(30443,plain,
% 3.32/3.51 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1733, 30442])).
% 3.32/3.51 tff(30444,plain,
% 3.32/3.51 (~b(s(s(s(s(s(z))))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[18460, 271, 3871, 30406, 30443])).
% 3.32/3.51 tff(30445,plain,
% 3.32/3.51 (r(s(s(s(s(s(z))))), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1682, 30444])).
% 3.32/3.51 tff(30446,plain,
% 3.32/3.51 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[25896, 30445, 30281, 30278])).
% 3.32/3.51 tff(30447,plain,
% 3.32/3.51 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[840, 30446, 28215])).
% 3.32/3.51 tff(30448,plain,
% 3.32/3.51 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30447, 30275])).
% 3.32/3.51 tff(30449,plain,
% 3.32/3.51 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[29482, 30419, 30417, 28259, 30308])).
% 3.32/3.51 tff(30450,plain,
% 3.32/3.51 ($false),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30449, 30448])).
% 3.32/3.51 tff(30451,plain,((~b(s(elem!1), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.51 tff(30452,plain,
% 3.32/3.51 (~b(s(elem!1), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30451, 30273, 1281, 601, 3871])).
% 3.32/3.51 tff(30453,plain,
% 3.32/3.51 (r(s(elem!1), z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[409, 30452])).
% 3.32/3.51 tff(30454,plain,
% 3.32/3.51 (~r(s(elem!1), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[5329, 30453, 909, 30209])).
% 3.32/3.51 tff(30455,plain,
% 3.32/3.51 (b(s(elem!1), s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[429, 30454, 422])).
% 3.32/3.51 tff(30456,plain,
% 3.32/3.51 (b(elem!1, s(z))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[28768, 30455, 28326])).
% 3.32/3.51 tff(30457,plain,
% 3.32/3.51 (~b(elem!1, z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[4775, 30456, 1281, 30271])).
% 3.32/3.51 tff(30458,plain,
% 3.32/3.51 (r(elem!1, z)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[284, 30457, 358])).
% 3.32/3.51 tff(30459,plain,
% 3.32/3.51 (~r(s(z), s(s(elem!1)))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[12439, 30458, 909, 30269])).
% 3.32/3.51 tff(30460,plain,
% 3.32/3.51 ($false),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30459, 30260])).
% 3.32/3.51 tff(30461,plain,(b(s(z), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(z))))) | (z = elem!1) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.51 tff(30462,plain,
% 3.32/3.51 (b(s(z), s(s(s(elem!1))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[30461, 909, 601, 1281, 422, 30259, 331, 2073])).
% 3.32/3.51 tff(30463,plain,
% 3.32/3.51 (b(s(z), s(elem!1))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[30462, 30123])).
% 3.32/3.51 tff(30464,plain,
% 3.32/3.51 (b(s(z), elem!1)),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[2562, 30462, 25718])).
% 3.32/3.51 tff(30465,plain,
% 3.32/3.51 (r(elem!1, s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[10306, 30464, 25718, 221, 2065, 30259])).
% 3.32/3.51 tff(30466,plain,
% 3.32/3.51 (~b(z, s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[19817, 30259, 1281, 2073])).
% 3.32/3.51 tff(30467,plain,
% 3.32/3.51 (r(z, s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[1214, 30466])).
% 3.32/3.51 tff(30468,plain,
% 3.32/3.51 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.51 inference(unit_resolution,[status(thm)],[28368, 30465, 28326])).
% 3.32/3.51 tff(30469,plain,
% 3.32/3.51 (elem!1 = s(s(elem!1))),
% 3.32/3.51 inference(transitivity,[status(thm)],[28196, 611])).
% 3.32/3.51 tff(30470,plain,
% 3.32/3.51 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30469])).
% 3.32/3.51 tff(30471,plain,
% 3.32/3.51 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.51 inference(symmetry,[status(thm)],[30470])).
% 3.32/3.51 tff(30472,plain,
% 3.32/3.51 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30471])).
% 3.32/3.51 tff(30473,plain,
% 3.32/3.51 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[611])).
% 3.32/3.51 tff(30474,plain,
% 3.32/3.51 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.32/3.51 inference(symmetry,[status(thm)],[30473])).
% 3.32/3.51 tff(30475,plain,
% 3.32/3.51 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.32/3.51 inference(modus_ponens,[status(thm)],[1722, 30474])).
% 3.32/3.51 tff(30476,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30477,plain,
% 3.32/3.51 (((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.51 inference(rewrite,[status(thm)],[])).
% 3.32/3.51 tff(30478,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.32/3.51 inference(monotonicity,[status(thm)],[30477])).
% 3.32/3.51 tff(30479,plain,
% 3.32/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.52 inference(transitivity,[status(thm)],[30478, 30476])).
% 3.32/3.52 tff(30480,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 3.32/3.52 inference(quant_inst,[status(thm)],[])).
% 3.32/3.52 tff(30481,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30480, 30479])).
% 3.32/3.52 tff(30482,plain,
% 3.32/3.52 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30481, 271, 750, 2073, 222])).
% 3.32/3.52 tff(30483,plain,
% 3.32/3.52 ($false),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30482, 30475])).
% 3.32/3.52 tff(30484,plain,((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.52 tff(30485,plain,
% 3.32/3.52 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30484, 222, 750, 2073, 601])).
% 3.32/3.52 tff(30486,plain,
% 3.32/3.52 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30485, 30472])).
% 3.32/3.52 tff(30487,plain,
% 3.32/3.52 (r(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1847, 30486, 28455])).
% 3.32/3.52 tff(30488,plain,
% 3.32/3.52 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[16341, 30487, 3891])).
% 3.32/3.52 tff(30489,plain,
% 3.32/3.52 (r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30488, 28492])).
% 3.32/3.52 tff(30490,plain,
% 3.32/3.52 (~b(s(s(s(elem!1))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[14970, 222, 2073, 750])).
% 3.32/3.52 tff(30491,plain,
% 3.32/3.52 (r(s(s(s(elem!1))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[8229, 30490])).
% 3.32/3.52 tff(30492,plain,
% 3.32/3.52 (~b(s(s(s(elem!1))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[12484, 750, 2073, 3871])).
% 3.32/3.52 tff(30493,plain,
% 3.32/3.52 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[16580, 30492])).
% 3.32/3.52 tff(30494,plain,
% 3.32/3.52 (~r(s(z), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[19684, 30491, 909, 30493])).
% 3.32/3.52 tff(30495,plain,
% 3.32/3.52 (b(s(z), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1756, 30494])).
% 3.32/3.52 tff(30496,plain,
% 3.32/3.52 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[23326, 30495, 3871, 222])).
% 3.32/3.52 tff(30497,plain,
% 3.32/3.52 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1733, 30496])).
% 3.32/3.52 tff(30498,plain,
% 3.32/3.52 (~r(s(s(s(z))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[11676, 30491, 30262, 7792])).
% 3.32/3.52 tff(30499,plain,
% 3.32/3.52 (b(s(s(s(z))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1155, 30498])).
% 3.32/3.52 tff(30500,plain,
% 3.32/3.52 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[4302, 30499, 1281, 3871])).
% 3.32/3.52 tff(30501,plain,
% 3.32/3.52 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1658, 30500])).
% 3.32/3.52 tff(30502,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30503,plain,
% 3.32/3.52 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30504,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.32/3.52 inference(monotonicity,[status(thm)],[30503])).
% 3.32/3.52 tff(30505,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.52 inference(transitivity,[status(thm)],[30504, 30502])).
% 3.32/3.52 tff(30506,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)))),
% 3.32/3.52 inference(quant_inst,[status(thm)],[])).
% 3.32/3.52 tff(30507,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30506, 30505])).
% 3.32/3.52 tff(30508,plain,
% 3.32/3.52 ($false),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30507, 121, 30501, 30497, 30491, 30489])).
% 3.32/3.52 tff(30509,plain,((~b(s(s(s(z))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.52 tff(30510,plain,
% 3.32/3.52 (~b(s(s(s(z))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30509, 30462, 601, 2073, 30259, 1281, 909, 30468])).
% 3.32/3.52 tff(30511,plain,
% 3.32/3.52 (r(s(s(s(z))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[2325, 30510])).
% 3.32/3.52 tff(30512,plain,
% 3.32/3.52 (~r(z, elem!1)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[19831, 30511, 30467, 30465])).
% 3.32/3.52 tff(30513,plain,
% 3.32/3.52 (b(z, elem!1)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[355, 30512, 331])).
% 3.32/3.52 tff(30514,plain,
% 3.32/3.52 (~b(s(elem!1), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[23220, 30513, 1281, 30463])).
% 3.32/3.52 tff(30515,plain,
% 3.32/3.52 (r(s(elem!1), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[409, 30514])).
% 3.32/3.52 tff(30516,plain,
% 3.32/3.52 (r(s(s(s(elem!1))), z)),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30515, 28511])).
% 3.32/3.52 tff(30517,plain,
% 3.32/3.52 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[28368, 10307, 2203])).
% 3.32/3.52 tff(30518,plain,
% 3.32/3.52 (~b(z, s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[19416, 10295, 1281, 3871])).
% 3.32/3.52 tff(30519,plain,
% 3.32/3.52 (r(z, s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1214, 30518])).
% 3.32/3.52 tff(30520,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30521,plain,
% 3.32/3.52 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30522,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.32/3.52 inference(monotonicity,[status(thm)],[30521])).
% 3.32/3.52 tff(30523,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.52 inference(transitivity,[status(thm)],[30522, 30520])).
% 3.32/3.52 tff(30524,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 3.32/3.52 inference(quant_inst,[status(thm)],[])).
% 3.32/3.52 tff(30525,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30524, 30523])).
% 3.32/3.52 tff(30526,plain,
% 3.32/3.52 ($false),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30525, 121, 6842, 2327, 30519, 30517])).
% 3.32/3.52 tff(30527,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~(s(elem!1) = elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.52 tff(30528,plain,
% 3.32/3.52 (~r(s(s(s(elem!1))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30527, 30511, 1281, 28326, 221, 30259, 25718, 2065, 30464])).
% 3.32/3.52 tff(30529,plain,
% 3.32/3.52 ($false),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30528, 30516])).
% 3.32/3.52 tff(30530,plain,((~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (z = elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.52 tff(30531,plain,
% 3.32/3.52 (~r(z, s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30530, 29768, 1281, 331, 601, 2065, 30121, 422, 30120])).
% 3.32/3.52 tff(30532,plain,
% 3.32/3.52 (b(z, s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[904, 30531])).
% 3.32/3.52 tff(30533,plain,
% 3.32/3.52 (~b(s(s(s(elem!1))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30266, 222, 2073, 3871])).
% 3.32/3.52 tff(30534,plain,
% 3.32/3.52 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[16580, 30533])).
% 3.32/3.52 tff(30535,plain,
% 3.32/3.52 (r(elem!1, s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[12809, 30534, 25718])).
% 3.32/3.52 tff(30536,plain,
% 3.32/3.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[11676, 28824, 30262, 24356])).
% 3.32/3.52 tff(30537,plain,
% 3.32/3.52 (~r(elem!1, s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[28368, 30536, 28326])).
% 3.32/3.52 tff(30538,plain,
% 3.32/3.52 (b(elem!1, s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1192, 30537, 28221])).
% 3.32/3.52 tff(30539,plain,
% 3.32/3.52 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[18462, 30538, 28455, 30535, 357, 30124, 222, 3871])).
% 3.32/3.52 tff(30540,plain,
% 3.32/3.52 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1733, 30539])).
% 3.32/3.52 tff(30541,plain,
% 3.32/3.52 (~r(z, s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[28653, 121, 30540, 24356, 30262])).
% 3.32/3.52 tff(30542,plain,
% 3.32/3.52 (b(z, s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1658, 30541])).
% 3.32/3.52 tff(30543,plain,
% 3.32/3.52 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.52 inference(monotonicity,[status(thm)],[213])).
% 3.32/3.52 tff(30544,plain,
% 3.32/3.52 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.52 inference(symmetry,[status(thm)],[30543])).
% 3.32/3.52 tff(30545,plain,
% 3.32/3.52 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[3061, 30544])).
% 3.32/3.52 tff(30546,plain,
% 3.32/3.52 (~r(s(z), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[17845, 30545])).
% 3.32/3.52 tff(30547,plain,
% 3.32/3.52 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1754, 21, 30546])).
% 3.32/3.52 tff(30548,plain,
% 3.32/3.52 (b(s(z), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30547, 5380])).
% 3.32/3.52 tff(30549,plain,
% 3.32/3.52 (s(s(elem!1)) = s(elem!1)),
% 3.32/3.52 inference(symmetry,[status(thm)],[25687])).
% 3.32/3.52 tff(30550,plain,
% 3.32/3.52 (r(s(z), s(s(elem!1))) <=> r(s(z), s(elem!1))),
% 3.32/3.52 inference(monotonicity,[status(thm)],[30549])).
% 3.32/3.52 tff(30551,plain,
% 3.32/3.52 (r(s(z), s(elem!1)) <=> r(s(z), s(s(elem!1)))),
% 3.32/3.52 inference(symmetry,[status(thm)],[30550])).
% 3.32/3.52 tff(30552,plain,
% 3.32/3.52 (r(s(z), s(s(elem!1)))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[431, 30551])).
% 3.32/3.52 tff(30553,plain,
% 3.32/3.52 (~r(s(s(s(s(s(z))))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[25896, 3061, 3456, 30552])).
% 3.32/3.52 tff(30554,plain,
% 3.32/3.52 (b(s(s(s(s(s(z))))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1680, 21, 1677, 30553])).
% 3.32/3.52 tff(30555,plain,
% 3.32/3.52 ($false),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[17857, 271, 220, 1639, 30554, 30548])).
% 3.32/3.52 tff(30556,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~(elem!1 = s(elem!1))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.52 tff(30557,plain,
% 3.32/3.52 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30556, 30542, 28458, 28256, 30535, 412, 220])).
% 3.32/3.52 tff(30558,plain,
% 3.32/3.52 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[840, 30557, 28215])).
% 3.32/3.52 tff(30559,plain,
% 3.32/3.52 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30558, 28214])).
% 3.32/3.52 tff(30560,plain,
% 3.32/3.52 (~r(s(s(s(s(s(z))))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[26340, 121, 30540, 24356, 30262])).
% 3.32/3.52 tff(30561,plain,
% 3.32/3.52 (b(s(s(s(s(s(z))))), z)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[6593, 21, 711, 30560])).
% 3.32/3.52 tff(30562,plain,
% 3.32/3.52 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30538, 28218])).
% 3.32/3.52 tff(30563,plain,
% 3.32/3.52 (b(s(elem!1), s(s(s(z))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30538, 28219])).
% 3.32/3.52 tff(30564,plain,
% 3.32/3.52 (~b(s(elem!1), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[7781, 30563, 2073, 3871])).
% 3.32/3.52 tff(30565,plain,
% 3.32/3.52 (r(s(elem!1), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[429, 30564, 422])).
% 3.32/3.52 tff(30566,plain,
% 3.32/3.52 (r(z, s(s(s(elem!1))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[19736, 33])).
% 3.32/3.52 tff(30567,plain,
% 3.32/3.52 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[24371, 30566, 1281, 220, 3871])).
% 3.32/3.52 tff(30568,plain,
% 3.32/3.52 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[932, 30567])).
% 3.32/3.52 tff(30569,plain,
% 3.32/3.52 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[26847, 30568, 572, 6842])).
% 3.32/3.52 tff(30570,plain,
% 3.32/3.52 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[28532, 30569, 601])).
% 3.32/3.52 tff(30571,plain,
% 3.32/3.52 (b(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1559, 30570, 28489])).
% 3.32/3.52 tff(30572,plain,
% 3.32/3.52 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[28738, 30571, 601])).
% 3.32/3.52 tff(30573,plain,
% 3.32/3.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[11676, 6842, 30262, 24356])).
% 3.32/3.52 tff(30574,plain,
% 3.32/3.52 (~r(elem!1, s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[28368, 30573, 28326])).
% 3.32/3.52 tff(30575,plain,
% 3.32/3.52 (b(elem!1, s(s(s(z))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1192, 30574, 28221])).
% 3.32/3.52 tff(30576,plain,
% 3.32/3.52 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30575, 28218])).
% 3.32/3.52 tff(30577,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30578,plain,
% 3.32/3.52 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30579,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.32/3.52 inference(monotonicity,[status(thm)],[30578])).
% 3.32/3.52 tff(30580,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.52 inference(transitivity,[status(thm)],[30579, 30577])).
% 3.32/3.52 tff(30581,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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)))))))),
% 3.32/3.52 inference(quant_inst,[status(thm)],[])).
% 3.32/3.52 tff(30582,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30581, 30580])).
% 3.32/3.52 tff(30583,plain,
% 3.32/3.52 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30582, 271, 30576, 2073, 30572])).
% 3.32/3.52 tff(30584,plain,
% 3.32/3.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1167, 21, 30583, 20146])).
% 3.32/3.52 tff(30585,plain,
% 3.32/3.52 (~b(z, s(elem!1))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[6491, 33, 3891])).
% 3.32/3.52 tff(30586,plain,
% 3.32/3.52 (r(z, s(elem!1))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1439, 30585])).
% 3.32/3.52 tff(30587,plain,
% 3.32/3.52 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[25903, 30586, 1281, 28458, 220, 411, 3456, 28554])).
% 3.32/3.52 tff(30588,plain,
% 3.32/3.52 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[840, 30587, 28215])).
% 3.32/3.52 tff(30589,plain,
% 3.32/3.52 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30588, 28214])).
% 3.32/3.52 tff(30590,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30591,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.52 inference(quant_inst,[status(thm)],[])).
% 3.32/3.52 tff(30592,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30591, 30590])).
% 3.32/3.52 tff(30593,plain,
% 3.32/3.52 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30592, 271, 30576, 30572, 30589])).
% 3.32/3.52 tff(30594,plain,
% 3.32/3.52 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[9512, 30593])).
% 3.32/3.52 tff(30595,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30596,plain,
% 3.32/3.52 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(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(s(z)))))))) <=> ((~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.52 inference(rewrite,[status(thm)],[])).
% 3.32/3.52 tff(30597,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.32/3.52 inference(monotonicity,[status(thm)],[30596])).
% 3.32/3.52 tff(30598,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.52 inference(transitivity,[status(thm)],[30597, 30595])).
% 3.32/3.52 tff(30599,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(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(s(z))))))))),
% 3.32/3.52 inference(quant_inst,[status(thm)],[])).
% 3.32/3.52 tff(30600,plain,
% 3.32/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.32/3.52 inference(modus_ponens,[status(thm)],[30599, 30598])).
% 3.32/3.52 tff(30601,plain,
% 3.32/3.52 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[30600, 271, 30576, 2073, 30589])).
% 3.32/3.52 tff(30602,plain,
% 3.32/3.52 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.52 inference(unit_resolution,[status(thm)],[1494, 30601])).
% 3.32/3.52 tff(30603,plain,
% 3.32/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30604,plain,
% 3.32/3.53 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30605,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30604])).
% 3.32/3.53 tff(30606,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(transitivity,[status(thm)],[30605, 30603])).
% 3.32/3.53 tff(30607,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.53 inference(quant_inst,[status(thm)],[])).
% 3.32/3.53 tff(30608,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30607, 30606])).
% 3.32/3.53 tff(30609,plain,
% 3.32/3.53 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30608, 271, 30576, 30572, 30589])).
% 3.32/3.53 tff(30610,plain,
% 3.32/3.53 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[1777, 30609])).
% 3.32/3.53 tff(30611,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30612,plain,
% 3.32/3.53 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30613,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30612])).
% 3.32/3.53 tff(30614,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.53 inference(transitivity,[status(thm)],[30613, 30611])).
% 3.32/3.53 tff(30615,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(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)))))))),
% 3.32/3.53 inference(quant_inst,[status(thm)],[])).
% 3.32/3.53 tff(30616,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30615, 30614])).
% 3.32/3.53 tff(30617,plain,
% 3.32/3.53 ($false),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30616, 121, 30610, 30602, 30594, 30584])).
% 3.32/3.53 tff(30618,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.53 tff(30619,plain,
% 3.32/3.53 (b(z, s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30618, 28824, 601, 572, 2073, 1281, 220, 30565, 30535, 3871])).
% 3.32/3.53 tff(30620,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30621,plain,
% 3.32/3.53 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30622,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30621])).
% 3.32/3.53 tff(30623,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(transitivity,[status(thm)],[30622, 30620])).
% 3.32/3.53 tff(30624,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.32/3.53 inference(quant_inst,[status(thm)],[])).
% 3.32/3.53 tff(30625,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30624, 30623])).
% 3.32/3.53 tff(30626,plain,
% 3.32/3.53 ($false),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30625, 271, 30619, 30562, 30561, 30559])).
% 3.32/3.53 tff(30627,plain,((~r(s(elem!1), z)) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.53 tff(30628,plain,
% 3.32/3.53 (~r(s(elem!1), z)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30627, 222, 601, 572, 2073, 1281, 3871, 422, 357, 220])).
% 3.32/3.53 tff(30629,plain,
% 3.32/3.53 (b(s(elem!1), z)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[409, 30628])).
% 3.32/3.53 tff(30630,plain,
% 3.32/3.53 (b(s(s(s(elem!1))), z)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[12308, 30629, 3891])).
% 3.32/3.53 tff(30631,plain,
% 3.32/3.53 (~b(z, s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30451, 30629, 1281, 601, 3871])).
% 3.32/3.53 tff(30632,plain,
% 3.32/3.53 (r(z, s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[19736, 30631])).
% 3.32/3.53 tff(30633,plain,
% 3.32/3.53 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[24371, 30632, 1281, 220, 3871])).
% 3.32/3.53 tff(30634,plain,
% 3.32/3.53 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[932, 30633])).
% 3.32/3.53 tff(30635,plain,
% 3.32/3.53 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[28695, 121, 572, 30534, 30634])).
% 3.32/3.53 tff(30636,plain,
% 3.32/3.53 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[28688, 121, 572, 30534, 30634])).
% 3.32/3.53 tff(30637,plain,
% 3.32/3.53 ($false),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[25036, 30636, 30635, 220, 1008, 2073, 30262, 30630])).
% 3.32/3.53 tff(30638,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.53 tff(30639,plain,
% 3.32/3.53 (~b(s(s(s(z))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30638, 3871, 28210, 30121, 572, 1281, 220, 601, 422, 357])).
% 3.32/3.53 tff(30640,plain,
% 3.32/3.53 (r(s(s(s(z))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[2325, 30639])).
% 3.32/3.53 tff(30641,plain,
% 3.32/3.53 (~b(z, s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[19817, 3871, 1281, 30121])).
% 3.32/3.53 tff(30642,plain,
% 3.32/3.53 (r(z, s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[1214, 30641])).
% 3.32/3.53 tff(30643,plain,
% 3.32/3.53 (~r(elem!1, s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[19831, 30199, 30642, 2327])).
% 3.32/3.53 tff(30644,plain,
% 3.32/3.53 (b(elem!1, s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[1192, 30643, 28221])).
% 3.32/3.53 tff(30645,plain,
% 3.32/3.53 (b(s(elem!1), s(s(s(z))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30644, 28219])).
% 3.32/3.53 tff(30646,plain,
% 3.32/3.53 (~b(s(elem!1), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[7781, 30645, 30121, 3871])).
% 3.32/3.53 tff(30647,plain,
% 3.32/3.53 (~b(s(s(elem!1)), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[28247, 30646, 609])).
% 3.32/3.53 tff(30648,plain,
% 3.32/3.53 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[24371, 111, 1281, 220, 3871])).
% 3.32/3.53 tff(30649,plain,
% 3.32/3.53 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[932, 30648])).
% 3.32/3.53 tff(30650,plain,
% 3.32/3.53 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[24945, 30649, 1281, 30642, 2327])).
% 3.32/3.53 tff(30651,plain,
% 3.32/3.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[10426, 30650])).
% 3.32/3.53 tff(30652,plain,
% 3.32/3.53 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.32/3.53 inference(transitivity,[status(thm)],[28207, 935])).
% 3.32/3.53 tff(30653,plain,
% 3.32/3.53 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30652])).
% 3.32/3.53 tff(30654,plain,
% 3.32/3.53 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[28209, 30653])).
% 3.32/3.53 tff(30655,plain,
% 3.32/3.53 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[28196])).
% 3.32/3.53 tff(30656,plain,
% 3.32/3.53 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30655])).
% 3.32/3.53 tff(30657,plain,
% 3.32/3.53 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30643, 30656])).
% 3.32/3.53 tff(30658,plain,
% 3.32/3.53 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[2071, 2065, 906])).
% 3.32/3.53 tff(30659,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30660,plain,
% 3.32/3.53 (((~b(s(s(s(z))), s(s(s(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(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30661,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30660])).
% 3.32/3.53 tff(30662,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.53 inference(transitivity,[status(thm)],[30661, 30659])).
% 3.32/3.53 tff(30663,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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)))))))),
% 3.32/3.53 inference(quant_inst,[status(thm)],[])).
% 3.32/3.53 tff(30664,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30663, 30662])).
% 3.32/3.53 tff(30665,plain,
% 3.32/3.53 (~b(s(z), s(s(s(s(z)))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30664, 271, 30658, 3871, 13508])).
% 3.32/3.53 tff(30666,plain,
% 3.32/3.53 (r(s(z), s(s(s(s(z)))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[16482, 30665])).
% 3.32/3.53 tff(30667,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30668,plain,
% 3.32/3.53 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30669,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.32/3.53 inference(monotonicity,[status(thm)],[30668])).
% 3.32/3.53 tff(30670,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.32/3.53 inference(transitivity,[status(thm)],[30669, 30667])).
% 3.32/3.53 tff(30671,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.53 inference(quant_inst,[status(thm)],[])).
% 3.32/3.53 tff(30672,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30671, 30670])).
% 3.32/3.53 tff(30673,plain,
% 3.32/3.53 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30672, 121, 12761, 911, 30666])).
% 3.32/3.53 tff(30674,plain,
% 3.32/3.53 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[1000, 21, 30673, 26550])).
% 3.32/3.53 tff(30675,plain,
% 3.32/3.53 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[6237, 21, 28366, 11664])).
% 3.32/3.53 tff(30676,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30677,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.53 inference(quant_inst,[status(thm)],[])).
% 3.32/3.53 tff(30678,plain,
% 3.32/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30677, 30676])).
% 3.32/3.53 tff(30679,plain,
% 3.32/3.53 ($false),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30678, 271, 30675, 30658, 13508, 30674])).
% 3.32/3.53 tff(30680,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.53 tff(30681,plain,
% 3.32/3.53 (~r(s(s(s(elem!1))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30680, 30657, 2065, 30654, 30651, 906, 3871, 30649])).
% 3.32/3.53 tff(30682,plain,
% 3.32/3.53 (~r(s(s(elem!1)), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[28239, 30681, 609])).
% 3.32/3.53 tff(30683,plain,
% 3.32/3.53 ($false),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[2143, 30682, 30647])).
% 3.32/3.53 tff(30684,plain,((~r(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.53 tff(30685,plain,
% 3.32/3.53 (~r(z, s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30684, 3871, 906, 2065, 601, 1281, 30640, 220])).
% 3.32/3.53 tff(30686,plain,
% 3.32/3.53 (b(z, s(s(s(elem!1))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[19736, 30685])).
% 3.32/3.53 tff(30687,plain,
% 3.32/3.53 (~b(s(elem!1), z)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30451, 30686, 1281, 601, 3871])).
% 3.32/3.53 tff(30688,plain,
% 3.32/3.53 (r(s(elem!1), z)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[409, 30687])).
% 3.32/3.53 tff(30689,plain,
% 3.32/3.53 (b(z, elem!1)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[13207, 30686, 28225])).
% 3.32/3.53 tff(30690,plain,
% 3.32/3.53 (~b(elem!1, s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[11002, 30689, 220, 3871])).
% 3.32/3.53 tff(30691,plain,
% 3.32/3.53 (r(elem!1, s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[299, 30690, 28851])).
% 3.32/3.53 tff(30692,plain,
% 3.32/3.53 (~b(s(s(elem!1)), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[28387, 30690, 601, 25718])).
% 3.32/3.53 tff(30693,plain,
% 3.32/3.53 (r(s(s(elem!1)), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[2143, 30692])).
% 3.32/3.53 tff(30694,plain,
% 3.32/3.53 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[28239, 30693, 609])).
% 3.32/3.53 tff(30695,plain,
% 3.32/3.53 (~r(z, s(s(s(s(s(z))))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30404, 30694, 601, 572, 30640, 3871, 220, 1281, 30691, 357])).
% 3.32/3.53 tff(30696,plain,
% 3.32/3.53 (b(z, s(s(s(s(s(z))))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[1658, 30695])).
% 3.32/3.53 tff(30697,plain,
% 3.32/3.53 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[30556, 30696, 28458, 28256, 30691, 30688, 220])).
% 3.32/3.53 tff(30698,plain,
% 3.32/3.53 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[840, 30697, 28215])).
% 3.32/3.53 tff(30699,plain,
% 3.32/3.53 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30698, 28214])).
% 3.32/3.53 tff(30700,plain,
% 3.32/3.53 (~r(elem!1, s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[11254, 30691, 357, 30640])).
% 3.32/3.53 tff(30701,plain,
% 3.32/3.53 (b(elem!1, s(s(s(z))))),
% 3.32/3.53 inference(unit_resolution,[status(thm)],[1192, 30700, 28221])).
% 3.32/3.53 tff(30702,plain,
% 3.32/3.53 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.53 inference(modus_ponens,[status(thm)],[30701, 28218])).
% 3.32/3.53 tff(30703,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30704,plain,
% 3.32/3.53 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.53 inference(rewrite,[status(thm)],[])).
% 3.32/3.53 tff(30705,plain,
% 3.32/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.32/3.54 inference(monotonicity,[status(thm)],[30704])).
% 3.32/3.54 tff(30706,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(transitivity,[status(thm)],[30705, 30703])).
% 3.32/3.54 tff(30707,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30708,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30707, 30706])).
% 3.32/3.54 tff(30709,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30708, 271, 30686, 30702, 30696, 30699])).
% 3.32/3.54 tff(30710,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30711,plain,
% 3.32/3.54 (~b(s(z), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30710, 30135, 601, 220, 1281, 30208, 906, 2065, 422])).
% 3.32/3.54 tff(30712,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30713,plain,
% 3.32/3.54 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30714,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.32/3.54 inference(monotonicity,[status(thm)],[30713])).
% 3.32/3.54 tff(30715,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.54 inference(transitivity,[status(thm)],[30714, 30712])).
% 3.32/3.54 tff(30716,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30717,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30716, 30715])).
% 3.32/3.54 tff(30718,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30717, 121, 572, 2327, 108, 7792])).
% 3.32/3.54 tff(30719,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30720,plain,
% 3.32/3.54 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30719, 2327, 572, 106])).
% 3.32/3.54 tff(30721,plain,
% 3.32/3.54 (~r(elem!1, s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[28368, 30720, 28326])).
% 3.32/3.54 tff(30722,plain,
% 3.32/3.54 (b(elem!1, s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1192, 30721, 28221])).
% 3.32/3.54 tff(30723,plain,
% 3.32/3.54 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30722, 28218])).
% 3.32/3.54 tff(30724,plain,
% 3.32/3.54 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[17876, 412, 220, 28256])).
% 3.32/3.54 tff(30725,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[4133, 28572])).
% 3.32/3.54 tff(30726,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30727,plain,
% 3.32/3.54 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30726, 30724, 601])).
% 3.32/3.54 tff(30728,plain,
% 3.32/3.54 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[840, 30727, 28215])).
% 3.32/3.54 tff(30729,plain,
% 3.32/3.54 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30728, 28214])).
% 3.32/3.54 tff(30730,plain,
% 3.32/3.54 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30719, 2327, 572, 108])).
% 3.32/3.54 tff(30731,plain,
% 3.32/3.54 (~r(elem!1, s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[28368, 30730, 28326])).
% 3.32/3.54 tff(30732,plain,
% 3.32/3.54 (b(elem!1, s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1192, 30731, 28221])).
% 3.32/3.54 tff(30733,plain,
% 3.32/3.54 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30732, 28218])).
% 3.32/3.54 tff(30734,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30735,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30736,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30735, 30734])).
% 3.32/3.54 tff(30737,plain,
% 3.32/3.54 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30736, 271, 30733, 2073, 30729])).
% 3.32/3.54 tff(30738,plain,
% 3.32/3.54 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1733, 30737])).
% 3.32/3.54 tff(30739,plain,
% 3.32/3.54 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30600, 271, 30733, 2073, 30729])).
% 3.32/3.54 tff(30740,plain,
% 3.32/3.54 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1494, 30739])).
% 3.32/3.54 tff(30741,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30742,plain,
% 3.32/3.54 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30743,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.32/3.54 inference(monotonicity,[status(thm)],[30742])).
% 3.32/3.54 tff(30744,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(transitivity,[status(thm)],[30743, 30741])).
% 3.32/3.54 tff(30745,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30746,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30745, 30744])).
% 3.32/3.54 tff(30747,plain,
% 3.32/3.54 (~r(s(z), s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30746, 121, 30740, 30738, 108])).
% 3.32/3.54 tff(30748,plain,
% 3.32/3.54 (b(s(z), s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1756, 30747])).
% 3.32/3.54 tff(30749,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30750,plain,
% 3.32/3.54 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~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(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30751,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 3.32/3.54 inference(monotonicity,[status(thm)],[30750])).
% 3.32/3.54 tff(30752,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.32/3.54 inference(transitivity,[status(thm)],[30751, 30749])).
% 3.32/3.54 tff(30753,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~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))))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30754,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30753, 30752])).
% 3.32/3.54 tff(30755,plain,
% 3.32/3.54 (~r(s(s(s(s(s(z))))), s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30754, 121, 30740, 30738, 108])).
% 3.32/3.54 tff(30756,plain,
% 3.32/3.54 (b(s(s(s(s(s(z))))), s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1682, 30755])).
% 3.32/3.54 tff(30757,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30758,plain,
% 3.32/3.54 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30759,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.32/3.54 inference(monotonicity,[status(thm)],[30758])).
% 3.32/3.54 tff(30760,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(transitivity,[status(thm)],[30759, 30757])).
% 3.32/3.54 tff(30761,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30762,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30761, 30760])).
% 3.32/3.54 tff(30763,plain,
% 3.32/3.54 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30762, 271, 1281, 220, 5393])).
% 3.32/3.54 tff(30764,plain,
% 3.32/3.54 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1658, 30763])).
% 3.32/3.54 tff(30765,plain,
% 3.32/3.54 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1785, 937, 5393, 5381])).
% 3.32/3.54 tff(30766,plain,
% 3.32/3.54 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1777, 30765])).
% 3.32/3.54 tff(30767,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(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(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(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(s(s(z))))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30768,plain,
% 3.32/3.54 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(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(s(s(z))))))))),
% 3.32/3.54 inference(rewrite,[status(thm)],[])).
% 3.32/3.54 tff(30769,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(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(s(s(z)))))))))),
% 3.32/3.54 inference(monotonicity,[status(thm)],[30768])).
% 3.32/3.54 tff(30770,plain,
% 3.32/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(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(s(s(z))))))))),
% 3.32/3.54 inference(transitivity,[status(thm)],[30769, 30767])).
% 3.32/3.54 tff(30771,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.54 inference(quant_inst,[status(thm)],[])).
% 3.32/3.54 tff(30772,plain,
% 3.32/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30771, 30770])).
% 3.32/3.54 tff(30773,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30772, 121, 30766, 30764, 1736, 24354])).
% 3.32/3.54 tff(30774,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30775,plain,
% 3.32/3.54 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30774, 30756, 30738, 30748, 1281, 220])).
% 3.32/3.54 tff(30776,plain,
% 3.32/3.54 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[932, 30775])).
% 3.32/3.54 tff(30777,plain,
% 3.32/3.54 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[26847, 30776, 572, 28824])).
% 3.32/3.54 tff(30778,plain,
% 3.32/3.54 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[28532, 30777, 601])).
% 3.32/3.54 tff(30779,plain,
% 3.32/3.54 (b(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1559, 30778, 28489])).
% 3.32/3.54 tff(30780,plain,
% 3.32/3.54 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30235, 30776, 108, 2327])).
% 3.32/3.54 tff(30781,plain,
% 3.32/3.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[10426, 30780])).
% 3.32/3.54 tff(30782,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30402, 271, 6202, 2073, 13508, 12562])).
% 3.32/3.54 tff(30783,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30784,plain,
% 3.32/3.54 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30783, 30781, 2073, 30733])).
% 3.32/3.54 tff(30785,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[28738, 30784, 30779, 601])).
% 3.32/3.54 tff(30786,plain,((~r(s(elem!1), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30787,plain,
% 3.32/3.54 (~r(s(elem!1), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30786, 2327, 2073, 106, 601, 572, 1281, 220])).
% 3.32/3.54 tff(30788,plain,
% 3.32/3.54 (b(s(elem!1), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[409, 30787])).
% 3.32/3.54 tff(30789,plain,
% 3.32/3.54 (b(z, elem!1)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[25998, 30788, 1281, 30191, 30198, 2467, 71])).
% 3.32/3.54 tff(30790,plain,
% 3.32/3.54 (~b(elem!1, s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[20398, 30789, 1281, 220])).
% 3.32/3.54 tff(30791,plain,
% 3.32/3.54 (r(elem!1, s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[299, 30790, 28851])).
% 3.32/3.54 tff(30792,plain,
% 3.32/3.54 (~r(elem!1, s(s(s(s(z)))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[21233, 911, 572, 3456])).
% 3.32/3.54 tff(30793,plain,
% 3.32/3.54 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[28440, 911, 572, 2327, 6202])).
% 3.32/3.54 tff(30794,plain,
% 3.32/3.54 (~b(elem!1, s(s(s(s(z)))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[28428, 30793, 601])).
% 3.32/3.54 tff(30795,plain,
% 3.32/3.54 ($false),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[20539, 30794, 30792, 20532])).
% 3.32/3.54 tff(30796,plain,((~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.54 tff(30797,plain,
% 3.32/3.54 (~r(s(s(s(s(z)))), s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30796, 30791, 601, 572, 20532, 2327, 30723])).
% 3.32/3.54 tff(30798,plain,
% 3.32/3.54 (b(s(s(s(s(z)))), s(z))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[932, 30797])).
% 3.32/3.54 tff(30799,plain,
% 3.32/3.54 (~b(s(s(s(s(z)))), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[22548, 30798, 1281, 220])).
% 3.32/3.54 tff(30800,plain,
% 3.32/3.54 (r(s(s(s(s(z)))), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1095, 30799])).
% 3.32/3.54 tff(30801,plain,
% 3.32/3.54 (~b(z, s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[2020, 30789, 30124, 30722])).
% 3.32/3.54 tff(30802,plain,
% 3.32/3.54 (r(z, s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1214, 30801])).
% 3.32/3.54 tff(30803,plain,
% 3.32/3.54 (~b(s(s(s(z))), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1956, 30789, 1422, 30788])).
% 3.32/3.54 tff(30804,plain,
% 3.32/3.54 (r(s(s(s(z))), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1155, 30803])).
% 3.32/3.54 tff(30805,plain,
% 3.32/3.54 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[26349, 30804, 1281, 220, 106, 30802])).
% 3.32/3.54 tff(30806,plain,
% 3.32/3.54 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1733, 30805])).
% 3.32/3.54 tff(30807,plain,
% 3.32/3.54 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[16371, 271, 30723, 2073, 30806])).
% 3.32/3.54 tff(30808,plain,
% 3.32/3.54 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30807, 28845])).
% 3.32/3.54 tff(30809,plain,
% 3.32/3.54 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[4138, 30808, 28482])).
% 3.32/3.54 tff(30810,plain,
% 3.32/3.54 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[17429, 30809, 3891])).
% 3.32/3.54 tff(30811,plain,
% 3.32/3.54 (b(s(s(s(elem!1))), z)),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[12308, 30788, 3891])).
% 3.32/3.54 tff(30812,plain,
% 3.32/3.54 (b(z, s(s(s(elem!1))))),
% 3.32/3.54 inference(modus_ponens,[status(thm)],[30789, 28197])).
% 3.32/3.54 tff(30813,plain,
% 3.32/3.54 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[30306, 30812, 1281, 601, 30811])).
% 3.32/3.54 tff(30814,plain,
% 3.32/3.54 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1658, 30813])).
% 3.32/3.54 tff(30815,plain,
% 3.32/3.54 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.54 inference(unit_resolution,[status(thm)],[1857, 30806, 30124, 30722])).
% 3.32/3.55 tff(30816,plain,
% 3.32/3.55 (r(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1847, 30815, 28455])).
% 3.32/3.55 tff(30817,plain,
% 3.32/3.55 (~r(s(z), s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[15700, 30810, 357, 30816])).
% 3.32/3.55 tff(30818,plain,
% 3.32/3.55 (b(s(z), s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1756, 30817])).
% 3.32/3.55 tff(30819,plain,
% 3.32/3.55 (~r(s(s(s(s(s(z))))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[16014, 30816, 357, 30791])).
% 3.32/3.55 tff(30820,plain,
% 3.32/3.55 (b(s(s(s(s(s(z))))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1682, 30819])).
% 3.32/3.55 tff(30821,plain,
% 3.32/3.55 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1785, 30798, 30820, 30818])).
% 3.32/3.55 tff(30822,plain,
% 3.32/3.55 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1777, 30821])).
% 3.32/3.55 tff(30823,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30824,plain,
% 3.32/3.55 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30825,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.32/3.55 inference(monotonicity,[status(thm)],[30824])).
% 3.32/3.55 tff(30826,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.55 inference(transitivity,[status(thm)],[30825, 30823])).
% 3.32/3.55 tff(30827,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.55 inference(quant_inst,[status(thm)],[])).
% 3.32/3.55 tff(30828,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30827, 30826])).
% 3.32/3.55 tff(30829,plain,
% 3.32/3.55 ($false),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30828, 121, 30822, 30814, 30810, 30800])).
% 3.32/3.55 tff(30830,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | b(s(elem!1), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.55 tff(30831,plain,
% 3.32/3.55 (~r(s(s(s(z))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30830, 30135, 220, 601, 1281, 28211, 30208, 30121, 30120, 2467, 30711])).
% 3.32/3.55 tff(30832,plain,
% 3.32/3.55 (b(s(s(s(z))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[2325, 30831])).
% 3.32/3.55 tff(30833,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), z)))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30834,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), z)))),
% 3.32/3.55 inference(quant_inst,[status(thm)],[])).
% 3.32/3.55 tff(30835,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(z))), z))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30834, 30833])).
% 3.32/3.55 tff(30836,plain,
% 3.32/3.55 (~b(s(s(s(z))), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30835, 271, 1281, 220, 30832])).
% 3.32/3.55 tff(30837,plain,
% 3.32/3.55 (r(s(s(s(z))), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1155, 30836])).
% 3.32/3.55 tff(30838,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30839,plain,
% 3.32/3.55 (((~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))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30840,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))))),
% 3.32/3.55 inference(monotonicity,[status(thm)],[30839])).
% 3.32/3.55 tff(30841,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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))))),
% 3.32/3.55 inference(transitivity,[status(thm)],[30840, 30838])).
% 3.32/3.55 tff(30842,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 3.32/3.55 inference(quant_inst,[status(thm)],[])).
% 3.32/3.55 tff(30843,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30842, 30841])).
% 3.32/3.55 tff(30844,plain,
% 3.32/3.55 (~b(z, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30843, 271, 1281, 220, 30832])).
% 3.32/3.55 tff(30845,plain,
% 3.32/3.55 (r(z, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1214, 30844])).
% 3.32/3.55 tff(30846,plain,
% 3.32/3.55 (r(s(z), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[105, 30711])).
% 3.32/3.55 tff(30847,plain,
% 3.32/3.55 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[26349, 30837, 1281, 220, 30846, 30845])).
% 3.32/3.55 tff(30848,plain,
% 3.32/3.55 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1733, 30847])).
% 3.32/3.55 tff(30849,plain,
% 3.32/3.55 (b(z, elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[25998, 394, 1281, 30191, 30198, 2467, 71])).
% 3.32/3.55 tff(30850,plain,
% 3.32/3.55 (b(z, s(s(s(elem!1))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30849, 28197])).
% 3.32/3.55 tff(30851,plain,
% 3.32/3.55 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30306, 30850, 1281, 601, 28259])).
% 3.32/3.55 tff(30852,plain,
% 3.32/3.55 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1658, 30851])).
% 3.32/3.55 tff(30853,plain,
% 3.32/3.55 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30375, 121, 1661, 109, 910])).
% 3.32/3.55 tff(30854,plain,
% 3.32/3.55 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[10426, 30853])).
% 3.32/3.55 tff(30855,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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)))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30856,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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)))))))),
% 3.32/3.55 inference(quant_inst,[status(thm)],[])).
% 3.32/3.55 tff(30857,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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))))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30856, 30855])).
% 3.32/3.55 tff(30858,plain,
% 3.32/3.55 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30857, 271, 2073, 1723, 30854])).
% 3.32/3.55 tff(30859,plain,
% 3.32/3.55 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[9512, 30858])).
% 3.32/3.55 tff(30860,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30861,plain,
% 3.32/3.55 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30862,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.32/3.55 inference(monotonicity,[status(thm)],[30861])).
% 3.32/3.55 tff(30863,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.55 inference(transitivity,[status(thm)],[30862, 30860])).
% 3.32/3.55 tff(30864,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.55 inference(quant_inst,[status(thm)],[])).
% 3.32/3.55 tff(30865,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30864, 30863])).
% 3.32/3.55 tff(30866,plain,
% 3.32/3.55 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30865, 271, 2073, 1723, 30854])).
% 3.32/3.55 tff(30867,plain,
% 3.32/3.55 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1777, 30866])).
% 3.32/3.55 tff(30868,plain,
% 3.32/3.55 ($false),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[29480, 121, 30867, 1661, 30859, 910])).
% 3.32/3.55 tff(30869,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.55 tff(30870,plain,
% 3.32/3.55 (~r(s(s(s(s(z)))), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30869, 30852, 2073, 1723, 109])).
% 3.32/3.55 tff(30871,plain,
% 3.32/3.55 (b(s(s(s(s(z)))), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1095, 30870])).
% 3.32/3.55 tff(30872,plain,
% 3.32/3.55 (~r(s(z), s(s(s(s(z)))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[28757, 30871, 572, 1008, 220, 28259, 601, 30850])).
% 3.32/3.55 tff(30873,plain,
% 3.32/3.55 (~b(s(z), s(s(s(s(z)))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[25001, 30871, 1281, 30850])).
% 3.32/3.55 tff(30874,plain,
% 3.32/3.55 ($false),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[16482, 30873, 30872])).
% 3.32/3.55 tff(30875,plain,((~b(s(elem!1), z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | b(s(elem!1), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.55 tff(30876,plain,
% 3.32/3.55 (~b(s(elem!1), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30875, 30135, 1281, 28210, 220, 601, 30121, 30848, 30837, 2467, 30711])).
% 3.32/3.55 tff(30877,plain,
% 3.32/3.55 (r(s(elem!1), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[409, 30876])).
% 3.32/3.55 tff(30878,plain,
% 3.32/3.55 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[17876, 30877, 220, 30209])).
% 3.32/3.55 tff(30879,plain,
% 3.32/3.55 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30726, 30878, 601])).
% 3.32/3.55 tff(30880,plain,
% 3.32/3.55 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[840, 30879, 28215])).
% 3.32/3.55 tff(30881,plain,
% 3.32/3.55 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30880, 28214])).
% 3.32/3.55 tff(30882,plain,
% 3.32/3.55 (r(s(s(s(elem!1))), z)),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30877, 28511])).
% 3.32/3.55 tff(30883,plain,
% 3.32/3.55 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[11674, 121, 30882, 30837, 30845])).
% 3.32/3.55 tff(30884,plain,
% 3.32/3.55 (~r(elem!1, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[28368, 30883, 28326])).
% 3.32/3.55 tff(30885,plain,
% 3.32/3.55 (b(elem!1, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1192, 30884, 28221])).
% 3.32/3.55 tff(30886,plain,
% 3.32/3.55 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30885, 28218])).
% 3.32/3.55 tff(30887,plain,
% 3.32/3.55 ($false),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[16371, 271, 30886, 30121, 30848, 30881])).
% 3.32/3.55 tff(30888,plain,(b(s(z), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | b(s(elem!1), elem!1) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.55 tff(30889,plain,
% 3.32/3.55 (b(s(z), s(s(s(elem!1))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30888, 30532, 601, 1281, 2467, 906, 2065, 422])).
% 3.32/3.55 tff(30890,plain,
% 3.32/3.55 (b(s(z), s(elem!1))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30889, 30123])).
% 3.32/3.55 tff(30891,plain,
% 3.32/3.55 (~b(s(elem!1), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[9241, 30890, 1281, 30532])).
% 3.32/3.55 tff(30892,plain,
% 3.32/3.55 (r(s(elem!1), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[409, 30891])).
% 3.32/3.55 tff(30893,plain,
% 3.32/3.55 (r(s(s(s(elem!1))), z)),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30892, 28511])).
% 3.32/3.55 tff(30894,plain,
% 3.32/3.55 (b(s(z), elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[2562, 30889, 25718])).
% 3.32/3.55 tff(30895,plain,
% 3.32/3.55 (b(s(z), s(s(elem!1)))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30889, 28841])).
% 3.32/3.55 tff(30896,plain,
% 3.32/3.55 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.55 inference(monotonicity,[status(thm)],[2590])).
% 3.32/3.55 tff(30897,plain,
% 3.32/3.55 (~b(s(s(s(z))), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[17276, 222, 220, 505])).
% 3.32/3.55 tff(30898,plain,
% 3.32/3.55 (r(s(s(s(z))), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1155, 30897])).
% 3.32/3.55 tff(30899,plain,
% 3.32/3.55 (b(s(z), elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[2562, 750, 2505])).
% 3.32/3.55 tff(30900,plain,
% 3.32/3.55 (~b(z, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[24799, 222, 220, 30899])).
% 3.32/3.55 tff(30901,plain,
% 3.32/3.55 (r(z, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1214, 30900])).
% 3.32/3.55 tff(30902,plain,
% 3.32/3.55 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[11676, 30901, 6842, 30898])).
% 3.32/3.55 tff(30903,plain,
% 3.32/3.55 (~r(elem!1, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[28368, 30902, 2203])).
% 3.32/3.55 tff(30904,plain,
% 3.32/3.55 (b(elem!1, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1192, 30903, 11082])).
% 3.32/3.55 tff(30905,plain,
% 3.32/3.55 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30904, 30896])).
% 3.32/3.55 tff(30906,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30907,plain,
% 3.32/3.55 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30908,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.32/3.55 inference(monotonicity,[status(thm)],[30907])).
% 3.32/3.55 tff(30909,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.32/3.55 inference(transitivity,[status(thm)],[30908, 30906])).
% 3.32/3.55 tff(30910,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 3.32/3.55 inference(quant_inst,[status(thm)],[])).
% 3.32/3.55 tff(30911,plain,
% 3.32/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30910, 30909])).
% 3.32/3.55 tff(30912,plain,
% 3.32/3.55 ($false),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30911, 271, 750, 30905, 2073, 222])).
% 3.32/3.55 tff(30913,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = elem!1)) | (~(s(elem!1) = elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.55 tff(30914,plain,
% 3.32/3.55 (~b(s(s(s(z))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30913, 30889, 30121, 25718, 28326, 30893, 30532, 30895])).
% 3.32/3.55 tff(30915,plain,
% 3.32/3.55 (r(s(s(s(z))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[2325, 30914])).
% 3.32/3.55 tff(30916,plain,
% 3.32/3.55 (~b(s(z), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30527, 30915, 1281, 28326, 29768, 30894, 25718, 2065, 30893])).
% 3.32/3.55 tff(30917,plain,
% 3.32/3.55 (r(s(z), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[105, 30916])).
% 3.32/3.55 tff(30918,plain,
% 3.32/3.55 (b(s(z), s(elem!1))),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[750, 30123])).
% 3.32/3.55 tff(30919,plain,
% 3.32/3.55 (~b(s(elem!1), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[9241, 30918, 1281, 220])).
% 3.32/3.55 tff(30920,plain,
% 3.32/3.55 (r(s(elem!1), z)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[409, 30919])).
% 3.32/3.55 tff(30921,plain,
% 3.32/3.55 (r(s(s(s(elem!1))), z)),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30920, 28511])).
% 3.32/3.55 tff(30922,plain,
% 3.32/3.55 (~b(s(s(s(z))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30913, 750, 2073, 25718, 28326, 30921, 220, 28848])).
% 3.32/3.55 tff(30923,plain,
% 3.32/3.55 (r(s(s(s(z))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[2325, 30922])).
% 3.32/3.55 tff(30924,plain,
% 3.32/3.55 (r(elem!1, s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[299, 24773, 258])).
% 3.32/3.55 tff(30925,plain,
% 3.32/3.55 (~b(elem!1, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[2020, 1326, 257, 1307])).
% 3.32/3.55 tff(30926,plain,
% 3.32/3.55 (r(elem!1, s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[1192, 30925, 1102])).
% 3.32/3.55 tff(30927,plain,
% 3.32/3.55 ($false),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[24792, 30926, 30924, 2327, 108])).
% 3.32/3.55 tff(30928,plain,((~b(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.55 tff(30929,plain,
% 3.32/3.55 (~b(z, elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30928, 1307, 108, 28221, 28851, 30124, 30923, 1281, 220])).
% 3.32/3.55 tff(30930,plain,
% 3.32/3.55 (r(z, elem!1)),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[355, 30929, 331])).
% 3.32/3.55 tff(30931,plain,
% 3.32/3.55 (r(elem!1, z)),
% 3.32/3.55 inference(modus_ponens,[status(thm)],[30920, 28512])).
% 3.32/3.55 tff(30932,plain,
% 3.32/3.55 (~b(z, s(s(s(elem!1))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[13207, 30929, 28225])).
% 3.32/3.55 tff(30933,plain,
% 3.32/3.55 (r(z, s(s(s(elem!1))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[19736, 30932])).
% 3.32/3.55 tff(30934,plain,
% 3.32/3.55 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[27041, 30933, 1281, 220, 1008, 750, 30931, 30930, 25718])).
% 3.32/3.55 tff(30935,plain,
% 3.32/3.55 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[932, 30934])).
% 3.32/3.55 tff(30936,plain,
% 3.32/3.55 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[30235, 30935, 108, 30923])).
% 3.32/3.55 tff(30937,plain,
% 3.32/3.55 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.55 inference(unit_resolution,[status(thm)],[10426, 30936])).
% 3.32/3.55 tff(30938,plain,
% 3.32/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.32/3.55 inference(rewrite,[status(thm)],[])).
% 3.32/3.55 tff(30939,plain,
% 3.32/3.55 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30940,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[30939])).
% 3.32/3.56 tff(30941,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.32/3.56 inference(transitivity,[status(thm)],[30940, 30938])).
% 3.32/3.56 tff(30942,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.32/3.56 inference(quant_inst,[status(thm)],[])).
% 3.32/3.56 tff(30943,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30942, 30941])).
% 3.32/3.56 tff(30944,plain,
% 3.32/3.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30943, 121, 30935, 30923, 108])).
% 3.32/3.56 tff(30945,plain,
% 3.32/3.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1167, 21, 30944, 20146])).
% 3.32/3.56 tff(30946,plain,
% 3.32/3.56 ($false),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30438, 271, 2073, 13508, 14893, 1066])).
% 3.32/3.56 tff(30947,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(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))))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.56 tff(30948,plain,
% 3.32/3.56 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30947, 30945, 2073, 30937])).
% 3.32/3.56 tff(30949,plain,
% 3.32/3.56 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1014, 30948, 1008])).
% 3.32/3.56 tff(30950,plain,
% 3.32/3.56 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[25701])).
% 3.32/3.56 tff(30951,plain,
% 3.32/3.56 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.56 inference(symmetry,[status(thm)],[30950])).
% 3.32/3.56 tff(30952,plain,
% 3.32/3.56 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[30951])).
% 3.32/3.56 tff(30953,plain,
% 3.32/3.56 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30948, 30952])).
% 3.32/3.56 tff(30954,plain,
% 3.32/3.56 (r(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1995, 30953, 28490])).
% 3.32/3.56 tff(30955,plain,
% 3.32/3.56 (~r(s(s(s(s(z)))), z)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[26940, 30954, 28225, 30933, 30920])).
% 3.32/3.56 tff(30956,plain,
% 3.32/3.56 (b(s(s(s(s(z)))), z)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1095, 30955])).
% 3.32/3.56 tff(30957,plain,
% 3.32/3.56 ($false),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[6706, 271, 1307, 1157, 1103, 14893])).
% 3.32/3.56 tff(30958,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.56 tff(30959,plain,
% 3.32/3.56 (~b(z, s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30958, 1307, 30956, 30945])).
% 3.32/3.56 tff(30960,plain,
% 3.32/3.56 (r(z, s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1121, 30959])).
% 3.32/3.56 tff(30961,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30962,plain,
% 3.32/3.56 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30963,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[30962])).
% 3.32/3.56 tff(30964,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.56 inference(transitivity,[status(thm)],[30963, 30961])).
% 3.32/3.56 tff(30965,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))),
% 3.32/3.56 inference(quant_inst,[status(thm)],[])).
% 3.32/3.56 tff(30966,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30965, 30964])).
% 3.32/3.56 tff(30967,plain,
% 3.32/3.56 ($false),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30966, 121, 30933, 30935, 30960, 30949])).
% 3.32/3.56 tff(30968,plain,((~b(z, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.32/3.56 tff(30969,plain,
% 3.32/3.56 (~b(z, s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30968, 30121, 28210, 601, 30917, 1281, 30532, 30889, 331])).
% 3.32/3.56 tff(30970,plain,
% 3.32/3.56 (r(z, s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1214, 30969])).
% 3.32/3.56 tff(30971,plain,
% 3.32/3.56 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[27041, 111, 1281, 220, 1008, 750, 30931, 30199, 25718])).
% 3.32/3.56 tff(30972,plain,
% 3.32/3.56 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[932, 30971])).
% 3.32/3.56 tff(30973,plain,
% 3.32/3.56 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30235, 30972, 108, 30923])).
% 3.32/3.56 tff(30974,plain,
% 3.32/3.56 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[10426, 30973])).
% 3.32/3.56 tff(30975,plain,
% 3.32/3.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30943, 121, 30972, 30923, 108])).
% 3.32/3.56 tff(30976,plain,
% 3.32/3.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1167, 21, 30975, 20146])).
% 3.32/3.56 tff(30977,plain,
% 3.32/3.56 (~r(elem!1, s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[19831, 30199, 30923, 1140])).
% 3.32/3.56 tff(30978,plain,
% 3.32/3.56 (b(elem!1, s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1192, 30977, 28221])).
% 3.32/3.56 tff(30979,plain,
% 3.32/3.56 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30978, 28218])).
% 3.32/3.56 tff(30980,plain,
% 3.32/3.56 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30783, 30979, 2073, 30974])).
% 3.32/3.56 tff(30981,plain,
% 3.32/3.56 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[28738, 30980, 601])).
% 3.32/3.56 tff(30982,plain,
% 3.32/3.56 (r(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1559, 30981, 28489])).
% 3.32/3.56 tff(30983,plain,
% 3.32/3.56 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[28532, 30982, 601])).
% 3.32/3.56 tff(30984,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30985,plain,
% 3.32/3.56 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30986,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[30985])).
% 3.32/3.56 tff(30987,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.56 inference(transitivity,[status(thm)],[30986, 30984])).
% 3.32/3.56 tff(30988,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 3.32/3.56 inference(quant_inst,[status(thm)],[])).
% 3.32/3.56 tff(30989,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30988, 30987])).
% 3.32/3.56 tff(30990,plain,
% 3.32/3.56 (~r(z, s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30989, 121, 111, 30921, 30983])).
% 3.32/3.56 tff(30991,plain,
% 3.32/3.56 (b(z, s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1121, 30990])).
% 3.32/3.56 tff(30992,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30993,plain,
% 3.32/3.56 (((~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(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(30994,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[30993])).
% 3.32/3.56 tff(30995,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.56 inference(transitivity,[status(thm)],[30994, 30992])).
% 3.32/3.56 tff(30996,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 3.32/3.56 inference(quant_inst,[status(thm)],[])).
% 3.32/3.56 tff(30997,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30996, 30995])).
% 3.32/3.56 tff(30998,plain,
% 3.32/3.56 (~b(s(s(s(z))), z)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30997, 271, 30991, 30974, 30976])).
% 3.32/3.56 tff(30999,plain,
% 3.32/3.56 (r(s(s(s(z))), z)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1155, 30998])).
% 3.32/3.56 tff(31000,plain,
% 3.32/3.56 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[26349, 30999, 1281, 220, 108, 1140])).
% 3.32/3.56 tff(31001,plain,
% 3.32/3.56 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1733, 31000])).
% 3.32/3.56 tff(31002,plain,
% 3.32/3.56 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1857, 31001, 30124, 30978])).
% 3.32/3.56 tff(31003,plain,
% 3.32/3.56 (r(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1847, 31002, 28455])).
% 3.32/3.56 tff(31004,plain,
% 3.32/3.56 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[28196])).
% 3.32/3.56 tff(31005,plain,
% 3.32/3.56 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.32/3.56 inference(symmetry,[status(thm)],[31004])).
% 3.32/3.56 tff(31006,plain,
% 3.32/3.56 (r(s(s(s(s(z)))), elem!1)),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[30983, 31005])).
% 3.32/3.56 tff(31007,plain,
% 3.32/3.56 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(31008,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[31007])).
% 3.32/3.56 tff(31009,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.32/3.56 inference(transitivity,[status(thm)],[31008, 26551])).
% 3.32/3.56 tff(31010,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.56 inference(quant_inst,[status(thm)],[])).
% 3.32/3.56 tff(31011,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[31010, 31009])).
% 3.32/3.56 tff(31012,plain,
% 3.32/3.56 (~r(s(s(s(s(z)))), z)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[31011, 121, 111, 30921, 30983])).
% 3.32/3.56 tff(31013,plain,
% 3.32/3.56 (b(s(s(s(s(z)))), z)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1095, 31012])).
% 3.32/3.56 tff(31014,plain,
% 3.32/3.56 (~b(s(z), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[24935, 30991, 1281, 31013])).
% 3.32/3.56 tff(31015,plain,
% 3.32/3.56 (r(s(z), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[16482, 31014])).
% 3.32/3.56 tff(31016,plain,
% 3.32/3.56 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30947, 30976, 2073, 30974])).
% 3.32/3.56 tff(31017,plain,
% 3.32/3.56 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1014, 31016, 1008])).
% 3.32/3.56 tff(31018,plain,
% 3.32/3.56 (~r(s(s(s(elem!1))), s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[16499, 31017, 31015, 30972])).
% 3.32/3.56 tff(31019,plain,
% 3.32/3.56 (~r(s(s(elem!1)), s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[28239, 31018, 609])).
% 3.32/3.56 tff(31020,plain,
% 3.32/3.56 (b(s(s(elem!1)), s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[2143, 31019])).
% 3.32/3.56 tff(31021,plain,
% 3.32/3.56 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[28875, 31001, 3891, 30180, 31020])).
% 3.32/3.56 tff(31022,plain,
% 3.32/3.56 (r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[840, 31021, 28215])).
% 3.32/3.56 tff(31023,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(31024,plain,
% 3.32/3.56 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(31025,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[31024])).
% 3.32/3.56 tff(31026,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.32/3.56 inference(transitivity,[status(thm)],[31025, 31023])).
% 3.32/3.56 tff(31027,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.56 inference(quant_inst,[status(thm)],[])).
% 3.32/3.56 tff(31028,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[31027, 31026])).
% 3.32/3.56 tff(31029,plain,
% 3.32/3.56 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[31028, 121])).
% 3.32/3.56 tff(31030,plain,
% 3.32/3.56 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[31029, 31022, 31006, 31003])).
% 3.32/3.56 tff(31031,plain,
% 3.32/3.56 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1777, 31030])).
% 3.32/3.56 tff(31032,plain,
% 3.32/3.56 ($false),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[30865, 271, 31031, 2073, 31001, 30974])).
% 3.32/3.56 tff(31033,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.56 tff(31034,plain,
% 3.32/3.56 (~r(z, s(s(s(elem!1))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[31033, 30121, 1281, 30532, 30917, 30970, 28210, 601, 30889])).
% 3.32/3.56 tff(31035,plain,
% 3.32/3.56 (b(z, s(s(s(elem!1))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[19736, 31034])).
% 3.32/3.56 tff(31036,plain,
% 3.32/3.56 (b(z, elem!1)),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[13207, 31035, 28225])).
% 3.32/3.56 tff(31037,plain,
% 3.32/3.56 (~b(elem!1, s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[20398, 31036, 1281, 30532])).
% 3.32/3.56 tff(31038,plain,
% 3.32/3.56 (r(elem!1, s(z))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[299, 31037, 28851])).
% 3.32/3.56 tff(31039,plain,
% 3.32/3.56 (~r(elem!1, s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[24792, 31038, 30915, 30917])).
% 3.32/3.56 tff(31040,plain,
% 3.32/3.56 (b(elem!1, s(s(s(z))))),
% 3.32/3.56 inference(unit_resolution,[status(thm)],[1192, 31039, 28221])).
% 3.32/3.56 tff(31041,plain,
% 3.32/3.56 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.56 inference(modus_ponens,[status(thm)],[31040, 28218])).
% 3.32/3.56 tff(31042,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(31043,plain,
% 3.32/3.56 (((~b(s(s(s(elem!1))), s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 3.32/3.56 inference(rewrite,[status(thm)],[])).
% 3.32/3.56 tff(31044,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 3.32/3.56 inference(monotonicity,[status(thm)],[31043])).
% 3.32/3.56 tff(31045,plain,
% 3.32/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 3.32/3.56 inference(transitivity,[status(thm)],[31044, 31042])).
% 3.32/3.56 tff(31046,plain,
% 3.32/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 3.32/3.57 inference(quant_inst,[status(thm)],[])).
% 3.32/3.57 tff(31047,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31046, 31045])).
% 3.32/3.57 tff(31048,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31047, 271, 750, 1281, 3407, 6202])).
% 3.32/3.57 tff(31049,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31050,plain,
% 3.32/3.57 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31049, 31035, 1281, 30889])).
% 3.32/3.57 tff(31051,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31050, 31041])).
% 3.32/3.57 tff(31052,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (z = elem!1) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(elem!1), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31053,plain,
% 3.32/3.57 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31052, 601, 1281, 9297, 9149, 2467, 2282])).
% 3.32/3.57 tff(31054,plain,
% 3.32/3.57 (r(s(s(s(z))), elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19994, 31053, 25718])).
% 3.32/3.57 tff(31055,plain,
% 3.32/3.57 (r(s(s(s(z))), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[23458, 31053, 3890])).
% 3.32/3.57 tff(31056,plain,
% 3.32/3.57 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 3.32/3.57 inference(symmetry,[status(thm)],[28511])).
% 3.32/3.57 tff(31057,plain,
% 3.32/3.57 (r(elem!1, z) <=> r(s(elem!1), z)),
% 3.32/3.57 inference(transitivity,[status(thm)],[28509, 31056])).
% 3.32/3.57 tff(31058,plain,
% 3.32/3.57 ((~r(elem!1, z)) <=> (~r(s(elem!1), z))),
% 3.32/3.57 inference(monotonicity,[status(thm)],[31057])).
% 3.32/3.57 tff(31059,plain,
% 3.32/3.57 (~b(z, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[21149, 3871, 1281, 222])).
% 3.32/3.57 tff(31060,plain,
% 3.32/3.57 (r(z, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1214, 31059])).
% 3.32/3.57 tff(31061,plain,
% 3.32/3.57 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(elem!1)))))),
% 3.32/3.57 inference(monotonicity,[status(thm)],[29081])).
% 3.32/3.57 tff(31062,plain,
% 3.32/3.57 (~b(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[30451, 3407, 1281, 601, 3871])).
% 3.32/3.57 tff(31063,plain,
% 3.32/3.57 (r(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[409, 31062])).
% 3.32/3.57 tff(31064,plain,
% 3.32/3.57 (~r(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[5155, 31063, 1500, 909])).
% 3.32/3.57 tff(31065,plain,
% 3.32/3.57 (b(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1155, 31064])).
% 3.32/3.57 tff(31066,plain,
% 3.32/3.57 (~b(z, s(s(elem!1)))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2650, 31065, 1281, 222])).
% 3.32/3.57 tff(31067,plain,
% 3.32/3.57 (~b(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31066, 31061])).
% 3.32/3.57 tff(31068,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[3407, 31067])).
% 3.32/3.57 tff(31069,plain,((~b(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31070,plain,
% 3.32/3.57 (~b(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31069, 3871, 1281, 222, 1500, 909, 601])).
% 3.32/3.57 tff(31071,plain,
% 3.32/3.57 (r(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19736, 31070])).
% 3.32/3.57 tff(31072,plain,
% 3.32/3.57 (r(z, elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[11073, 31071, 25718])).
% 3.32/3.57 tff(31073,plain,
% 3.32/3.57 (~r(elem!1, z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19871, 31072, 145, 31060])).
% 3.32/3.57 tff(31074,plain,
% 3.32/3.57 (~r(s(elem!1), z)),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31073, 31058])).
% 3.32/3.57 tff(31075,plain,
% 3.32/3.57 (b(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[409, 31074])).
% 3.32/3.57 tff(31076,plain,
% 3.32/3.57 (r(elem!1, s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[30204, 111, 909, 601, 1281, 572, 1242])).
% 3.32/3.57 tff(31077,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19790, 31076, 30199, 909, 572])).
% 3.32/3.57 tff(31078,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31079,plain,
% 3.32/3.57 (~r(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31078, 30135, 909, 601, 1281, 30187])).
% 3.32/3.57 tff(31080,plain,
% 3.32/3.57 (b(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19736, 31079])).
% 3.32/3.57 tff(31081,plain,
% 3.32/3.57 (~b(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[30451, 31080, 1281, 601, 3871])).
% 3.32/3.57 tff(31082,plain,
% 3.32/3.57 (b(z, elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[13207, 31080, 28225])).
% 3.32/3.57 tff(31083,plain,
% 3.32/3.57 (~b(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[4021, 1500, 1326, 412, 431, 909])).
% 3.32/3.57 tff(31084,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1155, 31083, 7885])).
% 3.32/3.57 tff(31085,plain,((~r(s(s(s(z))), s(elem!1))) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31086,plain,
% 3.32/3.57 (~r(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31085, 31082, 1500, 909, 30209])).
% 3.32/3.57 tff(31087,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[409, 31086, 31081])).
% 3.32/3.57 tff(31088,plain,(b(s(z), s(s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31089,plain,
% 3.32/3.57 (b(s(z), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31088, 3871, 909, 1281, 601, 1500])).
% 3.32/3.57 tff(31090,plain,
% 3.32/3.57 (b(s(z), s(elem!1))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31089, 30123])).
% 3.32/3.57 tff(31091,plain,
% 3.32/3.57 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[23890, 31075, 1281, 31090])).
% 3.32/3.57 tff(31092,plain,
% 3.32/3.57 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1658, 31091])).
% 3.32/3.57 tff(31093,plain,
% 3.32/3.57 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[11865, 31092, 31090, 31075, 909])).
% 3.32/3.57 tff(31094,plain,
% 3.32/3.57 (~b(s(s(elem!1)), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[22514, 31072, 1281, 3891, 222, 31060])).
% 3.32/3.57 tff(31095,plain,
% 3.32/3.57 (r(s(s(elem!1)), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2143, 31094])).
% 3.32/3.57 tff(31096,plain,
% 3.32/3.57 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[28239, 31095, 609])).
% 3.32/3.57 tff(31097,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.57 inference(rewrite,[status(thm)],[])).
% 3.32/3.57 tff(31098,plain,
% 3.32/3.57 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.57 inference(rewrite,[status(thm)],[])).
% 3.32/3.57 tff(31099,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.32/3.57 inference(monotonicity,[status(thm)],[31098])).
% 3.32/3.57 tff(31100,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.57 inference(transitivity,[status(thm)],[31099, 31097])).
% 3.32/3.57 tff(31101,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.32/3.57 inference(quant_inst,[status(thm)],[])).
% 3.32/3.57 tff(31102,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31101, 31100])).
% 3.32/3.57 tff(31103,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31102, 121, 111, 12761, 1661, 7793])).
% 3.32/3.57 tff(31104,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31105,plain,
% 3.32/3.57 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31104, 31092, 31071, 31096])).
% 3.32/3.57 tff(31106,plain,
% 3.32/3.57 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[17429, 31105, 3891])).
% 3.32/3.57 tff(31107,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[4138, 31106, 31093, 28482])).
% 3.32/3.57 tff(31108,plain,((~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31109,plain,
% 3.32/3.57 (~b(s(z), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31108, 222, 1281, 601, 145, 909, 1500])).
% 3.32/3.57 tff(31110,plain,
% 3.32/3.57 (r(s(z), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[105, 31109])).
% 3.32/3.57 tff(31111,plain,
% 3.32/3.57 (~r(z, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1508, 31110, 1500, 909])).
% 3.32/3.57 tff(31112,plain,
% 3.32/3.57 (b(z, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1214, 31111])).
% 3.32/3.57 tff(31113,plain,
% 3.32/3.57 (~b(s(z), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19761, 394, 1281, 1307])).
% 3.32/3.57 tff(31114,plain,
% 3.32/3.57 (r(s(z), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[444, 31113, 348])).
% 3.32/3.57 tff(31115,plain,
% 3.32/3.57 (~b(s(elem!1), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2029, 394, 222, 1307])).
% 3.32/3.57 tff(31116,plain,
% 3.32/3.57 (r(s(elem!1), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2044, 31115, 2037])).
% 3.32/3.57 tff(31117,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[3445, 31116, 31114, 145, 108])).
% 3.32/3.57 tff(31118,plain,((~b(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31119,plain,
% 3.32/3.57 (~b(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31118, 31110, 145, 28805, 348, 222, 31112, 1281])).
% 3.32/3.57 tff(31120,plain,
% 3.32/3.57 (r(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[409, 31119])).
% 3.32/3.57 tff(31121,plain,
% 3.32/3.57 (~r(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[5155, 31120, 1500, 909])).
% 3.32/3.57 tff(31122,plain,
% 3.32/3.57 (b(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1155, 31121])).
% 3.32/3.57 tff(31123,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[26525, 271, 1281, 31112, 222, 31122])).
% 3.32/3.57 tff(31124,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (s(z) = s(elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31125,plain,
% 3.32/3.57 (~b(s(s(s(z))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31124, 909, 31055, 1281, 31054, 348, 601])).
% 3.32/3.57 tff(31126,plain,
% 3.32/3.57 (r(s(s(s(z))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2325, 31125])).
% 3.32/3.57 tff(31127,plain,
% 3.32/3.57 (~r(s(z), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1508, 1140, 1500, 909])).
% 3.32/3.57 tff(31128,plain,
% 3.32/3.57 (b(s(z), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[105, 31127])).
% 3.32/3.57 tff(31129,plain,
% 3.32/3.57 (b(s(z), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31088, 31128, 909, 1281, 601, 1500])).
% 3.32/3.57 tff(31130,plain,
% 3.32/3.57 (b(s(z), s(elem!1))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31129, 30123])).
% 3.32/3.57 tff(31131,plain,
% 3.32/3.57 (~r(s(elem!1), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[3865, 412, 1500, 1140])).
% 3.32/3.57 tff(31132,plain,
% 3.32/3.57 (b(s(elem!1), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2044, 31131, 28805])).
% 3.32/3.57 tff(31133,plain,
% 3.32/3.57 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31132, 28216])).
% 3.32/3.57 tff(31134,plain,
% 3.32/3.57 (~r(z, elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19871, 28513, 145, 1140])).
% 3.32/3.57 tff(31135,plain,
% 3.32/3.57 (~r(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[11073, 31134, 25718])).
% 3.32/3.57 tff(31136,plain,
% 3.32/3.57 (b(z, s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19736, 31135])).
% 3.32/3.57 tff(31137,plain,
% 3.32/3.57 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31049, 31136, 1281, 750])).
% 3.32/3.57 tff(31138,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31137, 31133])).
% 3.32/3.57 tff(31139,plain,((~r(s(elem!1), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31140,plain,
% 3.32/3.57 (~r(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31139, 31129, 1281, 601, 145, 1140, 1500])).
% 3.32/3.57 tff(31141,plain,
% 3.32/3.57 (b(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[409, 31140])).
% 3.32/3.57 tff(31142,plain,
% 3.32/3.57 (~b(z, elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[23220, 31141, 1281, 31130])).
% 3.32/3.57 tff(31143,plain,
% 3.32/3.57 (r(z, elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[355, 31142, 331])).
% 3.32/3.57 tff(31144,plain,
% 3.32/3.57 (~r(elem!1, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19831, 31143, 2327, 1140])).
% 3.32/3.57 tff(31145,plain,
% 3.32/3.57 (b(elem!1, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1192, 31144, 28221])).
% 3.32/3.57 tff(31146,plain,
% 3.32/3.57 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[23890, 31141, 1281, 31130])).
% 3.32/3.57 tff(31147,plain,
% 3.32/3.57 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1658, 31146])).
% 3.32/3.57 tff(31148,plain,
% 3.32/3.57 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[16283, 31147, 145, 1140])).
% 3.32/3.57 tff(31149,plain,
% 3.32/3.57 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1733, 31148])).
% 3.32/3.57 tff(31150,plain,
% 3.32/3.57 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[11865, 31147, 31130, 31141, 909])).
% 3.32/3.57 tff(31151,plain,
% 3.32/3.57 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[25909, 31150, 28458])).
% 3.32/3.57 tff(31152,plain,
% 3.32/3.57 (r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[840, 31151, 28215])).
% 3.32/3.57 tff(31153,plain,
% 3.32/3.57 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[5017, 31152, 31143, 31147])).
% 3.32/3.57 tff(31154,plain,
% 3.32/3.57 (b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1847, 31153, 28455])).
% 3.32/3.57 tff(31155,plain,
% 3.32/3.57 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[5462, 31152, 3891])).
% 3.32/3.57 tff(31156,plain,
% 3.32/3.57 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[5531, 31155, 1140, 31147])).
% 3.32/3.57 tff(31157,plain,
% 3.32/3.57 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1494, 31156])).
% 3.32/3.57 tff(31158,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[18887, 31157, 31154, 31149, 31145])).
% 3.32/3.57 tff(31159,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (z = elem!1) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31160,plain,
% 3.32/3.57 (~r(z, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31159, 909, 31054, 31126, 9297, 1281, 601, 31055])).
% 3.32/3.57 tff(31161,plain,
% 3.32/3.57 (b(z, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1214, 31160])).
% 3.32/3.57 tff(31162,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[439, 30918])).
% 3.32/3.57 tff(31163,plain,((~b(s(z), s(s(s(elem!1))))) | b(s(z), s(elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31164,plain,
% 3.32/3.57 (~b(s(z), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31163, 31113, 601])).
% 3.32/3.57 tff(31165,plain,
% 3.32/3.57 (~b(s(z), elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[19692, 31164, 25718])).
% 3.32/3.57 tff(31166,plain,
% 3.32/3.57 (b(elem!1, s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[23319, 31165, 28851, 145, 2327])).
% 3.32/3.57 tff(31167,plain,
% 3.32/3.57 (~b(s(z), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31088, 31164, 909, 1281, 601, 1500])).
% 3.32/3.57 tff(31168,plain,
% 3.32/3.57 (b(z, elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[25998, 31167, 1281, 30191, 30198, 2467, 394])).
% 3.32/3.57 tff(31169,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[4775, 31168, 31166, 1281, 28798])).
% 3.32/3.57 tff(31170,plain,((~b(s(elem!1), z)) | (~b(s(z), z)) | b(s(elem!1), elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31171,plain,
% 3.32/3.57 (~b(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31170, 31126, 2467, 31054, 1281, 909, 601, 31055, 31161])).
% 3.32/3.57 tff(31172,plain,
% 3.32/3.57 (r(s(elem!1), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[409, 31171])).
% 3.32/3.57 tff(31173,plain,
% 3.32/3.57 (~r(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[5155, 31172, 31055, 909])).
% 3.32/3.57 tff(31174,plain,
% 3.32/3.57 (b(s(s(s(z))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1155, 31173])).
% 3.32/3.57 tff(31175,plain,
% 3.32/3.57 (r(s(s(s(z))), s(s(elem!1)))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[13482, 31054, 3891])).
% 3.32/3.57 tff(31176,plain,
% 3.32/3.57 (r(s(s(s(elem!1))), z)),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31172, 28511])).
% 3.32/3.57 tff(31177,plain,
% 3.32/3.57 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[12235, 3891, 9149])).
% 3.32/3.57 tff(31178,plain,
% 3.32/3.57 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31177, 28208])).
% 3.32/3.57 tff(31179,plain,
% 3.32/3.57 (~r(s(z), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[2640, 31172, 31055, 31126])).
% 3.32/3.57 tff(31180,plain,
% 3.32/3.57 (~r(s(z), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[28255, 31179, 609])).
% 3.32/3.57 tff(31181,plain,
% 3.32/3.57 (b(s(z), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[760, 31180])).
% 3.32/3.57 tff(31182,plain,
% 3.32/3.57 (~r(elem!1, s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[3464, 30199, 909, 108])).
% 3.32/3.57 tff(31183,plain,
% 3.32/3.57 (b(elem!1, s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[299, 31182, 28851])).
% 3.32/3.57 tff(31184,plain,
% 3.32/3.57 (~r(s(s(s(s(z)))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[30241, 108, 909, 2327])).
% 3.32/3.57 tff(31185,plain,
% 3.32/3.57 (b(s(s(s(s(z)))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[932, 31184])).
% 3.32/3.57 tff(31186,plain,
% 3.32/3.57 (~r(s(s(s(elem!1))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[12809, 31182, 25718])).
% 3.32/3.57 tff(31187,plain,
% 3.32/3.57 (b(s(s(s(elem!1))), s(z))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[16580, 31186])).
% 3.32/3.57 tff(31188,plain,
% 3.32/3.57 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[29196, 31187, 601, 750, 6842, 2327, 31185, 31183, 108])).
% 3.32/3.57 tff(31189,plain,
% 3.32/3.57 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1733, 31188])).
% 3.32/3.57 tff(31190,plain,
% 3.32/3.57 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[28970, 271, 1307, 31189, 1935])).
% 3.32/3.57 tff(31191,plain,
% 3.32/3.57 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1658, 31190])).
% 3.32/3.57 tff(31192,plain,
% 3.32/3.57 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[12573, 7792, 3891, 7794, 937, 750])).
% 3.32/3.57 tff(31193,plain,
% 3.32/3.57 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[10426, 31192])).
% 3.32/3.57 tff(31194,plain,
% 3.32/3.57 (~b(s(s(s(s(z)))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[13513, 31193, 1307, 1935])).
% 3.32/3.57 tff(31195,plain,
% 3.32/3.57 (r(s(s(s(s(z)))), z)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1095, 31194])).
% 3.32/3.57 tff(31196,plain,
% 3.32/3.57 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[29135, 31195, 909, 6842])).
% 3.32/3.57 tff(31197,plain,
% 3.32/3.57 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1014, 31196, 1008])).
% 3.32/3.57 tff(31198,plain,
% 3.32/3.57 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[12570, 31197, 750, 937])).
% 3.32/3.57 tff(31199,plain,
% 3.32/3.57 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[28738, 31198, 601])).
% 3.32/3.57 tff(31200,plain,
% 3.32/3.57 (r(s(s(s(s(z)))), s(elem!1))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1559, 31199, 28489])).
% 3.32/3.57 tff(31201,plain,
% 3.32/3.57 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[28532, 31200, 601])).
% 3.32/3.57 tff(31202,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.57 inference(rewrite,[status(thm)],[])).
% 3.32/3.57 tff(31203,plain,
% 3.32/3.57 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.57 inference(rewrite,[status(thm)],[])).
% 3.32/3.57 tff(31204,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.32/3.57 inference(monotonicity,[status(thm)],[31203])).
% 3.32/3.57 tff(31205,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.57 inference(transitivity,[status(thm)],[31204, 31202])).
% 3.32/3.57 tff(31206,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 3.32/3.57 inference(quant_inst,[status(thm)],[])).
% 3.32/3.57 tff(31207,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31206, 31205])).
% 3.32/3.57 tff(31208,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31207, 121, 111, 7792, 31195, 31201])).
% 3.32/3.57 tff(31209,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31210,plain,
% 3.32/3.57 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31209, 111, 601, 750, 31185, 1008, 909, 6842, 1307, 1935, 7794])).
% 3.32/3.57 tff(31211,plain,
% 3.32/3.57 (~r(elem!1, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[28368, 31210, 28326])).
% 3.32/3.57 tff(31212,plain,
% 3.32/3.57 (b(elem!1, s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[1192, 31211, 28221])).
% 3.32/3.57 tff(31213,plain,
% 3.32/3.57 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[1195, 30896])).
% 3.32/3.57 tff(31214,plain,
% 3.32/3.57 ($false),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[13108, 31213])).
% 3.32/3.57 tff(31215,plain,((~b(elem!1, s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(z)))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.57 tff(31216,plain,
% 3.32/3.57 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31215, 31212, 25718])).
% 3.32/3.57 tff(31217,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 3.32/3.57 inference(rewrite,[status(thm)],[])).
% 3.32/3.57 tff(31218,plain,
% 3.32/3.57 (((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), 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(elem!1)))))) <=> ((~b(s(s(s(elem!1))), 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(elem!1))))))),
% 3.32/3.57 inference(rewrite,[status(thm)],[])).
% 3.32/3.57 tff(31219,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1)))))))),
% 3.32/3.57 inference(monotonicity,[status(thm)],[31218])).
% 3.32/3.57 tff(31220,plain,
% 3.32/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 3.32/3.57 inference(transitivity,[status(thm)],[31219, 31217])).
% 3.32/3.57 tff(31221,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 3.32/3.57 inference(quant_inst,[status(thm)],[])).
% 3.32/3.57 tff(31222,plain,
% 3.32/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1)))))),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31221, 31220])).
% 3.32/3.57 tff(31223,plain,
% 3.32/3.57 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[31222, 271, 31216, 31189, 1935])).
% 3.32/3.57 tff(31224,plain,
% 3.32/3.57 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.57 inference(modus_ponens,[status(thm)],[31223, 28621])).
% 3.32/3.57 tff(31225,plain,
% 3.32/3.57 (r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.57 inference(unit_resolution,[status(thm)],[840, 31224, 28215])).
% 3.32/3.57 tff(31226,plain,
% 3.32/3.57 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.57 inference(transitivity,[status(thm)],[30473, 30471])).
% 3.32/3.58 tff(31227,plain,
% 3.32/3.58 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 3.32/3.58 inference(monotonicity,[status(thm)],[31226])).
% 3.32/3.58 tff(31228,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31229,plain,
% 3.32/3.58 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31230,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(s(z)))))))))),
% 3.32/3.58 inference(monotonicity,[status(thm)],[31229])).
% 3.32/3.58 tff(31231,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(transitivity,[status(thm)],[31230, 31228])).
% 3.32/3.58 tff(31232,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(quant_inst,[status(thm)],[])).
% 3.32/3.58 tff(31233,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31232, 31231])).
% 3.32/3.58 tff(31234,plain,
% 3.32/3.58 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31233, 271, 31216, 31189, 1935])).
% 3.32/3.58 tff(31235,plain,
% 3.32/3.58 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31234, 31227])).
% 3.32/3.58 tff(31236,plain,
% 3.32/3.58 (r(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1847, 31235, 28455])).
% 3.32/3.58 tff(31237,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[5017, 31236, 31225, 30199, 31191])).
% 3.32/3.58 tff(31238,plain,((~r(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31239,plain,
% 3.32/3.58 (~r(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31238, 108, 1935, 750, 1008, 909, 6842, 1307, 7794, 2327, 601])).
% 3.32/3.58 tff(31240,plain,
% 3.32/3.58 (b(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[19736, 31239])).
% 3.32/3.58 tff(31241,plain,
% 3.32/3.58 (b(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[13207, 31240, 28225])).
% 3.32/3.58 tff(31242,plain,
% 3.32/3.58 (~b(elem!1, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[4760, 31241, 1281, 29104])).
% 3.32/3.58 tff(31243,plain,
% 3.32/3.58 (r(elem!1, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[299, 31242, 28851])).
% 3.32/3.58 tff(31244,plain,
% 3.32/3.58 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31049, 31240, 1281, 750])).
% 3.32/3.58 tff(31245,plain,
% 3.32/3.58 (~b(elem!1, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31215, 31244, 25718])).
% 3.32/3.58 tff(31246,plain,
% 3.32/3.58 (r(elem!1, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1192, 31245, 28221])).
% 3.32/3.58 tff(31247,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[24792, 31246, 31243, 2327, 108])).
% 3.32/3.58 tff(31248,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31249,plain,
% 3.32/3.58 (~r(s(z), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31248, 31126, 1281, 31181, 31174, 31178, 909, 31176, 31161, 31175, 601])).
% 3.32/3.58 tff(31250,plain,
% 3.32/3.58 (b(s(z), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[105, 31249])).
% 3.32/3.58 tff(31251,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[5539, 271, 1281, 31161, 31250, 31174])).
% 3.32/3.58 tff(31252,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31253,plain,
% 3.32/3.58 (~r(z, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31252, 601, 1281, 2467, 348])).
% 3.32/3.58 tff(31254,plain,
% 3.32/3.58 (b(z, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[904, 31253])).
% 3.32/3.58 tff(31255,plain,
% 3.32/3.58 (~r(elem!1, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[4112, 108, 145, 357])).
% 3.32/3.58 tff(31256,plain,
% 3.32/3.58 (b(elem!1, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[299, 31255, 258])).
% 3.32/3.58 tff(31257,plain,
% 3.32/3.58 (~r(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[26024, 108, 1281, 145, 358, 220, 258, 357])).
% 3.32/3.58 tff(31258,plain,
% 3.32/3.58 (b(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[355, 31257, 331])).
% 3.32/3.58 tff(31259,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[20398, 31258, 31256, 1281, 220])).
% 3.32/3.58 tff(31260,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (z = elem!1) | (elem!1 = s(z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31261,plain,
% 3.32/3.58 (~r(s(z), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31260, 30208, 220, 331, 28851, 145, 1281])).
% 3.32/3.58 tff(31262,plain,
% 3.32/3.58 (b(s(z), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[105, 31261])).
% 3.32/3.58 tff(31263,plain,
% 3.32/3.58 (~r(elem!1, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[12657, 2327, 145, 572])).
% 3.32/3.58 tff(31264,plain,
% 3.32/3.58 (~r(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[2640, 2327, 1500, 28256])).
% 3.32/3.58 tff(31265,plain,
% 3.32/3.58 (b(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[409, 31264])).
% 3.32/3.58 tff(31266,plain,
% 3.32/3.58 (b(elem!1, s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[23319, 2327, 28851, 145, 1242])).
% 3.32/3.58 tff(31267,plain,
% 3.32/3.58 (~b(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[20398, 31266, 1281, 220])).
% 3.32/3.58 tff(31268,plain,
% 3.32/3.58 (r(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[355, 31267, 331])).
% 3.32/3.58 tff(31269,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[25755, 31268, 31265, 1281, 601, 31263, 30198, 30191, 1242])).
% 3.32/3.58 tff(31270,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | b(s(z), elem!1) | (z = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31271,plain,
% 3.32/3.58 (~r(s(s(s(z))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31270, 30187, 601, 1281, 331, 220, 1500, 145, 30135])).
% 3.32/3.58 tff(31272,plain,
% 3.32/3.58 (b(s(s(s(z))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[2325, 31271])).
% 3.32/3.58 tff(31273,plain,
% 3.32/3.58 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[30726, 28483, 601])).
% 3.32/3.58 tff(31274,plain,
% 3.32/3.58 (b(s(s(s(s(s(z))))), elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[840, 31273, 28215])).
% 3.32/3.58 tff(31275,plain,
% 3.32/3.58 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31274, 28214])).
% 3.32/3.58 tff(31276,plain,
% 3.32/3.58 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[11676, 28824, 109, 1140])).
% 3.32/3.58 tff(31277,plain,
% 3.32/3.58 (~r(elem!1, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[28368, 31276, 28326])).
% 3.32/3.58 tff(31278,plain,
% 3.32/3.58 (b(elem!1, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1192, 31277, 28221])).
% 3.32/3.58 tff(31279,plain,
% 3.32/3.58 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31215, 31278, 25718])).
% 3.32/3.58 tff(31280,plain,
% 3.32/3.58 (~r(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[3650, 412, 1500, 109])).
% 3.32/3.58 tff(31281,plain,
% 3.32/3.58 (~r(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[11073, 31280, 25718])).
% 3.32/3.58 tff(31282,plain,
% 3.32/3.58 (b(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[19736, 31281])).
% 3.32/3.58 tff(31283,plain,
% 3.32/3.58 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[30708, 271, 31282, 31279, 31275])).
% 3.32/3.58 tff(31284,plain,
% 3.32/3.58 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1658, 31283])).
% 3.32/3.58 tff(31285,plain,
% 3.32/3.58 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[16283, 31284, 145, 1140])).
% 3.32/3.58 tff(31286,plain,
% 3.32/3.58 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1733, 31285])).
% 3.32/3.58 tff(31287,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31288,plain,
% 3.32/3.58 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), 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(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31289,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.32/3.58 inference(monotonicity,[status(thm)],[31288])).
% 3.32/3.58 tff(31290,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.32/3.58 inference(transitivity,[status(thm)],[31289, 31287])).
% 3.32/3.58 tff(31291,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 3.32/3.58 inference(quant_inst,[status(thm)],[])).
% 3.32/3.58 tff(31292,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31291, 31290])).
% 3.32/3.58 tff(31293,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31292, 271, 31279, 222, 31286, 31275])).
% 3.32/3.58 tff(31294,plain,((~r(s(elem!1), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31295,plain,
% 3.32/3.58 (~r(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31294, 24356, 145, 1140, 222, 601, 220, 431, 1500])).
% 3.32/3.58 tff(31296,plain,
% 3.32/3.58 (b(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[409, 31295])).
% 3.32/3.58 tff(31297,plain,
% 3.32/3.58 (~b(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[30451, 31296, 1281, 601, 3871])).
% 3.32/3.58 tff(31298,plain,
% 3.32/3.58 (~b(z, s(elem!1))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[6491, 31297, 3891])).
% 3.32/3.58 tff(31299,plain,
% 3.32/3.58 (r(z, s(elem!1))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1439, 31298])).
% 3.32/3.58 tff(31300,plain,
% 3.32/3.58 (~r(s(elem!1), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[24514, 31299, 1500, 220, 431])).
% 3.32/3.58 tff(31301,plain,
% 3.32/3.58 (b(s(elem!1), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[429, 31300, 422])).
% 3.32/3.58 tff(31302,plain,
% 3.32/3.58 (~r(s(elem!1), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[10701, 31299, 1500, 1140])).
% 3.32/3.58 tff(31303,plain,
% 3.32/3.58 (b(s(elem!1), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[2044, 31302, 28805])).
% 3.32/3.58 tff(31304,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[3622, 31303, 31301, 222, 3871])).
% 3.32/3.58 tff(31305,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(elem!1))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31306,plain,
% 3.32/3.58 (~r(z, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31305, 31272, 422, 1500, 31262, 220, 30209, 1281, 601, 145])).
% 3.32/3.58 tff(31307,plain,
% 3.32/3.58 (~b(z, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[21149, 31272, 1281, 31262])).
% 3.32/3.58 tff(31308,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1214, 31307, 31306])).
% 3.32/3.58 tff(31309,plain,(b(s(z), s(s(s(elem!1)))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31310,plain,
% 3.32/3.58 (b(s(z), s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31309, 31055, 2282, 1281, 31254, 601, 31054, 9297])).
% 3.32/3.58 tff(31311,plain,
% 3.32/3.58 (b(s(z), elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[2562, 31310, 25718])).
% 3.32/3.58 tff(31312,plain,
% 3.32/3.58 (b(s(z), s(elem!1))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31163, 31310, 601])).
% 3.32/3.58 tff(31313,plain,
% 3.32/3.58 (~b(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[9241, 31312, 1281, 31254])).
% 3.32/3.58 tff(31314,plain,
% 3.32/3.58 (r(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[409, 31313])).
% 3.32/3.58 tff(31315,plain,
% 3.32/3.58 (~r(z, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31139, 31314, 1281, 601, 31054, 31310, 31055])).
% 3.32/3.58 tff(31316,plain,
% 3.32/3.58 (b(z, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1214, 31315])).
% 3.32/3.58 tff(31317,plain,
% 3.32/3.58 (~b(s(s(s(z))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[24799, 31316, 31254, 31311])).
% 3.32/3.58 tff(31318,plain,
% 3.32/3.58 (r(s(s(s(z))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[2325, 31317])).
% 3.32/3.58 tff(31319,plain,
% 3.32/3.58 (b(s(z), s(elem!1))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31163, 750, 601])).
% 3.32/3.58 tff(31320,plain,
% 3.32/3.58 (~b(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[9241, 31319, 1281, 220])).
% 3.32/3.58 tff(31321,plain,
% 3.32/3.58 (r(s(elem!1), z)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[409, 31320])).
% 3.32/3.58 tff(31322,plain,
% 3.32/3.58 (r(s(s(s(z))), s(elem!1))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[23458, 5499, 3890])).
% 3.32/3.58 tff(31323,plain,
% 3.32/3.58 (~r(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[3650, 24356, 31322, 31321])).
% 3.32/3.58 tff(31324,plain,
% 3.32/3.58 (~r(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[11073, 31323, 25718])).
% 3.32/3.58 tff(31325,plain,
% 3.32/3.58 (b(z, s(s(s(elem!1))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[19736, 31324])).
% 3.32/3.58 tff(31326,plain,
% 3.32/3.58 (~b(s(s(s(elem!1))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[17333, 31325, 220, 750])).
% 3.32/3.58 tff(31327,plain,
% 3.32/3.58 (r(s(s(s(elem!1))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[16580, 31326])).
% 3.32/3.58 tff(31328,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31329,plain,
% 3.32/3.58 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31330,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.32/3.58 inference(monotonicity,[status(thm)],[31329])).
% 3.32/3.58 tff(31331,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.58 inference(transitivity,[status(thm)],[31330, 31328])).
% 3.32/3.58 tff(31332,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 3.32/3.58 inference(quant_inst,[status(thm)],[])).
% 3.32/3.58 tff(31333,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31332, 31331])).
% 3.32/3.58 tff(31334,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31333, 271, 750, 1281, 3407, 1066])).
% 3.32/3.58 tff(31335,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31336,plain,
% 3.32/3.58 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31335, 31325, 1281, 750])).
% 3.32/3.58 tff(31337,plain,
% 3.32/3.58 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1014, 31336, 1008])).
% 3.32/3.58 tff(31338,plain,
% 3.32/3.58 (r(s(s(s(elem!1))), z)),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31321, 28511])).
% 3.32/3.58 tff(31339,plain,
% 3.32/3.58 (r(elem!1, z)),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31321, 28512])).
% 3.32/3.58 tff(31340,plain,
% 3.32/3.58 (r(s(s(s(z))), elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[19994, 5499, 25718])).
% 3.32/3.58 tff(31341,plain,
% 3.32/3.58 (~r(z, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31139, 31321, 1281, 601, 31340, 750, 31322])).
% 3.32/3.58 tff(31342,plain,
% 3.32/3.58 (b(z, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1214, 31341])).
% 3.32/3.58 tff(31343,plain,
% 3.32/3.58 (b(z, elem!1)),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[21396, 24356, 331, 1281, 31342, 3871, 31339])).
% 3.32/3.58 tff(31344,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31345,plain,
% 3.32/3.58 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31346,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 3.32/3.58 inference(monotonicity,[status(thm)],[31345])).
% 3.32/3.58 tff(31347,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(transitivity,[status(thm)],[31346, 31344])).
% 3.32/3.58 tff(31348,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 3.32/3.58 inference(quant_inst,[status(thm)],[])).
% 3.32/3.58 tff(31349,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31348, 31347])).
% 3.32/3.58 tff(31350,plain,
% 3.32/3.58 ($false),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31349, 271, 1326, 260, 220, 1849])).
% 3.32/3.58 tff(31351,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.58 tff(31352,plain,
% 3.32/3.58 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31351, 31343, 220, 29104])).
% 3.32/3.58 tff(31353,plain,
% 3.32/3.58 (r(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1847, 31352, 28455])).
% 3.32/3.58 tff(31354,plain,
% 3.32/3.58 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[16341, 31353, 3891])).
% 3.32/3.58 tff(31355,plain,
% 3.32/3.58 (r(s(s(s(z))), s(s(elem!1)))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[13482, 31340, 3891])).
% 3.32/3.58 tff(31356,plain,
% 3.32/3.58 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31049, 31325, 1281, 750])).
% 3.32/3.58 tff(31357,plain,
% 3.32/3.58 (~b(elem!1, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[31215, 31356, 25718])).
% 3.32/3.58 tff(31358,plain,
% 3.32/3.58 (r(elem!1, s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1192, 31357, 28221])).
% 3.32/3.58 tff(31359,plain,
% 3.32/3.58 (r(s(s(elem!1)), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[12242, 31358, 3891])).
% 3.32/3.58 tff(31360,plain,
% 3.32/3.58 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[16352, 31359, 31355, 31354])).
% 3.32/3.58 tff(31361,plain,
% 3.32/3.58 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1733, 31360])).
% 3.32/3.58 tff(31362,plain,
% 3.32/3.58 (~b(s(s(s(z))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[24799, 31342, 220, 29104])).
% 3.32/3.58 tff(31363,plain,
% 3.32/3.58 (r(s(s(s(z))), s(z))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[2325, 31362])).
% 3.32/3.58 tff(31364,plain,
% 3.32/3.58 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[28368, 31358, 28326])).
% 3.32/3.58 tff(31365,plain,
% 3.32/3.58 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[13558, 31364, 31363, 31337])).
% 3.32/3.58 tff(31366,plain,
% 3.32/3.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[10426, 31365])).
% 3.32/3.58 tff(31367,plain,
% 3.32/3.58 (r(s(elem!1), s(s(s(s(s(z))))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[25954, 31353, 28458])).
% 3.32/3.58 tff(31368,plain,
% 3.32/3.58 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.58 inference(modus_ponens,[status(thm)],[31336, 30952])).
% 3.32/3.58 tff(31369,plain,
% 3.32/3.58 (r(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.58 inference(unit_resolution,[status(thm)],[1995, 31368, 28490])).
% 3.32/3.58 tff(31370,assumption,(r(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 3.32/3.58 tff(31371,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31372,plain,
% 3.32/3.58 (((~b(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(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(rewrite,[status(thm)],[])).
% 3.32/3.58 tff(31373,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.32/3.58 inference(monotonicity,[status(thm)],[31372])).
% 3.32/3.58 tff(31374,plain,
% 3.32/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.58 inference(transitivity,[status(thm)],[31373, 31371])).
% 3.32/3.58 tff(31375,plain,
% 3.32/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31376,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31375, 31374])).
% 3.32/3.59 tff(31377,plain,
% 3.32/3.59 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31376, 271, 1723, 13508, 14893])).
% 3.32/3.59 tff(31378,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31379,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31380,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31379, 31378])).
% 3.32/3.59 tff(31381,plain,
% 3.32/3.59 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31380, 271, 1723, 13508, 14893])).
% 3.32/3.59 tff(31382,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 3.32/3.59 tff(31383,plain,
% 3.32/3.59 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1776, 4035, 31382])).
% 3.32/3.59 tff(31384,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 3.32/3.59 tff(31385,plain,
% 3.32/3.59 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[4037, 4035])).
% 3.32/3.59 tff(31386,plain,
% 3.32/3.59 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[4045, 31385, 31384])).
% 3.32/3.59 tff(31387,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31388,plain,
% 3.32/3.59 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31389,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.32/3.59 inference(monotonicity,[status(thm)],[31388])).
% 3.32/3.59 tff(31390,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.32/3.59 inference(transitivity,[status(thm)],[31389, 31387])).
% 3.32/3.59 tff(31391,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31392,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31391, 31390])).
% 3.32/3.59 tff(31393,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31392, 121, 1758, 2002, 9502, 31370])).
% 3.32/3.59 tff(31394,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31395,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31394, 31386, 31383, 31370, 2002])).
% 3.32/3.59 tff(31396,plain,((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31397,plain,
% 3.32/3.59 ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31396, 1772])).
% 3.32/3.59 tff(31398,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31397, 31381, 31377, 2002, 31370])).
% 3.32/3.59 tff(31399,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(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)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31400,plain,
% 3.32/3.59 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31399, 31369, 31367, 31361, 31366])).
% 3.32/3.59 tff(31401,plain,
% 3.32/3.59 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1167, 21, 31400, 20146])).
% 3.32/3.59 tff(31402,plain,
% 3.32/3.59 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[25477, 31401, 5499, 31337])).
% 3.32/3.59 tff(31403,plain,
% 3.32/3.59 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1777, 31402])).
% 3.32/3.59 tff(31404,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31405,plain,
% 3.32/3.59 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31406,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.32/3.59 inference(monotonicity,[status(thm)],[31405])).
% 3.32/3.59 tff(31407,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(transitivity,[status(thm)],[31406, 31404])).
% 3.32/3.59 tff(31408,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31409,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31408, 31407])).
% 3.32/3.59 tff(31410,plain,
% 3.32/3.59 (~b(s(s(s(s(z)))), z)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31409, 271, 6068, 1639, 1723])).
% 3.32/3.59 tff(31411,plain,
% 3.32/3.59 (r(s(s(s(s(z)))), z)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1095, 31410])).
% 3.32/3.59 tff(31412,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31413,plain,
% 3.32/3.59 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31414,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.32/3.59 inference(monotonicity,[status(thm)],[31413])).
% 3.32/3.59 tff(31415,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.32/3.59 inference(transitivity,[status(thm)],[31414, 31412])).
% 3.32/3.59 tff(31416,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31417,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31416, 31415])).
% 3.32/3.59 tff(31418,plain,
% 3.32/3.59 (~b(z, s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31417, 271, 6068, 1639, 1723])).
% 3.32/3.59 tff(31419,plain,
% 3.32/3.59 (r(z, s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1121, 31418])).
% 3.32/3.59 tff(31420,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[11616, 121, 109, 31419, 31411, 18818])).
% 3.32/3.59 tff(31421,plain,((~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31422,plain,
% 3.32/3.59 (~b(z, s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31421, 24356, 31401, 31403, 31361])).
% 3.32/3.59 tff(31423,plain,
% 3.32/3.59 (r(z, s(s(s(s(s(z))))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1658, 31422])).
% 3.32/3.59 tff(31424,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31425,plain,
% 3.32/3.59 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31426,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.32/3.59 inference(monotonicity,[status(thm)],[31425])).
% 3.32/3.59 tff(31427,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.59 inference(transitivity,[status(thm)],[31426, 31424])).
% 3.32/3.59 tff(31428,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31429,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31428, 31427])).
% 3.32/3.59 tff(31430,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31429, 121, 1661, 6842, 910, 13550])).
% 3.32/3.59 tff(31431,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31432,plain,
% 3.32/3.59 (~r(s(s(s(s(z)))), z)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31431, 31423, 31338, 31337])).
% 3.32/3.59 tff(31433,plain,
% 3.32/3.59 (b(s(s(s(s(z)))), z)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1095, 31432])).
% 3.32/3.59 tff(31434,plain,
% 3.32/3.59 (~b(s(z), s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[25001, 31433, 1281, 31325])).
% 3.32/3.59 tff(31435,plain,
% 3.32/3.59 (r(s(z), s(s(s(s(z)))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[16482, 31434])).
% 3.32/3.59 tff(31436,plain,
% 3.32/3.59 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[22548, 31433, 1281, 220])).
% 3.32/3.59 tff(31437,plain,
% 3.32/3.59 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[932, 31436])).
% 3.32/3.59 tff(31438,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[16499, 31437, 31435, 31337, 31327])).
% 3.32/3.59 tff(31439,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31440,plain,
% 3.32/3.59 (~b(s(z), s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31439, 31254, 1281, 31053, 601, 31178, 31310, 9297])).
% 3.32/3.59 tff(31441,plain,
% 3.32/3.59 (r(s(z), s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[105, 31440])).
% 3.32/3.59 tff(31442,plain,
% 3.32/3.59 (r(elem!1, z)),
% 3.32/3.59 inference(modus_ponens,[status(thm)],[31314, 28512])).
% 3.32/3.59 tff(31443,plain,
% 3.32/3.59 (~r(s(z), elem!1)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[15964, 31442, 31054, 31254, 31316])).
% 3.32/3.59 tff(31444,plain,
% 3.32/3.59 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31049, 3407, 1281, 750])).
% 3.32/3.59 tff(31445,plain,
% 3.32/3.59 (~b(elem!1, s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31215, 31444, 2505])).
% 3.32/3.59 tff(31446,plain,
% 3.32/3.59 (r(elem!1, s(z))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[20307, 3407, 1281, 2505, 232])).
% 3.32/3.59 tff(31447,plain,
% 3.32/3.59 (~r(elem!1, s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[24792, 31446, 2327, 108])).
% 3.32/3.59 tff(31448,plain,
% 3.32/3.59 ($false),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1192, 31447, 31445, 11082])).
% 3.32/3.59 tff(31449,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), z)) | r(s(z), elem!1) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.32/3.59 tff(31450,plain,
% 3.32/3.59 (~b(z, s(s(s(elem!1))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[31449, 31318, 31441, 25718, 1281, 31443, 31310])).
% 3.32/3.59 tff(31451,plain,
% 3.32/3.59 (r(z, s(s(s(elem!1))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[19736, 31450])).
% 3.32/3.59 tff(31452,plain,
% 3.32/3.59 (r(z, elem!1)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[11073, 31451, 25718])).
% 3.32/3.59 tff(31453,plain,
% 3.32/3.59 (~b(s(s(s(s(z)))), s(z))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[27041, 31451, 1281, 31254, 31178, 31310, 31442, 31452, 25718])).
% 3.32/3.59 tff(31454,plain,
% 3.32/3.59 (r(s(s(s(s(z)))), s(z))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[932, 31453])).
% 3.32/3.59 tff(31455,plain,
% 3.32/3.59 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[30235, 31454, 31441, 31318])).
% 3.32/3.59 tff(31456,plain,
% 3.32/3.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[10426, 31455])).
% 3.32/3.59 tff(31457,plain,
% 3.32/3.59 (~r(s(s(s(z))), z)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[3650, 31452, 31055, 31314])).
% 3.32/3.59 tff(31458,plain,
% 3.32/3.59 (b(s(s(s(z))), z)),
% 3.32/3.59 inference(unit_resolution,[status(thm)],[1155, 31457])).
% 3.32/3.59 tff(31459,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31460,plain,
% 3.32/3.59 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.59 inference(rewrite,[status(thm)],[])).
% 3.32/3.59 tff(31461,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.32/3.59 inference(monotonicity,[status(thm)],[31460])).
% 3.32/3.59 tff(31462,plain,
% 3.32/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.32/3.59 inference(transitivity,[status(thm)],[31461, 31459])).
% 3.32/3.59 tff(31463,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 3.32/3.59 inference(quant_inst,[status(thm)],[])).
% 3.32/3.59 tff(31464,plain,
% 3.32/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.32/3.60 inference(modus_ponens,[status(thm)],[31463, 31462])).
% 3.32/3.60 tff(31465,plain,
% 3.32/3.60 (~b(z, s(s(s(s(z)))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[31464, 271, 31316, 31458, 31456])).
% 3.32/3.60 tff(31466,plain,
% 3.32/3.60 (r(z, s(s(s(s(z)))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[1121, 31465])).
% 3.32/3.60 tff(31467,plain,
% 3.32/3.60 (~b(s(s(s(s(z)))), z)),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[13513, 31456, 31316, 31458])).
% 3.32/3.60 tff(31468,plain,
% 3.32/3.60 (r(s(s(s(s(z)))), z)),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[1095, 31467])).
% 3.32/3.60 tff(31469,plain,
% 3.32/3.60 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[26940, 31468, 28225, 31451, 31314])).
% 3.32/3.60 tff(31470,plain,
% 3.32/3.60 (b(s(elem!1), s(s(s(s(z)))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[1995, 31469, 28490])).
% 3.32/3.60 tff(31471,plain,
% 3.32/3.60 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.32/3.60 inference(modus_ponens,[status(thm)],[31470, 30950])).
% 3.32/3.60 tff(31472,plain,
% 3.32/3.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[30943, 121, 31454, 31318, 31441])).
% 3.32/3.60 tff(31473,plain,
% 3.32/3.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[1167, 21, 31472, 20146])).
% 3.32/3.60 tff(31474,plain,
% 3.32/3.60 (((~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(s(z)))))) | (~b(s(s(s(elem!1))), 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.60 inference(rewrite,[status(thm)],[])).
% 3.32/3.60 tff(31475,plain,
% 3.32/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(z))))))))),
% 3.32/3.60 inference(monotonicity,[status(thm)],[31474])).
% 3.32/3.60 tff(31476,plain,
% 3.32/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(s(s(s(z)))))))),
% 3.32/3.60 inference(transitivity,[status(thm)],[31475, 28433])).
% 3.32/3.60 tff(31477,plain,
% 3.32/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.32/3.60 inference(quant_inst,[status(thm)],[])).
% 3.32/3.60 tff(31478,plain,
% 3.32/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.32/3.60 inference(modus_ponens,[status(thm)],[31477, 31476])).
% 3.32/3.60 tff(31479,plain,
% 3.32/3.60 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[31478, 271, 31456, 31473, 31471])).
% 3.32/3.60 tff(31480,plain,
% 3.32/3.60 (~b(elem!1, s(s(s(z))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[31215, 31479, 25718])).
% 3.32/3.60 tff(31481,plain,
% 3.32/3.60 (r(elem!1, s(s(s(z))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[1192, 31480, 28221])).
% 3.32/3.60 tff(31482,plain,
% 3.32/3.60 (r(s(s(elem!1)), s(s(s(z))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[12242, 31481, 3891])).
% 3.32/3.60 tff(31483,plain,
% 3.32/3.60 (~r(elem!1, s(z))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[24792, 31481, 31318, 31441])).
% 3.32/3.60 tff(31484,plain,
% 3.32/3.60 (b(elem!1, s(z))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[299, 31483, 28851])).
% 3.32/3.60 tff(31485,plain,
% 3.32/3.60 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.32/3.60 inference(unit_resolution,[status(thm)],[15217, 1736, 1500, 108, 448])).
% 3.42/3.60 tff(31486,plain,
% 3.42/3.60 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[16352, 1736, 7794, 13992])).
% 3.42/3.60 tff(31487,plain,
% 3.42/3.60 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[16341, 31486, 2470])).
% 3.42/3.60 tff(31488,plain,
% 3.42/3.60 ($false),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[1847, 31487, 31485, 15994])).
% 3.42/3.60 tff(31489,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (elem!1 = s(s(s(s(s(z)))))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.60 tff(31490,plain,
% 3.42/3.60 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31489, 28455, 3891, 31055, 31441, 31484, 31175, 31482])).
% 3.42/3.60 tff(31491,plain,
% 3.42/3.60 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[1733, 31490])).
% 3.42/3.60 tff(31492,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31493,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.42/3.60 inference(quant_inst,[status(thm)],[])).
% 3.42/3.60 tff(31494,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31493, 31492])).
% 3.42/3.60 tff(31495,plain,
% 3.42/3.60 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31494, 271, 31491, 31458, 31456])).
% 3.42/3.60 tff(31496,plain,
% 3.42/3.60 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[9512, 31495])).
% 3.42/3.60 tff(31497,plain,
% 3.42/3.60 (~r(s(s(s(elem!1))), s(z))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[12809, 31483, 25718])).
% 3.42/3.60 tff(31498,plain,
% 3.42/3.60 (b(s(s(s(elem!1))), s(z))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[16580, 31497])).
% 3.42/3.60 tff(31499,plain,
% 3.42/3.60 (~b(z, s(s(s(s(s(z))))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[28972, 31498, 31054, 31254, 31310, 31316, 31441, 25718, 28215, 31458])).
% 3.42/3.60 tff(31500,plain,
% 3.42/3.60 (r(z, s(s(s(s(s(z))))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[1658, 31499])).
% 3.42/3.60 tff(31501,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31502,plain,
% 3.42/3.60 (((~b(s(s(s(z))), 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(s(z)))), s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31503,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31502])).
% 3.42/3.60 tff(31504,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.42/3.60 inference(transitivity,[status(thm)],[31503, 31501])).
% 3.42/3.60 tff(31505,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(z)))), s(s(s(s(s(z))))))))),
% 3.42/3.60 inference(quant_inst,[status(thm)],[])).
% 3.42/3.60 tff(31506,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31505, 31504])).
% 3.42/3.60 tff(31507,plain,
% 3.42/3.60 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31506, 271, 31491, 31458, 31456])).
% 3.42/3.60 tff(31508,plain,
% 3.42/3.60 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[1777, 31507])).
% 3.42/3.60 tff(31509,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31510,plain,
% 3.42/3.60 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31511,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31510])).
% 3.42/3.60 tff(31512,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.42/3.60 inference(transitivity,[status(thm)],[31511, 31509])).
% 3.42/3.60 tff(31513,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.42/3.60 inference(quant_inst,[status(thm)],[])).
% 3.42/3.60 tff(31514,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31513, 31512])).
% 3.42/3.60 tff(31515,plain,
% 3.42/3.60 ($false),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31514, 121, 31508, 31500, 31496, 31466])).
% 3.42/3.60 tff(31516,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | b(s(elem!1), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.60 tff(31517,plain,
% 3.42/3.60 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31516, 30118, 2467, 348])).
% 3.42/3.60 tff(31518,assumption,(~r(s(z), z)), introduced(assumption)).
% 3.42/3.60 tff(31519,plain,
% 3.42/3.60 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[19817, 1307, 19197, 3871])).
% 3.42/3.60 tff(31520,plain,
% 3.42/3.60 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[2071, 31519, 906])).
% 3.42/3.60 tff(31521,plain,
% 3.42/3.60 (s(z) = s(elem!1)),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[2063, 31520])).
% 3.42/3.60 tff(31522,plain,
% 3.42/3.60 (z = elem!1),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[343, 31521])).
% 3.42/3.60 tff(31523,plain,
% 3.42/3.60 (s(z) = s(elem!1)),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31522])).
% 3.42/3.60 tff(31524,plain,
% 3.42/3.60 (s(s(z)) = s(s(elem!1))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31523])).
% 3.42/3.60 tff(31525,plain,
% 3.42/3.60 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31524])).
% 3.42/3.60 tff(31526,plain,
% 3.42/3.60 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31525])).
% 3.42/3.60 tff(31527,plain,
% 3.42/3.60 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 3.42/3.60 inference(symmetry,[status(thm)],[31526])).
% 3.42/3.60 tff(31528,plain,
% 3.42/3.60 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31527])).
% 3.42/3.60 tff(31529,plain,
% 3.42/3.60 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31522])).
% 3.42/3.60 tff(31530,plain,
% 3.42/3.60 ((~b(z, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31529])).
% 3.42/3.60 tff(31531,plain,
% 3.42/3.60 (elem!1 = z),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[364, 31522])).
% 3.42/3.60 tff(31532,plain,
% 3.42/3.60 (b(s(elem!1), z)),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[20985, 31531, 19197])).
% 3.42/3.60 tff(31533,plain,
% 3.42/3.60 (b(elem!1, s(z))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[324, 31522, 220])).
% 3.42/3.60 tff(31534,plain,
% 3.42/3.60 (~b(z, elem!1)),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[20398, 31533, 19197, 220])).
% 3.42/3.60 tff(31535,plain,
% 3.42/3.60 (~(s(z) = elem!1)),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[229, 31534, 220])).
% 3.42/3.60 tff(31536,plain,
% 3.42/3.60 (~(elem!1 = s(z))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[242, 31535])).
% 3.42/3.60 tff(31537,plain,
% 3.42/3.60 (~b(z, s(s(s(elem!1))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[20833, 31536, 1, 19197, 3871, 6842, 31522, 31532])).
% 3.42/3.60 tff(31538,plain,
% 3.42/3.60 (~b(elem!1, s(s(s(elem!1))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31537, 31530])).
% 3.42/3.60 tff(31539,plain,
% 3.42/3.60 (~b(elem!1, s(s(s(z))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31538, 31528])).
% 3.42/3.60 tff(31540,plain,
% 3.42/3.60 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31522])).
% 3.42/3.60 tff(31541,plain,
% 3.42/3.60 (b(elem!1, s(s(s(z))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[1307, 31540])).
% 3.42/3.60 tff(31542,plain,
% 3.42/3.60 ($false),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31541, 31539])).
% 3.42/3.60 tff(31543,plain,((~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.60 tff(31544,plain,
% 3.42/3.60 (~b(z, s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31543, 20245, 3871, 1, 220, 906])).
% 3.42/3.60 tff(31545,plain,
% 3.42/3.60 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[11676, 6533, 24432, 6842])).
% 3.42/3.60 tff(31546,plain,
% 3.42/3.60 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[24945, 911, 2326, 19197, 6533])).
% 3.42/3.60 tff(31547,plain,
% 3.42/3.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[10426, 31546])).
% 3.42/3.60 tff(31548,plain,
% 3.42/3.60 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[11676, 6533, 24356, 6842])).
% 3.42/3.60 tff(31549,plain,
% 3.42/3.60 (~(z = elem!1)),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[18101, 14005, 911])).
% 3.42/3.60 tff(31550,plain,
% 3.42/3.60 (~(s(z) = s(elem!1))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[343, 31549])).
% 3.42/3.60 tff(31551,plain,
% 3.42/3.60 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[2063, 31550])).
% 3.42/3.60 tff(31552,plain,
% 3.42/3.60 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[2071, 31551, 906])).
% 3.42/3.60 tff(31553,plain,
% 3.42/3.60 (~b(s(elem!1), s(z))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[16834, 271, 11211, 1281, 220])).
% 3.42/3.60 tff(31554,plain,
% 3.42/3.60 (r(s(elem!1), s(z))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[429, 31553, 2282])).
% 3.42/3.60 tff(31555,plain,
% 3.42/3.60 (~b(s(z), s(elem!1))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[9241, 11211, 1281, 220])).
% 3.42/3.60 tff(31556,plain,
% 3.42/3.60 (r(s(z), s(elem!1))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[444, 31555, 348])).
% 3.42/3.60 tff(31557,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31558,plain,
% 3.42/3.60 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31559,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31558])).
% 3.42/3.60 tff(31560,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.60 inference(transitivity,[status(thm)],[31559, 31557])).
% 3.42/3.60 tff(31561,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.60 inference(quant_inst,[status(thm)],[])).
% 3.42/3.60 tff(31562,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31561, 31560])).
% 3.42/3.60 tff(31563,plain,
% 3.42/3.60 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31562, 121, 31556, 911, 31554])).
% 3.42/3.60 tff(31564,plain,
% 3.42/3.60 (~(s(s(s(z))) = s(elem!1))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[11011, 10994, 24356])).
% 3.42/3.60 tff(31565,plain,
% 3.42/3.60 (~(s(elem!1) = s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[2035, 31564])).
% 3.42/3.60 tff(31566,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31567,plain,
% 3.42/3.60 (((~r(s(z), s(elem!1))) | (~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(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31568,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31567])).
% 3.42/3.60 tff(31569,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.42/3.60 inference(transitivity,[status(thm)],[31568, 31566])).
% 3.42/3.60 tff(31570,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 3.42/3.60 inference(quant_inst,[status(thm)],[])).
% 3.42/3.60 tff(31571,plain,
% 3.42/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 3.42/3.60 inference(modus_ponens,[status(thm)],[31570, 31569])).
% 3.42/3.60 tff(31572,plain,
% 3.42/3.60 (~r(s(elem!1), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[31571, 121, 31556, 31554, 2327])).
% 3.42/3.60 tff(31573,plain,
% 3.42/3.60 (b(s(elem!1), s(s(s(z))))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[2044, 31572, 31565])).
% 3.42/3.60 tff(31574,plain,
% 3.42/3.60 (~r(s(s(s(z))), s(elem!1))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[8142, 121, 31556, 31554, 2327])).
% 3.42/3.60 tff(31575,plain,
% 3.42/3.60 (b(s(s(s(z))), s(elem!1))),
% 3.42/3.60 inference(unit_resolution,[status(thm)],[1816, 31574, 31564])).
% 3.42/3.60 tff(31576,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31577,plain,
% 3.42/3.60 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.60 inference(rewrite,[status(thm)],[])).
% 3.42/3.60 tff(31578,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 3.42/3.60 inference(monotonicity,[status(thm)],[31577])).
% 3.42/3.60 tff(31579,plain,
% 3.42/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.61 inference(transitivity,[status(thm)],[31578, 31576])).
% 3.42/3.61 tff(31580,plain,
% 3.42/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 3.42/3.61 inference(quant_inst,[status(thm)],[])).
% 3.42/3.61 tff(31581,plain,
% 3.42/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31580, 31579])).
% 3.42/3.61 tff(31582,plain,
% 3.42/3.61 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31581, 271, 31575, 31573, 13508])).
% 3.42/3.61 tff(31583,plain,
% 3.42/3.61 (s(elem!1) = s(s(s(s(z))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1995, 31582, 31563])).
% 3.42/3.61 tff(31584,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31583])).
% 3.42/3.61 tff(31585,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(symmetry,[status(thm)],[31584])).
% 3.42/3.61 tff(31586,plain,
% 3.42/3.61 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31585])).
% 3.42/3.61 tff(31587,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.42/3.61 inference(rewrite,[status(thm)],[])).
% 3.42/3.61 tff(31588,plain,
% 3.42/3.61 (((~b(s(s(s(z))), s(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(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.42/3.61 inference(rewrite,[status(thm)],[])).
% 3.42/3.61 tff(31589,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31588])).
% 3.42/3.61 tff(31590,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(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, X3: $i, X2: $i, X1: $i] : ((~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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.42/3.61 inference(transitivity,[status(thm)],[31589, 31587])).
% 3.42/3.61 tff(31591,plain,
% 3.42/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(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)))))))),
% 3.42/3.61 inference(quant_inst,[status(thm)],[])).
% 3.42/3.61 tff(31592,plain,
% 3.42/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31591, 31590])).
% 3.42/3.61 tff(31593,plain,
% 3.42/3.61 (~b(s(z), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31592, 271, 31575, 3871, 13508])).
% 3.42/3.61 tff(31594,plain,
% 3.42/3.61 (r(s(z), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[16482, 31593])).
% 3.42/3.61 tff(31595,plain,
% 3.42/3.61 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[16499, 31594, 911, 12761])).
% 3.42/3.61 tff(31596,plain,
% 3.42/3.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31595, 31586])).
% 3.42/3.61 tff(31597,plain,
% 3.42/3.61 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2114, 31575, 2073, 11211])).
% 3.42/3.61 tff(31598,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[681, 31597, 82])).
% 3.42/3.61 tff(31599,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31598, 31596])).
% 3.42/3.61 tff(31600,plain,(r(s(elem!1), z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31601,plain,
% 3.42/3.61 (r(s(elem!1), z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31600, 31552, 911, 12761, 3871, 82, 13508, 2326, 1281, 220, 31550])).
% 3.42/3.61 tff(31602,plain,
% 3.42/3.61 (~r(s(elem!1), s(s(s(z))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[15486, 121, 412, 24356, 6533])).
% 3.42/3.61 tff(31603,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.42/3.61 inference(monotonicity,[status(thm)],[244])).
% 3.42/3.61 tff(31604,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.61 inference(symmetry,[status(thm)],[31603])).
% 3.42/3.61 tff(31605,plain,
% 3.42/3.61 (b(s(z), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[10599, 244, 3871])).
% 3.42/3.61 tff(31606,plain,
% 3.42/3.61 (~b(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[6548, 244, 1209])).
% 3.42/3.61 tff(31607,plain,
% 3.42/3.61 (r(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[355, 31606, 331])).
% 3.42/3.61 tff(31608,plain,
% 3.42/3.61 (~(s(z) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[229, 31606, 220])).
% 3.42/3.61 tff(31609,plain,
% 3.42/3.61 (~(elem!1 = s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[242, 31608])).
% 3.42/3.61 tff(31610,plain,
% 3.42/3.61 (b(elem!1, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[22265, 31609, 412, 109, 31607, 1209, 3871, 344, 377])).
% 3.42/3.61 tff(31611,plain,
% 3.42/3.61 (~b(s(s(s(elem!1))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[13752, 31610, 750, 31605])).
% 3.42/3.61 tff(31612,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[486, 31611, 9552])).
% 3.42/3.61 tff(31613,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31612, 31604])).
% 3.42/3.61 tff(31614,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[28366, 31613])).
% 3.42/3.61 tff(31615,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(s(elem!1))), s(s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~b(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31616,plain,
% 3.42/3.61 (~(s(s(s(z))) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31615, 750, 28366, 412, 24356, 1209, 3871, 377, 220, 31549])).
% 3.42/3.61 tff(31617,plain,
% 3.42/3.61 (b(s(s(s(z))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[255, 31616, 221])).
% 3.42/3.61 tff(31618,plain,
% 3.42/3.61 (~(s(z) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[8109, 31617, 2319])).
% 3.42/3.61 tff(31619,plain,
% 3.42/3.61 (~(elem!1 = z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[333, 31549])).
% 3.42/3.61 tff(31620,plain,
% 3.42/3.61 (b(elem!1, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[22265, 378, 412, 109, 243, 1209, 3871, 348, 377])).
% 3.42/3.61 tff(31621,plain,
% 3.42/3.61 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2562, 1242, 750])).
% 3.42/3.61 tff(31622,plain,
% 3.42/3.61 (s(s(s(z))) = s(elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[13140, 2618, 412, 257, 307, 1140])).
% 3.42/3.61 tff(31623,plain,
% 3.42/3.61 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31622])).
% 3.42/3.61 tff(31624,plain,
% 3.42/3.61 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31623])).
% 3.42/3.61 tff(31625,plain,
% 3.42/3.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[28366, 31624])).
% 3.42/3.61 tff(31626,plain,
% 3.42/3.61 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[681, 31625, 82])).
% 3.42/3.61 tff(31627,plain,
% 3.42/3.61 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31622])).
% 3.42/3.61 tff(31628,plain,
% 3.42/3.61 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31627])).
% 3.42/3.61 tff(31629,plain,
% 3.42/3.61 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[906, 31628])).
% 3.42/3.61 tff(31630,plain,
% 3.42/3.61 (~b(s(s(s(elem!1))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[11152, 31629, 307, 31625, 82])).
% 3.42/3.61 tff(31631,plain,
% 3.42/3.61 (b(elem!1, s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[12884, 31630, 378, 481, 111])).
% 3.42/3.61 tff(31632,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[12887, 31631, 31626, 2618, 307])).
% 3.42/3.61 tff(31633,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31634,plain,
% 3.42/3.61 (~b(s(elem!1), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31633, 31621, 378, 307, 111, 82, 28366, 906, 412, 257, 1140])).
% 3.42/3.61 tff(31635,plain,
% 3.42/3.61 (r(s(elem!1), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2243, 31634, 2564])).
% 3.42/3.61 tff(31636,plain,
% 3.42/3.61 (~r(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[5358, 31635, 378, 412])).
% 3.42/3.61 tff(31637,plain,
% 3.42/3.61 (b(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[284, 31636, 259])).
% 3.42/3.61 tff(31638,plain,
% 3.42/3.61 (~r(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[5343, 31635, 378, 412])).
% 3.42/3.61 tff(31639,plain,
% 3.42/3.61 (b(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[299, 31638, 243])).
% 3.42/3.61 tff(31640,plain,
% 3.42/3.61 (~b(z, s(s(elem!1)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[5420, 31637, 1281, 31639])).
% 3.42/3.61 tff(31641,plain,
% 3.42/3.61 (r(z, s(s(elem!1)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2106, 31640])).
% 3.42/3.61 tff(31642,plain,
% 3.42/3.61 (~b(s(elem!1), s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1290, 31639, 1281, 307])).
% 3.42/3.61 tff(31643,plain,
% 3.42/3.61 (r(s(elem!1), s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[429, 31642, 422])).
% 3.42/3.61 tff(31644,plain,
% 3.42/3.61 (~r(z, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[25779, 31643, 1281, 378, 259, 10603, 31635, 31639])).
% 3.42/3.61 tff(31645,plain,
% 3.42/3.61 (b(z, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1439, 31644])).
% 3.42/3.61 tff(31646,plain,
% 3.42/3.61 (~b(elem!1, s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[6868, 31645, 82, 412, 378, 31641, 307, 31637])).
% 3.42/3.61 tff(31647,plain,
% 3.42/3.61 (~(elem!1 = s(s(s(elem!1))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31621, 655])).
% 3.42/3.61 tff(31648,plain,
% 3.42/3.61 (~r(elem!1, s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[6817, 31635, 412, 378])).
% 3.42/3.61 tff(31649,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[660, 21, 31648, 31647, 31646])).
% 3.42/3.61 tff(31650,plain,(b(s(z), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (elem!1 = z) | (s(elem!1) = s(z)) | (s(elem!1) = elem!1) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (s(z) = elem!1) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31651,plain,
% 3.42/3.61 (b(s(z), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31650, 378, 412, 82, 31620, 1281, 259, 2282, 3500, 111, 28366, 906, 257, 6533, 231, 750])).
% 3.42/3.61 tff(31652,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[10652, 271, 31620, 31651, 3871, 257])).
% 3.42/3.61 tff(31653,plain,((~r(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(z) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31654,plain,
% 3.42/3.61 (~r(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31653, 31617, 3871, 412, 82, 1281, 31619, 111, 28366, 906, 31618, 750, 24356, 1209, 31550, 377])).
% 3.42/3.61 tff(31655,plain,
% 3.42/3.61 (b(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[355, 31654, 31549])).
% 3.42/3.61 tff(31656,plain,
% 3.42/3.61 (~b(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[21813, 31655, 377, 1281, 31619, 412])).
% 3.42/3.61 tff(31657,plain,
% 3.42/3.61 (~(elem!1 = s(s(s(z))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1100, 31616])).
% 3.42/3.61 tff(31658,plain,
% 3.42/3.61 (~(elem!1 = s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[242, 31618])).
% 3.42/3.61 tff(31659,plain,
% 3.42/3.61 (r(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[299, 31656, 31658])).
% 3.42/3.61 tff(31660,plain,
% 3.42/3.61 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1516, 31657])).
% 3.42/3.61 tff(31661,plain,
% 3.42/3.61 (b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1559, 31660, 14005])).
% 3.42/3.61 tff(31662,plain,
% 3.42/3.61 (~r(s(z), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[24983, 31617, 31661, 412, 24356, 6533, 13508, 911, 2326, 31659, 31657])).
% 3.42/3.61 tff(31663,plain,
% 3.42/3.61 (~r(s(z), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[9267, 31662, 377, 1281, 31618, 31656, 31550, 31655])).
% 3.42/3.61 tff(31664,plain,
% 3.42/3.61 (b(s(z), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[444, 31663, 31550])).
% 3.42/3.61 tff(31665,plain,
% 3.42/3.61 (~b(s(elem!1), s(s(s(z))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[3879, 31664, 31617, 3871])).
% 3.42/3.61 tff(31666,plain,
% 3.42/3.61 (s(elem!1) = s(s(s(z)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2042, 21, 31665, 31602])).
% 3.42/3.61 tff(31667,plain,
% 3.42/3.61 (s(s(elem!1)) = s(s(s(s(z))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31666])).
% 3.42/3.61 tff(31668,plain,
% 3.42/3.61 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31667])).
% 3.42/3.61 tff(31669,plain,
% 3.42/3.61 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31668])).
% 3.42/3.61 tff(31670,plain,
% 3.42/3.61 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 3.42/3.61 inference(symmetry,[status(thm)],[31669])).
% 3.42/3.61 tff(31671,plain,
% 3.42/3.61 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(z, s(s(s(elem!1)))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31670])).
% 3.42/3.61 tff(31672,plain,
% 3.42/3.61 (b(s(z), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[236, 31662, 31618])).
% 3.42/3.61 tff(31673,plain,
% 3.42/3.61 (~b(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[12145, 31672, 220, 31655])).
% 3.42/3.61 tff(31674,plain,
% 3.42/3.61 (r(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[284, 31673, 31619])).
% 3.42/3.61 tff(31675,plain,
% 3.42/3.61 (~b(elem!1, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[20382, 31672, 1281, 31655])).
% 3.42/3.61 tff(31676,plain,
% 3.42/3.61 (r(elem!1, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[392, 31675, 377])).
% 3.42/3.61 tff(31677,plain,
% 3.42/3.61 (~r(z, s(s(s(s(s(z))))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[15803, 31676, 412, 31674])).
% 3.42/3.61 tff(31678,plain,
% 3.42/3.61 (~r(z, s(s(s(elem!1))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31677, 31671])).
% 3.42/3.61 tff(31679,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[111, 31678])).
% 3.42/3.61 tff(31680,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(z, s(s(s(z)))) | r(s(s(s(s(z)))), s(elem!1)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31681,plain,
% 3.42/3.61 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31680, 412, 111, 3871, 377, 220, 1281, 13508, 911, 82, 28366, 906, 1209, 14005, 2319, 221])).
% 3.42/3.61 tff(31682,plain,
% 3.42/3.61 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[760, 31681])).
% 3.42/3.61 tff(31683,plain,
% 3.42/3.61 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[21371, 121, 31682, 911, 2326])).
% 3.42/3.61 tff(31684,plain,
% 3.42/3.61 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1167, 21, 31683, 20146])).
% 3.42/3.61 tff(31685,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.42/3.61 inference(rewrite,[status(thm)],[])).
% 3.42/3.61 tff(31686,plain,
% 3.42/3.61 (((~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(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))))))),
% 3.42/3.61 inference(rewrite,[status(thm)],[])).
% 3.42/3.61 tff(31687,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[31686])).
% 3.42/3.61 tff(31688,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.42/3.61 inference(transitivity,[status(thm)],[31687, 31685])).
% 3.42/3.61 tff(31689,plain,
% 3.42/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.42/3.61 inference(quant_inst,[status(thm)],[])).
% 3.42/3.61 tff(31690,plain,
% 3.42/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31689, 31688])).
% 3.42/3.61 tff(31691,plain,
% 3.42/3.61 (~b(s(z), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31690, 271, 3871, 13508, 31684])).
% 3.42/3.61 tff(31692,plain,
% 3.42/3.61 (r(s(z), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[16482, 31691])).
% 3.42/3.61 tff(31693,plain,
% 3.42/3.61 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[16499, 31692, 911, 12761])).
% 3.42/3.61 tff(31694,plain,
% 3.42/3.61 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 3.42/3.61 inference(symmetry,[status(thm)],[9466])).
% 3.42/3.61 tff(31695,plain,
% 3.42/3.61 (b(s(s(s(s(z)))), elem!1)),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[13508, 9464])).
% 3.42/3.61 tff(31696,plain,
% 3.42/3.61 (b(s(elem!1), elem!1)),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31695, 31694])).
% 3.42/3.61 tff(31697,plain,
% 3.42/3.61 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.61 inference(monotonicity,[status(thm)],[2606])).
% 3.42/3.61 tff(31698,plain,
% 3.42/3.61 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(symmetry,[status(thm)],[31697])).
% 3.42/3.61 tff(31699,plain,
% 3.42/3.61 (~(s(s(z)) = s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[960, 31608])).
% 3.42/3.61 tff(31700,plain,
% 3.42/3.61 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[953, 31699])).
% 3.42/3.61 tff(31701,plain,
% 3.42/3.61 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[946, 31700])).
% 3.42/3.61 tff(31702,plain,
% 3.42/3.61 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1014, 31701, 1007])).
% 3.42/3.61 tff(31703,plain,
% 3.42/3.61 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31702, 31698])).
% 3.42/3.61 tff(31704,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[12887, 31703, 31696, 27998, 31610])).
% 3.42/3.61 tff(31705,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~b(z, s(z))) | (z = elem!1) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31706,plain,
% 3.42/3.61 (~(s(s(s(z))) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31705, 31693, 13508, 412, 24356, 1209, 3871, 377, 220, 31549, 31552])).
% 3.42/3.61 tff(31707,plain,
% 3.42/3.61 (b(s(s(s(z))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[255, 31706, 221])).
% 3.42/3.61 tff(31708,plain,
% 3.42/3.61 (~(s(z) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[8109, 31707, 2319])).
% 3.42/3.61 tff(31709,plain,
% 3.42/3.61 (~(elem!1 = s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[242, 31708])).
% 3.42/3.61 tff(31710,plain,
% 3.42/3.61 (~(elem!1 = s(s(s(z))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1100, 31706])).
% 3.42/3.61 tff(31711,plain,
% 3.42/3.61 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1516, 31710])).
% 3.42/3.61 tff(31712,plain,
% 3.42/3.61 (b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1559, 31711, 14005])).
% 3.42/3.61 tff(31713,plain,
% 3.42/3.61 (~r(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[22265, 317, 412, 109, 258, 1209, 3871, 344, 377])).
% 3.42/3.61 tff(31714,plain,
% 3.42/3.61 (b(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[355, 31713, 331])).
% 3.42/3.61 tff(31715,plain,
% 3.42/3.61 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[11073, 31713, 111])).
% 3.42/3.61 tff(31716,plain,
% 3.42/3.61 (~b(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[21813, 31714, 377, 1281, 358, 412])).
% 3.42/3.61 tff(31717,plain,
% 3.42/3.61 (r(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[299, 31716, 258])).
% 3.42/3.61 tff(31718,plain,
% 3.42/3.61 (~r(s(s(s(elem!1))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[22268, 31717, 12761, 572])).
% 3.42/3.61 tff(31719,plain,
% 3.42/3.61 (b(s(s(s(elem!1))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[486, 31718, 31715])).
% 3.42/3.61 tff(31720,plain,
% 3.42/3.61 (~b(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[11686, 31719, 257, 31714, 13970])).
% 3.42/3.61 tff(31721,plain,
% 3.42/3.61 (r(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[284, 31720, 358])).
% 3.42/3.61 tff(31722,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[21651, 121, 3502, 31721, 412, 6533])).
% 3.42/3.61 tff(31723,plain,(b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(z)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (z = elem!1) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31724,plain,
% 3.42/3.61 (b(elem!1, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31723, 412, 31707, 12761, 31682, 31709, 377, 1281, 111, 31549, 24356, 1209, 3871])).
% 3.42/3.61 tff(31725,plain,
% 3.42/3.61 (~b(s(z), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[24003, 31724, 3871, 31707])).
% 3.42/3.61 tff(31726,plain,
% 3.42/3.61 (r(s(z), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[236, 31725, 31708])).
% 3.42/3.61 tff(31727,plain,
% 3.42/3.61 (~r(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[24983, 31726, 31707, 412, 24356, 6533, 13508, 911, 2326, 31712, 31710])).
% 3.42/3.61 tff(31728,plain,
% 3.42/3.61 (b(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[299, 31727, 31709])).
% 3.42/3.61 tff(31729,plain,
% 3.42/3.61 (~(s(elem!1) = s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[350, 31550])).
% 3.42/3.61 tff(31730,plain,
% 3.42/3.61 (~r(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[24983, 357, 257, 412, 109, 1140, 13508, 911, 2327, 1562, 1102])).
% 3.42/3.61 tff(31731,plain,
% 3.42/3.61 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[12809, 31730, 12761])).
% 3.42/3.61 tff(31732,plain,
% 3.42/3.61 (~b(s(elem!1), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31633, 31731, 257, 378, 111, 82, 28366, 906, 412, 307, 1140])).
% 3.42/3.61 tff(31733,plain,
% 3.42/3.61 (r(s(elem!1), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2243, 31732, 2564])).
% 3.42/3.61 tff(31734,plain,
% 3.42/3.61 (~r(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[5358, 31733, 378, 412])).
% 3.42/3.61 tff(31735,plain,
% 3.42/3.61 (b(elem!1, z)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[284, 31734, 259])).
% 3.42/3.61 tff(31736,plain,
% 3.42/3.61 (b(elem!1, s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[299, 31730, 258])).
% 3.42/3.61 tff(31737,plain,
% 3.42/3.61 (~b(s(elem!1), s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1290, 31736, 1281, 307])).
% 3.42/3.61 tff(31738,plain,
% 3.42/3.61 (r(s(elem!1), s(z))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[429, 31737, 422])).
% 3.42/3.61 tff(31739,plain,
% 3.42/3.61 (~r(z, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[25779, 31738, 1281, 378, 259, 357, 31733, 31736])).
% 3.42/3.61 tff(31740,plain,
% 3.42/3.61 (b(z, s(elem!1))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[1439, 31739])).
% 3.42/3.61 tff(31741,plain,
% 3.42/3.61 (~b(z, s(s(elem!1)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[5420, 31735, 1281, 31736])).
% 3.42/3.61 tff(31742,plain,
% 3.42/3.61 (r(z, s(s(elem!1)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[2106, 31741])).
% 3.42/3.61 tff(31743,plain,
% 3.42/3.61 (~b(elem!1, s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[6868, 31742, 82, 412, 378, 31740, 307, 31735])).
% 3.42/3.61 tff(31744,plain,
% 3.42/3.61 (~r(elem!1, s(s(s(elem!1))))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[6817, 31733, 412, 378])).
% 3.42/3.61 tff(31745,plain,
% 3.42/3.61 (elem!1 = s(s(s(elem!1)))),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[660, 21, 31744, 31743])).
% 3.42/3.61 tff(31746,plain,
% 3.42/3.61 (s(s(s(elem!1))) = elem!1),
% 3.42/3.61 inference(modus_ponens,[status(thm)],[31745, 653])).
% 3.42/3.61 tff(31747,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31731, 31746])).
% 3.42/3.61 tff(31748,plain,((~r(s(z), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (elem!1 = z) | (s(elem!1) = elem!1) | (s(elem!1) = s(z)) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31749,plain,
% 3.42/3.61 (~r(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31748, 31726, 412, 82, 31724, 1281, 31619, 3500, 31729, 31707, 111, 28366, 906, 6533, 12761, 31709, 24356, 13508, 911, 2326, 31712, 31710])).
% 3.42/3.61 tff(31750,plain,
% 3.42/3.61 (b(z, elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[355, 31749, 31549])).
% 3.42/3.61 tff(31751,plain,
% 3.42/3.61 ($false),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[20398, 31750, 31728, 1281, 220])).
% 3.42/3.61 tff(31752,plain,((~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | b(z, s(s(s(z)))) | r(s(s(s(s(z)))), s(elem!1)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.61 tff(31753,plain,
% 3.42/3.61 (r(s(s(s(z))), elem!1)),
% 3.42/3.61 inference(unit_resolution,[status(thm)],[31752, 31601, 220, 82, 111, 28366, 906, 12761, 13508, 911, 3871, 8336, 1209, 14005, 2319, 1281])).
% 3.42/3.61 tff(31754,plain,
% 3.42/3.61 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 3.42/3.61 inference(rewrite,[status(thm)],[])).
% 3.42/3.61 tff(31755,plain,
% 3.42/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31754])).
% 3.42/3.62 tff(31756,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31755, 22276])).
% 3.42/3.62 tff(31757,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 3.42/3.62 inference(quant_inst,[status(thm)],[])).
% 3.42/3.62 tff(31758,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31757, 31756])).
% 3.42/3.62 tff(31759,plain,
% 3.42/3.62 (~b(elem!1, s(z))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31758, 271, 1281, 261, 220])).
% 3.42/3.62 tff(31760,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31761,plain,
% 3.42/3.62 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31762,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31761])).
% 3.42/3.62 tff(31763,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31762, 31760])).
% 3.42/3.62 tff(31764,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 3.42/3.62 inference(quant_inst,[status(thm)],[])).
% 3.42/3.62 tff(31765,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31764, 31763])).
% 3.42/3.62 tff(31766,plain,
% 3.42/3.62 (~b(s(z), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31765, 271, 1281, 261, 220])).
% 3.42/3.62 tff(31767,plain,
% 3.42/3.62 (elem!1 = s(z)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[23319, 31766, 2327, 145, 31759])).
% 3.42/3.62 tff(31768,plain,
% 3.42/3.62 (r(s(s(elem!1)), s(z))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[6824, 2359, 145])).
% 3.42/3.62 tff(31769,plain,
% 3.42/3.62 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[1224])).
% 3.42/3.62 tff(31770,plain,
% 3.42/3.62 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 3.42/3.62 inference(symmetry,[status(thm)],[31769])).
% 3.42/3.62 tff(31771,plain,
% 3.42/3.62 (r(z, s(s(elem!1)))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[1140, 31770])).
% 3.42/3.62 tff(31772,plain,
% 3.42/3.62 (~r(s(elem!1), s(s(elem!1)))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[5431, 31771, 412, 31768])).
% 3.42/3.62 tff(31773,plain,
% 3.42/3.62 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[26395, 2359, 1562])).
% 3.42/3.62 tff(31774,plain,
% 3.42/3.62 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[2073, 21522])).
% 3.42/3.62 tff(31775,plain,
% 3.42/3.62 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.62 inference(symmetry,[status(thm)],[11160])).
% 3.42/3.62 tff(31776,plain,
% 3.42/3.62 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.62 inference(symmetry,[status(thm)],[11159])).
% 3.42/3.62 tff(31777,plain,
% 3.42/3.62 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31776, 31775])).
% 3.42/3.62 tff(31778,plain,
% 3.42/3.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[13508, 31777])).
% 3.42/3.62 tff(31779,plain,
% 3.42/3.62 (~b(s(elem!1), s(s(elem!1)))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[1459, 31778, 31774, 31773])).
% 3.42/3.62 tff(31780,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[526, 31779, 31772, 216])).
% 3.42/3.62 tff(31781,plain,((~(elem!1 = s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31782,plain,
% 3.42/3.62 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31781, 31767, 412, 13508, 1140, 2073, 145, 216])).
% 3.42/3.62 tff(31783,plain,
% 3.42/3.62 (~(s(s(s(z))) = elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[10599, 31766, 3871])).
% 3.42/3.62 tff(31784,plain,
% 3.42/3.62 (~(elem!1 = s(s(s(z))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[1100, 31783])).
% 3.42/3.62 tff(31785,plain,
% 3.42/3.62 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[1516, 31784])).
% 3.42/3.62 tff(31786,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[1559, 31785, 31782, 14005])).
% 3.42/3.62 tff(31787,plain,((~b(elem!1, z)) | r(s(s(s(s(z)))), s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31788,plain,
% 3.42/3.62 (~b(elem!1, z)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31787, 14005, 31601, 13508, 6533, 31552, 31753, 216, 2326, 3871, 1281, 220])).
% 3.42/3.62 tff(31789,plain,
% 3.42/3.62 (~(s(z) = elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[20120, 31788, 1281])).
% 3.42/3.62 tff(31790,plain,
% 3.42/3.62 (~(elem!1 = s(z))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[242, 31789])).
% 3.42/3.62 tff(31791,plain,
% 3.42/3.62 (r(elem!1, z)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[284, 31788, 31619])).
% 3.42/3.62 tff(31792,plain,
% 3.42/3.62 (~r(z, elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[19871, 31791, 31753, 6533])).
% 3.42/3.62 tff(31793,plain,
% 3.42/3.62 (b(z, elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[355, 31792, 31549])).
% 3.42/3.62 tff(31794,plain,
% 3.42/3.62 (~b(elem!1, s(z))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[21813, 31793, 8336, 1281, 31619, 31601])).
% 3.42/3.62 tff(31795,plain,
% 3.42/3.62 (~r(elem!1, s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[24748, 31791, 31601, 6533])).
% 3.42/3.62 tff(31796,plain,
% 3.42/3.62 (b(elem!1, s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[392, 31795, 8336])).
% 3.42/3.62 tff(31797,plain,
% 3.42/3.62 (~b(s(z), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[20382, 31793, 1281, 31796])).
% 3.42/3.62 tff(31798,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[23319, 31797, 31794, 2326, 31753, 31790])).
% 3.42/3.62 tff(31799,plain,(r(s(s(s(s(z)))), s(elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | b(z, s(s(s(z)))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31800,plain,
% 3.42/3.62 (r(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31799, 13508, 1281, 216, 3871, 220, 82, 111, 31548, 906, 12761, 911, 1209, 2319])).
% 3.42/3.62 tff(31801,plain,
% 3.42/3.62 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31600, 348, 911, 12761, 3871, 82, 13508, 2327, 1281, 220, 10994])).
% 3.42/3.62 tff(31802,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[2071, 31801, 9149, 906])).
% 3.42/3.62 tff(31803,plain,((s(z) = s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31804,plain,
% 3.42/3.62 (s(z) = s(elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31803, 10994, 911, 12761, 3871, 82, 13508, 2327, 1281, 220, 906])).
% 3.42/3.62 tff(31805,plain,
% 3.42/3.62 (s(s(z)) = s(s(elem!1))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31804])).
% 3.42/3.62 tff(31806,plain,
% 3.42/3.62 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31805])).
% 3.42/3.62 tff(31807,plain,
% 3.42/3.62 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31806])).
% 3.42/3.62 tff(31808,plain,
% 3.42/3.62 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 3.42/3.62 inference(symmetry,[status(thm)],[31807])).
% 3.42/3.62 tff(31809,plain,
% 3.42/3.62 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31808])).
% 3.42/3.62 tff(31810,plain,
% 3.42/3.62 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.42/3.62 inference(symmetry,[status(thm)],[31809])).
% 3.42/3.62 tff(31811,plain,
% 3.42/3.62 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31804])).
% 3.42/3.62 tff(31812,plain,
% 3.42/3.62 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31811, 1927])).
% 3.42/3.62 tff(31813,plain,
% 3.42/3.62 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31812])).
% 3.42/3.62 tff(31814,plain,
% 3.42/3.62 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[927, 31813])).
% 3.42/3.62 tff(31815,plain,
% 3.42/3.62 (z = elem!1),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[343, 31804])).
% 3.42/3.62 tff(31816,plain,
% 3.42/3.62 (elem!1 = z),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[364, 31815])).
% 3.42/3.62 tff(31817,plain,
% 3.42/3.62 (b(s(z), s(s(s(elem!1))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[9876, 31816, 3871])).
% 3.42/3.62 tff(31818,plain,
% 3.42/3.62 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[754, 31817, 31815])).
% 3.42/3.62 tff(31819,plain,
% 3.42/3.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31808])).
% 3.42/3.62 tff(31820,plain,
% 3.42/3.62 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.42/3.62 inference(symmetry,[status(thm)],[31819])).
% 3.42/3.62 tff(31821,plain,
% 3.42/3.62 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31806])).
% 3.42/3.62 tff(31822,plain,
% 3.42/3.62 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[13508, 31821])).
% 3.42/3.62 tff(31823,plain,
% 3.42/3.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31822, 31820])).
% 3.42/3.62 tff(31824,plain,
% 3.42/3.62 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31804])).
% 3.42/3.62 tff(31825,plain,
% 3.42/3.62 (r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[12761, 31824])).
% 3.42/3.62 tff(31826,plain,
% 3.42/3.62 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31815])).
% 3.42/3.62 tff(31827,plain,
% 3.42/3.62 (r(elem!1, s(s(s(elem!1))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[111, 31826])).
% 3.42/3.62 tff(31828,plain,
% 3.42/3.62 (r(s(s(s(z))), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[475, 31815, 24356])).
% 3.42/3.62 tff(31829,plain,
% 3.42/3.62 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[149, 31828, 31815])).
% 3.42/3.62 tff(31830,plain,
% 3.42/3.62 (s(elem!1) = s(z)),
% 3.42/3.62 inference(symmetry,[status(thm)],[338])).
% 3.42/3.62 tff(31831,plain,
% 3.42/3.62 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31830])).
% 3.42/3.62 tff(31832,plain,
% 3.42/3.62 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.62 inference(symmetry,[status(thm)],[31831])).
% 3.42/3.62 tff(31833,plain,
% 3.42/3.62 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31832])).
% 3.42/3.62 tff(31834,plain,
% 3.42/3.62 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[1677, 31833])).
% 3.42/3.62 tff(31835,plain,
% 3.42/3.62 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[835, 831, 107])).
% 3.42/3.62 tff(31836,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31837,plain,
% 3.42/3.62 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31838,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31837])).
% 3.42/3.62 tff(31839,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31838, 31836])).
% 3.42/3.62 tff(31840,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(quant_inst,[status(thm)],[])).
% 3.42/3.62 tff(31841,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31840, 31839])).
% 3.42/3.62 tff(31842,plain,
% 3.42/3.62 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31841, 271, 10033, 10032, 31835])).
% 3.42/3.62 tff(31843,plain,
% 3.42/3.62 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[7634, 21, 31842])).
% 3.42/3.62 tff(31844,plain,
% 3.42/3.62 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31843, 18924])).
% 3.42/3.62 tff(31845,plain,
% 3.42/3.62 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.62 inference(monotonicity,[status(thm)],[107])).
% 3.42/3.62 tff(31846,plain,
% 3.42/3.62 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 3.42/3.62 inference(symmetry,[status(thm)],[31845])).
% 3.42/3.62 tff(31847,plain,
% 3.42/3.62 (b(s(s(s(s(s(z))))), z)),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[831, 31846])).
% 3.42/3.62 tff(31848,plain,
% 3.42/3.62 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[24620, 31847, 220, 394])).
% 3.42/3.62 tff(31849,plain,
% 3.42/3.62 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[4138, 31848, 4132])).
% 3.42/3.62 tff(31850,plain,
% 3.42/3.62 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[18190, 31849, 107])).
% 3.42/3.62 tff(31851,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31852,plain,
% 3.42/3.62 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31853,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31852])).
% 3.42/3.62 tff(31854,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31853, 31851])).
% 3.42/3.62 tff(31855,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.42/3.62 inference(quant_inst,[status(thm)],[])).
% 3.42/3.62 tff(31856,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31855, 31854])).
% 3.42/3.62 tff(31857,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31856, 121, 684, 7473, 31850, 31844])).
% 3.42/3.62 tff(31858,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~(z = elem!1)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31859,plain,
% 3.42/3.62 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31858, 7473, 684, 9878, 31834, 220, 394])).
% 3.42/3.62 tff(31860,plain,
% 3.42/3.62 (r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[840, 31859, 9949])).
% 3.42/3.62 tff(31861,plain,
% 3.42/3.62 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[9962, 31860, 338])).
% 3.42/3.62 tff(31862,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31863,plain,
% 3.42/3.62 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31864,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31863])).
% 3.42/3.62 tff(31865,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31864, 31862])).
% 3.42/3.62 tff(31866,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(quant_inst,[status(thm)],[])).
% 3.42/3.62 tff(31867,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31866, 31865])).
% 3.42/3.62 tff(31868,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31867, 121, 139, 727, 31861, 7473])).
% 3.42/3.62 tff(31869,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31870,plain,
% 3.42/3.62 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31869, 31829, 31827, 31804, 31825, 220, 11211])).
% 3.42/3.62 tff(31871,plain,
% 3.42/3.62 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[7296, 31870, 31815])).
% 3.42/3.62 tff(31872,plain,
% 3.42/3.62 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[1494, 31871])).
% 3.42/3.62 tff(31873,plain,
% 3.42/3.62 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[18038, 31872, 31815])).
% 3.42/3.62 tff(31874,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.42/3.62 tff(31875,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31876,plain,
% 3.42/3.62 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(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(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(rewrite,[status(thm)],[])).
% 3.42/3.62 tff(31877,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31876])).
% 3.42/3.62 tff(31878,plain,
% 3.42/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(transitivity,[status(thm)],[31877, 31875])).
% 3.42/3.62 tff(31879,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.62 inference(quant_inst,[status(thm)],[])).
% 3.42/3.62 tff(31880,plain,
% 3.42/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31879, 31878])).
% 3.42/3.62 tff(31881,plain,
% 3.42/3.62 ($false),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31880, 271, 739, 7979, 18043, 31874])).
% 3.42/3.62 tff(31882,plain,((~b(s(s(s(elem!1))), s(s(s(s(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(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.62 tff(31883,plain,
% 3.42/3.62 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[31882, 31873, 31823, 31818])).
% 3.42/3.62 tff(31884,plain,
% 3.42/3.62 (~b(s(z), s(s(s(s(z)))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[19599, 31883, 31804])).
% 3.42/3.62 tff(31885,plain,
% 3.42/3.62 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[19605, 31884, 31815])).
% 3.42/3.62 tff(31886,plain,
% 3.42/3.62 (r(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.62 inference(unit_resolution,[status(thm)],[1995, 31885, 31814])).
% 3.42/3.62 tff(31887,plain,
% 3.42/3.62 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[31886, 31810])).
% 3.42/3.62 tff(31888,plain,
% 3.42/3.62 (s(elem!1) = s(z)),
% 3.42/3.62 inference(symmetry,[status(thm)],[31804])).
% 3.42/3.62 tff(31889,plain,
% 3.42/3.62 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31888])).
% 3.42/3.62 tff(31890,plain,
% 3.42/3.62 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.62 inference(symmetry,[status(thm)],[31889])).
% 3.42/3.62 tff(31891,plain,
% 3.42/3.62 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31890])).
% 3.42/3.62 tff(31892,plain,
% 3.42/3.62 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.62 inference(modus_ponens,[status(thm)],[1677, 31891])).
% 3.42/3.62 tff(31893,plain,
% 3.42/3.62 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31815])).
% 3.42/3.62 tff(31894,plain,
% 3.42/3.62 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 3.42/3.62 inference(symmetry,[status(thm)],[31893])).
% 3.42/3.62 tff(31895,plain,
% 3.42/3.62 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.42/3.62 inference(monotonicity,[status(thm)],[31815])).
% 3.42/3.63 tff(31896,plain,
% 3.42/3.63 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31895])).
% 3.42/3.63 tff(31897,plain,
% 3.42/3.63 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[711, 31896])).
% 3.42/3.63 tff(31898,plain,
% 3.42/3.63 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31806])).
% 3.42/3.63 tff(31899,plain,
% 3.42/3.63 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.63 inference(symmetry,[status(thm)],[31898])).
% 3.42/3.63 tff(31900,plain,
% 3.42/3.63 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31807])).
% 3.42/3.63 tff(31901,plain,
% 3.42/3.63 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 3.42/3.63 inference(symmetry,[status(thm)],[31900])).
% 3.42/3.63 tff(31902,plain,
% 3.42/3.63 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31901])).
% 3.42/3.63 tff(31903,plain,
% 3.42/3.63 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.63 inference(transitivity,[status(thm)],[31902, 31899])).
% 3.42/3.63 tff(31904,plain,
% 3.42/3.63 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31903])).
% 3.42/3.63 tff(31905,plain,
% 3.42/3.63 (b(elem!1, s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[327, 31815, 220])).
% 3.42/3.63 tff(31906,plain,
% 3.42/3.63 (~(s(z) = elem!1)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[1276, 31905, 31555])).
% 3.42/3.63 tff(31907,plain,
% 3.42/3.63 (~(s(s(z)) = s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[960, 31906])).
% 3.42/3.63 tff(31908,plain,
% 3.42/3.63 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[953, 31907])).
% 3.42/3.63 tff(31909,plain,
% 3.42/3.63 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[946, 31908])).
% 3.42/3.63 tff(31910,plain,
% 3.42/3.63 (r(s(z), s(s(s(s(z)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[16482, 31884])).
% 3.42/3.63 tff(31911,plain,
% 3.42/3.63 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[16499, 31910, 911, 12761])).
% 3.42/3.63 tff(31912,plain,
% 3.42/3.63 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[1014, 31911, 31909])).
% 3.42/3.63 tff(31913,plain,
% 3.42/3.63 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[18804, 31912, 31815])).
% 3.42/3.63 tff(31914,plain,
% 3.42/3.63 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[10182, 31815, 1551])).
% 3.42/3.63 tff(31915,plain,
% 3.42/3.63 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[9938, 9939])).
% 3.42/3.63 tff(31916,plain,
% 3.42/3.63 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.63 inference(symmetry,[status(thm)],[31915])).
% 3.42/3.63 tff(31917,plain,
% 3.42/3.63 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31916])).
% 3.42/3.63 tff(31918,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31919,plain,
% 3.42/3.63 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(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)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31920,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31919])).
% 3.42/3.63 tff(31921,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(transitivity,[status(thm)],[31920, 31918])).
% 3.42/3.63 tff(31922,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(quant_inst,[status(thm)],[])).
% 3.42/3.63 tff(31923,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31922, 31921])).
% 3.42/3.63 tff(31924,plain,
% 3.42/3.63 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31923, 271, 18990, 7979, 18789])).
% 3.42/3.63 tff(31925,plain,
% 3.42/3.63 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31924, 31917])).
% 3.42/3.63 tff(31926,plain,
% 3.42/3.63 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[1777, 31925])).
% 3.42/3.63 tff(31927,plain,
% 3.42/3.63 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31926, 20802])).
% 3.42/3.63 tff(31928,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.42/3.63 tff(31929,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31930,plain,
% 3.42/3.63 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31931,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31930])).
% 3.42/3.63 tff(31932,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(transitivity,[status(thm)],[31931, 31929])).
% 3.42/3.63 tff(31933,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.42/3.63 inference(quant_inst,[status(thm)],[])).
% 3.42/3.63 tff(31934,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31933, 31932])).
% 3.42/3.63 tff(31935,plain,
% 3.42/3.63 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31934, 271, 739, 18990, 18789])).
% 3.42/3.63 tff(31936,plain,
% 3.42/3.63 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[9896, 31935, 9878])).
% 3.42/3.63 tff(31937,plain,
% 3.42/3.63 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[4138, 31936, 31834])).
% 3.42/3.63 tff(31938,plain,
% 3.42/3.63 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[18190, 31937, 9878])).
% 3.42/3.63 tff(31939,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31940,plain,
% 3.42/3.63 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31941,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31940])).
% 3.42/3.63 tff(31942,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(transitivity,[status(thm)],[31941, 31939])).
% 3.42/3.63 tff(31943,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 3.42/3.63 inference(quant_inst,[status(thm)],[])).
% 3.42/3.63 tff(31944,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31943, 31942])).
% 3.42/3.63 tff(31945,plain,
% 3.42/3.63 ($false),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31944, 121, 6898, 31938, 31928, 31927])).
% 3.42/3.63 tff(31946,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~(s(z) = s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.63 tff(31947,plain,
% 3.42/3.63 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31946, 31914, 31887, 31804, 31823, 31913, 31818])).
% 3.42/3.63 tff(31948,plain,
% 3.42/3.63 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31947, 31904])).
% 3.42/3.63 tff(31949,plain,
% 3.42/3.63 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[1733, 31948])).
% 3.42/3.63 tff(31950,plain,
% 3.42/3.63 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[6039, 31949, 31815])).
% 3.42/3.63 tff(31951,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31952,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.42/3.63 inference(quant_inst,[status(thm)],[])).
% 3.42/3.63 tff(31953,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31952, 31951])).
% 3.42/3.63 tff(31954,plain,
% 3.42/3.63 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31953, 121, 31825, 31827, 31950])).
% 3.42/3.63 tff(31955,plain,
% 3.42/3.63 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[9962, 31954, 31804])).
% 3.42/3.63 tff(31956,plain,
% 3.42/3.63 (b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[840, 31955, 31897])).
% 3.42/3.63 tff(31957,plain,
% 3.42/3.63 (b(s(s(s(s(s(z))))), z)),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31956, 31894])).
% 3.42/3.63 tff(31958,plain,
% 3.42/3.63 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[24620, 31957, 220, 11211])).
% 3.42/3.63 tff(31959,plain,
% 3.42/3.63 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[4138, 31958, 31892])).
% 3.42/3.63 tff(31960,plain,
% 3.42/3.63 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[18190, 31959, 31815])).
% 3.42/3.63 tff(31961,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31962,plain,
% 3.42/3.63 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(31963,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31962])).
% 3.42/3.63 tff(31964,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.42/3.63 inference(transitivity,[status(thm)],[31963, 31961])).
% 3.42/3.63 tff(31965,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.42/3.63 inference(quant_inst,[status(thm)],[])).
% 3.42/3.63 tff(31966,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31965, 31964])).
% 3.42/3.63 tff(31967,plain,
% 3.42/3.63 ($false),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31966, 121, 31825, 31950, 31960, 31887])).
% 3.42/3.63 tff(31968,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.63 tff(31969,plain,
% 3.42/3.63 (r(s(elem!1), z)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31968, 13508, 911, 12761, 220, 111, 3871, 31800, 82, 2326, 1281, 906])).
% 3.42/3.63 tff(31970,plain,
% 3.42/3.63 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[25005])).
% 3.42/3.63 tff(31971,plain,
% 3.42/3.63 (r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[1551, 31970])).
% 3.42/3.63 tff(31972,plain,
% 3.42/3.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[25005])).
% 3.42/3.63 tff(31973,plain,
% 3.42/3.63 (s(s(s(z))) = s(s(elem!1))),
% 3.42/3.63 inference(transitivity,[status(thm)],[775, 31972, 55])).
% 3.42/3.63 tff(31974,plain,
% 3.42/3.63 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31973])).
% 3.42/3.63 tff(31975,plain,
% 3.42/3.63 (r(z, s(s(elem!1)))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[1140, 31974])).
% 3.42/3.63 tff(31976,plain,
% 3.42/3.63 ($false),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[6850, 31975, 31971, 6842, 412])).
% 3.42/3.63 tff(31977,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.63 tff(31978,plain,
% 3.42/3.63 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31977, 31969, 6842, 6533, 31800])).
% 3.42/3.63 tff(31979,plain,
% 3.42/3.63 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[30680, 13508, 31548, 31978, 12761, 911, 3871, 906])).
% 3.42/3.63 tff(31980,plain,
% 3.42/3.63 (s(z) = s(elem!1)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[2063, 31979])).
% 3.42/3.63 tff(31981,plain,
% 3.42/3.63 (z = elem!1),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[343, 31980])).
% 3.42/3.63 tff(31982,plain,
% 3.42/3.63 (s(z) = s(elem!1)),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31981])).
% 3.42/3.63 tff(31983,plain,
% 3.42/3.63 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31982])).
% 3.42/3.63 tff(31984,plain,
% 3.42/3.63 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 3.42/3.63 inference(symmetry,[status(thm)],[31983])).
% 3.42/3.63 tff(31985,plain,
% 3.42/3.63 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31981])).
% 3.42/3.63 tff(31986,plain,
% 3.42/3.63 (r(s(elem!1), elem!1)),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31969, 31985])).
% 3.42/3.63 tff(31987,plain,
% 3.42/3.63 (r(s(z), elem!1)),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31986, 31984])).
% 3.42/3.63 tff(31988,plain,
% 3.42/3.63 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31981])).
% 3.42/3.63 tff(31989,plain,
% 3.42/3.63 ((~r(s(z), z)) <=> (~r(s(z), elem!1))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[31988])).
% 3.42/3.63 tff(31990,plain,
% 3.42/3.63 (~r(s(z), elem!1)),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[31518, 31989])).
% 3.42/3.63 tff(31991,plain,
% 3.42/3.63 ($false),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31990, 31987])).
% 3.42/3.63 tff(31992,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(z), z) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(s(elem!1))) | b(z, s(s(s(z)))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.63 tff(31993,plain,
% 3.42/3.63 (~r(s(s(s(elem!1))), s(z))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31992, 31547, 31518, 911, 3871, 906, 6842, 220, 111, 79, 19197, 211, 1209, 2319])).
% 3.42/3.63 tff(31994,plain,
% 3.42/3.63 (b(s(s(s(elem!1))), s(z))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[16580, 31993])).
% 3.42/3.63 tff(31995,plain,
% 3.42/3.63 (~(s(z) = s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[19469, 31994, 2319])).
% 3.42/3.63 tff(31996,plain,
% 3.42/3.63 (~(s(z) = elem!1)),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[1238, 31993, 911])).
% 3.42/3.63 tff(31997,plain,
% 3.42/3.63 (~(elem!1 = s(z))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[242, 31996])).
% 3.42/3.63 tff(31998,plain,
% 3.42/3.63 (r(s(elem!1), s(z))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[429, 2282, 24240])).
% 3.42/3.63 tff(31999,plain,
% 3.42/3.63 (r(s(z), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[444, 348, 24242])).
% 3.42/3.63 tff(32000,plain,
% 3.42/3.63 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[27054, 121, 31999, 911, 31998])).
% 3.42/3.63 tff(32001,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(32002,plain,
% 3.42/3.63 (((~r(s(z), s(elem!1))) | (~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(s(z)))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.42/3.63 inference(rewrite,[status(thm)],[])).
% 3.42/3.63 tff(32003,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 3.42/3.63 inference(monotonicity,[status(thm)],[32002])).
% 3.42/3.63 tff(32004,plain,
% 3.42/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.42/3.63 inference(transitivity,[status(thm)],[32003, 32001])).
% 3.42/3.63 tff(32005,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 3.42/3.63 inference(quant_inst,[status(thm)],[])).
% 3.42/3.63 tff(32006,plain,
% 3.42/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.42/3.63 inference(modus_ponens,[status(thm)],[32005, 32004])).
% 3.42/3.63 tff(32007,plain,
% 3.42/3.63 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[32006, 121, 31999, 911, 2327])).
% 3.42/3.63 tff(32008,plain,
% 3.42/3.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[1167, 21, 32007, 20146])).
% 3.42/3.63 tff(32009,plain,
% 3.42/3.63 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[24945, 911, 2327, 19197, 6533])).
% 3.42/3.63 tff(32010,plain,
% 3.42/3.63 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[10426, 32009])).
% 3.42/3.63 tff(32011,plain,
% 3.42/3.63 (~r(s(elem!1), s(s(s(z))))),
% 3.42/3.63 inference(unit_resolution,[status(thm)],[31571, 121, 31999, 31998, 2327])).
% 3.42/3.64 tff(32012,plain,
% 3.42/3.64 (b(s(elem!1), s(s(s(z))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2044, 32011, 6284])).
% 3.42/3.64 tff(32013,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(z)))), s(elem!1))))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32014,plain,
% 3.42/3.64 (((~b(s(s(s(z))), 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(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), 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(z)))), s(elem!1))))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32015,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(z)))), s(elem!1)))))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32014])).
% 3.42/3.64 tff(32016,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(z)))), s(elem!1))))),
% 3.42/3.64 inference(transitivity,[status(thm)],[32015, 32013])).
% 3.42/3.64 tff(32017,plain,
% 3.42/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(z)))), s(elem!1))))),
% 3.42/3.64 inference(quant_inst,[status(thm)],[])).
% 3.42/3.64 tff(32018,plain,
% 3.42/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(z)))), s(elem!1)))),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[32017, 32016])).
% 3.42/3.64 tff(32019,plain,
% 3.42/3.64 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32018, 271, 32012, 32010, 32008])).
% 3.42/3.64 tff(32020,plain,
% 3.42/3.64 (s(s(s(s(z)))) = s(elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1559, 32019, 32000])).
% 3.42/3.64 tff(32021,plain,
% 3.42/3.64 (elem!1 = s(s(s(z)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1516, 32020])).
% 3.42/3.64 tff(32022,plain,
% 3.42/3.64 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32021])).
% 3.42/3.64 tff(32023,plain,
% 3.42/3.64 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(symmetry,[status(thm)],[32022])).
% 3.42/3.64 tff(32024,plain,
% 3.42/3.64 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32023])).
% 3.42/3.64 tff(32025,plain,
% 3.42/3.64 (~r(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[31545, 32024])).
% 3.42/3.64 tff(32026,plain,
% 3.42/3.64 (~r(s(s(s(z))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[8142, 121, 31999, 31998, 2327])).
% 3.42/3.64 tff(32027,plain,
% 3.42/3.64 (b(s(s(s(z))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1816, 32026, 2033])).
% 3.42/3.64 tff(32028,plain,
% 3.42/3.64 (s(s(s(z))) = elem!1),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1100, 32021])).
% 3.42/3.64 tff(32029,plain,
% 3.42/3.64 (b(elem!1, s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6165, 32028, 32027])).
% 3.42/3.64 tff(32030,plain,
% 3.42/3.64 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12484, 19776, 503, 3871])).
% 3.42/3.64 tff(32031,plain,
% 3.42/3.64 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[760, 32030])).
% 3.42/3.64 tff(32032,plain,
% 3.42/3.64 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2114, 32027, 394, 19776])).
% 3.42/3.64 tff(32033,plain,
% 3.42/3.64 (r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[681, 32032, 79])).
% 3.42/3.64 tff(32034,plain,
% 3.42/3.64 (~r(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9617, 32033, 31999, 32031])).
% 3.42/3.64 tff(32035,plain,
% 3.42/3.64 (b(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2243, 32034, 2207])).
% 3.42/3.64 tff(32036,plain,
% 3.42/3.64 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32021])).
% 3.42/3.64 tff(32037,plain,
% 3.42/3.64 (r(s(s(s(z))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.42/3.64 inference(symmetry,[status(thm)],[32036])).
% 3.42/3.64 tff(32038,plain,
% 3.42/3.64 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(elem!1, s(elem!1)))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32037])).
% 3.42/3.64 tff(32039,plain,
% 3.42/3.64 (~r(elem!1, s(elem!1))),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[32026, 32038])).
% 3.42/3.64 tff(32040,plain,
% 3.42/3.64 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[14823, 32039, 394, 9297, 32032, 32035, 32029, 32025])).
% 3.42/3.64 tff(32041,plain,
% 3.42/3.64 (~b(elem!1, z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[402, 32029, 394, 220])).
% 3.42/3.64 tff(32042,plain,
% 3.42/3.64 (r(elem!1, z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[284, 32041, 9298])).
% 3.42/3.64 tff(32043,plain,
% 3.42/3.64 (~b(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6548, 32028, 1209])).
% 3.42/3.64 tff(32044,plain,
% 3.42/3.64 (r(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[355, 32043, 9297])).
% 3.42/3.64 tff(32045,plain,
% 3.42/3.64 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2611, 32028])).
% 3.42/3.64 tff(32046,plain,
% 3.42/3.64 (b(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[486, 32025, 32045])).
% 3.42/3.64 tff(32047,plain,
% 3.42/3.64 (~r(s(s(elem!1)), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[20430, 32046, 6842, 1, 198, 32044, 32029, 32042])).
% 3.42/3.64 tff(32048,plain,
% 3.42/3.64 (b(s(s(elem!1)), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2430, 32047])).
% 3.42/3.64 tff(32049,plain,
% 3.42/3.64 (~r(z, s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[17205, 32048, 258, 32040, 220, 9297, 68])).
% 3.42/3.64 tff(32050,plain,
% 3.42/3.64 (b(z, s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2106, 32049])).
% 3.42/3.64 tff(32051,plain,
% 3.42/3.64 (~b(s(z), s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[17014, 32048, 19197, 220])).
% 3.42/3.64 tff(32052,plain,
% 3.42/3.64 (r(s(z), s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2167, 32051])).
% 3.42/3.64 tff(32053,plain,
% 3.42/3.64 (~b(s(s(elem!1)), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2528, 32050, 394, 32048])).
% 3.42/3.64 tff(32054,plain,
% 3.42/3.64 (r(s(s(elem!1)), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[701, 32053, 3313])).
% 3.42/3.64 tff(32055,plain,
% 3.42/3.64 (~r(s(elem!1), s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[3275, 32054, 31999, 32052])).
% 3.42/3.64 tff(32056,plain,
% 3.42/3.64 (b(s(elem!1), s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[526, 32055, 211])).
% 3.42/3.64 tff(32057,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32058,plain,
% 3.42/3.64 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32059,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32058])).
% 3.42/3.64 tff(32060,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.42/3.64 inference(transitivity,[status(thm)],[32059, 32057])).
% 3.42/3.64 tff(32061,plain,
% 3.42/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 3.42/3.64 inference(quant_inst,[status(thm)],[])).
% 3.42/3.64 tff(32062,plain,
% 3.42/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[32061, 32060])).
% 3.42/3.64 tff(32063,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32062, 271, 32040, 394, 32056, 32050])).
% 3.42/3.64 tff(32064,plain,((s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(s(s(z)))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32065,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32064, 24455, 11211, 220, 258, 68, 6842, 1, 1209, 348, 2327, 911, 503, 3871, 906])).
% 3.42/3.64 tff(32066,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(s(s(z)))) | (s(z) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32067,plain,
% 3.42/3.64 (r(s(elem!1), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32066, 31997, 220, 68, 6842, 1, 1209, 31995, 2326, 911, 31994, 3871, 906])).
% 3.42/3.64 tff(32068,plain,
% 3.42/3.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[7238, 121, 111, 32067, 6842])).
% 3.42/3.64 tff(32069,plain,
% 3.42/3.64 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[681, 32068, 79])).
% 3.42/3.64 tff(32070,plain,
% 3.42/3.64 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6215, 121, 111, 32067, 6842])).
% 3.42/3.64 tff(32071,plain,
% 3.42/3.64 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2293, 21, 32070, 85])).
% 3.42/3.64 tff(32072,plain,
% 3.42/3.64 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2063, 31995])).
% 3.42/3.64 tff(32073,plain,
% 3.42/3.64 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2071, 32072, 906])).
% 3.42/3.64 tff(32074,plain,
% 3.42/3.64 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12484, 32073, 31994, 3871])).
% 3.42/3.64 tff(32075,plain,
% 3.42/3.64 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[760, 32074])).
% 3.42/3.64 tff(32076,plain,
% 3.42/3.64 (~r(elem!1, z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[24748, 3502, 412, 6533])).
% 3.42/3.64 tff(32077,plain,
% 3.42/3.64 (b(elem!1, z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[284, 32076, 9298])).
% 3.42/3.64 tff(32078,plain,
% 3.42/3.64 (~r(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[22265, 317, 412, 109, 258, 1209, 3871, 348, 377])).
% 3.42/3.64 tff(32079,plain,
% 3.42/3.64 (b(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[355, 32078, 9297])).
% 3.42/3.64 tff(32080,plain,
% 3.42/3.64 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[7179, 3502, 676])).
% 3.42/3.64 tff(32081,plain,
% 3.42/3.64 (~b(s(z), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[3964, 32077, 1281, 32079])).
% 3.42/3.64 tff(32082,plain,
% 3.42/3.64 (~b(elem!1, s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[21813, 32079, 377, 1281, 9298, 412])).
% 3.42/3.64 tff(32083,plain,
% 3.42/3.64 (~r(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[18965, 32082, 258, 572, 32081])).
% 3.42/3.64 tff(32084,plain,
% 3.42/3.64 (b(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[486, 32083, 32080])).
% 3.42/3.64 tff(32085,plain,
% 3.42/3.64 (~(s(s(s(z))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6548, 32079, 1209])).
% 3.42/3.64 tff(32086,plain,
% 3.42/3.64 (~r(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[23319, 32081, 2327, 32082, 258])).
% 3.42/3.64 tff(32087,plain,
% 3.42/3.64 (b(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[255, 32086, 32085])).
% 3.42/3.64 tff(32088,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[11686, 32087, 32084, 32079, 32077, 15822])).
% 3.42/3.64 tff(32089,plain,(b(elem!1, s(elem!1)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | b(z, s(s(s(z)))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | r(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32090,plain,
% 3.42/3.64 (b(elem!1, s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32089, 31997, 2326, 32075, 19197, 1209, 219, 32067, 32068, 24432, 3871, 31995])).
% 3.42/3.64 tff(32091,plain,
% 3.42/3.64 (~b(elem!1, s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6866, 271, 32090, 32071, 32069])).
% 3.42/3.64 tff(32092,plain,
% 3.42/3.64 (~b(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[11152, 32090, 32068, 32070, 79])).
% 3.42/3.64 tff(32093,plain,
% 3.42/3.64 (~(z = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[500, 31995])).
% 3.42/3.64 tff(32094,plain,
% 3.42/3.64 (~(s(s(s(z))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9580, 32091, 32073])).
% 3.42/3.64 tff(32095,plain,
% 3.42/3.64 (~b(s(z), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[24003, 257, 3871, 307])).
% 3.42/3.64 tff(32096,plain,
% 3.42/3.64 (b(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[355, 1391, 331])).
% 3.42/3.64 tff(32097,plain,
% 3.42/3.64 (~b(elem!1, s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[21813, 32096, 377, 1281, 358, 412])).
% 3.42/3.64 tff(32098,plain,
% 3.42/3.64 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[11073, 1391, 111])).
% 3.42/3.64 tff(32099,plain,
% 3.42/3.64 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[486, 32098, 479])).
% 3.42/3.64 tff(32100,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[18965, 32099, 32097, 258, 572, 1242])).
% 3.42/3.64 tff(32101,plain,(r(z, elem!1) | (elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | b(s(z), elem!1) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32102,plain,
% 3.42/3.64 (r(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32101, 32095, 572, 258, 479, 377, 1281, 412, 111, 331])).
% 3.42/3.64 tff(32103,plain,
% 3.42/3.64 (s(s(s(elem!1))) = elem!1),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12884, 32102, 479, 657, 111])).
% 3.42/3.64 tff(32104,plain,
% 3.42/3.64 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32103])).
% 3.42/3.64 tff(32105,plain,
% 3.42/3.64 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.64 inference(symmetry,[status(thm)],[32104])).
% 3.42/3.64 tff(32106,plain,
% 3.42/3.64 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32105])).
% 3.42/3.64 tff(32107,plain,
% 3.42/3.64 (~(s(s(s(z))) = s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2596, 32103])).
% 3.42/3.64 tff(32108,plain,
% 3.42/3.64 (~b(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[13140, 32107, 412, 257, 307, 1140])).
% 3.42/3.64 tff(32109,plain,
% 3.42/3.64 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[32108, 32106])).
% 3.42/3.64 tff(32110,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[739, 32109])).
% 3.42/3.64 tff(32111,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(z))))) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(z)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | (z = elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32112,plain,
% 3.42/3.64 (~b(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32111, 32071, 32067, 32090, 6533, 32092, 32091, 111, 32075, 31997, 219, 19197, 32093, 3871])).
% 3.42/3.64 tff(32113,plain,
% 3.42/3.64 (r(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[255, 32112, 32094])).
% 3.42/3.64 tff(32114,plain,
% 3.42/3.64 (~r(elem!1, s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12657, 32113, 2326, 32075])).
% 3.42/3.64 tff(32115,plain,
% 3.42/3.64 (b(elem!1, s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[299, 32114, 31997])).
% 3.42/3.64 tff(32116,plain,
% 3.42/3.64 (~b(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[20398, 32115, 19197, 220])).
% 3.42/3.64 tff(32117,plain,
% 3.42/3.64 (r(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[355, 32116, 32093])).
% 3.42/3.64 tff(32118,plain,
% 3.42/3.64 (s(s(s(elem!1))) = elem!1),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12884, 32117, 32092, 32091, 111])).
% 3.42/3.64 tff(32119,plain,
% 3.42/3.64 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32118])).
% 3.42/3.64 tff(32120,plain,
% 3.42/3.64 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.64 inference(symmetry,[status(thm)],[32119])).
% 3.42/3.64 tff(32121,plain,
% 3.42/3.64 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32120])).
% 3.42/3.64 tff(32122,plain,
% 3.42/3.64 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[32112, 32121])).
% 3.42/3.64 tff(32123,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32073, 32122])).
% 3.42/3.64 tff(32124,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | b(z, s(s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(s(z))), s(z)) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32125,plain,
% 3.42/3.64 (~r(s(s(s(s(z)))), s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32124, 2319, 220, 3871, 1209, 6842, 68, 1, 906, 111, 31518])).
% 3.42/3.64 tff(32126,plain,
% 3.42/3.64 (b(s(s(s(s(z)))), s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[932, 32125])).
% 3.42/3.64 tff(32127,plain,
% 3.42/3.64 (~b(s(s(s(s(z)))), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[22548, 32126, 19197, 220])).
% 3.42/3.64 tff(32128,plain,
% 3.42/3.64 (r(s(s(s(s(z)))), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1095, 32127])).
% 3.42/3.64 tff(32129,plain,
% 3.42/3.64 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[27490, 121, 111, 6842, 32128])).
% 3.42/3.64 tff(32130,plain,
% 3.42/3.64 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[26553, 121, 111, 6842, 32128])).
% 3.42/3.64 tff(32131,plain,
% 3.42/3.64 (~b(s(s(s(s(z)))), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[22548, 1347, 1281, 220])).
% 3.42/3.64 tff(32132,plain,
% 3.42/3.64 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[27354, 11211, 32131])).
% 3.42/3.64 tff(32133,plain,
% 3.42/3.64 (~(s(s(s(z))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2605, 32132])).
% 3.42/3.64 tff(32134,plain,
% 3.42/3.64 (r(s(elem!1), s(z))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[429, 2282, 424])).
% 3.42/3.64 tff(32135,plain,
% 3.42/3.64 (~r(s(s(s(z))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[8142, 121, 23248, 32134, 2327])).
% 3.42/3.64 tff(32136,plain,
% 3.42/3.64 (b(s(s(s(z))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1816, 32135, 2033])).
% 3.42/3.64 tff(32137,plain,
% 3.42/3.64 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2114, 32136, 11211, 19776])).
% 3.42/3.64 tff(32138,plain,
% 3.42/3.64 (r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[681, 32137, 82])).
% 3.42/3.64 tff(32139,plain,
% 3.42/3.64 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1014, 19200, 1007])).
% 3.42/3.64 tff(32140,plain,
% 3.42/3.64 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[25008, 19200])).
% 3.42/3.64 tff(32141,plain,
% 3.42/3.64 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[25011, 32140])).
% 3.42/3.64 tff(32142,plain,
% 3.42/3.64 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12570, 32141, 937, 32139])).
% 3.42/3.64 tff(32143,plain,
% 3.42/3.64 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[760, 32142])).
% 3.42/3.64 tff(32144,plain,
% 3.42/3.64 (~r(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9617, 32143, 431, 684])).
% 3.42/3.64 tff(32145,plain,
% 3.42/3.64 (b(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2243, 32144, 3500])).
% 3.42/3.64 tff(32146,plain,
% 3.42/3.64 (~r(elem!1, s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[24472, 32145, 1140, 220, 82, 431, 411, 3871, 258, 10994, 377, 348])).
% 3.42/3.64 tff(32147,plain,
% 3.42/3.64 (b(elem!1, s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[392, 32146, 377])).
% 3.42/3.64 tff(32148,plain,
% 3.42/3.64 (~b(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[4598, 32147, 11211, 32145])).
% 3.42/3.64 tff(32149,plain,
% 3.42/3.64 (r(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[355, 32148, 9297])).
% 3.42/3.64 tff(32150,plain,
% 3.42/3.64 (~b(elem!1, z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[402, 32147, 11211, 220])).
% 3.42/3.64 tff(32151,plain,
% 3.42/3.64 (r(elem!1, z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[284, 32150, 9298])).
% 3.42/3.64 tff(32152,plain,
% 3.42/3.64 (~b(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[3288, 32147, 11211, 1422])).
% 3.42/3.64 tff(32153,plain,
% 3.42/3.64 (r(s(s(s(z))), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[255, 32152, 907])).
% 3.42/3.64 tff(32154,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[19871, 32153, 32151, 32149, 1140])).
% 3.42/3.64 tff(32155,plain,((elem!1 = s(z)) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(z))) | (elem!1 = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(elem!1), z) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32156,plain,
% 3.42/3.64 (elem!1 = s(z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32155, 32136, 907, 1140, 220, 377, 82, 23248, 32134, 3871, 10994, 348, 32138, 1347, 25010, 1007])).
% 3.42/3.64 tff(32157,plain,
% 3.42/3.64 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[11319, 32156, 922, 19776, 3871])).
% 3.42/3.64 tff(32158,plain,
% 3.42/3.64 (~r(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9617, 32157, 23248, 32138])).
% 3.42/3.64 tff(32159,plain,
% 3.42/3.64 (b(elem!1, s(s(s(z))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[11114, 32156, 3871])).
% 3.42/3.64 tff(32160,plain,
% 3.42/3.64 (s(z) = elem!1),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[242, 32156])).
% 3.42/3.64 tff(32161,plain,
% 3.42/3.64 (b(z, elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[229, 32160, 220])).
% 3.42/3.64 tff(32162,plain,
% 3.42/3.64 (~b(s(elem!1), elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9291, 32161, 11211, 32159])).
% 3.42/3.64 tff(32163,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2243, 32162, 32158, 3500])).
% 3.42/3.64 tff(32164,plain,((s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(s(z)))), s(z)) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | (elem!1 = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), z) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(elem!1), s(z)) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32165,plain,
% 3.42/3.64 (s(z) = s(elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32164, 32133, 3871, 922, 220, 1140, 377, 82, 10994, 25010, 1007, 31564, 2327, 906, 31553, 31555])).
% 3.42/3.64 tff(32166,plain,
% 3.42/3.64 (z = elem!1),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[343, 32165])).
% 3.42/3.64 tff(32167,plain,
% 3.42/3.64 (b(elem!1, s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[327, 32166, 220])).
% 3.42/3.64 tff(32168,plain,
% 3.42/3.64 (~(s(z) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1276, 32167, 31555])).
% 3.42/3.64 tff(32169,plain,
% 3.42/3.64 (~(s(s(z)) = s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[960, 32168])).
% 3.42/3.64 tff(32170,plain,
% 3.42/3.64 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[953, 32169])).
% 3.42/3.64 tff(32171,plain,
% 3.42/3.64 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[946, 32170])).
% 3.42/3.64 tff(32172,plain,
% 3.42/3.64 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[25008, 32171])).
% 3.42/3.64 tff(32173,plain,
% 3.42/3.64 (elem!1 = z),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[364, 32166])).
% 3.42/3.64 tff(32174,plain,
% 3.42/3.64 (b(s(z), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9876, 32173, 3871])).
% 3.42/3.64 tff(32175,plain,
% 3.42/3.64 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[1014, 32171, 1007])).
% 3.42/3.64 tff(32176,plain,
% 3.42/3.64 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[12570, 32175, 1347, 32174])).
% 3.42/3.64 tff(32177,plain,
% 3.42/3.64 ($false),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[25011, 32176, 32172])).
% 3.42/3.64 tff(32178,plain,(r(s(elem!1), z) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | r(s(s(s(s(z)))), s(z)) | (~r(z, s(s(s(z))))) | (elem!1 = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.64 tff(32179,plain,
% 3.42/3.64 (r(s(elem!1), z)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32178, 32130, 32129, 3871, 220, 32125, 6533, 219, 79, 2326, 906, 19197])).
% 3.42/3.64 tff(32180,plain,
% 3.42/3.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[7238, 121, 111, 32179, 6842])).
% 3.42/3.64 tff(32181,plain,
% 3.42/3.64 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[681, 32180, 79])).
% 3.42/3.64 tff(32182,plain,
% 3.42/3.64 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6215, 121, 111, 32179, 6842])).
% 3.42/3.64 tff(32183,plain,
% 3.42/3.64 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[2293, 21, 32182, 85])).
% 3.42/3.64 tff(32184,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32185,plain,
% 3.42/3.64 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32186,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))))),
% 3.42/3.64 inference(monotonicity,[status(thm)],[32185])).
% 3.42/3.64 tff(32187,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 3.42/3.64 inference(transitivity,[status(thm)],[32186, 32184])).
% 3.42/3.64 tff(32188,plain,
% 3.42/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 3.42/3.64 inference(quant_inst,[status(thm)],[])).
% 3.42/3.64 tff(32189,plain,
% 3.42/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 3.42/3.64 inference(modus_ponens,[status(thm)],[32188, 32187])).
% 3.42/3.64 tff(32190,plain,
% 3.42/3.64 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32189, 121, 111, 32179, 32128])).
% 3.42/3.64 tff(32191,plain,
% 3.42/3.64 (b(elem!1, s(elem!1))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[32089, 32143, 2327, 412, 1281, 1209, 377, 258, 676, 109, 3871, 348])).
% 3.42/3.64 tff(32192,plain,
% 3.42/3.64 (~b(elem!1, s(s(s(elem!1))))),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[6866, 271, 32191, 739, 638])).
% 3.42/3.64 tff(32193,plain,
% 3.42/3.64 (~(s(s(s(z))) = elem!1)),
% 3.42/3.64 inference(unit_resolution,[status(thm)],[9580, 32192, 2073])).
% 3.42/3.64 tff(32194,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32195,plain,
% 3.42/3.64 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.64 inference(rewrite,[status(thm)],[])).
% 3.42/3.64 tff(32196,plain,
% 3.42/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~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(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32195])).
% 3.42/3.65 tff(32197,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~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(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.65 inference(transitivity,[status(thm)],[32196, 32194])).
% 3.42/3.65 tff(32198,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(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))))),
% 3.42/3.65 inference(quant_inst,[status(thm)],[])).
% 3.42/3.65 tff(32199,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32198, 32197])).
% 3.42/3.65 tff(32200,plain,
% 3.42/3.65 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32199, 271, 739, 32139, 32141])).
% 3.42/3.65 tff(32201,plain,
% 3.42/3.65 (s(s(s(s(z)))) = s(elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1559, 32200, 14005])).
% 3.42/3.65 tff(32202,plain,
% 3.42/3.65 (elem!1 = s(s(s(z)))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1516, 32201])).
% 3.42/3.65 tff(32203,plain,
% 3.42/3.65 ($false),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1100, 32202, 32193])).
% 3.42/3.65 tff(32204,plain,((elem!1 = s(z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(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))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | b(z, s(s(s(z)))) | (elem!1 = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.65 tff(32205,plain,
% 3.42/3.65 (elem!1 = s(z)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32204, 19776, 14005, 739, 638, 2326, 412, 1281, 1209, 8336, 676, 24356, 3871, 348, 937, 25010, 1007])).
% 3.42/3.65 tff(32206,plain,
% 3.42/3.65 (s(z) = elem!1),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[242, 32205])).
% 3.42/3.65 tff(32207,plain,
% 3.42/3.65 (s(s(z)) = s(elem!1)),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32206])).
% 3.42/3.65 tff(32208,plain,
% 3.42/3.65 (s(s(s(z))) = s(s(elem!1))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32207])).
% 3.42/3.65 tff(32209,plain,
% 3.42/3.65 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32208])).
% 3.42/3.65 tff(32210,plain,
% 3.42/3.65 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32209, 32208])).
% 3.42/3.65 tff(32211,plain,
% 3.42/3.65 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.65 inference(symmetry,[status(thm)],[32210])).
% 3.42/3.65 tff(32212,plain,
% 3.42/3.65 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32211])).
% 3.42/3.65 tff(32213,plain,
% 3.42/3.65 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32208])).
% 3.42/3.65 tff(32214,plain,
% 3.42/3.65 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32213])).
% 3.42/3.65 tff(32215,plain,
% 3.42/3.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[28366, 32214])).
% 3.42/3.65 tff(32216,plain,
% 3.42/3.65 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32215, 32212])).
% 3.42/3.65 tff(32217,plain,
% 3.42/3.65 (b(z, elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[229, 32206, 220])).
% 3.42/3.65 tff(32218,plain,
% 3.42/3.65 (~(s(s(s(z))) = elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[6548, 32217, 1209])).
% 3.42/3.65 tff(32219,plain,
% 3.42/3.65 (~b(s(s(s(z))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[8109, 32206, 2319])).
% 3.42/3.65 tff(32220,plain,
% 3.42/3.65 (r(s(s(s(z))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[255, 32219, 32218])).
% 3.42/3.65 tff(32221,plain,
% 3.42/3.65 (b(elem!1, z)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[20120, 32206, 1281])).
% 3.42/3.65 tff(32222,plain,
% 3.42/3.65 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[31787, 32221, 412, 14005, 6533, 19776, 32220, 216, 2326, 3871, 1281, 220])).
% 3.42/3.65 tff(32223,plain,
% 3.42/3.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[10426, 32222])).
% 3.42/3.65 tff(32224,plain,
% 3.42/3.65 ($false),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32223, 32216])).
% 3.42/3.65 tff(32225,plain,((s(z) = s(elem!1)) | r(s(s(s(elem!1))), s(s(s(z)))) | (~r(s(elem!1), z)) | r(s(s(s(s(z)))), s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(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)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | r(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.65 tff(32226,plain,
% 3.42/3.65 (s(z) = s(elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32225, 32179, 31545, 32190, 211, 3871, 19197, 220, 1209, 2319, 32183, 32181, 32180, 32126, 32130, 32129, 906])).
% 3.42/3.65 tff(32227,plain,
% 3.42/3.65 (z = elem!1),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[343, 32226])).
% 3.42/3.65 tff(32228,plain,
% 3.42/3.65 (r(s(s(s(z))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[475, 32227, 24432])).
% 3.42/3.65 tff(32229,plain,
% 3.42/3.65 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[149, 32227, 32228])).
% 3.42/3.65 tff(32230,plain,
% 3.42/3.65 (b(elem!1, s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[327, 32227, 220])).
% 3.42/3.65 tff(32231,plain,
% 3.42/3.65 (elem!1 = z),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[364, 32227])).
% 3.42/3.65 tff(32232,plain,
% 3.42/3.65 (b(s(elem!1), z)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[20985, 32231, 19197])).
% 3.42/3.65 tff(32233,plain,
% 3.42/3.65 (b(s(elem!1), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[2488, 32232, 32227])).
% 3.42/3.65 tff(32234,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.42/3.65 inference(rewrite,[status(thm)],[])).
% 3.42/3.65 tff(32235,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.42/3.65 inference(quant_inst,[status(thm)],[])).
% 3.42/3.65 tff(32236,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32235, 32234])).
% 3.42/3.65 tff(32237,plain,
% 3.42/3.65 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32236, 271, 2618, 638])).
% 3.42/3.65 tff(32238,plain,
% 3.42/3.65 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32237, 1586])).
% 3.42/3.65 tff(32239,plain,
% 3.42/3.65 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1594, 21, 1591, 32238])).
% 3.42/3.65 tff(32240,plain,
% 3.42/3.65 (~b(elem!1, s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[3217, 271, 307, 2618, 638])).
% 3.42/3.65 tff(32241,plain,
% 3.42/3.65 (r(elem!1, s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[660, 21, 726, 32240])).
% 3.42/3.65 tff(32242,plain,
% 3.42/3.65 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[5899, 121, 139, 32241, 32239])).
% 3.42/3.65 tff(32243,plain,
% 3.42/3.65 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[20547, 271, 307, 2618])).
% 3.42/3.65 tff(32244,plain,
% 3.42/3.65 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32243, 1586])).
% 3.42/3.65 tff(32245,plain,
% 3.42/3.65 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[5877, 21, 32244])).
% 3.42/3.65 tff(32246,plain,
% 3.42/3.65 ($false),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32245, 32242, 5874])).
% 3.42/3.65 tff(32247,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (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)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.65 tff(32248,plain,
% 3.42/3.65 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32247, 32233, 32181, 32230, 32227, 1577, 32229])).
% 3.42/3.65 tff(32249,plain,
% 3.42/3.65 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[27354, 32232, 32127])).
% 3.42/3.65 tff(32250,plain,
% 3.42/3.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[14008, 32249])).
% 3.42/3.65 tff(32251,plain,
% 3.42/3.65 (b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1559, 32250, 32190])).
% 3.42/3.65 tff(32252,plain,
% 3.42/3.65 ($false),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1566, 32251, 32248, 32227])).
% 3.42/3.65 tff(32253,plain,(b(s(s(s(z))), s(z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | b(z, s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.65 tff(32254,plain,
% 3.42/3.65 (b(s(s(s(z))), s(z))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32253, 1209, 3871, 220, 906, 111, 6842, 68, 1, 31518])).
% 3.42/3.65 tff(32255,plain,
% 3.42/3.65 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[11676, 1140, 24432, 6842])).
% 3.42/3.65 tff(32256,plain,
% 3.42/3.65 (~b(s(s(s(elem!1))), s(z))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[30266, 19776, 3871, 222])).
% 3.42/3.65 tff(32257,plain,
% 3.42/3.65 (r(s(s(s(elem!1))), s(z))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[16580, 32256])).
% 3.42/3.65 tff(32258,plain,
% 3.42/3.65 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[6237, 21, 28366])).
% 3.42/3.65 tff(32259,plain,
% 3.42/3.65 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32258, 15822])).
% 3.42/3.65 tff(32260,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.42/3.65 inference(rewrite,[status(thm)],[])).
% 3.42/3.65 tff(32261,plain,
% 3.42/3.65 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.42/3.65 inference(rewrite,[status(thm)],[])).
% 3.42/3.65 tff(32262,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32261])).
% 3.42/3.65 tff(32263,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.42/3.65 inference(transitivity,[status(thm)],[32262, 32260])).
% 3.42/3.65 tff(32264,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 3.42/3.65 inference(quant_inst,[status(thm)],[])).
% 3.42/3.65 tff(32265,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32264, 32263])).
% 3.42/3.65 tff(32266,plain,
% 3.42/3.65 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32265, 271, 32259, 19776, 3871])).
% 3.42/3.65 tff(32267,plain,
% 3.42/3.65 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[760, 32266])).
% 3.42/3.65 tff(32268,plain,
% 3.42/3.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[13251, 121, 32267, 32257, 24452])).
% 3.42/3.65 tff(32269,plain,
% 3.42/3.65 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[681, 32268, 82])).
% 3.42/3.65 tff(32270,plain,
% 3.42/3.65 (~b(s(s(s(z))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[2114, 32269, 19776, 11211])).
% 3.42/3.65 tff(32271,plain,
% 3.42/3.65 (r(s(s(s(z))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1816, 32270, 24455])).
% 3.42/3.65 tff(32272,plain,
% 3.42/3.65 (~(s(elem!1) = s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[2035, 24455])).
% 3.42/3.65 tff(32273,plain,
% 3.42/3.65 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[13276, 121, 32267, 32257, 24452])).
% 3.42/3.65 tff(32274,plain,
% 3.42/3.65 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[2293, 21, 32273, 2280])).
% 3.42/3.65 tff(32275,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.42/3.65 inference(rewrite,[status(thm)],[])).
% 3.42/3.65 tff(32276,plain,
% 3.42/3.65 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~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(elem!1), s(s(s(z))))))),
% 3.42/3.65 inference(rewrite,[status(thm)],[])).
% 3.42/3.65 tff(32277,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32276])).
% 3.42/3.65 tff(32278,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.42/3.65 inference(transitivity,[status(thm)],[32277, 32275])).
% 3.42/3.65 tff(32279,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))))),
% 3.42/3.65 inference(quant_inst,[status(thm)],[])).
% 3.42/3.65 tff(32280,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z)))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32279, 32278])).
% 3.42/3.65 tff(32281,plain,
% 3.42/3.65 (~b(s(elem!1), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32280, 271, 19776, 32274, 32269])).
% 3.42/3.65 tff(32282,plain,
% 3.42/3.65 (r(s(elem!1), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[2044, 32281, 32272])).
% 3.42/3.65 tff(32283,plain,
% 3.42/3.65 (elem!1 = s(z)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[24630, 32282, 220, 1140, 222, 3871, 32259, 32257, 32270, 82, 1, 32267, 111, 10994, 348])).
% 3.42/3.65 tff(32284,plain,
% 3.42/3.65 (s(z) = elem!1),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[242, 32283])).
% 3.42/3.65 tff(32285,plain,
% 3.42/3.65 (~b(elem!1, s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1276, 32284, 24236])).
% 3.42/3.65 tff(32286,plain,
% 3.42/3.65 (b(z, elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[229, 32284, 220])).
% 3.42/3.65 tff(32287,plain,
% 3.42/3.65 (r(s(s(s(z))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[11532, 32284, 2207, 3871, 11211, 32286, 9149, 32285])).
% 3.42/3.65 tff(32288,plain,
% 3.42/3.65 (r(elem!1, s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[392, 32285, 219])).
% 3.42/3.65 tff(32289,plain,
% 3.42/3.65 ($false),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[19641, 32288, 32287, 24452, 32271])).
% 3.42/3.65 tff(32290,plain,((s(z) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | r(s(elem!1), z) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.65 tff(32291,plain,
% 3.42/3.65 (s(z) = s(elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32290, 10994, 220, 1140, 222, 79, 1, 111, 3871, 32255, 906])).
% 3.42/3.65 tff(32292,plain,
% 3.42/3.65 (s(s(z)) = s(s(elem!1))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32291])).
% 3.42/3.65 tff(32293,plain,
% 3.42/3.65 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32292])).
% 3.42/3.65 tff(32294,plain,
% 3.42/3.65 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32293])).
% 3.42/3.65 tff(32295,plain,
% 3.42/3.65 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32294])).
% 3.42/3.65 tff(32296,plain,
% 3.42/3.65 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 3.42/3.65 inference(symmetry,[status(thm)],[32295])).
% 3.42/3.65 tff(32297,plain,
% 3.42/3.65 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32296])).
% 3.42/3.65 tff(32298,plain,
% 3.42/3.65 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.65 inference(symmetry,[status(thm)],[32297])).
% 3.42/3.65 tff(32299,plain,
% 3.42/3.65 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32293])).
% 3.42/3.65 tff(32300,plain,
% 3.42/3.65 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.65 inference(transitivity,[status(thm)],[32299, 32298])).
% 3.42/3.65 tff(32301,plain,
% 3.42/3.65 (z = elem!1),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[343, 32291])).
% 3.42/3.65 tff(32302,plain,
% 3.42/3.65 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32301])).
% 3.42/3.65 tff(32303,plain,
% 3.42/3.65 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32302])).
% 3.42/3.65 tff(32304,plain,
% 3.42/3.65 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[711, 32303])).
% 3.42/3.65 tff(32305,plain,
% 3.42/3.65 (s(elem!1) = s(z)),
% 3.42/3.65 inference(symmetry,[status(thm)],[32291])).
% 3.42/3.65 tff(32306,plain,
% 3.42/3.65 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32305])).
% 3.42/3.65 tff(32307,plain,
% 3.42/3.65 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.65 inference(symmetry,[status(thm)],[32306])).
% 3.42/3.65 tff(32308,plain,
% 3.42/3.65 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32307])).
% 3.42/3.65 tff(32309,plain,
% 3.42/3.65 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[1677, 32308])).
% 3.42/3.65 tff(32310,plain,
% 3.42/3.65 (b(elem!1, s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[327, 32301, 220])).
% 3.42/3.65 tff(32311,plain,
% 3.42/3.65 (elem!1 = z),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[364, 32301])).
% 3.42/3.65 tff(32312,plain,
% 3.42/3.65 (b(s(z), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[9876, 32311, 3871])).
% 3.42/3.65 tff(32313,plain,
% 3.42/3.65 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[754, 32312, 32301])).
% 3.42/3.65 tff(32314,plain,
% 3.42/3.65 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32293])).
% 3.42/3.65 tff(32315,plain,
% 3.42/3.65 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32291])).
% 3.42/3.65 tff(32316,plain,
% 3.42/3.65 (b(s(s(s(z))), s(elem!1))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[222, 32315])).
% 3.42/3.65 tff(32317,plain,
% 3.42/3.65 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32316, 32314])).
% 3.42/3.65 tff(32318,plain,
% 3.42/3.65 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32301])).
% 3.42/3.65 tff(32319,plain,
% 3.42/3.65 (r(elem!1, s(s(s(elem!1))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[111, 32318])).
% 3.42/3.65 tff(32320,plain,
% 3.42/3.65 (~b(elem!1, s(s(elem!1)))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[3324, 2494, 394, 307])).
% 3.42/3.65 tff(32321,plain,
% 3.42/3.65 (r(elem!1, s(s(elem!1)))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[599, 32320, 68])).
% 3.42/3.65 tff(32322,plain,
% 3.42/3.65 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[5254, 2494, 638, 739])).
% 3.42/3.65 tff(32323,plain,
% 3.42/3.65 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[556, 32322, 1])).
% 3.42/3.65 tff(32324,plain,
% 3.42/3.65 ($false),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[17583, 32323, 32321, 6842, 727])).
% 3.42/3.65 tff(32325,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.65 tff(32326,plain,
% 3.42/3.65 (~b(s(s(elem!1)), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32325, 32319, 6842, 1, 68, 32317, 32313, 11211, 32310])).
% 3.42/3.65 tff(32327,plain,
% 3.42/3.65 (r(s(s(elem!1)), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[701, 32326, 3313])).
% 3.42/3.65 tff(32328,plain,
% 3.42/3.65 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32291])).
% 3.42/3.65 tff(32329,plain,
% 3.42/3.65 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.65 inference(transitivity,[status(thm)],[32328, 1927])).
% 3.42/3.65 tff(32330,plain,
% 3.42/3.65 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.65 inference(transitivity,[status(thm)],[32329, 10146])).
% 3.42/3.65 tff(32331,plain,
% 3.42/3.65 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32330])).
% 3.42/3.65 tff(32332,plain,
% 3.42/3.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[927, 32331])).
% 3.42/3.65 tff(32333,plain,
% 3.42/3.65 (r(s(s(s(z))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[475, 32301, 24432])).
% 3.42/3.65 tff(32334,plain,
% 3.42/3.65 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[149, 32301, 32333])).
% 3.42/3.65 tff(32335,plain,
% 3.42/3.65 (b(s(elem!1), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[2488, 32301, 11211])).
% 3.42/3.65 tff(32336,plain,
% 3.42/3.65 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32247, 32317, 32301, 32310, 32335, 1577, 32334])).
% 3.42/3.65 tff(32337,plain,
% 3.42/3.65 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1566, 32336, 32301])).
% 3.42/3.65 tff(32338,plain,
% 3.42/3.65 (r(s(s(s(s(z)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1559, 32337, 32332])).
% 3.42/3.65 tff(32339,plain,
% 3.42/3.65 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[10182, 32338, 32301])).
% 3.42/3.65 tff(32340,plain,
% 3.42/3.65 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32305, 32296])).
% 3.42/3.65 tff(32341,plain,
% 3.42/3.65 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.65 inference(symmetry,[status(thm)],[32340])).
% 3.42/3.65 tff(32342,plain,
% 3.42/3.65 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32341])).
% 3.42/3.65 tff(32343,plain,
% 3.42/3.65 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 3.42/3.65 inference(monotonicity,[status(thm)],[32291])).
% 3.42/3.65 tff(32344,plain,
% 3.42/3.65 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 3.42/3.65 inference(symmetry,[status(thm)],[32343])).
% 3.42/3.65 tff(32345,plain,
% 3.42/3.65 (b(s(z), elem!1)),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32335, 32344])).
% 3.42/3.65 tff(32346,plain,
% 3.42/3.65 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[5389, 5381, 307, 260])).
% 3.42/3.65 tff(32347,plain,
% 3.42/3.65 (r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[840, 32346, 9949])).
% 3.42/3.65 tff(32348,plain,
% 3.42/3.65 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[9962, 32347, 338])).
% 3.42/3.65 tff(32349,plain,
% 3.42/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.42/3.65 inference(rewrite,[status(thm)],[])).
% 3.42/3.65 tff(32350,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.42/3.65 inference(quant_inst,[status(thm)],[])).
% 3.42/3.65 tff(32351,plain,
% 3.42/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32350, 32349])).
% 3.42/3.65 tff(32352,plain,
% 3.42/3.65 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[32351, 121, 139, 727, 32348])).
% 3.42/3.65 tff(32353,plain,
% 3.42/3.65 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[6039, 32352, 9878])).
% 3.42/3.65 tff(32354,plain,
% 3.42/3.65 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[1733, 32353])).
% 3.42/3.65 tff(32355,plain,
% 3.42/3.65 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[32354, 19548])).
% 3.42/3.65 tff(32356,plain,
% 3.42/3.65 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 3.42/3.65 inference(monotonicity,[status(thm)],[31830, 9940])).
% 3.42/3.65 tff(32357,plain,
% 3.42/3.65 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.65 inference(symmetry,[status(thm)],[32356])).
% 3.42/3.65 tff(32358,plain,
% 3.42/3.65 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.65 inference(modus_ponens,[status(thm)],[5381, 32357])).
% 3.42/3.65 tff(32359,plain,
% 3.42/3.65 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[5389, 5381, 260, 307])).
% 3.42/3.65 tff(32360,plain,
% 3.42/3.65 (r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[840, 32359, 9949])).
% 3.42/3.65 tff(32361,plain,
% 3.42/3.65 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.42/3.65 inference(unit_resolution,[status(thm)],[9962, 32360, 338])).
% 3.42/3.65 tff(32362,plain,
% 3.42/3.65 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[31867, 121, 139, 727, 32361])).
% 3.42/3.66 tff(32363,plain,
% 3.42/3.66 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[7296, 32362, 9878])).
% 3.42/3.66 tff(32364,plain,
% 3.42/3.66 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[1494, 32363])).
% 3.42/3.66 tff(32365,plain,
% 3.42/3.66 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18038, 32364, 9878])).
% 3.42/3.66 tff(32366,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32367,plain,
% 3.42/3.66 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32368,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32367])).
% 3.42/3.66 tff(32369,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32368, 32366])).
% 3.42/3.66 tff(32370,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32371,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32370, 32369])).
% 3.42/3.66 tff(32372,plain,
% 3.42/3.66 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32371, 271, 739, 18990, 32365])).
% 3.42/3.66 tff(32373,plain,
% 3.42/3.66 ($false),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32372, 32358])).
% 3.42/3.66 tff(32374,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.66 tff(32375,plain,
% 3.42/3.66 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32374, 5381, 739, 338, 139, 727, 260, 307])).
% 3.42/3.66 tff(32376,plain,
% 3.42/3.66 ($false),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32375, 32355])).
% 3.42/3.66 tff(32377,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.66 tff(32378,plain,
% 3.42/3.66 (~b(s(z), s(s(s(s(s(z))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32377, 32291, 32334, 32319, 32313, 32345, 32310])).
% 3.42/3.66 tff(32379,plain,
% 3.42/3.66 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32378, 32342])).
% 3.42/3.66 tff(32380,plain,
% 3.42/3.66 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[814, 32301])).
% 3.42/3.66 tff(32381,plain,
% 3.42/3.66 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32380, 7608])).
% 3.42/3.66 tff(32382,plain,
% 3.42/3.66 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18925, 32381, 32379])).
% 3.42/3.66 tff(32383,plain,
% 3.42/3.66 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[20801])).
% 3.42/3.66 tff(32384,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32385,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32386,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(elem!1)))))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32385, 32384])).
% 3.42/3.66 tff(32387,plain,
% 3.42/3.66 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32386, 121, 6898, 7472, 18328])).
% 3.42/3.66 tff(32388,plain,
% 3.42/3.66 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32387, 32383])).
% 3.42/3.66 tff(32389,plain,
% 3.42/3.66 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[1777, 32388])).
% 3.42/3.66 tff(32390,plain,
% 3.42/3.66 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32389, 31915])).
% 3.42/3.66 tff(32391,plain,
% 3.42/3.66 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[9939, 9936])).
% 3.42/3.66 tff(32392,plain,
% 3.42/3.66 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32391])).
% 3.42/3.66 tff(32393,plain,
% 3.42/3.66 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[877, 32392])).
% 3.42/3.66 tff(32394,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32395,plain,
% 3.42/3.66 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32396,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32395])).
% 3.42/3.66 tff(32397,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32396, 32394])).
% 3.42/3.66 tff(32398,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32399,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32398, 32397])).
% 3.42/3.66 tff(32400,plain,
% 3.42/3.66 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32399, 121, 683, 6898, 18328])).
% 3.42/3.66 tff(32401,plain,
% 3.42/3.66 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 32400])).
% 3.42/3.66 tff(32402,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32403,plain,
% 3.42/3.66 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32404,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32403])).
% 3.42/3.66 tff(32405,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32404, 32402])).
% 3.42/3.66 tff(32406,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32407,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32406, 32405])).
% 3.42/3.66 tff(32408,plain,
% 3.42/3.66 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32407, 121, 683, 6898, 18328])).
% 3.42/3.66 tff(32409,plain,
% 3.42/3.66 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18082, 32408, 18648])).
% 3.42/3.66 tff(32410,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32411,plain,
% 3.42/3.66 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32412,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32411])).
% 3.42/3.66 tff(32413,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32412, 32410])).
% 3.42/3.66 tff(32414,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32415,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32414, 32413])).
% 3.42/3.66 tff(32416,plain,
% 3.42/3.66 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32415, 121, 683, 7472, 18328])).
% 3.42/3.66 tff(32417,plain,
% 3.42/3.66 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18291, 32416, 18289])).
% 3.42/3.66 tff(32418,plain,
% 3.42/3.66 ($false),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18552, 271, 32417, 32409, 32401, 7564])).
% 3.42/3.66 tff(32419,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.66 tff(32420,plain,
% 3.42/3.66 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32419, 18328, 5951, 32393, 683, 7472, 6898])).
% 3.42/3.66 tff(32421,plain,
% 3.42/3.66 ($false),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32420, 32390])).
% 3.42/3.66 tff(32422,plain,((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.66 tff(32423,plain,
% 3.42/3.66 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32422, 32382, 32339, 32291, 5834, 32327])).
% 3.42/3.66 tff(32424,plain,
% 3.42/3.66 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18190, 32423, 32301])).
% 3.42/3.66 tff(32425,plain,
% 3.42/3.66 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[4138, 32424, 32309])).
% 3.42/3.66 tff(32426,plain,
% 3.42/3.66 (~b(s(s(s(s(s(z))))), z)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[24620, 32425, 220, 11211])).
% 3.42/3.66 tff(32427,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 3.42/3.66 tff(32428,plain,
% 3.42/3.66 ($false),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32427, 31847])).
% 3.42/3.66 tff(32429,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.66 tff(32430,plain,
% 3.42/3.66 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32429, 32426, 32301])).
% 3.42/3.66 tff(32431,plain,
% 3.42/3.66 (r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[840, 32430, 32304])).
% 3.42/3.66 tff(32432,plain,
% 3.42/3.66 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[9962, 32431, 32291])).
% 3.42/3.66 tff(32433,plain,
% 3.42/3.66 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32351, 121, 32334, 32319, 32432])).
% 3.42/3.66 tff(32434,plain,
% 3.42/3.66 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[6039, 32433, 32301])).
% 3.42/3.66 tff(32435,plain,
% 3.42/3.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[1733, 32434])).
% 3.42/3.66 tff(32436,plain,
% 3.42/3.66 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32435, 32300])).
% 3.42/3.66 tff(32437,plain,
% 3.42/3.66 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[9896, 32425, 32301])).
% 3.42/3.66 tff(32438,plain,
% 3.42/3.66 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[18992, 32437, 32317, 32313])).
% 3.42/3.66 tff(32439,plain,
% 3.42/3.66 ($false),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32438, 32436])).
% 3.42/3.66 tff(32440,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.66 tff(32441,plain,
% 3.42/3.66 (r(s(elem!1), z)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32440, 32254, 6842, 1, 68, 111, 220, 3871, 6533, 906])).
% 3.42/3.66 tff(32442,plain,
% 3.42/3.66 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[6215, 121, 111, 32441, 6842])).
% 3.42/3.66 tff(32443,plain,
% 3.42/3.66 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[7238, 121, 111, 32441, 6842])).
% 3.42/3.66 tff(32444,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32445,plain,
% 3.42/3.66 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32446,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32445])).
% 3.42/3.66 tff(32447,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32446, 32444])).
% 3.42/3.66 tff(32448,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32449,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32448, 32447])).
% 3.42/3.66 tff(32450,plain,
% 3.42/3.66 (~r(s(s(s(z))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32449, 121, 111, 412, 24432])).
% 3.42/3.66 tff(32451,plain,
% 3.42/3.66 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[2293, 21, 11148, 85])).
% 3.42/3.66 tff(32452,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32453,plain,
% 3.42/3.66 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.42/3.66 inference(rewrite,[status(thm)],[])).
% 3.42/3.66 tff(32454,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32453])).
% 3.42/3.66 tff(32455,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32454, 32452])).
% 3.42/3.66 tff(32456,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~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))))),
% 3.42/3.66 inference(quant_inst,[status(thm)],[])).
% 3.42/3.66 tff(32457,plain,
% 3.42/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32456, 32455])).
% 3.42/3.66 tff(32458,plain,
% 3.42/3.66 (~b(s(s(s(z))), s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[32457, 271, 32259, 19776, 32451])).
% 3.42/3.66 tff(32459,plain,
% 3.42/3.66 (s(s(s(z))) = s(elem!1)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[1816, 32458, 32450])).
% 3.42/3.66 tff(32460,plain,
% 3.42/3.66 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[2596, 32459])).
% 3.42/3.66 tff(32461,plain,
% 3.42/3.66 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32459])).
% 3.42/3.66 tff(32462,plain,
% 3.42/3.66 (s(s(z)) = elem!1),
% 3.42/3.66 inference(transitivity,[status(thm)],[92, 32461, 70])).
% 3.42/3.66 tff(32463,plain,
% 3.42/3.66 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32462])).
% 3.42/3.66 tff(32464,plain,
% 3.42/3.66 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 3.42/3.66 inference(transitivity,[status(thm)],[32463, 238])).
% 3.42/3.66 tff(32465,plain,
% 3.42/3.66 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 3.42/3.66 inference(transitivity,[status(thm)],[32464, 1218])).
% 3.42/3.66 tff(32466,plain,
% 3.42/3.66 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32465])).
% 3.42/3.66 tff(32467,plain,
% 3.42/3.66 (~(elem!1 = s(z))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[3595, 32466])).
% 3.42/3.66 tff(32468,plain,
% 3.42/3.66 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32459])).
% 3.42/3.66 tff(32469,plain,
% 3.42/3.66 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32468])).
% 3.42/3.66 tff(32470,plain,
% 3.42/3.66 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 3.42/3.66 inference(symmetry,[status(thm)],[32469])).
% 3.42/3.66 tff(32471,plain,
% 3.42/3.66 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32468])).
% 3.42/3.66 tff(32472,plain,
% 3.42/3.66 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32471])).
% 3.42/3.66 tff(32473,plain,
% 3.42/3.66 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32468])).
% 3.42/3.66 tff(32474,plain,
% 3.42/3.66 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 3.42/3.66 inference(monotonicity,[status(thm)],[32473])).
% 3.42/3.66 tff(32475,plain,
% 3.42/3.66 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 3.42/3.66 inference(symmetry,[status(thm)],[32474])).
% 3.42/3.66 tff(32476,plain,
% 3.42/3.66 (r(z, s(s(s(s(s(z))))))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[111, 32475])).
% 3.42/3.66 tff(32477,plain,
% 3.42/3.66 (~b(s(s(s(s(z)))), s(z))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[30408, 32476, 19197, 3871, 220, 222])).
% 3.42/3.66 tff(32478,plain,
% 3.42/3.66 (~b(s(s(elem!1)), s(z))),
% 3.42/3.66 inference(modus_ponens,[status(thm)],[32477, 32472])).
% 3.42/3.66 tff(32479,plain,
% 3.42/3.66 (r(s(s(elem!1)), s(z))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 32478])).
% 3.42/3.66 tff(32480,plain,
% 3.42/3.66 (~b(z, s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[16218, 32459, 1209])).
% 3.42/3.66 tff(32481,plain,
% 3.42/3.66 (r(z, s(elem!1))),
% 3.42/3.66 inference(unit_resolution,[status(thm)],[1439, 32480])).
% 3.42/3.66 tff(32482,plain,
% 3.42/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32483,plain,
% 3.42/3.67 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32484,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32483])).
% 3.42/3.67 tff(32485,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32484, 32482])).
% 3.42/3.67 tff(32486,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.42/3.67 inference(quant_inst,[status(thm)],[])).
% 3.42/3.67 tff(32487,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32486, 32485])).
% 3.42/3.67 tff(32488,plain,
% 3.42/3.67 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32487, 121, 32267, 32479, 32257])).
% 3.42/3.67 tff(32489,plain,
% 3.42/3.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[586, 32488, 563])).
% 3.42/3.67 tff(32490,plain,
% 3.42/3.67 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[681, 676, 79])).
% 3.42/3.67 tff(32491,plain,
% 3.42/3.67 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2881, 121, 32267, 32479, 32257])).
% 3.42/3.67 tff(32492,plain,
% 3.42/3.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[556, 32491, 1])).
% 3.42/3.67 tff(32493,plain,
% 3.42/3.67 (~b(s(elem!1), s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[1459, 32492, 32490, 32489])).
% 3.42/3.67 tff(32494,plain,
% 3.42/3.67 (r(s(elem!1), s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[526, 32493, 211])).
% 3.42/3.67 tff(32495,plain,
% 3.42/3.67 (~r(z, s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[17708, 32494, 32481, 32479])).
% 3.42/3.67 tff(32496,plain,
% 3.42/3.67 (b(z, s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2106, 32495])).
% 3.42/3.67 tff(32497,plain,
% 3.42/3.67 (b(z, s(s(s(s(z)))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32496, 32470])).
% 3.42/3.67 tff(32498,plain,
% 3.42/3.67 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32468])).
% 3.42/3.67 tff(32499,plain,
% 3.42/3.67 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.67 inference(symmetry,[status(thm)],[32498])).
% 3.42/3.67 tff(32500,plain,
% 3.42/3.67 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32473])).
% 3.42/3.67 tff(32501,plain,
% 3.42/3.67 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.42/3.67 inference(symmetry,[status(thm)],[32500])).
% 3.42/3.67 tff(32502,plain,
% 3.42/3.67 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32501, 32499])).
% 3.42/3.67 tff(32503,plain,
% 3.42/3.67 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32492, 32502])).
% 3.42/3.67 tff(32504,plain,
% 3.42/3.67 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32468])).
% 3.42/3.67 tff(32505,plain,
% 3.42/3.67 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 3.42/3.67 inference(symmetry,[status(thm)],[32504])).
% 3.42/3.67 tff(32506,plain,
% 3.42/3.67 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32505])).
% 3.42/3.67 tff(32507,plain,
% 3.42/3.67 (~(elem!1 = s(s(s(s(z)))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[68, 32506])).
% 3.42/3.67 tff(32508,plain,
% 3.42/3.67 (r(s(s(s(s(z)))), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[932, 32477])).
% 3.42/3.67 tff(32509,plain,
% 3.42/3.67 (~b(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[11002, 1326, 220, 3871])).
% 3.42/3.67 tff(32510,plain,
% 3.42/3.67 (r(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[299, 32509, 258])).
% 3.42/3.67 tff(32511,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32512,plain,
% 3.42/3.67 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32513,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32512])).
% 3.42/3.67 tff(32514,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32513, 32511])).
% 3.42/3.67 tff(32515,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 3.42/3.67 inference(quant_inst,[status(thm)],[])).
% 3.42/3.67 tff(32516,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32515, 32514])).
% 3.42/3.67 tff(32517,plain,
% 3.42/3.67 ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32516, 271])).
% 3.42/3.67 tff(32518,plain,
% 3.42/3.67 (~b(elem!1, s(s(s(s(z)))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32517, 1326, 6068, 1157])).
% 3.42/3.67 tff(32519,plain,
% 3.42/3.67 (r(elem!1, s(s(s(s(z)))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[20539, 32518, 20532])).
% 3.42/3.67 tff(32520,plain,
% 3.42/3.67 ($false),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[21233, 32519, 32510, 572, 911])).
% 3.42/3.67 tff(32521,plain,((~b(z, elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(z))))) | (elem!1 = s(z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.67 tff(32522,plain,
% 3.42/3.67 (~b(z, elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32521, 32267, 32508, 32507, 32467, 32503, 32497, 220, 3871])).
% 3.42/3.67 tff(32523,plain,
% 3.42/3.67 (r(z, elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[355, 32522, 9297])).
% 3.42/3.67 tff(32524,plain,
% 3.42/3.67 (b(elem!1, s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[22265, 32523, 412, 24432, 32467, 1209, 3871, 348, 219])).
% 3.42/3.67 tff(32525,plain,
% 3.42/3.67 (~b(s(s(s(elem!1))), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[11152, 32524, 676, 11148, 79])).
% 3.42/3.67 tff(32526,plain,
% 3.42/3.67 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[486, 32525, 32460])).
% 3.42/3.67 tff(32527,plain,
% 3.42/3.67 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32459])).
% 3.42/3.67 tff(32528,plain,
% 3.42/3.67 (b(s(elem!1), s(z))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[222, 32527])).
% 3.42/3.67 tff(32529,plain,
% 3.42/3.67 (b(s(z), s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[4929, 32459, 3871])).
% 3.42/3.67 tff(32530,plain,
% 3.42/3.67 (~b(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[456, 32524, 32529, 32528])).
% 3.42/3.67 tff(32531,plain,
% 3.42/3.67 (r(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[299, 32530, 32467])).
% 3.42/3.67 tff(32532,plain,
% 3.42/3.67 ($false),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[22268, 32531, 32526, 32257, 32267])).
% 3.42/3.67 tff(32533,plain,((s(z) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | (~r(s(elem!1), z)) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.67 tff(32534,plain,
% 3.42/3.67 (s(z) = s(elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32533, 32443, 32442, 32441, 1209, 3871, 220, 1, 32254, 111, 68, 31545, 906])).
% 3.42/3.67 tff(32535,plain,
% 3.42/3.67 (r(s(z), z) <=> r(s(elem!1), z)),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32534])).
% 3.42/3.67 tff(32536,plain,
% 3.42/3.67 (r(s(elem!1), z) <=> r(s(z), z)),
% 3.42/3.67 inference(symmetry,[status(thm)],[32535])).
% 3.42/3.67 tff(32537,plain,
% 3.42/3.67 (r(s(z), z)),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32441, 32536])).
% 3.42/3.67 tff(32538,plain,
% 3.42/3.67 ($false),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[31518, 32537])).
% 3.42/3.67 tff(32539,plain,(b(z, s(s(s(z)))) | r(s(z), z) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.67 tff(32540,plain,
% 3.42/3.67 (elem!1 = s(s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32539, 31544, 3871, 220, 1, 111, 31518, 906, 20245])).
% 3.42/3.67 tff(32541,plain,
% 3.42/3.67 (s(elem!1) = s(s(s(elem!1)))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32540])).
% 3.42/3.67 tff(32542,plain,
% 3.42/3.67 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32541])).
% 3.42/3.67 tff(32543,plain,
% 3.42/3.67 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32542, 935])).
% 3.42/3.67 tff(32544,plain,
% 3.42/3.67 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32543])).
% 3.42/3.67 tff(32545,plain,
% 3.42/3.67 (~(s(s(s(z))) = elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[3906, 32540])).
% 3.42/3.67 tff(32546,plain,
% 3.42/3.67 (~(elem!1 = s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[1100, 32545])).
% 3.42/3.67 tff(32547,plain,
% 3.42/3.67 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[1516, 32546])).
% 3.42/3.67 tff(32548,plain,
% 3.42/3.67 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[17419, 32547])).
% 3.42/3.67 tff(32549,plain,
% 3.42/3.67 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32548, 32544])).
% 3.42/3.67 tff(32550,plain,
% 3.42/3.67 (~b(s(elem!1), z)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[12308, 32540, 8226])).
% 3.42/3.67 tff(32551,plain,
% 3.42/3.67 (~(elem!1 = z)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[20985, 32550, 19197])).
% 3.42/3.67 tff(32552,plain,
% 3.42/3.67 (~(z = elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[364, 32551])).
% 3.42/3.67 tff(32553,plain,
% 3.42/3.67 (~(s(z) = s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[343, 32552])).
% 3.42/3.67 tff(32554,plain,
% 3.42/3.67 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2063, 32553])).
% 3.42/3.67 tff(32555,plain,
% 3.42/3.67 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2071, 32554, 906])).
% 3.42/3.67 tff(32556,plain,
% 3.42/3.67 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[11663, 32554])).
% 3.42/3.67 tff(32557,plain,
% 3.42/3.67 (r(z, s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[1214, 31544])).
% 3.42/3.67 tff(32558,plain,
% 3.42/3.67 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[11676, 32557, 24432, 20245])).
% 3.42/3.67 tff(32559,plain,
% 3.42/3.67 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[6237, 21, 32558, 32556])).
% 3.42/3.67 tff(32560,plain,
% 3.42/3.67 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32265, 271, 32559, 32555, 3871])).
% 3.42/3.67 tff(32561,plain,
% 3.42/3.67 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[760, 32560])).
% 3.42/3.67 tff(32562,plain,
% 3.42/3.67 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32540])).
% 3.42/3.67 tff(32563,plain,
% 3.42/3.67 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 3.42/3.67 inference(symmetry,[status(thm)],[32562])).
% 3.42/3.67 tff(32564,plain,
% 3.42/3.67 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32563, 1218])).
% 3.42/3.67 tff(32565,plain,
% 3.42/3.67 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32564])).
% 3.42/3.67 tff(32566,plain,
% 3.42/3.67 (~(elem!1 = s(z))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[2137, 32565])).
% 3.42/3.67 tff(32567,plain,
% 3.42/3.67 (~(s(s(s(z))) = s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[3917, 32553, 32540])).
% 3.42/3.67 tff(32568,plain,
% 3.42/3.67 (~(s(elem!1) = s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2035, 32567])).
% 3.42/3.67 tff(32569,plain,
% 3.42/3.67 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32541])).
% 3.42/3.67 tff(32570,plain,
% 3.42/3.67 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 3.42/3.67 inference(symmetry,[status(thm)],[32569])).
% 3.42/3.67 tff(32571,plain,
% 3.42/3.67 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32570])).
% 3.42/3.67 tff(32572,plain,
% 3.42/3.67 (~r(s(elem!1), s(s(s(z))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32558, 32571])).
% 3.42/3.67 tff(32573,plain,
% 3.42/3.67 (b(s(elem!1), s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2044, 32572, 32568])).
% 3.42/3.67 tff(32574,plain,
% 3.42/3.67 (r(s(elem!1), z)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[409, 32550])).
% 3.42/3.67 tff(32575,plain,
% 3.42/3.67 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32541])).
% 3.42/3.67 tff(32576,plain,
% 3.42/3.67 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32575])).
% 3.42/3.67 tff(32577,plain,
% 3.42/3.67 (~b(s(elem!1), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[7781, 32573, 32555, 3871])).
% 3.42/3.67 tff(32578,plain,
% 3.42/3.67 (~b(s(s(s(elem!1))), s(z))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32577, 32576])).
% 3.42/3.67 tff(32579,plain,
% 3.42/3.67 (r(s(s(s(elem!1))), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[66, 21, 32578, 63])).
% 3.42/3.67 tff(32580,plain,
% 3.42/3.67 (~r(z, elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[22265, 317, 412, 24356, 12075, 1209, 3871, 22132, 377])).
% 3.42/3.67 tff(32581,plain,
% 3.42/3.67 (b(z, elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[355, 32580, 365])).
% 3.42/3.67 tff(32582,plain,
% 3.42/3.67 (~b(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[11002, 32581, 220, 3871])).
% 3.42/3.67 tff(32583,plain,
% 3.42/3.67 (~b(s(s(elem!1)), s(z))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32582, 12397])).
% 3.42/3.67 tff(32584,plain,
% 3.42/3.67 (r(s(s(elem!1)), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 32583])).
% 3.42/3.67 tff(32585,plain,
% 3.42/3.67 (b(elem!1, z)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[284, 32076, 259])).
% 3.42/3.67 tff(32586,plain,
% 3.42/3.67 (~b(s(z), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[3964, 32585, 1281, 32581])).
% 3.42/3.67 tff(32587,plain,
% 3.42/3.67 (r(s(z), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[236, 32586, 12077])).
% 3.42/3.67 tff(32588,plain,
% 3.42/3.67 (r(s(z), s(s(elem!1)))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32587, 12386])).
% 3.42/3.67 tff(32589,plain,
% 3.42/3.67 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[3502, 12281])).
% 3.42/3.67 tff(32590,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32591,plain,
% 3.42/3.67 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32592,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32591])).
% 3.42/3.67 tff(32593,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32592, 32590])).
% 3.42/3.67 tff(32594,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.42/3.67 inference(quant_inst,[status(thm)],[])).
% 3.42/3.67 tff(32595,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32594, 32593])).
% 3.42/3.67 tff(32596,plain,
% 3.42/3.67 ($false),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32595, 121, 32589, 32588, 32584, 12761])).
% 3.42/3.67 tff(32597,plain,(b(elem!1, s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (elem!1 = z) | (~r(s(elem!1), z)) | b(z, s(s(s(z)))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.67 tff(32598,plain,
% 3.42/3.67 (b(elem!1, s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32597, 32579, 32540, 19197, 220, 3871, 32551, 32574, 31544, 219])).
% 3.42/3.67 tff(32599,plain,
% 3.42/3.67 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32541])).
% 3.42/3.67 tff(32600,plain,
% 3.42/3.67 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 3.42/3.67 inference(symmetry,[status(thm)],[32599])).
% 3.42/3.67 tff(32601,plain,
% 3.42/3.67 (r(z, s(elem!1))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[111, 32600])).
% 3.42/3.67 tff(32602,plain,
% 3.42/3.67 (~(s(s(s(z))) = s(elem!1))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[3917, 22132, 2470])).
% 3.42/3.67 tff(32603,plain,
% 3.42/3.67 (~r(elem!1, s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[6723, 145, 1140, 378])).
% 3.42/3.67 tff(32604,plain,
% 3.42/3.67 (b(elem!1, s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[1192, 32603, 12183])).
% 3.42/3.67 tff(32605,plain,
% 3.42/3.67 (~b(s(s(s(z))), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[10690, 32604, 3870, 307])).
% 3.42/3.67 tff(32606,plain,
% 3.42/3.67 (r(s(s(s(z))), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2325, 32605])).
% 3.42/3.67 tff(32607,plain,
% 3.42/3.67 (b(s(s(elem!1)), s(s(s(z))))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[5482, 32604, 2470])).
% 3.42/3.67 tff(32608,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32609,plain,
% 3.42/3.67 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.42/3.67 inference(rewrite,[status(thm)],[])).
% 3.42/3.67 tff(32610,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 3.42/3.67 inference(monotonicity,[status(thm)],[32609])).
% 3.42/3.67 tff(32611,plain,
% 3.42/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.42/3.67 inference(transitivity,[status(thm)],[32610, 32608])).
% 3.42/3.67 tff(32612,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))),
% 3.42/3.67 inference(quant_inst,[status(thm)],[])).
% 3.42/3.67 tff(32613,plain,
% 3.42/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 3.42/3.67 inference(modus_ponens,[status(thm)],[32612, 32611])).
% 3.42/3.67 tff(32614,plain,
% 3.42/3.67 (~b(s(z), s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32613, 271, 2073, 3871, 32607])).
% 3.42/3.67 tff(32615,plain,
% 3.42/3.67 (r(s(z), s(s(elem!1)))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2167, 32614])).
% 3.42/3.67 tff(32616,plain,
% 3.42/3.67 (~b(s(s(elem!1)), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[13672, 271, 2073, 3871, 32607])).
% 3.42/3.67 tff(32617,plain,
% 3.42/3.67 (r(s(s(elem!1)), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2143, 32616])).
% 3.42/3.67 tff(32618,plain,
% 3.42/3.67 (r(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[12129, 32617, 2470])).
% 3.42/3.67 tff(32619,plain,
% 3.42/3.67 ($false),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[12518, 32618, 32615, 32606, 145])).
% 3.42/3.67 tff(32620,plain,((~r(s(s(s(z))), elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.67 tff(32621,plain,
% 3.42/3.67 (~r(s(s(s(z))), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[32620, 378, 2073, 3871, 3870, 307, 1140, 2470])).
% 3.42/3.67 tff(32622,plain,
% 3.42/3.67 (b(s(s(s(z))), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[255, 32621, 3907])).
% 3.42/3.67 tff(32623,plain,
% 3.42/3.67 (~b(s(elem!1), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[13140, 32622, 412, 32602, 307, 1140])).
% 3.42/3.67 tff(32624,plain,
% 3.42/3.67 (r(s(elem!1), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[2243, 32623, 2564])).
% 3.42/3.67 tff(32625,plain,
% 3.42/3.67 (~r(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[5343, 32624, 412, 378])).
% 3.42/3.67 tff(32626,plain,
% 3.42/3.67 (~b(s(z), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[24003, 32622, 3871, 307])).
% 3.42/3.67 tff(32627,plain,
% 3.42/3.67 (r(s(z), elem!1)),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[236, 32626, 12077])).
% 3.42/3.67 tff(32628,plain,
% 3.42/3.67 (~b(s(elem!1), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[7781, 3870, 2073, 3871])).
% 3.42/3.67 tff(32629,plain,
% 3.42/3.67 (r(s(elem!1), s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[429, 32628, 22133])).
% 3.42/3.67 tff(32630,plain,
% 3.42/3.67 (~b(elem!1, s(z))),
% 3.42/3.67 inference(unit_resolution,[status(thm)],[25779, 32624, 1281, 1441, 259, 32629, 378, 32627])).
% 3.42/3.67 tff(32631,plain,
% 3.42/3.68 ($false),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[299, 32630, 32625, 12075])).
% 3.42/3.68 tff(32632,plain,((~r(z, elem!1)) | (~b(s(z), z)) | (~r(z, s(elem!1))) | (elem!1 = z) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.68 tff(32633,plain,
% 3.42/3.68 (~r(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32632, 32601, 19197, 32551, 32574, 2207, 32598, 32557, 3871, 32555, 32573, 32540])).
% 3.42/3.68 tff(32634,plain,
% 3.42/3.68 (b(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[355, 32633, 32552])).
% 3.42/3.68 tff(32635,plain,
% 3.42/3.68 (~b(elem!1, s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[11002, 32634, 220, 3871])).
% 3.42/3.68 tff(32636,plain,
% 3.42/3.68 (~b(s(z), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[20382, 32634, 19197, 32598])).
% 3.42/3.68 tff(32637,plain,
% 3.42/3.68 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32540])).
% 3.42/3.68 tff(32638,plain,
% 3.42/3.68 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 3.42/3.68 inference(symmetry,[status(thm)],[32637])).
% 3.42/3.68 tff(32639,plain,
% 3.42/3.68 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32541])).
% 3.42/3.68 tff(32640,plain,
% 3.42/3.68 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.42/3.68 inference(symmetry,[status(thm)],[32639])).
% 3.42/3.68 tff(32641,plain,
% 3.42/3.68 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 3.42/3.68 inference(transitivity,[status(thm)],[32640, 32638])).
% 3.42/3.68 tff(32642,plain,
% 3.42/3.68 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32540])).
% 3.42/3.68 tff(32643,plain,
% 3.42/3.68 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32642])).
% 3.42/3.68 tff(32644,plain,
% 3.42/3.68 (~b(s(s(elem!1)), s(z))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32635, 32643])).
% 3.42/3.68 tff(32645,plain,
% 3.42/3.68 (r(s(s(elem!1)), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2141, 21, 2138, 32644])).
% 3.42/3.68 tff(32646,plain,
% 3.42/3.68 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32540])).
% 3.42/3.68 tff(32647,plain,
% 3.42/3.68 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32563])).
% 3.42/3.68 tff(32648,plain,
% 3.42/3.68 (~(s(z) = elem!1)),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[2137, 32647])).
% 3.42/3.68 tff(32649,plain,
% 3.42/3.68 (r(s(z), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[236, 32636, 32648])).
% 3.42/3.68 tff(32650,plain,
% 3.42/3.68 (r(s(z), s(s(elem!1)))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32649, 32646])).
% 3.42/3.68 tff(32651,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32652,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32653,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32652, 32651])).
% 3.42/3.68 tff(32654,plain,
% 3.42/3.68 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32653, 121, 32650, 32645, 32579])).
% 3.42/3.68 tff(32655,plain,
% 3.42/3.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[586, 32654, 563])).
% 3.42/3.68 tff(32656,plain,
% 3.42/3.68 (b(s(elem!1), elem!1)),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32655, 32641])).
% 3.42/3.68 tff(32657,plain,
% 3.42/3.68 (~b(s(s(s(z))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[13140, 32656, 32574, 32567, 32598, 32557])).
% 3.42/3.68 tff(32658,plain,
% 3.42/3.68 (r(s(s(s(z))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[255, 32657, 32545])).
% 3.42/3.68 tff(32659,plain,
% 3.42/3.68 (~r(s(s(s(z))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[23319, 32658, 32636, 32635, 32566])).
% 3.42/3.68 tff(32660,plain,
% 3.42/3.68 (b(s(s(s(z))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2325, 32659])).
% 3.42/3.68 tff(32661,plain,
% 3.42/3.68 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[6358, 32567, 32540])).
% 3.42/3.68 tff(32662,plain,
% 3.42/3.68 (~r(z, s(s(s(s(s(z))))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[30408, 937, 1281, 3871, 220, 222])).
% 3.42/3.68 tff(32663,plain,
% 3.42/3.68 (b(z, s(s(s(s(s(z))))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1658, 32662])).
% 3.42/3.68 tff(32664,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32665,plain,
% 3.42/3.68 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32666,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32665])).
% 3.42/3.68 tff(32667,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 3.42/3.68 inference(transitivity,[status(thm)],[32666, 32664])).
% 3.42/3.68 tff(32668,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32669,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32668, 32667])).
% 3.42/3.68 tff(32670,plain,
% 3.42/3.68 ($false),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32669, 271, 307, 1326, 831, 1639])).
% 3.42/3.68 tff(32671,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.68 tff(32672,plain,
% 3.42/3.68 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32671, 32663, 307, 1326])).
% 3.42/3.68 tff(32673,plain,
% 3.42/3.68 (r(s(z), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[236, 27263, 12077])).
% 3.42/3.68 tff(32674,plain,
% 3.42/3.68 (r(s(z), s(s(elem!1)))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32673, 12386])).
% 3.42/3.68 tff(32675,plain,
% 3.42/3.68 (r(elem!1, s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[299, 32509, 12075])).
% 3.42/3.68 tff(32676,plain,
% 3.42/3.68 (~b(s(s(s(s(s(z))))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[28683, 937, 1140, 2470, 4132, 12761, 572, 24356, 3871, 222])).
% 3.42/3.68 tff(32677,plain,
% 3.42/3.68 (r(s(s(s(s(s(z))))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1682, 32676])).
% 3.42/3.68 tff(32678,plain,
% 3.42/3.68 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[25896, 32677, 32675, 32674])).
% 3.42/3.68 tff(32679,plain,
% 3.42/3.68 ($false),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[840, 32678, 32672, 17421])).
% 3.42/3.68 tff(32680,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(z, s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.68 tff(32681,plain,
% 3.42/3.68 (~b(s(s(s(s(z)))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32680, 32598, 32634, 32557, 32540, 32661, 32579, 32561, 3871, 32660, 19197, 220])).
% 3.42/3.68 tff(32682,plain,
% 3.42/3.68 (r(s(s(s(s(z)))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[932, 32681])).
% 3.42/3.68 tff(32683,plain,
% 3.42/3.68 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[26847, 32682, 32561, 20245])).
% 3.42/3.68 tff(32684,plain,
% 3.42/3.68 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1000, 21, 32683, 32549])).
% 3.42/3.68 tff(32685,plain,
% 3.42/3.68 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[12592, 121, 32650, 32645, 32682])).
% 3.42/3.68 tff(32686,plain,
% 3.42/3.68 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[12235, 32554, 32540])).
% 3.42/3.68 tff(32687,plain,
% 3.42/3.68 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[12253, 21, 32686, 32685])).
% 3.42/3.68 tff(32688,plain,
% 3.42/3.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2479, 32598, 32540])).
% 3.42/3.68 tff(32689,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32690,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32691,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32690, 32689])).
% 3.42/3.68 tff(32692,plain,
% 3.42/3.68 ($false),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32691, 271, 32688, 32655, 32687, 32684])).
% 3.42/3.68 tff(32693,plain,(b(s(s(s(elem!1))), z) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.68 tff(32694,plain,
% 3.42/3.68 (b(s(s(s(elem!1))), z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32693, 20246, 220, 26317, 906, 1, 31518])).
% 3.42/3.68 tff(32695,plain,
% 3.42/3.68 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24396, 271, 19197, 220, 32694])).
% 3.42/3.68 tff(32696,plain,
% 3.42/3.68 (~(elem!1 = z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[9876, 32695, 20246])).
% 3.42/3.68 tff(32697,plain,
% 3.42/3.68 (~(z = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[364, 32696])).
% 3.42/3.68 tff(32698,plain,
% 3.42/3.68 (~(s(z) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[343, 32697])).
% 3.42/3.68 tff(32699,plain,
% 3.42/3.68 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2063, 32698])).
% 3.42/3.68 tff(32700,plain,
% 3.42/3.68 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2071, 32699, 906])).
% 3.42/3.68 tff(32701,plain,
% 3.42/3.68 (~b(z, s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[19817, 32700, 19197, 20246])).
% 3.42/3.68 tff(32702,plain,
% 3.42/3.68 (~b(s(s(s(s(z)))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24371, 20246, 26317, 19197, 220])).
% 3.42/3.68 tff(32703,plain,
% 3.42/3.68 (r(s(s(s(s(z)))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[932, 32702])).
% 3.42/3.68 tff(32704,plain,
% 3.42/3.68 (~b(s(s(s(elem!1))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24388, 271, 19197, 220, 32694])).
% 3.42/3.68 tff(32705,plain,
% 3.42/3.68 (r(s(s(s(elem!1))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[16580, 32704])).
% 3.42/3.68 tff(32706,plain,
% 3.42/3.68 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[760, 32695])).
% 3.42/3.68 tff(32707,plain,
% 3.42/3.68 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[28695, 121, 32706, 32705, 32703])).
% 3.42/3.68 tff(32708,plain,
% 3.42/3.68 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[28688, 121, 32706, 32705, 32703])).
% 3.42/3.68 tff(32709,plain,
% 3.42/3.68 (r(z, s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1214, 32701])).
% 3.42/3.68 tff(32710,plain,
% 3.42/3.68 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[25036, 32694, 220, 32709, 32700, 32708, 32707])).
% 3.42/3.68 tff(32711,plain,
% 3.42/3.68 (s(s(s(z))) = s(s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[946, 32710])).
% 3.42/3.68 tff(32712,plain,
% 3.42/3.68 (s(s(z)) = s(elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[953, 32711])).
% 3.42/3.68 tff(32713,plain,
% 3.42/3.68 (s(z) = elem!1),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[960, 32712])).
% 3.42/3.68 tff(32714,plain,
% 3.42/3.68 (b(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[229, 32713, 220])).
% 3.42/3.68 tff(32715,plain,
% 3.42/3.68 (~(s(s(s(z))) = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[6548, 32714, 32701])).
% 3.42/3.68 tff(32716,plain,
% 3.42/3.68 (~(elem!1 = s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1100, 32715])).
% 3.42/3.68 tff(32717,plain,
% 3.42/3.68 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1516, 32716])).
% 3.42/3.68 tff(32718,plain,
% 3.42/3.68 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[17419, 32717])).
% 3.42/3.68 tff(32719,plain,
% 3.42/3.68 (~(elem!1 = z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[9876, 24397, 3871])).
% 3.42/3.68 tff(32720,plain,
% 3.42/3.68 (~(z = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[364, 32719])).
% 3.42/3.68 tff(32721,plain,
% 3.42/3.68 (~(s(z) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[343, 32720])).
% 3.42/3.68 tff(32722,plain,
% 3.42/3.68 (~b(s(elem!1), z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24421, 19000, 111, 1281, 220, 1638, 32721])).
% 3.42/3.68 tff(32723,plain,
% 3.42/3.68 (r(s(elem!1), z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[409, 32722])).
% 3.42/3.68 tff(32724,plain,
% 3.42/3.68 (~b(s(s(s(s(z)))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24371, 3871, 111, 1281, 220])).
% 3.42/3.68 tff(32725,plain,
% 3.42/3.68 (r(s(s(s(s(z)))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[932, 32724])).
% 3.42/3.68 tff(32726,plain,
% 3.42/3.68 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[28695, 121, 24398, 24390, 32725])).
% 3.42/3.68 tff(32727,plain,
% 3.42/3.68 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[28688, 121, 24398, 24390, 32725])).
% 3.42/3.68 tff(32728,plain,
% 3.42/3.68 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[25019, 271, 2073, 32139, 32141])).
% 3.42/3.68 tff(32729,plain,
% 3.42/3.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[10426, 32728])).
% 3.42/3.68 tff(32730,plain,
% 3.42/3.68 (~b(z, s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[19817, 2073, 1281, 3871])).
% 3.42/3.68 tff(32731,plain,
% 3.42/3.68 (r(z, s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1214, 32730])).
% 3.42/3.68 tff(32732,plain,
% 3.42/3.68 (~b(s(s(s(z))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[31723, 258, 572, 12761, 317, 412, 377, 1281, 111, 331, 109, 32730, 3871])).
% 3.42/3.68 tff(32733,plain,
% 3.42/3.68 (~r(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[22265, 258, 317, 109, 412, 32730, 3871, 344, 377])).
% 3.42/3.68 tff(32734,plain,
% 3.42/3.68 (b(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[355, 32733, 331])).
% 3.42/3.68 tff(32735,plain,
% 3.42/3.68 (~(s(s(s(z))) = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[6548, 32734, 32730])).
% 3.42/3.68 tff(32736,plain,
% 3.42/3.68 (r(s(s(s(z))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[255, 32735, 32732])).
% 3.42/3.68 tff(32737,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32738,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32739,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32738, 32737])).
% 3.42/3.68 tff(32740,plain,
% 3.42/3.68 (~r(s(s(s(s(z)))), z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32739, 121, 32736, 32731, 32729])).
% 3.42/3.68 tff(32741,plain,
% 3.42/3.68 (b(s(s(s(s(z)))), z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1095, 32740])).
% 3.42/3.68 tff(32742,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32743,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32744,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32743, 32742])).
% 3.42/3.68 tff(32745,plain,
% 3.42/3.68 ($false),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32744, 271, 32734, 1638, 32741, 32141])).
% 3.42/3.68 tff(32746,plain,((elem!1 = s(z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (z = elem!1) | b(elem!1, s(elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.68 tff(32747,plain,
% 3.42/3.68 (elem!1 = s(z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32746, 317, 2073, 32727, 32726, 32720, 1638, 24356, 32723, 3871, 8336, 24398, 24390, 1281, 111])).
% 3.42/3.68 tff(32748,plain,
% 3.42/3.68 (~b(s(z), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[3576, 32747, 317])).
% 3.42/3.68 tff(32749,plain,
% 3.42/3.68 (r(s(z), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[444, 32748, 32721])).
% 3.42/3.68 tff(32750,plain,
% 3.42/3.68 (~(elem!1 = s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32597, 32723, 24390, 1281, 220, 3871, 32719, 317, 32730, 8336])).
% 3.42/3.68 tff(32751,plain,
% 3.42/3.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[78, 32750])).
% 3.42/3.68 tff(32752,plain,
% 3.42/3.68 (s(z) = elem!1),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[242, 32747])).
% 3.42/3.68 tff(32753,plain,
% 3.42/3.68 (b(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[229, 32752, 220])).
% 3.42/3.68 tff(32754,plain,
% 3.42/3.68 (~(s(s(s(z))) = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[6548, 32753, 32730])).
% 3.42/3.68 tff(32755,plain,
% 3.42/3.68 (~(elem!1 = s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1100, 32754])).
% 3.42/3.68 tff(32756,plain,
% 3.42/3.68 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1516, 32755])).
% 3.42/3.68 tff(32757,plain,
% 3.42/3.68 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[17419, 32756])).
% 3.42/3.68 tff(32758,plain,
% 3.42/3.68 (s(s(z)) = s(elem!1)),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32752])).
% 3.42/3.68 tff(32759,plain,
% 3.42/3.68 (s(s(s(z))) = s(s(elem!1))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32758])).
% 3.42/3.68 tff(32760,plain,
% 3.42/3.68 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32759])).
% 3.42/3.68 tff(32761,plain,
% 3.42/3.68 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32760])).
% 3.42/3.68 tff(32762,plain,
% 3.42/3.68 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.68 inference(symmetry,[status(thm)],[32761])).
% 3.42/3.68 tff(32763,plain,
% 3.42/3.68 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32762])).
% 3.42/3.68 tff(32764,plain,
% 3.42/3.68 (r(s(s(s(elem!1))), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1234, 32747, 32725])).
% 3.42/3.68 tff(32765,plain,
% 3.42/3.68 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[13101, 32764, 111, 32723])).
% 3.42/3.68 tff(32766,plain,
% 3.42/3.68 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32765, 32763])).
% 3.42/3.68 tff(32767,plain,
% 3.42/3.68 (b(s(elem!1), s(s(s(s(z)))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1995, 32766, 32757])).
% 3.42/3.68 tff(32768,plain,
% 3.42/3.68 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[23654, 32767, 32752])).
% 3.42/3.68 tff(32769,plain,
% 3.42/3.68 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32759])).
% 3.42/3.68 tff(32770,plain,
% 3.42/3.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[2073, 32769])).
% 3.42/3.68 tff(32771,plain,
% 3.42/3.68 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32759])).
% 3.42/3.68 tff(32772,plain,
% 3.42/3.68 (r(s(s(elem!1)), z)),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[24356, 32771])).
% 3.42/3.68 tff(32773,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32774,plain,
% 3.42/3.68 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32775,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32774])).
% 3.42/3.68 tff(32776,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 3.42/3.68 inference(transitivity,[status(thm)],[32775, 32773])).
% 3.42/3.68 tff(32777,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32778,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32777, 32776])).
% 3.42/3.68 tff(32779,plain,
% 3.42/3.68 (~r(s(s(elem!1)), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32778, 121, 111, 32723, 32772])).
% 3.42/3.68 tff(32780,plain,
% 3.42/3.68 (b(s(s(elem!1)), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[701, 32779, 8423])).
% 3.42/3.68 tff(32781,plain,
% 3.42/3.68 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[5254, 32780, 32770, 32768])).
% 3.42/3.68 tff(32782,plain,
% 3.42/3.68 (r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[681, 32781, 32751])).
% 3.42/3.68 tff(32783,plain,
% 3.42/3.68 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32759])).
% 3.42/3.68 tff(32784,plain,
% 3.42/3.68 (b(elem!1, s(s(s(z))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[11114, 32747, 3871])).
% 3.42/3.68 tff(32785,plain,
% 3.42/3.68 (b(elem!1, s(s(elem!1)))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32784, 32783])).
% 3.42/3.68 tff(32786,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32787,plain,
% 3.42/3.68 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 3.42/3.68 inference(rewrite,[status(thm)],[])).
% 3.42/3.68 tff(32788,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))))),
% 3.42/3.68 inference(monotonicity,[status(thm)],[32787])).
% 3.42/3.68 tff(32789,plain,
% 3.42/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 3.42/3.68 inference(transitivity,[status(thm)],[32788, 32786])).
% 3.42/3.68 tff(32790,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.42/3.68 inference(quant_inst,[status(thm)],[])).
% 3.42/3.68 tff(32791,plain,
% 3.42/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))),
% 3.42/3.68 inference(modus_ponens,[status(thm)],[32790, 32789])).
% 3.42/3.68 tff(32792,plain,
% 3.42/3.68 (~r(s(elem!1), s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32791, 121, 111, 32723, 32772])).
% 3.42/3.68 tff(32793,plain,
% 3.42/3.68 (b(s(elem!1), s(s(elem!1)))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[526, 32792, 216])).
% 3.42/3.68 tff(32794,plain,
% 3.42/3.68 (~b(s(elem!1), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[14419, 32793, 32785, 32770])).
% 3.42/3.68 tff(32795,plain,
% 3.42/3.68 (r(s(elem!1), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2243, 32794, 8337])).
% 3.42/3.68 tff(32796,plain,
% 3.42/3.68 ($false),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[9617, 32795, 32782, 32749, 24398])).
% 3.42/3.68 tff(32797,plain,(b(elem!1, s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.68 tff(32798,plain,
% 3.42/3.68 (b(elem!1, s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[32797, 26317, 211, 32700, 220, 20246, 32694, 19197])).
% 3.42/3.68 tff(32799,plain,
% 3.42/3.68 (b(s(z), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1276, 32713, 32798])).
% 3.42/3.68 tff(32800,plain,
% 3.42/3.68 (r(s(z), s(s(s(s(z)))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1053, 32713, 32706])).
% 3.42/3.68 tff(32801,plain,
% 3.42/3.68 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[13597, 271, 11211, 220, 1638])).
% 3.42/3.68 tff(32802,plain,
% 3.42/3.68 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24396, 271, 19197, 220, 1638])).
% 3.42/3.68 tff(32803,plain,
% 3.42/3.68 (~(elem!1 = z)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[9876, 32802, 3871])).
% 3.42/3.68 tff(32804,plain,
% 3.42/3.68 (~(z = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[364, 32803])).
% 3.42/3.68 tff(32805,plain,
% 3.42/3.68 (~(s(z) = s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[343, 32804])).
% 3.42/3.68 tff(32806,plain,
% 3.42/3.68 (~(s(elem!1) = s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[350, 32805])).
% 3.42/3.68 tff(32807,plain,
% 3.42/3.68 (r(s(elem!1), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[429, 24234, 32806])).
% 3.42/3.68 tff(32808,plain,
% 3.42/3.68 (~b(s(s(s(elem!1))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[24388, 271, 19197, 220, 1638])).
% 3.42/3.68 tff(32809,plain,
% 3.42/3.68 (r(s(s(s(elem!1))), s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[16580, 32808])).
% 3.42/3.68 tff(32810,plain,
% 3.42/3.68 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[760, 32802])).
% 3.42/3.68 tff(32811,plain,
% 3.42/3.68 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[13251, 121, 32810, 32809, 32807])).
% 3.42/3.68 tff(32812,plain,
% 3.42/3.68 (s(s(s(elem!1))) = s(elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[681, 32811, 32801])).
% 3.42/3.68 tff(32813,plain,
% 3.42/3.68 (elem!1 = s(s(elem!1))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[78, 32812])).
% 3.42/3.68 tff(32814,plain,
% 3.42/3.68 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[2063, 32805])).
% 3.42/3.68 tff(32815,plain,
% 3.42/3.68 (~r(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[22490, 32813, 19197, 906, 307, 3871, 24455, 32814, 11211])).
% 3.42/3.68 tff(32816,plain,
% 3.42/3.68 (b(z, elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[355, 32815, 32804])).
% 3.42/3.68 tff(32817,plain,
% 3.42/3.68 (~b(s(elem!1), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[4598, 32816, 11211, 307])).
% 3.42/3.68 tff(32818,plain,
% 3.42/3.68 (~b(elem!1, s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[11002, 32816, 220, 3871])).
% 3.42/3.68 tff(32819,plain,
% 3.42/3.68 (~(s(z) = elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[1276, 24236, 307])).
% 3.42/3.68 tff(32820,plain,
% 3.42/3.68 (~(elem!1 = s(z))),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[242, 32819])).
% 3.42/3.68 tff(32821,plain,
% 3.42/3.68 (~b(s(z), elem!1)),
% 3.42/3.68 inference(unit_resolution,[status(thm)],[20382, 32816, 19197, 307])).
% 3.42/3.68 tff(32822,plain,
% 3.42/3.68 (~r(s(s(s(elem!1))), elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[18965, 32821, 32810, 32820, 32818])).
% 3.42/3.69 tff(32823,plain,
% 3.42/3.69 ($false),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[12364, 32822, 32817, 1, 32813])).
% 3.42/3.69 tff(32824,plain,(r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.69 tff(32825,plain,
% 3.42/3.69 (r(s(elem!1), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32824, 32798, 1, 220, 20246, 906, 32694])).
% 3.42/3.69 tff(32826,plain,
% 3.42/3.69 (elem!1 = s(z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1221, 32713])).
% 3.42/3.69 tff(32827,plain,
% 3.42/3.69 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32713])).
% 3.42/3.69 tff(32828,plain,
% 3.42/3.69 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 3.42/3.69 inference(transitivity,[status(thm)],[32827, 2212])).
% 3.42/3.69 tff(32829,plain,
% 3.42/3.69 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32828])).
% 3.42/3.69 tff(32830,plain,
% 3.42/3.69 (~(s(s(elem!1)) = elem!1)),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[2137, 32829])).
% 3.42/3.69 tff(32831,plain,
% 3.42/3.69 (r(s(s(elem!1)), s(z))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[23042, 32830, 32826, 32825, 32703, 32800, 32709, 20246, 32799, 32714, 26445, 32715, 32718])).
% 3.42/3.69 tff(32832,plain,
% 3.42/3.69 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32710])).
% 3.42/3.69 tff(32833,plain,
% 3.42/3.69 (s(s(elem!1)) = s(s(s(z)))),
% 3.42/3.69 inference(transitivity,[status(thm)],[56, 32832, 774])).
% 3.42/3.69 tff(32834,plain,
% 3.42/3.69 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32833])).
% 3.42/3.69 tff(32835,plain,
% 3.42/3.69 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32834])).
% 3.42/3.69 tff(32836,plain,
% 3.42/3.69 (r(z, s(s(elem!1)))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32709, 32835])).
% 3.42/3.69 tff(32837,plain,
% 3.42/3.69 (~r(s(elem!1), s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[5431, 32836, 32825, 32831])).
% 3.42/3.69 tff(32838,plain,
% 3.42/3.69 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32833, 32710])).
% 3.42/3.69 tff(32839,plain,
% 3.42/3.69 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32838])).
% 3.42/3.69 tff(32840,plain,
% 3.42/3.69 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32710])).
% 3.42/3.69 tff(32841,plain,
% 3.42/3.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32700, 32840])).
% 3.42/3.69 tff(32842,plain,
% 3.42/3.69 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32841, 32839])).
% 3.42/3.69 tff(32843,plain,
% 3.42/3.69 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32833])).
% 3.42/3.69 tff(32844,plain,
% 3.42/3.69 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32843])).
% 3.42/3.69 tff(32845,plain,
% 3.42/3.69 (b(elem!1, s(s(s(z))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[11114, 32826, 20246])).
% 3.42/3.69 tff(32846,plain,
% 3.42/3.69 (b(elem!1, s(s(elem!1)))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32845, 32844])).
% 3.42/3.69 tff(32847,plain,
% 3.42/3.69 (~b(s(elem!1), s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[9687, 32846, 32798, 32842])).
% 3.42/3.69 tff(32848,plain,
% 3.42/3.69 ($false),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[526, 32847, 32837, 211])).
% 3.42/3.69 tff(32849,plain,(r(s(z), s(s(s(z)))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.69 tff(32850,plain,
% 3.42/3.69 (r(s(z), s(s(s(z))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32849, 906, 1, 11199, 31518])).
% 3.42/3.69 tff(32851,plain,
% 3.42/3.69 (~b(s(elem!1), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[27984, 9983, 11199, 348, 1, 906, 108, 71])).
% 3.42/3.69 tff(32852,plain,
% 3.42/3.69 (r(s(elem!1), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[409, 32851])).
% 3.42/3.69 tff(32853,plain,
% 3.42/3.69 (b(z, elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[355, 1391, 9297])).
% 3.42/3.69 tff(32854,plain,
% 3.42/3.69 (~b(s(elem!1), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[27984, 9983, 220, 348, 1, 906, 108, 71])).
% 3.42/3.69 tff(32855,plain,
% 3.42/3.69 (r(s(elem!1), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[409, 32854])).
% 3.42/3.69 tff(32856,plain,
% 3.42/3.69 (~b(elem!1, s(z))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[20398, 32853, 19197, 220])).
% 3.42/3.69 tff(32857,plain,
% 3.42/3.69 (r(elem!1, s(z))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[299, 243, 24871])).
% 3.42/3.69 tff(32858,plain,
% 3.42/3.69 (~r(s(s(s(z))), elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[4112, 32857, 108, 1244])).
% 3.42/3.69 tff(32859,plain,
% 3.42/3.69 (~r(s(z), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[9263, 32857, 19197, 379, 1326, 348])).
% 3.42/3.69 tff(32860,plain,
% 3.42/3.69 (b(s(z), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[444, 32859, 348])).
% 3.42/3.69 tff(32861,plain,
% 3.42/3.69 (~(s(s(s(z))) = s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[9276, 32860, 71])).
% 3.42/3.69 tff(32862,plain,
% 3.42/3.69 (r(s(s(s(z))), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1816, 32861, 3506])).
% 3.42/3.69 tff(32863,plain,
% 3.42/3.69 (s(s(s(z))) = elem!1),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[24754, 32862, 412, 1326, 9298, 379, 32858])).
% 3.42/3.69 tff(32864,plain,
% 3.42/3.69 (~(s(s(s(elem!1))) = elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2611, 32863])).
% 3.42/3.69 tff(32865,plain,
% 3.42/3.69 (~r(elem!1, s(s(s(z))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[17626, 32862, 412, 379])).
% 3.42/3.69 tff(32866,plain,
% 3.42/3.69 (~(elem!1 = s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[3906, 32863])).
% 3.42/3.69 tff(32867,plain,
% 3.42/3.69 (~b(elem!1, z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[11686, 908, 1326, 504, 11665])).
% 3.42/3.69 tff(32868,plain,
% 3.42/3.69 (r(elem!1, z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[284, 32867, 259])).
% 3.42/3.69 tff(32869,plain,
% 3.42/3.69 (~b(z, s(s(s(z))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2020, 19232, 908, 1326])).
% 3.42/3.69 tff(32870,plain,
% 3.42/3.69 (r(z, s(s(s(z))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1214, 32869])).
% 3.42/3.69 tff(32871,plain,
% 3.42/3.69 ($false),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[24748, 32870, 32868, 379, 412])).
% 3.42/3.69 tff(32872,plain,((s(s(s(z))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.42/3.69 tff(32873,plain,
% 3.42/3.69 (s(s(s(z))) = elem!1),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32872, 504, 412, 9298, 1326, 379, 15822, 10297, 221])).
% 3.42/3.69 tff(32874,plain,
% 3.42/3.69 (s(elem!1) = s(s(s(s(z))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2605, 32873])).
% 3.42/3.69 tff(32875,plain,
% 3.42/3.69 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32876,plain,
% 3.42/3.69 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(z))))), z)),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32875])).
% 3.42/3.69 tff(32877,plain,
% 3.42/3.69 ((~r(s(s(elem!1)), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32876])).
% 3.42/3.69 tff(32878,plain,
% 3.42/3.69 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32879,plain,
% 3.42/3.69 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32878])).
% 3.42/3.69 tff(32880,plain,
% 3.42/3.69 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(elem!1)))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32879])).
% 3.42/3.69 tff(32881,plain,
% 3.42/3.69 (b(s(z), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[444, 438, 348])).
% 3.42/3.69 tff(32882,plain,
% 3.42/3.69 (b(s(z), s(s(s(s(z)))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[9597, 32874, 32881])).
% 3.42/3.69 tff(32883,plain,
% 3.42/3.69 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32884,plain,
% 3.42/3.69 (b(s(elem!1), s(z))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[429, 423, 2282])).
% 3.42/3.69 tff(32885,plain,
% 3.42/3.69 (b(s(s(s(s(z)))), s(z))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32884, 32883])).
% 3.42/3.69 tff(32886,plain,
% 3.42/3.69 (~b(z, s(s(s(s(z)))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[21223, 32885, 19197, 32882])).
% 3.42/3.69 tff(32887,plain,
% 3.42/3.69 (~b(z, s(elem!1))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32886, 32880])).
% 3.42/3.69 tff(32888,plain,
% 3.42/3.69 (r(z, s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1439, 32887])).
% 3.42/3.69 tff(32889,plain,
% 3.42/3.69 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32890,plain,
% 3.42/3.69 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32889])).
% 3.42/3.69 tff(32891,plain,
% 3.42/3.69 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32892,plain,
% 3.42/3.69 (r(s(s(s(s(z)))), z)),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[412, 32891])).
% 3.42/3.69 tff(32893,plain,
% 3.42/3.69 (b(elem!1, s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[9580, 32873, 2073])).
% 3.42/3.69 tff(32894,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32895,plain,
% 3.42/3.69 (((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32896,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32895])).
% 3.42/3.69 tff(32897,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.42/3.69 inference(transitivity,[status(thm)],[32896, 32894])).
% 3.42/3.69 tff(32898,plain,
% 3.42/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 3.42/3.69 inference(quant_inst,[status(thm)],[])).
% 3.42/3.69 tff(32899,plain,
% 3.42/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32898, 32897])).
% 3.42/3.69 tff(32900,plain,
% 3.42/3.69 (~b(s(s(s(elem!1))), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32899, 271, 1326, 504, 32893])).
% 3.42/3.69 tff(32901,plain,
% 3.42/3.69 (r(s(s(s(elem!1))), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[8229, 32900])).
% 3.42/3.69 tff(32902,plain,
% 3.42/3.69 (((~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(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32903,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32902])).
% 3.42/3.69 tff(32904,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 3.42/3.69 inference(transitivity,[status(thm)],[32903, 4378])).
% 3.42/3.69 tff(32905,plain,
% 3.42/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 3.42/3.69 inference(quant_inst,[status(thm)],[])).
% 3.42/3.69 tff(32906,plain,
% 3.42/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32905, 32904])).
% 3.42/3.69 tff(32907,plain,
% 3.42/3.69 (~b(z, s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32906, 271, 1326, 504, 32893])).
% 3.42/3.69 tff(32908,plain,
% 3.42/3.69 (r(z, s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[36, 21, 32907, 32])).
% 3.42/3.69 tff(32909,plain,
% 3.42/3.69 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[26553, 121, 32908, 32901, 32892])).
% 3.42/3.69 tff(32910,plain,
% 3.42/3.69 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1000, 21, 32909, 25009])).
% 3.42/3.69 tff(32911,plain,
% 3.42/3.69 (b(s(elem!1), s(s(s(elem!1))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32910, 32890])).
% 3.42/3.69 tff(32912,plain,
% 3.42/3.69 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32913,plain,
% 3.42/3.69 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32912])).
% 3.42/3.69 tff(32914,plain,
% 3.42/3.69 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32913])).
% 3.42/3.69 tff(32915,plain,
% 3.42/3.69 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[27490, 121, 32908, 32901, 32892])).
% 3.42/3.69 tff(32916,plain,
% 3.42/3.69 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32915, 32914])).
% 3.42/3.69 tff(32917,plain,
% 3.42/3.69 (b(s(s(s(elem!1))), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[681, 32916, 79])).
% 3.42/3.69 tff(32918,plain,
% 3.42/3.69 (~b(s(s(s(elem!1))), s(z))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2310, 32908, 423, 79, 348, 438, 412])).
% 3.42/3.69 tff(32919,plain,
% 3.42/3.69 (r(s(s(s(elem!1))), s(z))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[16580, 32918])).
% 3.42/3.69 tff(32920,plain,
% 3.42/3.69 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(z))))), z)),
% 3.42/3.69 inference(monotonicity,[status(thm)],[9696])).
% 3.42/3.69 tff(32921,plain,
% 3.42/3.69 (r(s(s(s(s(s(z))))), z) <=> r(s(s(elem!1)), z)),
% 3.42/3.69 inference(symmetry,[status(thm)],[32920])).
% 3.42/3.69 tff(32922,plain,
% 3.42/3.69 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(elem!1)), z))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32921])).
% 3.42/3.69 tff(32923,plain,
% 3.42/3.69 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[9696])).
% 3.42/3.69 tff(32924,plain,
% 3.42/3.69 (~r(s(s(elem!1)), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[14657, 2417, 412, 1441])).
% 3.42/3.69 tff(32925,plain,
% 3.42/3.69 (b(s(s(elem!1)), s(elem!1))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[701, 32924, 3313])).
% 3.42/3.69 tff(32926,plain,
% 3.42/3.69 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[5254, 32925, 638, 739])).
% 3.42/3.69 tff(32927,plain,
% 3.42/3.69 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[556, 32926, 1])).
% 3.42/3.69 tff(32928,plain,
% 3.42/3.69 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32927, 32923])).
% 3.42/3.69 tff(32929,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32930,plain,
% 3.42/3.69 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32931,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32930])).
% 3.42/3.69 tff(32932,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 3.42/3.69 inference(transitivity,[status(thm)],[32931, 32929])).
% 3.42/3.69 tff(32933,plain,
% 3.42/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.42/3.69 inference(quant_inst,[status(thm)],[])).
% 3.42/3.69 tff(32934,plain,
% 3.42/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32933, 32932])).
% 3.42/3.69 tff(32935,plain,
% 3.42/3.69 (~r(s(s(s(s(s(z))))), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32934, 121, 111, 12761, 32928])).
% 3.42/3.69 tff(32936,plain,
% 3.42/3.69 (~r(s(s(elem!1)), z)),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32935, 32922])).
% 3.42/3.69 tff(32937,plain,
% 3.42/3.69 ($false),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2417, 32936])).
% 3.42/3.69 tff(32938,plain,((~r(s(s(elem!1)), z)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.42/3.69 tff(32939,plain,
% 3.42/3.69 (~r(s(s(elem!1)), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[32938, 32874, 32908, 32919, 1, 32917, 32911, 412, 32888])).
% 3.42/3.69 tff(32940,plain,
% 3.42/3.69 (~r(s(s(s(s(s(z))))), z)),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32939, 32877])).
% 3.42/3.69 tff(32941,plain,
% 3.42/3.69 (b(s(s(s(s(s(z))))), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[6593, 21, 711, 32940])).
% 3.42/3.69 tff(32942,plain,
% 3.42/3.69 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32873])).
% 3.42/3.69 tff(32943,plain,
% 3.42/3.69 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.42/3.69 inference(transitivity,[status(thm)],[32942, 1836])).
% 3.42/3.69 tff(32944,plain,
% 3.42/3.69 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32943])).
% 3.42/3.69 tff(32945,plain,
% 3.42/3.69 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[1489, 32944])).
% 3.42/3.69 tff(32946,plain,
% 3.42/3.69 (b(s(s(elem!1)), z)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2430, 32939])).
% 3.42/3.69 tff(32947,plain,
% 3.42/3.69 (~b(s(z), s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[17014, 32946, 19197, 220])).
% 3.42/3.69 tff(32948,plain,
% 3.42/3.69 (r(s(z), s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[2167, 32947])).
% 3.42/3.69 tff(32949,plain,
% 3.42/3.69 (r(s(z), s(s(s(s(s(z))))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[9700, 32948, 32874])).
% 3.42/3.69 tff(32950,plain,
% 3.42/3.69 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32873])).
% 3.42/3.69 tff(32951,plain,
% 3.42/3.69 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.69 inference(symmetry,[status(thm)],[32950])).
% 3.42/3.69 tff(32952,plain,
% 3.42/3.69 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32875])).
% 3.42/3.69 tff(32953,plain,
% 3.42/3.69 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.69 inference(transitivity,[status(thm)],[32952, 32951])).
% 3.42/3.69 tff(32954,plain,
% 3.42/3.69 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1014, 32915, 1008])).
% 3.42/3.69 tff(32955,plain,
% 3.42/3.69 (~b(s(z), s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[12570, 32910, 32885, 32954])).
% 3.42/3.69 tff(32956,plain,
% 3.42/3.69 (r(s(z), s(s(s(elem!1))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[760, 32955])).
% 3.42/3.69 tff(32957,plain,
% 3.42/3.69 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[10857, 32946, 32908, 32956])).
% 3.42/3.69 tff(32958,plain,
% 3.42/3.69 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[586, 32957, 563])).
% 3.42/3.69 tff(32959,plain,
% 3.42/3.69 (~r(s(s(elem!1)), elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1633, 32948, 357, 379])).
% 3.42/3.69 tff(32960,plain,
% 3.42/3.69 (b(s(s(elem!1)), elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[862, 32959, 198])).
% 3.42/3.69 tff(32961,plain,
% 3.42/3.69 (~b(elem!1, s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[594, 32960, 504, 32958])).
% 3.42/3.69 tff(32962,plain,
% 3.42/3.69 (r(elem!1, s(s(elem!1)))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[599, 32961, 68])).
% 3.42/3.69 tff(32963,plain,
% 3.42/3.69 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[32962, 32953])).
% 3.42/3.69 tff(32964,plain,
% 3.42/3.69 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[18909, 32963, 108, 32949])).
% 3.42/3.69 tff(32965,plain,
% 3.42/3.69 (b(s(s(s(s(s(z))))), elem!1)),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[840, 32964, 32945])).
% 3.42/3.69 tff(32966,plain,
% 3.42/3.69 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32874])).
% 3.42/3.69 tff(32967,plain,
% 3.42/3.69 (r(elem!1, s(s(s(s(z)))))),
% 3.42/3.69 inference(modus_ponens,[status(thm)],[379, 32966])).
% 3.42/3.69 tff(32968,plain,
% 3.42/3.69 (r(z, s(s(s(s(z)))))),
% 3.42/3.69 inference(unit_resolution,[status(thm)],[1121, 32886])).
% 3.42/3.69 tff(32969,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32970,plain,
% 3.42/3.69 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.42/3.69 inference(rewrite,[status(thm)],[])).
% 3.42/3.69 tff(32971,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 3.42/3.69 inference(monotonicity,[status(thm)],[32970])).
% 3.42/3.69 tff(32972,plain,
% 3.42/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.52/3.70 inference(transitivity,[status(thm)],[32971, 32969])).
% 3.52/3.70 tff(32973,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 3.52/3.70 inference(quant_inst,[status(thm)],[])).
% 3.52/3.70 tff(32974,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[32973, 32972])).
% 3.52/3.70 tff(32975,plain,
% 3.52/3.70 (~r(elem!1, z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[32974, 121, 32968, 32967, 32892])).
% 3.52/3.70 tff(32976,plain,
% 3.52/3.70 (b(elem!1, z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[284, 32975, 9298])).
% 3.52/3.70 tff(32977,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(32978,plain,
% 3.52/3.70 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(32979,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[32978])).
% 3.52/3.70 tff(32980,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 3.52/3.70 inference(transitivity,[status(thm)],[32979, 32977])).
% 3.52/3.70 tff(32981,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 3.52/3.70 inference(quant_inst,[status(thm)],[])).
% 3.52/3.70 tff(32982,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[32981, 32980])).
% 3.52/3.70 tff(32983,plain,
% 3.52/3.70 ($false),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[32982, 271, 1326, 32976, 32965, 32941])).
% 3.52/3.70 tff(32984,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(elem!1), s(z)) | (s(z) = s(elem!1)) | r(s(z), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.70 tff(32985,plain,
% 3.52/3.70 (~b(s(s(s(elem!1))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[32984, 32866, 108, 1326, 1244, 379, 220, 1, 412, 13988, 423, 348, 32859, 2073, 32865, 32858])).
% 3.52/3.70 tff(32986,plain,
% 3.52/3.70 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[78, 32866])).
% 3.52/3.70 tff(32987,plain,
% 3.52/3.70 (~r(s(s(s(elem!1))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[3823, 32986, 379, 412, 32884, 1244])).
% 3.52/3.70 tff(32988,plain,
% 3.52/3.70 ($false),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[486, 32987, 32985, 32864])).
% 3.52/3.70 tff(32989,plain,((s(z) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(elem!1), s(z)) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(s(z))), s(elem!1)) | b(s(z), s(s(s(z)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.70 tff(32990,plain,
% 3.52/3.70 (s(z) = elem!1),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[32989, 3506, 412, 108, 1326, 220, 1, 423, 348, 2073, 379, 71, 1242])).
% 3.52/3.70 tff(32991,plain,
% 3.52/3.70 (s(s(z)) = s(elem!1)),
% 3.52/3.70 inference(monotonicity,[status(thm)],[32990])).
% 3.52/3.70 tff(32992,plain,
% 3.52/3.70 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[32991])).
% 3.52/3.70 tff(32993,plain,
% 3.52/3.70 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 3.52/3.70 inference(transitivity,[status(thm)],[32992, 3535])).
% 3.52/3.70 tff(32994,plain,
% 3.52/3.70 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[32993])).
% 3.52/3.70 tff(32995,plain,
% 3.52/3.70 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[1136, 32994])).
% 3.52/3.70 tff(32996,plain,
% 3.52/3.70 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[32990])).
% 3.52/3.70 tff(32997,plain,
% 3.52/3.70 (r(elem!1, s(s(s(z))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[108, 32996])).
% 3.52/3.70 tff(32998,plain,
% 3.52/3.70 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[17626, 32997, 412, 379])).
% 3.52/3.70 tff(32999,plain,
% 3.52/3.70 ($false),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1816, 32998, 32995, 3506])).
% 3.52/3.70 tff(33000,plain,(b(s(s(s(z))), s(elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(elem!1), s(z)) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(z), s(s(s(z)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.70 tff(33001,plain,
% 3.52/3.70 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33000, 423, 9983, 108, 32853, 220, 1, 32855, 348, 19776, 71, 1242])).
% 3.52/3.70 tff(33002,plain,
% 3.52/3.70 (~(s(s(s(z))) = elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[6165, 33001, 317])).
% 3.52/3.70 tff(33003,plain,
% 3.52/3.70 (r(elem!1, s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[299, 243, 32856])).
% 3.52/3.70 tff(33004,plain,
% 3.52/3.70 (~r(s(z), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[9263, 33003, 19197, 379, 32853, 348])).
% 3.52/3.70 tff(33005,plain,
% 3.52/3.70 (b(s(z), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[444, 33004, 348])).
% 3.52/3.70 tff(33006,plain,
% 3.52/3.70 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[9276, 33005, 71])).
% 3.52/3.70 tff(33007,plain,
% 3.52/3.70 (~r(s(s(s(z))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[4112, 33003, 108, 1244])).
% 3.52/3.70 tff(33008,plain,
% 3.52/3.70 (b(s(s(s(z))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[255, 33007, 907])).
% 3.52/3.70 tff(33009,plain,
% 3.52/3.70 (~b(s(s(s(z))), s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24796, 33005, 447, 1422])).
% 3.52/3.70 tff(33010,plain,
% 3.52/3.70 (r(s(s(s(z))), s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[2325, 33009])).
% 3.52/3.70 tff(33011,plain,
% 3.52/3.70 (~r(elem!1, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[11254, 33010, 33003, 1244])).
% 3.52/3.70 tff(33012,plain,
% 3.52/3.70 (b(elem!1, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1192, 33011, 1101])).
% 3.52/3.70 tff(33013,plain,
% 3.52/3.70 (~b(z, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[2020, 33012, 33008, 32853])).
% 3.52/3.70 tff(33014,plain,
% 3.52/3.70 (r(z, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1214, 33013])).
% 3.52/3.70 tff(33015,plain,
% 3.52/3.70 (~b(s(elem!1), z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[27984, 379, 220, 348, 1, 906, 108, 71])).
% 3.52/3.70 tff(33016,plain,
% 3.52/3.70 (r(s(elem!1), z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[409, 33015])).
% 3.52/3.70 tff(33017,plain,
% 3.52/3.70 (~b(s(s(s(elem!1))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[32872, 33011, 33016, 9298, 32853, 379, 15822, 907, 33007])).
% 3.52/3.70 tff(33018,plain,
% 3.52/3.70 (~r(elem!1, z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24748, 33014, 379, 33016])).
% 3.52/3.70 tff(33019,plain,
% 3.52/3.70 (b(elem!1, z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[284, 33018, 9298])).
% 3.52/3.70 tff(33020,plain,
% 3.52/3.70 (s(s(s(elem!1))) = s(elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[3823, 139, 379, 412, 447, 357])).
% 3.52/3.70 tff(33021,plain,
% 3.52/3.70 (elem!1 = s(s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[78, 33020])).
% 3.52/3.70 tff(33022,plain,
% 3.52/3.70 (s(elem!1) = s(s(s(elem!1)))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33021])).
% 3.52/3.70 tff(33023,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33022])).
% 3.52/3.70 tff(33024,plain,
% 3.52/3.70 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33022])).
% 3.52/3.70 tff(33025,plain,
% 3.52/3.70 (b(s(s(s(elem!1))), s(z))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[447, 33024])).
% 3.52/3.70 tff(33026,plain,
% 3.52/3.70 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33022])).
% 3.52/3.70 tff(33027,plain,
% 3.52/3.70 (~b(z, s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[22213, 271, 19197, 220, 447])).
% 3.52/3.70 tff(33028,plain,
% 3.52/3.70 (r(z, s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1439, 33027])).
% 3.52/3.70 tff(33029,plain,
% 3.52/3.70 (r(z, s(s(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33028, 33026])).
% 3.52/3.70 tff(33030,plain,
% 3.52/3.70 (~r(s(z), s(s(s(elem!1))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[18965, 139, 1242, 258, 24871])).
% 3.52/3.70 tff(33031,plain,
% 3.52/3.70 (b(s(z), s(s(s(elem!1))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[760, 33030])).
% 3.52/3.70 tff(33032,plain,
% 3.52/3.70 (~b(s(s(s(z))), z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1947, 261, 1326, 257])).
% 3.52/3.70 tff(33033,plain,
% 3.52/3.70 (r(s(s(s(z))), z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1155, 33032])).
% 3.52/3.70 tff(33034,plain,
% 3.52/3.70 (~r(elem!1, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[11254, 2327, 24872, 357])).
% 3.52/3.70 tff(33035,plain,
% 3.52/3.70 (b(elem!1, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1192, 33034, 1102])).
% 3.52/3.70 tff(33036,plain,
% 3.52/3.70 (~b(z, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[2020, 33035, 257, 1326])).
% 3.52/3.70 tff(33037,plain,
% 3.52/3.70 (r(z, s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1214, 33036])).
% 3.52/3.70 tff(33038,plain,
% 3.52/3.70 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33021])).
% 3.52/3.70 tff(33039,plain,
% 3.52/3.70 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[139, 33038])).
% 3.52/3.70 tff(33040,plain,
% 3.52/3.70 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33022])).
% 3.52/3.70 tff(33041,plain,
% 3.52/3.70 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33021])).
% 3.52/3.70 tff(33042,plain,
% 3.52/3.70 (r(s(s(elem!1)), s(elem!1))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[379, 33041])).
% 3.52/3.70 tff(33043,plain,
% 3.52/3.70 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33042, 33040])).
% 3.52/3.70 tff(33044,plain,
% 3.52/3.70 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[12235, 33021, 2065])).
% 3.52/3.70 tff(33045,plain,
% 3.52/3.70 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33021])).
% 3.52/3.70 tff(33046,plain,
% 3.52/3.70 (b(s(s(elem!1)), z)),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[261, 33045])).
% 3.52/3.70 tff(33047,plain,
% 3.52/3.70 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33021])).
% 3.52/3.70 tff(33048,plain,
% 3.52/3.70 (b(z, s(s(elem!1)))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[1326, 33047])).
% 3.52/3.70 tff(33049,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[2471])).
% 3.52/3.70 tff(33050,plain,
% 3.52/3.70 (~b(s(s(s(s(z)))), s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[22548, 1103, 1281, 220])).
% 3.52/3.70 tff(33051,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[932, 33050])).
% 3.52/3.70 tff(33052,plain,
% 3.52/3.70 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24945, 33051, 2327, 1281, 1140])).
% 3.52/3.70 tff(33053,plain,
% 3.52/3.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[10426, 33052])).
% 3.52/3.70 tff(33054,plain,
% 3.52/3.70 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24983, 33053, 412, 3456, 257, 1140, 109, 33051, 2327, 357, 1102])).
% 3.52/3.70 tff(33055,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1559, 33054, 1517])).
% 3.52/3.70 tff(33056,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33055, 33049])).
% 3.52/3.70 tff(33057,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(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(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(33058,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(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(s(elem!1)))))),
% 3.52/3.70 inference(quant_inst,[status(thm)],[])).
% 3.52/3.70 tff(33059,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(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(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33058, 33057])).
% 3.52/3.70 tff(33060,plain,
% 3.52/3.70 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33059, 121, 623, 573, 33056])).
% 3.52/3.70 tff(33061,plain,
% 3.52/3.70 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[12253, 21, 13528, 33060])).
% 3.52/3.70 tff(33062,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(33063,plain,
% 3.52/3.70 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(33064,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33063])).
% 3.52/3.70 tff(33065,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 3.52/3.70 inference(transitivity,[status(thm)],[33064, 33062])).
% 3.52/3.70 tff(33066,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 3.52/3.70 inference(quant_inst,[status(thm)],[])).
% 3.52/3.70 tff(33067,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33066, 33065])).
% 3.52/3.70 tff(33068,plain,
% 3.52/3.70 ($false),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33067, 271, 1894, 2449, 33061, 1103])).
% 3.52/3.70 tff(33069,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.70 tff(33070,plain,
% 3.52/3.70 (~b(s(s(s(s(z)))), z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33069, 33048, 33046, 33044, 33043, 33039, 33021, 412, 24872, 257, 33037, 33033, 2327, 357, 1102, 19197, 220])).
% 3.52/3.70 tff(33071,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1095, 33070])).
% 3.52/3.70 tff(33072,plain,
% 3.52/3.70 (~b(s(s(s(s(z)))), s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1023, 33071, 1, 257, 33031, 33029, 906, 33025])).
% 3.52/3.70 tff(33073,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(z))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[932, 33072])).
% 3.52/3.70 tff(33074,plain,
% 3.52/3.70 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24945, 33073, 2327, 19197, 33037])).
% 3.52/3.70 tff(33075,plain,
% 3.52/3.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[10426, 33074])).
% 3.52/3.70 tff(33076,plain,
% 3.52/3.70 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24983, 33075, 412, 24872, 257, 33037, 33033, 33073, 2327, 357, 1102])).
% 3.52/3.70 tff(33077,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1559, 33076, 1517])).
% 3.52/3.70 tff(33078,plain,
% 3.52/3.70 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33077, 33023])).
% 3.52/3.70 tff(33079,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(33080,plain,
% 3.52/3.70 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.52/3.70 inference(rewrite,[status(thm)],[])).
% 3.52/3.70 tff(33081,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33080])).
% 3.52/3.70 tff(33082,plain,
% 3.52/3.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 3.52/3.70 inference(transitivity,[status(thm)],[33081, 33079])).
% 3.52/3.70 tff(33083,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 3.52/3.70 inference(quant_inst,[status(thm)],[])).
% 3.52/3.70 tff(33084,plain,
% 3.52/3.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[33083, 33082])).
% 3.52/3.70 tff(33085,plain,
% 3.52/3.70 ($false),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33084, 121, 33029, 33039, 33071, 33078])).
% 3.52/3.70 tff(33086,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(z), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.70 tff(33087,plain,
% 3.52/3.70 (~r(s(s(s(elem!1))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33086, 33008, 33016, 33010, 1244, 1101, 1, 906, 220, 447, 33019, 32853, 379, 9149, 1242, 243])).
% 3.52/3.70 tff(33088,plain,
% 3.52/3.70 (s(s(s(elem!1))) = elem!1),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[486, 33087, 33017])).
% 3.52/3.70 tff(33089,plain,
% 3.52/3.70 (~b(z, s(s(s(elem!1))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[25064, 33088, 19197, 447, 220, 33016, 19776, 13988, 33014, 379, 33003, 33008, 1244, 1101, 1422, 33005, 2207, 32853, 33006, 9298])).
% 3.52/3.70 tff(33090,plain,
% 3.52/3.70 (~r(z, s(s(s(elem!1))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[11073, 33088, 1391])).
% 3.52/3.70 tff(33091,plain,
% 3.52/3.70 ($false),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[36, 21, 33090, 33089, 32])).
% 3.52/3.70 tff(33092,plain,((s(z) = elem!1) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), elem!1) | (s(s(s(z))) = elem!1) | b(s(z), s(s(s(z)))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.70 tff(33093,plain,
% 3.52/3.70 (s(z) = elem!1),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[33092, 32884, 220, 9983, 33001, 1391, 1, 906, 1242, 33002, 71, 348, 108])).
% 3.52/3.70 tff(33094,plain,
% 3.52/3.70 (elem!1 = s(z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1221, 33093])).
% 3.52/3.70 tff(33095,plain,
% 3.52/3.70 (~b(s(z), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[3576, 33094, 317])).
% 3.52/3.70 tff(33096,plain,
% 3.52/3.70 (r(s(z), s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[444, 33095, 348])).
% 3.52/3.70 tff(33097,plain,
% 3.52/3.70 (s(s(z)) = s(elem!1)),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33093])).
% 3.52/3.70 tff(33098,plain,
% 3.52/3.70 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33097])).
% 3.52/3.70 tff(33099,plain,
% 3.52/3.70 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 3.52/3.70 inference(transitivity,[status(thm)],[33098, 3535])).
% 3.52/3.70 tff(33100,plain,
% 3.52/3.70 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33099])).
% 3.52/3.70 tff(33101,plain,
% 3.52/3.70 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[1136, 33100])).
% 3.52/3.70 tff(33102,plain,
% 3.52/3.70 (b(elem!1, z)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[20120, 33093, 19197])).
% 3.52/3.70 tff(33103,plain,
% 3.52/3.70 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33093])).
% 3.52/3.70 tff(33104,plain,
% 3.52/3.70 (b(s(elem!1), elem!1)),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[32884, 33103])).
% 3.52/3.70 tff(33105,plain,
% 3.52/3.70 (~b(s(s(s(z))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[23566, 33104, 33102, 33101, 32853])).
% 3.52/3.70 tff(33106,plain,
% 3.52/3.70 (r(s(s(s(z))), elem!1)),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[255, 33105, 33002])).
% 3.52/3.70 tff(33107,plain,
% 3.52/3.70 (~r(s(elem!1), s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[3445, 33106, 108, 33096])).
% 3.52/3.70 tff(33108,plain,
% 3.52/3.70 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[24187, 33107, 33093])).
% 3.52/3.70 tff(33109,plain,
% 3.52/3.70 (b(s(elem!1), s(s(elem!1)))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[526, 33108, 211])).
% 3.52/3.70 tff(33110,plain,
% 3.52/3.70 (s(s(s(z))) = s(s(elem!1))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33097])).
% 3.52/3.70 tff(33111,plain,
% 3.52/3.70 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.70 inference(monotonicity,[status(thm)],[33110])).
% 3.52/3.70 tff(33112,plain,
% 3.52/3.70 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.70 inference(modus_ponens,[status(thm)],[19776, 33111])).
% 3.52/3.70 tff(33113,plain,
% 3.52/3.70 (~(elem!1 = s(s(s(z))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1100, 33002])).
% 3.52/3.70 tff(33114,plain,
% 3.52/3.70 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1516, 33113])).
% 3.52/3.70 tff(33115,plain,
% 3.52/3.70 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[17419, 33114])).
% 3.52/3.70 tff(33116,plain,
% 3.52/3.70 (~b(z, s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[3747, 271, 33104, 32853, 33102])).
% 3.52/3.70 tff(33117,plain,
% 3.52/3.70 (r(z, s(elem!1))),
% 3.52/3.70 inference(unit_resolution,[status(thm)],[1439, 33116])).
% 3.52/3.70 tff(33118,plain,
% 3.52/3.70 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[27109, 33117, 32855, 33093, 33115, 19197, 220, 33112, 33109])).
% 3.52/3.71 tff(33119,plain,
% 3.52/3.71 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33110])).
% 3.52/3.71 tff(33120,plain,
% 3.52/3.71 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33093])).
% 3.52/3.71 tff(33121,plain,
% 3.52/3.71 (r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[108, 33120])).
% 3.52/3.71 tff(33122,plain,
% 3.52/3.71 (r(elem!1, s(s(elem!1)))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33121, 33119])).
% 3.52/3.71 tff(33123,plain,
% 3.52/3.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33110])).
% 3.52/3.71 tff(33124,plain,
% 3.52/3.71 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33123])).
% 3.52/3.71 tff(33125,plain,
% 3.52/3.71 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.71 inference(transitivity,[status(thm)],[33124, 200])).
% 3.52/3.71 tff(33126,plain,
% 3.52/3.71 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33125])).
% 3.52/3.71 tff(33127,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33115, 33126])).
% 3.52/3.71 tff(33128,plain,
% 3.52/3.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[25513, 33118, 9983, 32855])).
% 3.52/3.71 tff(33129,plain,
% 3.52/3.71 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[681, 33128, 33127])).
% 3.52/3.71 tff(33130,plain,
% 3.52/3.71 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1459, 33129, 33112, 33109])).
% 3.52/3.71 tff(33131,plain,
% 3.52/3.71 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[586, 33130, 563])).
% 3.52/3.71 tff(33132,plain,
% 3.52/3.71 (s(s(elem!1)) = s(s(s(z)))),
% 3.52/3.71 inference(symmetry,[status(thm)],[33110])).
% 3.52/3.71 tff(33133,plain,
% 3.52/3.71 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33132])).
% 3.52/3.71 tff(33134,plain,
% 3.52/3.71 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.52/3.71 inference(symmetry,[status(thm)],[33133])).
% 3.52/3.71 tff(33135,plain,
% 3.52/3.71 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33001, 33134])).
% 3.52/3.71 tff(33136,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[2603, 26290])).
% 3.52/3.71 tff(33137,plain,
% 3.52/3.71 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[681, 25522, 33136])).
% 3.52/3.71 tff(33138,plain,
% 3.52/3.71 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[5254, 33137, 543, 2494])).
% 3.52/3.71 tff(33139,plain,
% 3.52/3.71 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23654, 33138, 223])).
% 3.52/3.71 tff(33140,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1995, 33139, 2603])).
% 3.52/3.71 tff(33141,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33140, 27096])).
% 3.52/3.71 tff(33142,plain,
% 3.52/3.71 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[13101, 139, 111, 412])).
% 3.52/3.71 tff(33143,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33142, 33141])).
% 3.52/3.71 tff(33144,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33145,plain,
% 3.52/3.71 (~r(z, s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33144, 33118, 33115, 33112, 33135, 9983, 32855, 33093])).
% 3.52/3.71 tff(33146,plain,
% 3.52/3.71 (b(z, s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[19736, 33145])).
% 3.52/3.71 tff(33147,plain,
% 3.52/3.71 (~b(s(s(elem!1)), z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[5267, 33146, 33129, 33112])).
% 3.52/3.71 tff(33148,plain,
% 3.52/3.71 (r(s(s(elem!1)), z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2430, 33147])).
% 3.52/3.71 tff(33149,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[14145, 33148, 33131, 33122, 33118])).
% 3.52/3.71 tff(33150,plain,(r(s(elem!1), s(z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | b(elem!1, s(elem!1)) | r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33151,plain,
% 3.52/3.71 (r(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33150, 1242, 108, 348, 317, 1391, 1, 906, 220, 71])).
% 3.52/3.71 tff(33152,plain,
% 3.52/3.71 (s(z) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23287, 33151, 9983, 32856, 1242])).
% 3.52/3.71 tff(33153,plain,
% 3.52/3.71 (s(s(z)) = s(elem!1)),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33152])).
% 3.52/3.71 tff(33154,plain,
% 3.52/3.71 (s(s(s(z))) = s(s(elem!1))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33153])).
% 3.52/3.71 tff(33155,plain,
% 3.52/3.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33154])).
% 3.52/3.71 tff(33156,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33155])).
% 3.52/3.71 tff(33157,plain,
% 3.52/3.71 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33152])).
% 3.52/3.71 tff(33158,plain,
% 3.52/3.71 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 3.52/3.71 inference(transitivity,[status(thm)],[33157, 159])).
% 3.52/3.71 tff(33159,plain,
% 3.52/3.71 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33158])).
% 3.52/3.71 tff(33160,plain,
% 3.52/3.71 (~(elem!1 = s(s(s(z))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[97, 33159])).
% 3.52/3.71 tff(33161,plain,
% 3.52/3.71 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1516, 33160])).
% 3.52/3.71 tff(33162,plain,
% 3.52/3.71 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[17419, 33161])).
% 3.52/3.71 tff(33163,plain,
% 3.52/3.71 (s(s(elem!1)) = s(s(s(z)))),
% 3.52/3.71 inference(symmetry,[status(thm)],[33154])).
% 3.52/3.71 tff(33164,plain,
% 3.52/3.71 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33163])).
% 3.52/3.71 tff(33165,plain,
% 3.52/3.71 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.52/3.71 inference(symmetry,[status(thm)],[33164])).
% 3.52/3.71 tff(33166,plain,
% 3.52/3.71 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33153])).
% 3.52/3.71 tff(33167,plain,
% 3.52/3.71 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 3.52/3.71 inference(transitivity,[status(thm)],[33166, 3535])).
% 3.52/3.71 tff(33168,plain,
% 3.52/3.71 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33167])).
% 3.52/3.71 tff(33169,plain,
% 3.52/3.71 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[1136, 33168])).
% 3.52/3.71 tff(33170,plain,
% 3.52/3.71 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33152])).
% 3.52/3.71 tff(33171,plain,
% 3.52/3.71 (r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[108, 33170])).
% 3.52/3.71 tff(33172,plain,
% 3.52/3.71 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33152])).
% 3.52/3.71 tff(33173,plain,
% 3.52/3.71 (r(s(elem!1), elem!1)),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33151, 33172])).
% 3.52/3.71 tff(33174,plain,
% 3.52/3.71 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[3849, 33173, 33171, 9983])).
% 3.52/3.71 tff(33175,plain,
% 3.52/3.71 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1816, 33174, 33169])).
% 3.52/3.71 tff(33176,plain,
% 3.52/3.71 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33175, 33165])).
% 3.52/3.71 tff(33177,plain,
% 3.52/3.71 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33154])).
% 3.52/3.71 tff(33178,plain,
% 3.52/3.71 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[19776, 33177])).
% 3.52/3.71 tff(33179,plain,
% 3.52/3.71 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33152])).
% 3.52/3.71 tff(33180,plain,
% 3.52/3.71 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33179])).
% 3.52/3.71 tff(33181,plain,
% 3.52/3.71 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[2137, 33180])).
% 3.52/3.71 tff(33182,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[78, 33181])).
% 3.52/3.71 tff(33183,plain,
% 3.52/3.71 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33154])).
% 3.52/3.71 tff(33184,plain,
% 3.52/3.71 (r(elem!1, s(s(elem!1)))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33171, 33183])).
% 3.52/3.71 tff(33185,plain,
% 3.52/3.71 (elem!1 = s(z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1221, 33152])).
% 3.52/3.71 tff(33186,plain,
% 3.52/3.71 (~b(s(z), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[3576, 33185, 317])).
% 3.52/3.71 tff(33187,plain,
% 3.52/3.71 (r(s(z), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[444, 33186, 348])).
% 3.52/3.71 tff(33188,plain,
% 3.52/3.71 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[6652])).
% 3.52/3.71 tff(33189,plain,
% 3.52/3.71 (~(elem!1 = s(s(s(z))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[97, 33188])).
% 3.52/3.71 tff(33190,plain,
% 3.52/3.71 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1516, 33189])).
% 3.52/3.71 tff(33191,plain,
% 3.52/3.71 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[17419, 33190])).
% 3.52/3.71 tff(33192,plain,
% 3.52/3.71 (~b(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[11686, 27097, 1326, 20121, 11665])).
% 3.52/3.71 tff(33193,plain,
% 3.52/3.71 (r(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[255, 33192, 6655])).
% 3.52/3.71 tff(33194,plain,
% 3.52/3.71 (~r(s(elem!1), s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[3445, 33193, 108, 431])).
% 3.52/3.71 tff(33195,plain,
% 3.52/3.71 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24187, 33194, 223])).
% 3.52/3.71 tff(33196,plain,
% 3.52/3.71 (b(s(elem!1), s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[526, 33195, 216])).
% 3.52/3.71 tff(33197,plain,
% 3.52/3.71 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[10076, 33196, 543, 27097])).
% 3.52/3.71 tff(33198,plain,
% 3.52/3.71 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23654, 33197, 223])).
% 3.52/3.71 tff(33199,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1995, 33198, 33191])).
% 3.52/3.71 tff(33200,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33199, 27096])).
% 3.52/3.71 tff(33201,plain,
% 3.52/3.71 (~r(z, s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[27109, 33196, 412, 223, 33191, 1281, 220, 543, 147])).
% 3.52/3.71 tff(33202,plain,
% 3.52/3.71 (b(z, s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1439, 33201])).
% 3.52/3.71 tff(33203,plain,
% 3.52/3.71 (~b(z, s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[8781, 33202, 33196, 543])).
% 3.52/3.71 tff(33204,plain,
% 3.52/3.71 (r(z, s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2106, 33203])).
% 3.52/3.71 tff(33205,plain,
% 3.52/3.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[6850, 27095, 412, 33204])).
% 3.52/3.71 tff(33206,plain,
% 3.52/3.71 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[681, 33205, 6656])).
% 3.52/3.71 tff(33207,plain,
% 3.52/3.71 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1459, 33206, 543, 33196])).
% 3.52/3.71 tff(33208,plain,
% 3.52/3.71 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[586, 33207, 6943])).
% 3.52/3.71 tff(33209,plain,
% 3.52/3.71 (~b(z, s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[7173, 27097, 20121, 1326])).
% 3.52/3.71 tff(33210,plain,
% 3.52/3.71 (r(z, s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[19736, 33209])).
% 3.52/3.71 tff(33211,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.52/3.71 inference(rewrite,[status(thm)],[])).
% 3.52/3.71 tff(33212,plain,
% 3.52/3.71 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.52/3.71 inference(rewrite,[status(thm)],[])).
% 3.52/3.71 tff(33213,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33212])).
% 3.52/3.71 tff(33214,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 3.52/3.71 inference(transitivity,[status(thm)],[33213, 33211])).
% 3.52/3.71 tff(33215,plain,
% 3.52/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 3.52/3.71 inference(quant_inst,[status(thm)],[])).
% 3.52/3.71 tff(33216,plain,
% 3.52/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33215, 33214])).
% 3.52/3.71 tff(33217,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33216, 121, 33210, 33208, 412, 33200])).
% 3.52/3.71 tff(33218,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33219,plain,
% 3.52/3.71 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33218, 33178, 563, 32855, 33152, 19197, 220, 211, 108, 33187, 32853, 15822])).
% 3.52/3.71 tff(33220,plain,
% 3.52/3.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[720, 33219, 33184, 33173])).
% 3.52/3.71 tff(33221,plain,
% 3.52/3.71 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[681, 33220, 33182])).
% 3.52/3.71 tff(33222,plain,
% 3.52/3.71 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[5254, 33221, 33178, 33176])).
% 3.52/3.71 tff(33223,plain,
% 3.52/3.71 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23654, 33222, 33152])).
% 3.52/3.71 tff(33224,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1995, 33223, 33162])).
% 3.52/3.71 tff(33225,plain,
% 3.52/3.71 (r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33224, 33156])).
% 3.52/3.71 tff(33226,plain,
% 3.52/3.71 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[9184, 33219, 9983, 33173])).
% 3.52/3.71 tff(33227,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33226, 33225])).
% 3.52/3.71 tff(33228,plain,(b(s(z), elem!1) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | b(elem!1, s(elem!1)) | r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33229,plain,
% 3.52/3.71 (b(s(z), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33228, 1391, 108, 348, 317, 220, 1, 906, 71])).
% 3.52/3.71 tff(33230,plain,
% 3.52/3.71 (~b(elem!1, z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[12145, 33229, 220, 32853])).
% 3.52/3.71 tff(33231,plain,
% 3.52/3.71 (r(elem!1, z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[284, 33230, 9298])).
% 3.52/3.71 tff(33232,plain,
% 3.52/3.71 (~r(z, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24748, 33231, 9983, 32855])).
% 3.52/3.71 tff(33233,plain,
% 3.52/3.71 (b(z, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1214, 33232])).
% 3.52/3.71 tff(33234,plain,
% 3.52/3.71 (~b(s(s(s(z))), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24799, 33229, 220, 33233])).
% 3.52/3.71 tff(33235,plain,
% 3.52/3.71 (r(s(s(s(z))), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2325, 33234])).
% 3.52/3.71 tff(33236,plain,
% 3.52/3.71 (~(s(z) = elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[20120, 33230, 19197])).
% 3.52/3.71 tff(33237,plain,
% 3.52/3.71 (~(elem!1 = s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[242, 33236])).
% 3.52/3.71 tff(33238,plain,
% 3.52/3.71 (r(elem!1, s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[299, 33237, 32856])).
% 3.52/3.71 tff(33239,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 3.52/3.71 inference(rewrite,[status(thm)],[])).
% 3.52/3.71 tff(33240,plain,
% 3.52/3.71 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 3.52/3.71 inference(rewrite,[status(thm)],[])).
% 3.52/3.71 tff(33241,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33240])).
% 3.52/3.71 tff(33242,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 3.52/3.71 inference(transitivity,[status(thm)],[33241, 33239])).
% 3.52/3.71 tff(33243,plain,
% 3.52/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 3.52/3.71 inference(quant_inst,[status(thm)],[])).
% 3.52/3.71 tff(33244,plain,
% 3.52/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33243, 33242])).
% 3.52/3.71 tff(33245,plain,
% 3.52/3.71 (~r(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33244, 121, 33238, 33235, 108])).
% 3.52/3.71 tff(33246,plain,
% 3.52/3.71 (~r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24792, 33235, 33238, 108])).
% 3.52/3.71 tff(33247,plain,
% 3.52/3.71 (~r(s(z), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[9263, 33238, 19197, 9983, 32853, 348])).
% 3.52/3.71 tff(33248,plain,
% 3.52/3.71 (~(s(s(z)) = s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[960, 33236])).
% 3.52/3.71 tff(33249,plain,
% 3.52/3.71 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[953, 33248])).
% 3.52/3.71 tff(33250,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[946, 33249])).
% 3.52/3.71 tff(33251,plain,
% 3.52/3.71 (b(s(z), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[444, 33247, 348])).
% 3.52/3.71 tff(33252,plain,
% 3.52/3.71 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[9276, 33251, 71])).
% 3.52/3.71 tff(33253,plain,
% 3.52/3.71 (~r(z, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24748, 1409, 9983, 412])).
% 3.52/3.71 tff(33254,plain,
% 3.52/3.71 (b(z, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1214, 33253])).
% 3.52/3.71 tff(33255,plain,
% 3.52/3.71 (s(s(s(z))) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[255, 2346, 221])).
% 3.52/3.71 tff(33256,plain,
% 3.52/3.71 (~b(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[6165, 33255, 317])).
% 3.52/3.71 tff(33257,plain,
% 3.52/3.71 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[3906, 33255])).
% 3.52/3.71 tff(33258,plain,
% 3.52/3.71 (s(s(s(z))) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[255, 3757, 2346])).
% 3.52/3.71 tff(33259,plain,
% 3.52/3.71 (r(s(z), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[250, 33258, 108])).
% 3.52/3.71 tff(33260,plain,
% 3.52/3.71 (~b(s(s(s(z))), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23140, 33258, 24871])).
% 3.52/3.71 tff(33261,plain,
% 3.52/3.71 (r(s(s(s(z))), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2325, 33260])).
% 3.52/3.71 tff(33262,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2611, 33258])).
% 3.52/3.71 tff(33263,plain,
% 3.52/3.71 (b(s(s(s(elem!1))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[486, 33262, 147])).
% 3.52/3.71 tff(33264,plain,
% 3.52/3.71 (r(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[32984, 33263, 108, 1326, 68, 379, 220, 1, 412, 1008, 33259, 348, 438, 2073, 24743, 3757])).
% 3.52/3.71 tff(33265,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24825, 33264, 33261, 1500, 33259])).
% 3.52/3.71 tff(33266,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(z), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33267,plain,
% 3.52/3.71 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33266, 33257, 1326, 108, 9983, 220, 1, 412, 1008, 348, 438, 2073, 147, 2346])).
% 3.52/3.71 tff(33268,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1816, 33267, 33256, 2033])).
% 3.52/3.71 tff(33269,plain,(b(s(s(s(z))), elem!1) | (s(s(s(z))) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(z), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | b(elem!1, s(elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33270,plain,
% 3.52/3.71 (b(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33269, 147, 1326, 108, 220, 1, 412, 1008, 348, 438, 2073, 2033, 317, 221])).
% 3.52/3.71 tff(33271,plain,
% 3.52/3.71 (~b(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2020, 33270, 33254, 1326])).
% 3.52/3.71 tff(33272,plain,
% 3.52/3.71 (elem!1 = s(s(s(z)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1192, 33271, 10297])).
% 3.52/3.71 tff(33273,plain,
% 3.52/3.71 (s(s(s(z))) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1100, 33272])).
% 3.52/3.71 tff(33274,plain,
% 3.52/3.71 (~b(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[6165, 33273, 317])).
% 3.52/3.71 tff(33275,plain,
% 3.52/3.71 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[3906, 33273])).
% 3.52/3.71 tff(33276,plain,
% 3.52/3.71 (elem!1 = s(s(s(z)))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1192, 24743, 11112])).
% 3.52/3.71 tff(33277,plain,
% 3.52/3.71 (s(s(s(z))) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1100, 33276])).
% 3.52/3.71 tff(33278,plain,
% 3.52/3.71 (r(s(z), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[250, 33277, 108])).
% 3.52/3.71 tff(33279,plain,
% 3.52/3.71 (~b(s(s(s(z))), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23140, 33277, 24871])).
% 3.52/3.71 tff(33280,plain,
% 3.52/3.71 (r(s(s(s(z))), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2325, 33279])).
% 3.52/3.71 tff(33281,plain,
% 3.52/3.71 (~r(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[15964, 33278, 1409, 220, 24776])).
% 3.52/3.71 tff(33282,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2611, 33277])).
% 3.52/3.71 tff(33283,plain,
% 3.52/3.71 (b(s(s(s(elem!1))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[486, 33282, 147])).
% 3.52/3.71 tff(33284,plain,
% 3.52/3.71 (r(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[32984, 33283, 108, 1326, 68, 379, 220, 1, 412, 1008, 33278, 348, 438, 2073, 24743, 33281])).
% 3.52/3.71 tff(33285,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24825, 33284, 33280, 1500, 33278])).
% 3.52/3.71 tff(33286,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(z), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, z)) | r(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33287,plain,
% 3.52/3.71 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33286, 33275, 1326, 108, 9983, 220, 1, 412, 1008, 348, 438, 2073, 1409, 147, 33271])).
% 3.52/3.71 tff(33288,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1816, 33287, 33274, 2033])).
% 3.52/3.71 tff(33289,plain,(r(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(z), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, z)) | b(elem!1, s(elem!1)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33290,plain,
% 3.52/3.71 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33289, 33252, 32853, 108, 220, 1, 32855, 33250, 348, 33247, 19776, 33231, 317, 33246, 33245])).
% 3.52/3.71 tff(33291,plain,
% 3.52/3.71 (r(s(s(s(z))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1816, 16598, 2033])).
% 3.52/3.71 tff(33292,plain,
% 3.52/3.71 (~b(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[3823, 27993, 379, 412, 139, 17291])).
% 3.52/3.71 tff(33293,plain,
% 3.52/3.71 (r(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[429, 33292, 422])).
% 3.52/3.71 tff(33294,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24825, 33293, 33291, 2327, 27993])).
% 3.52/3.71 tff(33295,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (s(s(s(z))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | b(elem!1, s(elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33296,plain,
% 3.52/3.71 (~(s(s(s(z))) = elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33295, 33235, 2282, 33252, 9983, 32855, 33290, 317, 108])).
% 3.52/3.71 tff(33297,plain,
% 3.52/3.71 (b(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[255, 33296, 33245])).
% 3.52/3.71 tff(33298,plain,
% 3.52/3.71 (~(elem!1 = s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1100, 33296])).
% 3.52/3.71 tff(33299,plain,
% 3.52/3.71 (b(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1192, 33298, 33246])).
% 3.52/3.71 tff(33300,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[2020, 33299, 33297, 33233, 32853])).
% 3.52/3.71 tff(33301,plain,(r(z, elem!1) | b(elem!1, s(elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33302,plain,
% 3.52/3.71 (r(z, elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33301, 317, 108, 11199, 1, 348, 71, 906])).
% 3.52/3.71 tff(33303,plain,
% 3.52/3.71 (~r(elem!1, z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24723, 9983, 33302, 32852])).
% 3.52/3.71 tff(33304,plain,
% 3.52/3.71 (b(elem!1, z)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[284, 33303, 9298])).
% 3.52/3.71 tff(33305,plain,
% 3.52/3.71 (~b(elem!1, s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[31758, 271, 19197, 33304, 11199])).
% 3.52/3.71 tff(33306,plain,
% 3.52/3.71 (~r(z, s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[12090, 33302, 9983, 32852])).
% 3.52/3.71 tff(33307,plain,
% 3.52/3.71 (b(z, s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[1439, 33306])).
% 3.52/3.71 tff(33308,plain,
% 3.52/3.71 (~b(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[24719, 33307, 11199, 19197])).
% 3.52/3.71 tff(33309,plain,
% 3.52/3.71 (r(s(elem!1), s(z))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[429, 33308, 2282])).
% 3.52/3.71 tff(33310,plain,
% 3.52/3.71 (~b(s(z), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[31765, 271, 19197, 33304, 11199])).
% 3.52/3.71 tff(33311,plain,
% 3.52/3.71 (s(z) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[23287, 33310, 9983, 33309, 33305])).
% 3.52/3.71 tff(33312,plain,
% 3.52/3.71 (r(z, s(z)) <=> r(z, elem!1)),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33311])).
% 3.52/3.71 tff(33313,plain,
% 3.52/3.71 (r(z, elem!1) <=> r(z, s(z))),
% 3.52/3.71 inference(symmetry,[status(thm)],[33312])).
% 3.52/3.71 tff(33314,plain,
% 3.52/3.71 (r(z, s(z))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33302, 33313])).
% 3.52/3.71 tff(33315,plain,
% 3.52/3.71 ($false),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[899, 33314])).
% 3.52/3.71 tff(33316,plain,(b(elem!1, s(elem!1)) | r(z, s(z)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.71 tff(33317,plain,
% 3.52/3.71 (b(elem!1, s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[33316, 348, 108, 1, 899, 71, 906])).
% 3.52/3.71 tff(33318,plain,
% 3.52/3.71 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[28184, 2344, 307, 1, 108, 906, 220, 348, 71])).
% 3.52/3.71 tff(33319,plain,
% 3.52/3.71 (~(elem!1 = s(s(s(elem!1))))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[19808, 2346, 19776])).
% 3.52/3.71 tff(33320,plain,
% 3.52/3.71 (~(s(s(s(elem!1))) = elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[13222, 33319])).
% 3.52/3.71 tff(33321,plain,
% 3.52/3.71 (s(z) = elem!1),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[236, 232, 1242])).
% 3.52/3.71 tff(33322,plain,
% 3.52/3.71 (s(s(z)) = s(elem!1)),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33321])).
% 3.52/3.71 tff(33323,plain,
% 3.52/3.71 (s(s(s(z))) = s(s(elem!1))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33322])).
% 3.52/3.71 tff(33324,plain,
% 3.52/3.71 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33323])).
% 3.52/3.71 tff(33325,plain,
% 3.52/3.71 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33321])).
% 3.52/3.71 tff(33326,plain,
% 3.52/3.71 (r(elem!1, s(s(s(z))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[108, 33325])).
% 3.52/3.71 tff(33327,plain,
% 3.52/3.71 (r(elem!1, s(s(elem!1)))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[33326, 33324])).
% 3.52/3.71 tff(33328,plain,
% 3.52/3.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[718, 121, 622, 33327, 139])).
% 3.52/3.71 tff(33329,plain,
% 3.52/3.71 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33323])).
% 3.52/3.71 tff(33330,plain,
% 3.52/3.71 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.52/3.71 inference(monotonicity,[status(thm)],[33329])).
% 3.52/3.71 tff(33331,plain,
% 3.52/3.71 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.71 inference(modus_ponens,[status(thm)],[906, 33330])).
% 3.52/3.71 tff(33332,plain,
% 3.52/3.71 (r(s(s(s(z))), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[255, 251, 2346])).
% 3.52/3.71 tff(33333,plain,
% 3.52/3.71 (r(s(s(elem!1)), elem!1)),
% 3.52/3.71 inference(unit_resolution,[status(thm)],[14112, 33321, 33332])).
% 3.52/3.71 tff(33334,plain,
% 3.52/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33335,plain,
% 3.52/3.72 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33336,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33335])).
% 3.52/3.72 tff(33337,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.72 inference(transitivity,[status(thm)],[33336, 33334])).
% 3.52/3.72 tff(33338,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.52/3.72 inference(quant_inst,[status(thm)],[])).
% 3.52/3.72 tff(33339,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33338, 33337])).
% 3.52/3.72 tff(33340,plain,
% 3.52/3.72 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33339, 121, 622, 33327, 33333])).
% 3.52/3.72 tff(33341,plain,
% 3.52/3.72 ($false),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[13884, 33340, 33331, 2344, 2467, 481, 33328])).
% 3.52/3.72 tff(33342,plain,(r(s(z), elem!1) | r(elem!1, s(elem!1)) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.72 tff(33343,plain,
% 3.52/3.72 (r(s(z), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33342, 33320, 2467, 2344, 622, 139, 906, 108, 2346, 1242])).
% 3.52/3.72 tff(33344,plain,
% 3.52/3.72 (~(elem!1 = s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[25463, 33343])).
% 3.52/3.72 tff(33345,plain,
% 3.52/3.72 (r(elem!1, s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[299, 33344, 294])).
% 3.52/3.72 tff(33346,plain,
% 3.52/3.72 (~r(s(s(s(z))), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[4112, 33345, 108, 33343])).
% 3.52/3.72 tff(33347,plain,
% 3.52/3.72 (s(s(s(z))) = elem!1),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[255, 33346, 2346])).
% 3.52/3.72 tff(33348,plain,
% 3.52/3.72 (elem!1 = s(s(s(z)))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33347])).
% 3.52/3.72 tff(33349,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33348])).
% 3.52/3.72 tff(33350,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 3.52/3.72 inference(symmetry,[status(thm)],[33349])).
% 3.52/3.72 tff(33351,plain,
% 3.52/3.72 (s(elem!1) = s(s(s(s(z))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[2605, 33347])).
% 3.52/3.72 tff(33352,plain,
% 3.52/3.72 (s(s(s(s(z)))) = s(elem!1)),
% 3.52/3.72 inference(symmetry,[status(thm)],[33351])).
% 3.52/3.72 tff(33353,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33352, 33347])).
% 3.52/3.72 tff(33354,plain,
% 3.52/3.72 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33353])).
% 3.52/3.72 tff(33355,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[622, 33354])).
% 3.52/3.72 tff(33356,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), elem!1)),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33355, 33350])).
% 3.52/3.72 tff(33357,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33351])).
% 3.52/3.72 tff(33358,plain,
% 3.52/3.72 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[3888, 33345, 139, 622])).
% 3.52/3.72 tff(33359,plain,
% 3.52/3.72 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[3906, 33347])).
% 3.52/3.72 tff(33360,plain,
% 3.52/3.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[78, 33359])).
% 3.52/3.72 tff(33361,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[681, 33360, 33358])).
% 3.52/3.72 tff(33362,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33361, 33357])).
% 3.52/3.72 tff(33363,plain,
% 3.52/3.72 (~r(s(z), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[6525, 33345, 622, 33343])).
% 3.52/3.72 tff(33364,plain,
% 3.52/3.72 (b(s(z), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[444, 33363, 348])).
% 3.52/3.72 tff(33365,plain,
% 3.52/3.72 (b(s(z), s(s(s(s(z)))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[9597, 33351, 33364])).
% 3.52/3.72 tff(33366,plain,
% 3.52/3.72 (~r(s(s(s(elem!1))), s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[4618, 121, 33343, 139, 33345])).
% 3.52/3.72 tff(33367,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[16580, 33366])).
% 3.52/3.72 tff(33368,plain,
% 3.52/3.72 (~b(s(s(s(s(z)))), s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1075, 33367, 33365, 33362])).
% 3.52/3.72 tff(33369,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[932, 33368])).
% 3.52/3.72 tff(33370,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33371,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.52/3.72 inference(quant_inst,[status(thm)],[])).
% 3.52/3.72 tff(33372,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33371, 33370])).
% 3.52/3.72 tff(33373,plain,
% 3.52/3.72 ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33372, 121, 33343, 33345])).
% 3.52/3.72 tff(33374,plain,
% 3.52/3.72 (~r(s(s(s(s(z)))), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33373, 33369])).
% 3.52/3.72 tff(33375,plain,
% 3.52/3.72 ($false),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33374, 33356])).
% 3.52/3.72 tff(33376,plain,(b(s(s(s(z))), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z)) | b(s(elem!1), elem!1) | r(elem!1, s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.72 tff(33377,plain,
% 3.52/3.72 (b(s(s(s(z))), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33376, 24773, 8448, 348, 108, 139, 2467, 2344, 906, 27263])).
% 3.52/3.72 tff(33378,plain,
% 3.52/3.72 (~(s(elem!1) = s(s(s(z))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[8462, 33377, 2467])).
% 3.52/3.72 tff(33379,plain,
% 3.52/3.72 (~b(z, s(s(s(z))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1978, 33377, 307, 1326])).
% 3.52/3.72 tff(33380,plain,
% 3.52/3.72 (r(z, s(s(s(z))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1214, 33379])).
% 3.52/3.72 tff(33381,plain,
% 3.52/3.72 (~b(s(s(s(z))), z)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1940, 33377, 307, 1326])).
% 3.52/3.72 tff(33382,plain,
% 3.52/3.72 (r(s(s(s(z))), z)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1155, 33381])).
% 3.52/3.72 tff(33383,plain,
% 3.52/3.72 (~r(s(elem!1), s(s(s(z))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[15486, 121, 412, 33382, 33380])).
% 3.52/3.72 tff(33384,plain,
% 3.52/3.72 (b(s(elem!1), s(s(s(z))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[2044, 33383, 33378])).
% 3.52/3.72 tff(33385,plain,
% 3.52/3.72 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[22644, 121, 412, 33382, 33380])).
% 3.52/3.72 tff(33386,plain,
% 3.52/3.72 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[9276, 9034, 71])).
% 3.52/3.72 tff(33387,plain,
% 3.52/3.72 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1816, 33386, 1510])).
% 3.52/3.72 tff(33388,plain,
% 3.52/3.72 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33387, 7849])).
% 3.52/3.72 tff(33389,plain,
% 3.52/3.72 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[24187, 223, 2038])).
% 3.52/3.72 tff(33390,plain,
% 3.52/3.72 (b(s(elem!1), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[526, 33389, 216])).
% 3.52/3.72 tff(33391,plain,
% 3.52/3.72 ($false),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[857, 271, 307, 33390, 1383, 33388])).
% 3.52/3.72 tff(33392,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(elem!1)) | (s(elem!1) = s(s(elem!1))) | b(s(z), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.72 tff(33393,plain,
% 3.52/3.72 (~(s(z) = elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33392, 33377, 307, 33385, 216, 71, 33383])).
% 3.52/3.72 tff(33394,plain,
% 3.52/3.72 (r(s(z), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[236, 33393, 27263])).
% 3.52/3.72 tff(33395,plain,
% 3.52/3.72 (~(elem!1 = s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[242, 33393])).
% 3.52/3.72 tff(33396,plain,
% 3.52/3.72 (r(elem!1, s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[299, 33395, 24773])).
% 3.52/3.72 tff(33397,plain,
% 3.52/3.72 (~r(s(z), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[6525, 33396, 8448, 33394])).
% 3.52/3.72 tff(33398,plain,
% 3.52/3.72 (b(s(z), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[444, 33397, 348])).
% 3.52/3.72 tff(33399,plain,
% 3.52/3.72 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[9276, 33398, 71])).
% 3.52/3.72 tff(33400,plain,
% 3.52/3.72 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1816, 33399, 33385])).
% 3.52/3.72 tff(33401,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33402,plain,
% 3.52/3.72 (((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33403,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33402])).
% 3.52/3.72 tff(33404,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.52/3.72 inference(transitivity,[status(thm)],[33403, 33401])).
% 3.52/3.72 tff(33405,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 3.52/3.72 inference(quant_inst,[status(thm)],[])).
% 3.52/3.72 tff(33406,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33405, 33404])).
% 3.52/3.72 tff(33407,plain,
% 3.52/3.72 ($false),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33406, 271, 307, 33400, 33384, 33377])).
% 3.52/3.72 tff(33408,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | b(s(z), s(s(s(z)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), z)) | b(s(elem!1), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | r(elem!1, s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.72 tff(33409,plain,
% 3.52/3.72 (~b(z, elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33408, 2467, 71, 348, 216, 412, 307, 108, 139, 2344, 906, 1281, 220])).
% 3.52/3.72 tff(33410,plain,
% 3.52/3.72 (~(s(z) = elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[229, 33409, 220])).
% 3.52/3.72 tff(33411,plain,
% 3.52/3.72 (~(elem!1 = s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[242, 33410])).
% 3.52/3.72 tff(33412,plain,
% 3.52/3.72 (r(z, elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[355, 33409, 9297])).
% 3.52/3.72 tff(33413,plain,
% 3.52/3.72 (~r(elem!1, s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[5343, 33412, 412, 8448])).
% 3.52/3.72 tff(33414,plain,
% 3.52/3.72 (b(elem!1, s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[299, 33413, 33411])).
% 3.52/3.72 tff(33415,plain,
% 3.52/3.72 (~r(elem!1, z)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[5358, 33412, 412, 8448])).
% 3.52/3.72 tff(33416,plain,
% 3.52/3.72 (b(elem!1, z)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[284, 33415, 9298])).
% 3.52/3.72 tff(33417,plain,
% 3.52/3.72 (~b(s(z), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[8962, 33416, 220, 33414])).
% 3.52/3.72 tff(33418,plain,
% 3.52/3.72 (r(s(z), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[236, 33417, 33410])).
% 3.52/3.72 tff(33419,plain,
% 3.52/3.72 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[13202])).
% 3.52/3.72 tff(33420,plain,
% 3.52/3.72 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), elem!1)),
% 3.52/3.72 inference(symmetry,[status(thm)],[33419])).
% 3.52/3.72 tff(33421,plain,
% 3.52/3.72 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(elem!1), elem!1))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33420])).
% 3.52/3.72 tff(33422,plain,
% 3.52/3.72 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[13101, 26241, 139, 412])).
% 3.52/3.72 tff(33423,plain,
% 3.52/3.72 (~r(s(elem!1), elem!1)),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33422, 33421])).
% 3.52/3.72 tff(33424,plain,
% 3.52/3.72 ($false),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[622, 33423])).
% 3.52/3.72 tff(33425,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.72 tff(33426,plain,
% 3.52/3.72 (~(elem!1 = s(s(s(elem!1))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33425, 8448, 139, 412, 33409])).
% 3.52/3.72 tff(33427,plain,
% 3.52/3.72 (~r(elem!1, s(s(s(elem!1))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[6817, 33412, 412, 8448])).
% 3.52/3.72 tff(33428,plain,
% 3.52/3.72 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[660, 21, 33427])).
% 3.52/3.72 tff(33429,plain,
% 3.52/3.72 (b(elem!1, s(s(s(elem!1))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33428, 33426])).
% 3.52/3.72 tff(33430,plain,
% 3.52/3.72 (s(s(s(elem!1))) = s(elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[26272, 33429, 412, 307, 8448, 33412, 1281, 9298, 33418, 2282, 33411])).
% 3.52/3.72 tff(33431,plain,
% 3.52/3.72 (elem!1 = s(s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[78, 33430])).
% 3.52/3.72 tff(33432,plain,
% 3.52/3.72 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33431])).
% 3.52/3.72 tff(33433,plain,
% 3.52/3.72 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 3.52/3.72 inference(symmetry,[status(thm)],[33432])).
% 3.52/3.72 tff(33434,plain,
% 3.52/3.72 ((~b(s(s(elem!1)), z)) <=> (~b(elem!1, z))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33433])).
% 3.52/3.72 tff(33435,plain,
% 3.52/3.72 (~r(s(s(elem!1)), s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[12129, 33431, 33413])).
% 3.52/3.72 tff(33436,plain,
% 3.52/3.72 (b(s(s(elem!1)), s(z))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[2143, 33435])).
% 3.52/3.72 tff(33437,plain,
% 3.52/3.72 (~b(s(s(elem!1)), z)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[16949, 33436, 1281, 220])).
% 3.52/3.72 tff(33438,plain,
% 3.52/3.72 (~b(elem!1, z)),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33437, 33434])).
% 3.52/3.72 tff(33439,plain,
% 3.52/3.72 ($false),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33416, 33438])).
% 3.52/3.72 tff(33440,plain,(b(s(elem!1), elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | b(s(z), s(s(s(z)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.72 tff(33441,plain,
% 3.52/3.72 (b(s(elem!1), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33440, 28095, 220, 19197, 307, 33318, 71, 348, 211, 108, 2344, 906])).
% 3.52/3.72 tff(33442,plain,
% 3.52/3.72 (elem!1 = s(z)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[27249, 2356, 139, 412, 220, 2618, 307, 1, 108, 348, 232])).
% 3.52/3.72 tff(33443,plain,
% 3.52/3.72 (s(z) = elem!1),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[242, 33442])).
% 3.52/3.72 tff(33444,plain,
% 3.52/3.72 (s(s(z)) = s(elem!1)),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33443])).
% 3.52/3.72 tff(33445,plain,
% 3.52/3.72 (s(s(s(z))) = s(s(elem!1))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33444])).
% 3.52/3.72 tff(33446,plain,
% 3.52/3.72 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33445])).
% 3.52/3.72 tff(33447,plain,
% 3.52/3.72 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33446])).
% 3.52/3.72 tff(33448,plain,
% 3.52/3.72 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33447])).
% 3.52/3.72 tff(33449,plain,
% 3.52/3.72 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33448])).
% 3.52/3.72 tff(33450,plain,
% 3.52/3.72 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33449])).
% 3.52/3.72 tff(33451,plain,
% 3.52/3.72 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33447])).
% 3.52/3.72 tff(33452,plain,
% 3.52/3.72 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33451])).
% 3.52/3.72 tff(33453,plain,
% 3.52/3.72 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.52/3.72 inference(symmetry,[status(thm)],[33452])).
% 3.52/3.72 tff(33454,plain,
% 3.52/3.72 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33453])).
% 3.52/3.72 tff(33455,plain,
% 3.52/3.72 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[3049, 33443])).
% 3.52/3.72 tff(33456,plain,
% 3.52/3.72 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33455, 33454])).
% 3.52/3.72 tff(33457,plain,
% 3.52/3.72 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33446])).
% 3.52/3.72 tff(33458,plain,
% 3.52/3.72 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.72 inference(transitivity,[status(thm)],[33457, 200])).
% 3.52/3.72 tff(33459,plain,
% 3.52/3.72 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33458])).
% 3.52/3.72 tff(33460,plain,
% 3.52/3.72 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[17419, 2358])).
% 3.52/3.72 tff(33461,plain,
% 3.52/3.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33460, 33459])).
% 3.52/3.72 tff(33462,plain,
% 3.52/3.72 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33445])).
% 3.52/3.72 tff(33463,plain,
% 3.52/3.72 (b(z, elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[229, 33443, 220])).
% 3.52/3.72 tff(33464,plain,
% 3.52/3.72 (~b(z, s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[4606, 271, 307, 2618, 33463])).
% 3.52/3.72 tff(33465,plain,
% 3.52/3.72 (r(z, s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1439, 33464])).
% 3.52/3.72 tff(33466,plain,
% 3.52/3.72 (r(s(s(elem!1)), elem!1)),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[14112, 33443, 2356])).
% 3.52/3.72 tff(33467,plain,
% 3.52/3.72 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33445])).
% 3.52/3.72 tff(33468,plain,
% 3.52/3.72 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33443])).
% 3.52/3.72 tff(33469,plain,
% 3.52/3.72 (r(elem!1, s(s(s(z))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[108, 33468])).
% 3.52/3.72 tff(33470,plain,
% 3.52/3.72 (r(elem!1, s(s(elem!1)))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33469, 33467])).
% 3.52/3.72 tff(33471,plain,
% 3.52/3.72 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[5091, 121, 33470, 139, 33466])).
% 3.52/3.72 tff(33472,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[586, 33471, 563])).
% 3.52/3.72 tff(33473,plain,
% 3.52/3.72 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[2837, 26696])).
% 3.52/3.72 tff(33474,plain,
% 3.52/3.72 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[2363])).
% 3.52/3.72 tff(33475,plain,
% 3.52/3.72 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33474])).
% 3.52/3.72 tff(33476,plain,
% 3.52/3.72 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[23706])).
% 3.52/3.72 tff(33477,plain,
% 3.52/3.72 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.72 inference(transitivity,[status(thm)],[33476, 33475])).
% 3.52/3.72 tff(33478,plain,
% 3.52/3.72 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33477])).
% 3.52/3.72 tff(33479,plain,
% 3.52/3.72 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[2363])).
% 3.52/3.72 tff(33480,plain,
% 3.52/3.72 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33479])).
% 3.52/3.72 tff(33481,plain,
% 3.52/3.72 (~b(z, s(s(elem!1)))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[1209, 33480])).
% 3.52/3.72 tff(33482,plain,
% 3.52/3.72 (r(z, s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[2106, 33481])).
% 3.52/3.72 tff(33483,plain,
% 3.52/3.72 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[17708, 33482, 1441, 31768])).
% 3.52/3.72 tff(33484,plain,
% 3.52/3.72 (b(s(elem!1), s(s(elem!1)))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[526, 33483, 216])).
% 3.52/3.72 tff(33485,plain,
% 3.52/3.72 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[2363])).
% 3.52/3.72 tff(33486,plain,
% 3.52/3.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[2073, 33485])).
% 3.52/3.72 tff(33487,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33488,plain,
% 3.52/3.72 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33489,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[33488])).
% 3.52/3.72 tff(33490,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.52/3.72 inference(transitivity,[status(thm)],[33489, 33487])).
% 3.52/3.72 tff(33491,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.52/3.72 inference(quant_inst,[status(thm)],[])).
% 3.52/3.72 tff(33492,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33491, 33490])).
% 3.52/3.72 tff(33493,plain,
% 3.52/3.72 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[33492, 271, 33486, 33484, 589])).
% 3.52/3.72 tff(33494,plain,
% 3.52/3.72 (~b(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[23654, 33493, 2359])).
% 3.52/3.72 tff(33495,plain,
% 3.52/3.72 (r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1995, 33494, 26383])).
% 3.52/3.72 tff(33496,plain,
% 3.52/3.72 (r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33495, 23641])).
% 3.52/3.72 tff(33497,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[2364])).
% 3.52/3.72 tff(33498,plain,
% 3.52/3.72 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[2363])).
% 3.52/3.72 tff(33499,plain,
% 3.52/3.72 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33498])).
% 3.52/3.72 tff(33500,plain,
% 3.52/3.72 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.72 inference(monotonicity,[status(thm)],[2364])).
% 3.52/3.72 tff(33501,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.52/3.72 inference(symmetry,[status(thm)],[33500])).
% 3.52/3.72 tff(33502,plain,
% 3.52/3.72 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.72 inference(transitivity,[status(thm)],[33501, 33499])).
% 3.52/3.72 tff(33503,plain,
% 3.52/3.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[589, 33502])).
% 3.52/3.72 tff(33504,plain,
% 3.52/3.72 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[31781, 6533, 412, 2073, 145, 239, 33503, 216])).
% 3.52/3.72 tff(33505,plain,
% 3.52/3.72 (r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.72 inference(unit_resolution,[status(thm)],[1559, 33504, 1548])).
% 3.52/3.72 tff(33506,plain,
% 3.52/3.72 (r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.72 inference(modus_ponens,[status(thm)],[33505, 33497])).
% 3.52/3.72 tff(33507,plain,
% 3.52/3.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.72 inference(rewrite,[status(thm)],[])).
% 3.52/3.72 tff(33508,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.72 inference(quant_inst,[status(thm)],[])).
% 3.52/3.72 tff(33509,plain,
% 3.52/3.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33508, 33507])).
% 3.52/3.73 tff(33510,plain,
% 3.52/3.73 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33509, 271, 543, 589, 5044])).
% 3.52/3.73 tff(33511,plain,
% 3.52/3.73 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[8221, 33510, 1591])).
% 3.52/3.73 tff(33512,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33513,plain,
% 3.52/3.73 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33514,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33513])).
% 3.52/3.73 tff(33515,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.52/3.73 inference(transitivity,[status(thm)],[33514, 33512])).
% 3.52/3.73 tff(33516,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.52/3.73 inference(quant_inst,[status(thm)],[])).
% 3.52/3.73 tff(33517,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33516, 33515])).
% 3.52/3.73 tff(33518,plain,
% 3.52/3.73 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33517, 271, 543, 517, 5044])).
% 3.52/3.73 tff(33519,plain,
% 3.52/3.73 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[3112, 21, 3109, 33518])).
% 3.52/3.73 tff(33520,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33521,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.52/3.73 inference(quant_inst,[status(thm)],[])).
% 3.52/3.73 tff(33522,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33521, 33520])).
% 3.52/3.73 tff(33523,plain,
% 3.52/3.73 ($false),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33522, 121, 684, 798, 33519, 33511])).
% 3.52/3.73 tff(33524,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.73 tff(33525,plain,
% 3.52/3.73 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33524, 33506, 33496, 3109, 1591, 33486, 589, 33484])).
% 3.52/3.73 tff(33526,plain,
% 3.52/3.73 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33525, 33478])).
% 3.52/3.73 tff(33527,plain,
% 3.52/3.73 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1733, 33526])).
% 3.52/3.73 tff(33528,plain,
% 3.52/3.73 (~r(z, s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[16283, 33527, 145, 6533])).
% 3.52/3.73 tff(33529,plain,
% 3.52/3.73 (b(z, s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1658, 33528])).
% 3.52/3.73 tff(33530,plain,
% 3.52/3.73 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[32671, 33529, 307, 1326])).
% 3.52/3.73 tff(33531,plain,
% 3.52/3.73 (r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[840, 33530, 10355])).
% 3.52/3.73 tff(33532,plain,
% 3.52/3.73 (r(s(s(s(s(s(z))))), s(z))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33531, 23703])).
% 3.52/3.73 tff(33533,plain,
% 3.52/3.73 (~r(s(s(s(s(s(z))))), s(z))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[23750, 33527, 108, 145])).
% 3.52/3.73 tff(33534,plain,
% 3.52/3.73 ($false),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33533, 33532])).
% 3.52/3.73 tff(33535,plain,(b(z, s(s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.73 tff(33536,plain,
% 3.52/3.73 (b(z, s(s(s(z))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33535, 33463, 307, 2356, 108, 33473, 1577, 33472, 211, 33465, 2358, 412, 2073, 33442])).
% 3.52/3.73 tff(33537,plain,
% 3.52/3.73 (b(z, s(s(elem!1)))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33536, 33462])).
% 3.52/3.73 tff(33538,plain,
% 3.52/3.73 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33445])).
% 3.52/3.73 tff(33539,plain,
% 3.52/3.73 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[2073, 33538])).
% 3.52/3.73 tff(33540,plain,
% 3.52/3.73 (~b(s(s(s(elem!1))), z)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1900, 271, 33539, 33472, 33537])).
% 3.52/3.73 tff(33541,plain,
% 3.52/3.73 (r(s(s(s(elem!1))), z)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[8229, 33540])).
% 3.52/3.73 tff(33542,plain,
% 3.52/3.73 (~b(z, s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1911, 271, 33539, 33472, 33537])).
% 3.52/3.73 tff(33543,plain,
% 3.52/3.73 (r(z, s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[19736, 33542])).
% 3.52/3.73 tff(33544,plain,
% 3.52/3.73 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[7238, 121, 33543, 412, 33541])).
% 3.52/3.73 tff(33545,plain,
% 3.52/3.73 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[681, 33544, 33461])).
% 3.52/3.73 tff(33546,plain,
% 3.52/3.73 (~b(elem!1, s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[12887, 33545, 307, 2618])).
% 3.52/3.73 tff(33547,plain,
% 3.52/3.73 (~b(s(z), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[8233, 33546, 33443])).
% 3.52/3.73 tff(33548,plain,
% 3.52/3.73 (r(s(z), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[760, 33547])).
% 3.52/3.73 tff(33549,plain,
% 3.52/3.73 (r(elem!1, s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1045, 33548, 33443])).
% 3.52/3.73 tff(33550,plain,
% 3.52/3.73 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.73 inference(transitivity,[status(thm)],[33458, 2839])).
% 3.52/3.73 tff(33551,plain,
% 3.52/3.73 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33550])).
% 3.52/3.73 tff(33552,plain,
% 3.52/3.73 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33460, 33551])).
% 3.52/3.73 tff(33553,plain,
% 3.52/3.73 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[13101, 33543, 139, 412])).
% 3.52/3.73 tff(33554,plain,
% 3.52/3.73 (b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[2293, 21, 33553, 33552])).
% 3.52/3.73 tff(33555,plain,
% 3.52/3.73 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[10173, 33554, 307, 33545, 1577, 33549, 33456, 139])).
% 3.52/3.73 tff(33556,plain,
% 3.52/3.73 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33555, 33450])).
% 3.52/3.73 tff(33557,plain,
% 3.52/3.73 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33444])).
% 3.52/3.73 tff(33558,plain,
% 3.52/3.73 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33557])).
% 3.52/3.73 tff(33559,plain,
% 3.52/3.73 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[877, 33558])).
% 3.52/3.73 tff(33560,plain,
% 3.52/3.73 (~b(s(elem!1), s(s(elem!1)))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1459, 33545, 33539, 33472])).
% 3.52/3.73 tff(33561,plain,
% 3.52/3.73 (r(s(elem!1), s(s(elem!1)))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[526, 33560, 211])).
% 3.52/3.73 tff(33562,plain,
% 3.52/3.73 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33444])).
% 3.52/3.73 tff(33563,plain,
% 3.52/3.73 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 3.52/3.73 inference(symmetry,[status(thm)],[33562])).
% 3.52/3.73 tff(33564,plain,
% 3.52/3.73 (r(s(s(z)), z)),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[412, 33563])).
% 3.52/3.73 tff(33565,plain,
% 3.52/3.73 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33444])).
% 3.52/3.73 tff(33566,plain,
% 3.52/3.73 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 3.52/3.73 inference(symmetry,[status(thm)],[33565])).
% 3.52/3.73 tff(33567,plain,
% 3.52/3.73 (r(z, s(s(z)))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33465, 33566])).
% 3.52/3.73 tff(33568,plain,
% 3.52/3.73 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33444])).
% 3.52/3.73 tff(33569,plain,
% 3.52/3.73 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 3.52/3.73 inference(symmetry,[status(thm)],[33568])).
% 3.52/3.73 tff(33570,plain,
% 3.52/3.73 (s(s(elem!1)) = s(s(s(z)))),
% 3.52/3.73 inference(symmetry,[status(thm)],[33445])).
% 3.52/3.73 tff(33571,plain,
% 3.52/3.73 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33570])).
% 3.52/3.73 tff(33572,plain,
% 3.52/3.73 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 3.52/3.73 inference(transitivity,[status(thm)],[33571, 33569])).
% 3.52/3.73 tff(33573,plain,
% 3.52/3.73 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(z))), s(s(z))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33572])).
% 3.52/3.73 tff(33574,plain,
% 3.52/3.73 (~b(s(s(elem!1)), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[5254, 33554, 33539, 33545])).
% 3.52/3.73 tff(33575,plain,
% 3.52/3.73 (~b(s(s(s(z))), s(s(z)))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33574, 33573])).
% 3.52/3.73 tff(33576,plain,
% 3.52/3.73 (r(s(s(s(z))), s(s(z)))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1368, 33575])).
% 3.52/3.73 tff(33577,plain,
% 3.52/3.73 (~r(s(s(s(z))), z)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[21564, 33576, 33567, 33564])).
% 3.52/3.73 tff(33578,plain,
% 3.52/3.73 (b(s(s(s(z))), z)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1155, 33577])).
% 3.52/3.73 tff(33579,plain,
% 3.52/3.73 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33446])).
% 3.52/3.73 tff(33580,plain,
% 3.52/3.73 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.73 inference(symmetry,[status(thm)],[33579])).
% 3.52/3.73 tff(33581,plain,
% 3.52/3.73 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33580])).
% 3.52/3.73 tff(33582,plain,
% 3.52/3.73 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33553, 33581])).
% 3.52/3.73 tff(33583,plain,
% 3.52/3.73 (b(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1995, 33582, 33460])).
% 3.52/3.73 tff(33584,plain,
% 3.52/3.73 (r(elem!1, s(s(s(z))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[108, 17590])).
% 3.52/3.73 tff(33585,plain,
% 3.52/3.73 (r(elem!1, s(s(elem!1)))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33584, 6711])).
% 3.52/3.73 tff(33586,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33587,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~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))))))),
% 3.52/3.73 inference(quant_inst,[status(thm)],[])).
% 3.52/3.73 tff(33588,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~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)))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33587, 33586])).
% 3.52/3.73 tff(33589,plain,
% 3.52/3.73 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33588, 121, 33585, 139, 3081])).
% 3.52/3.73 tff(33590,plain,
% 3.52/3.73 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33589, 14669])).
% 3.52/3.73 tff(33591,plain,
% 3.52/3.73 (~b(z, s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[28951, 3061, 220, 1935, 145, 108])).
% 3.52/3.73 tff(33592,plain,
% 3.52/3.73 (r(z, s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1658, 33591])).
% 3.52/3.73 tff(33593,plain,
% 3.52/3.73 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[6368, 33592, 1441, 627])).
% 3.52/3.73 tff(33594,plain,
% 3.52/3.73 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[4138, 33593, 4962])).
% 3.52/3.73 tff(33595,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33596,plain,
% 3.52/3.73 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33597,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33596])).
% 3.52/3.73 tff(33598,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.52/3.73 inference(transitivity,[status(thm)],[33597, 33595])).
% 3.52/3.73 tff(33599,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.52/3.73 inference(quant_inst,[status(thm)],[])).
% 3.52/3.73 tff(33600,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33599, 33598])).
% 3.52/3.73 tff(33601,plain,
% 3.52/3.73 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33600, 121, 33585, 139, 3081])).
% 3.52/3.73 tff(33602,plain,
% 3.52/3.73 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[6896, 33601, 223])).
% 3.52/3.73 tff(33603,plain,
% 3.52/3.73 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1777, 33602])).
% 3.52/3.73 tff(33604,plain,
% 3.52/3.73 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[14690, 33603, 14671, 33594])).
% 3.52/3.73 tff(33605,plain,
% 3.52/3.73 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[9512, 33604])).
% 3.52/3.73 tff(33606,plain,
% 3.52/3.73 ($false),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33605, 33590])).
% 3.52/3.73 tff(33607,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.73 tff(33608,plain,
% 3.52/3.73 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33607, 33443, 33583, 139, 33465, 33561, 220, 33578, 2356, 108])).
% 3.52/3.73 tff(33609,plain,
% 3.52/3.73 (b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[840, 33608, 33455])).
% 3.52/3.73 tff(33610,plain,
% 3.52/3.73 (~b(z, s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[32671, 33609, 307, 33463])).
% 3.52/3.73 tff(33611,plain,
% 3.52/3.73 (r(z, s(s(s(s(s(z))))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1658, 33610])).
% 3.52/3.73 tff(33612,plain,
% 3.52/3.73 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[6368, 33611, 33465, 33561])).
% 3.52/3.73 tff(33613,plain,
% 3.52/3.73 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[4138, 33612, 33559])).
% 3.52/3.73 tff(33614,plain,
% 3.52/3.73 ($false),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33613, 33556])).
% 3.52/3.73 tff(33615,plain,(b(s(s(s(z))), elem!1) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.73 tff(33616,plain,
% 3.52/3.73 (b(s(s(s(z))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33615, 232, 139, 220, 108, 2618, 412, 2073, 1, 348, 307])).
% 3.52/3.73 tff(33617,plain,
% 3.52/3.73 (~b(s(s(s(elem!1))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[23787, 33616, 2073, 307])).
% 3.52/3.73 tff(33618,plain,
% 3.52/3.73 (elem!1 = s(z)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[27190, 33616, 139, 1, 220, 33617, 307, 2618, 412, 348, 232])).
% 3.52/3.73 tff(33619,plain,
% 3.52/3.73 (s(z) = elem!1),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[242, 33618])).
% 3.52/3.73 tff(33620,plain,
% 3.52/3.73 (b(s(z), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[1276, 33619, 307])).
% 3.52/3.73 tff(33621,plain,
% 3.52/3.73 (b(z, elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[229, 33619, 220])).
% 3.52/3.73 tff(33622,plain,
% 3.52/3.73 (b(elem!1, z)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[20120, 33619, 19197])).
% 3.52/3.73 tff(33623,plain,
% 3.52/3.73 (s(s(s(z))) = s(elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[23566, 33622, 2618, 33616, 33621])).
% 3.52/3.73 tff(33624,plain,
% 3.52/3.73 ($false),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[9276, 33623, 33620, 71])).
% 3.52/3.73 tff(33625,plain,(r(s(z), elem!1) | b(s(z), s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.73 tff(33626,plain,
% 3.52/3.73 (r(s(z), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33625, 2618, 71, 307, 220, 139, 1, 412, 348, 2073, 108])).
% 3.52/3.73 tff(33627,plain,
% 3.52/3.73 (~(elem!1 = s(z))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[25463, 33626])).
% 3.52/3.73 tff(33628,plain,
% 3.52/3.73 (~r(s(s(s(z))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[26024, 378, 33626, 220, 9298, 19197, 33627, 108])).
% 3.52/3.73 tff(33629,plain,
% 3.52/3.73 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[10594])).
% 3.52/3.73 tff(33630,plain,
% 3.52/3.73 (~b(s(z), elem!1)),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[71, 33629])).
% 3.52/3.73 tff(33631,plain,
% 3.52/3.73 (~(elem!1 = s(z))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[25463, 357])).
% 3.52/3.73 tff(33632,plain,
% 3.52/3.73 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 3.52/3.73 inference(transitivity,[status(thm)],[28004, 1837])).
% 3.52/3.73 tff(33633,plain,
% 3.52/3.73 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33632])).
% 3.52/3.73 tff(33634,plain,
% 3.52/3.73 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[1489, 33633])).
% 3.52/3.73 tff(33635,plain,
% 3.52/3.73 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 3.52/3.73 inference(symmetry,[status(thm)],[23145])).
% 3.52/3.73 tff(33636,plain,
% 3.52/3.73 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[4024])).
% 3.52/3.73 tff(33637,plain,
% 3.52/3.73 (b(elem!1, s(s(s(s(z)))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[307, 33636])).
% 3.52/3.73 tff(33638,plain,
% 3.52/3.73 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.52/3.73 inference(monotonicity,[status(thm)],[4024])).
% 3.52/3.73 tff(33639,plain,
% 3.52/3.73 (b(s(s(s(s(z)))), elem!1)),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[2618, 33638])).
% 3.52/3.73 tff(33640,plain,
% 3.52/3.73 (~b(s(z), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[3019, 448, 307, 2618])).
% 3.52/3.73 tff(33641,plain,
% 3.52/3.73 (r(s(z), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[444, 33640, 348])).
% 3.52/3.73 tff(33642,plain,
% 3.52/3.73 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[17876, 33641, 412, 220])).
% 3.52/3.73 tff(33643,plain,
% 3.52/3.73 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[4138, 33642, 24523])).
% 3.52/3.73 tff(33644,plain,
% 3.52/3.73 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(symmetry,[status(thm)],[4039])).
% 3.52/3.73 tff(33645,plain,
% 3.52/3.73 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33644])).
% 3.52/3.73 tff(33646,plain,
% 3.52/3.73 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[31384, 33645])).
% 3.52/3.73 tff(33647,plain,
% 3.52/3.73 ($false),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[9894, 33646])).
% 3.52/3.73 tff(33648,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.73 tff(33649,plain,
% 3.52/3.73 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33648, 33643, 4024])).
% 3.52/3.73 tff(33650,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(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)))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33651,plain,
% 3.52/3.73 (((~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(s(z))))), elem!1)) | (~b(s(s(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)))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33652,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(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))))))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33651])).
% 3.52/3.73 tff(33653,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(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)))))))),
% 3.52/3.73 inference(transitivity,[status(thm)],[33652, 33650])).
% 3.52/3.73 tff(33654,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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)))),
% 3.52/3.73 inference(quant_inst,[status(thm)],[])).
% 3.52/3.73 tff(33655,plain,
% 3.52/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(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))))))),
% 3.52/3.73 inference(modus_ponens,[status(thm)],[33654, 33653])).
% 3.52/3.73 tff(33656,plain,
% 3.52/3.73 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[33655, 271, 33649, 33639, 33637])).
% 3.52/3.73 tff(33657,plain,
% 3.52/3.73 (r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.73 inference(unit_resolution,[status(thm)],[840, 33656, 4997])).
% 3.52/3.73 tff(33658,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33659,plain,
% 3.52/3.73 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.52/3.73 inference(rewrite,[status(thm)],[])).
% 3.52/3.73 tff(33660,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.52/3.73 inference(monotonicity,[status(thm)],[33659])).
% 3.52/3.73 tff(33661,plain,
% 3.52/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33660, 33658])).
% 3.52/3.74 tff(33662,plain,
% 3.52/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.52/3.74 inference(quant_inst,[status(thm)],[])).
% 3.52/3.74 tff(33663,plain,
% 3.52/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33662, 33661])).
% 3.52/3.74 tff(33664,plain,
% 3.52/3.74 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33663, 271, 33649, 33639, 33637])).
% 3.52/3.74 tff(33665,plain,
% 3.52/3.74 (r(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1847, 33664, 15994])).
% 3.52/3.74 tff(33666,plain,
% 3.52/3.74 (~r(z, s(s(s(s(s(z))))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[5017, 33665, 378, 33657])).
% 3.52/3.74 tff(33667,plain,
% 3.52/3.74 (b(z, s(s(s(s(s(z))))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1658, 33666])).
% 3.52/3.74 tff(33668,plain,
% 3.52/3.74 (b(z, s(s(elem!1)))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33667, 33635])).
% 3.52/3.74 tff(33669,plain,
% 3.52/3.74 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[9696, 4024])).
% 3.52/3.74 tff(33670,plain,
% 3.52/3.74 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33669])).
% 3.52/3.74 tff(33671,plain,
% 3.52/3.74 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33649, 33670])).
% 3.52/3.74 tff(33672,plain,
% 3.52/3.74 (~b(s(s(elem!1)), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[6807, 33671, 307, 2618])).
% 3.52/3.74 tff(33673,plain,
% 3.52/3.74 (r(s(s(elem!1)), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[862, 33672, 851])).
% 3.52/3.74 tff(33674,plain,
% 3.52/3.74 (~r(elem!1, z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[6958, 33673, 139, 1, 563, 378])).
% 3.52/3.74 tff(33675,plain,
% 3.52/3.74 (b(elem!1, z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[284, 33674, 9298])).
% 3.52/3.74 tff(33676,plain,
% 3.52/3.74 (~b(z, s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[5420, 33675, 19197, 448])).
% 3.52/3.74 tff(33677,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33676, 33668])).
% 3.52/3.74 tff(33678,plain,((~b(elem!1, s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (elem!1 = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33679,plain,
% 3.52/3.74 (~b(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33678, 2606, 139, 1, 378, 16513, 33634, 28006, 307, 2618, 412, 220, 348])).
% 3.52/3.74 tff(33680,plain,
% 3.52/3.74 (~r(s(z), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[18965, 33679, 139, 33631, 33630])).
% 3.52/3.74 tff(33681,plain,
% 3.52/3.74 (b(s(z), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[760, 33680])).
% 3.52/3.74 tff(33682,plain,
% 3.52/3.74 (r(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[299, 33679, 33631])).
% 3.52/3.74 tff(33683,plain,
% 3.52/3.74 (~r(s(s(s(elem!1))), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[4618, 121, 357, 139, 33682])).
% 3.52/3.74 tff(33684,plain,
% 3.52/3.74 (b(s(s(s(elem!1))), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[16580, 33683])).
% 3.52/3.74 tff(33685,plain,
% 3.52/3.74 (~r(z, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[26178, 121, 378, 139, 33682])).
% 3.52/3.74 tff(33686,plain,
% 3.52/3.74 (b(z, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[19736, 33685])).
% 3.52/3.74 tff(33687,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[17333, 33686, 33684, 220, 33681])).
% 3.52/3.74 tff(33688,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33689,plain,
% 3.52/3.74 (~(s(s(s(z))) = elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33688, 378, 220, 139, 33626, 1, 307, 2618, 412, 348, 71])).
% 3.52/3.74 tff(33690,plain,
% 3.52/3.74 (b(s(s(s(z))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[255, 33689, 33628])).
% 3.52/3.74 tff(33691,plain,
% 3.52/3.74 (~b(s(s(s(z))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[13128, 271, 307, 2618, 33690])).
% 3.52/3.74 tff(33692,plain,
% 3.52/3.74 (~r(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[26182, 378, 33626, 139, 220])).
% 3.52/3.74 tff(33693,plain,
% 3.52/3.74 (b(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[299, 33692, 33627])).
% 3.52/3.74 tff(33694,plain,
% 3.52/3.74 (~b(s(z), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3019, 33693, 307, 2618])).
% 3.52/3.74 tff(33695,plain,
% 3.52/3.74 (r(s(z), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[444, 33694, 348])).
% 3.52/3.74 tff(33696,plain,
% 3.52/3.74 (~b(s(elem!1), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1290, 33693, 19197, 307])).
% 3.52/3.74 tff(33697,plain,
% 3.52/3.74 (r(s(elem!1), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[429, 33696, 2282])).
% 3.52/3.74 tff(33698,plain,
% 3.52/3.74 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[23235, 33697, 33695, 108])).
% 3.52/3.74 tff(33699,plain,
% 3.52/3.74 (s(s(s(z))) = s(elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1816, 33698, 33691])).
% 3.52/3.74 tff(33700,plain,
% 3.52/3.74 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33699])).
% 3.52/3.74 tff(33701,plain,
% 3.52/3.74 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33700])).
% 3.52/3.74 tff(33702,plain,
% 3.52/3.74 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33701])).
% 3.52/3.74 tff(33703,plain,
% 3.52/3.74 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33699])).
% 3.52/3.74 tff(33704,plain,
% 3.52/3.74 (s(s(z)) = elem!1),
% 3.52/3.74 inference(transitivity,[status(thm)],[92, 33703, 70])).
% 3.52/3.74 tff(33705,plain,
% 3.52/3.74 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33704])).
% 3.52/3.74 tff(33706,plain,
% 3.52/3.74 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33705, 1837])).
% 3.52/3.74 tff(33707,plain,
% 3.52/3.74 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33706])).
% 3.52/3.74 tff(33708,plain,
% 3.52/3.74 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[877, 33707])).
% 3.52/3.74 tff(33709,plain,
% 3.52/3.74 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33699])).
% 3.52/3.74 tff(33710,plain,
% 3.52/3.74 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33709])).
% 3.52/3.74 tff(33711,plain,
% 3.52/3.74 (b(elem!1, s(s(s(z))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[307, 33710])).
% 3.52/3.74 tff(33712,plain,
% 3.52/3.74 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33699])).
% 3.52/3.74 tff(33713,plain,
% 3.52/3.74 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33712])).
% 3.52/3.74 tff(33714,plain,
% 3.52/3.74 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33713])).
% 3.52/3.74 tff(33715,plain,
% 3.52/3.74 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[17876, 33695, 412, 220])).
% 3.52/3.74 tff(33716,plain,
% 3.52/3.74 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33715, 33714])).
% 3.52/3.74 tff(33717,plain,
% 3.52/3.74 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1733, 33716])).
% 3.52/3.74 tff(33718,plain,
% 3.52/3.74 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1857, 33717, 33690, 33711])).
% 3.52/3.74 tff(33719,plain,
% 3.52/3.74 (r(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1847, 33718, 33708])).
% 3.52/3.74 tff(33720,plain,
% 3.52/3.74 (r(elem!1, s(s(s(elem!1))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33719, 33702])).
% 3.52/3.74 tff(33721,plain,
% 3.52/3.74 (~b(s(s(s(elem!1))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[23787, 33690, 2073, 307])).
% 3.52/3.74 tff(33722,plain,
% 3.52/3.74 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3790, 33721, 2618])).
% 3.52/3.74 tff(33723,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[78, 33722])).
% 3.52/3.74 tff(33724,plain,
% 3.52/3.74 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33701])).
% 3.52/3.74 tff(33725,plain,
% 3.52/3.74 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33724])).
% 3.52/3.74 tff(33726,plain,
% 3.52/3.74 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33715, 33725])).
% 3.52/3.74 tff(33727,plain,
% 3.52/3.74 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[681, 33726, 33723])).
% 3.52/3.74 tff(33728,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2596, 33699])).
% 3.52/3.74 tff(33729,plain,
% 3.52/3.74 (~b(elem!1, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[12887, 33727, 307, 2618])).
% 3.52/3.74 tff(33730,plain,
% 3.52/3.74 (~r(z, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[12884, 33729, 378, 33721, 33728])).
% 3.52/3.74 tff(33731,plain,
% 3.52/3.74 (b(z, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[19736, 33730])).
% 3.52/3.74 tff(33732,plain,
% 3.52/3.74 (~b(s(z), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[21846, 33731, 19197, 33727])).
% 3.52/3.74 tff(33733,plain,
% 3.52/3.74 (r(s(z), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[760, 33732])).
% 3.52/3.74 tff(33734,plain,
% 3.52/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 3.52/3.74 inference(rewrite,[status(thm)],[])).
% 3.52/3.74 tff(33735,plain,
% 3.52/3.74 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 3.52/3.74 inference(rewrite,[status(thm)],[])).
% 3.52/3.74 tff(33736,plain,
% 3.52/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33735])).
% 3.52/3.74 tff(33737,plain,
% 3.52/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33736, 33734])).
% 3.52/3.74 tff(33738,plain,
% 3.52/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 3.52/3.74 inference(quant_inst,[status(thm)],[])).
% 3.52/3.74 tff(33739,plain,
% 3.52/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33738, 33737])).
% 3.52/3.74 tff(33740,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33739, 121, 33626, 33733, 139, 33720])).
% 3.52/3.74 tff(33741,plain,((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33742,plain,
% 3.52/3.74 (~r(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33741, 33318, 307, 33441, 28095, 220, 108, 348, 19776, 1, 71])).
% 3.52/3.74 tff(33743,plain,
% 3.52/3.74 (b(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[355, 33742, 9297])).
% 3.52/3.74 tff(33744,plain,
% 3.52/3.74 (~b(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[20398, 33743, 19197, 220])).
% 3.52/3.74 tff(33745,plain,
% 3.52/3.74 (r(s(z), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33625, 33441, 71, 307, 220, 33318, 1, 28095, 348, 19776, 108])).
% 3.52/3.74 tff(33746,plain,
% 3.52/3.74 (~(elem!1 = s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[25463, 33745])).
% 3.52/3.74 tff(33747,plain,
% 3.52/3.74 (~b(s(z), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[20382, 33743, 19197, 307])).
% 3.52/3.74 tff(33748,plain,
% 3.52/3.74 (~r(s(z), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[18965, 33747, 33318, 33746, 33744])).
% 3.52/3.74 tff(33749,plain,
% 3.52/3.74 (b(s(z), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[760, 33748])).
% 3.52/3.74 tff(33750,plain,
% 3.52/3.74 (r(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[299, 33744, 33746])).
% 3.52/3.74 tff(33751,plain,
% 3.52/3.74 (~r(s(s(s(elem!1))), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[4618, 121, 33745, 33318, 33750])).
% 3.52/3.74 tff(33752,plain,
% 3.52/3.74 (b(s(s(s(elem!1))), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[16580, 33751])).
% 3.52/3.74 tff(33753,plain,
% 3.52/3.74 (~b(z, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[17333, 33752, 220, 33749])).
% 3.52/3.74 tff(33754,plain,
% 3.52/3.74 (r(z, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[19736, 33753])).
% 3.52/3.74 tff(33755,plain,
% 3.52/3.74 (~r(s(s(s(z))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[4112, 33750, 108, 33745])).
% 3.52/3.74 tff(33756,plain,
% 3.52/3.74 (~b(s(s(s(elem!1))), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[27482, 271, 33749, 220, 33752])).
% 3.52/3.74 tff(33757,plain,
% 3.52/3.74 (r(s(s(s(elem!1))), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[8229, 33756])).
% 3.52/3.74 tff(33758,plain,
% 3.52/3.74 (~b(z, s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[4606, 271, 307, 33441, 33743])).
% 3.52/3.74 tff(33759,plain,
% 3.52/3.74 (r(z, s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1439, 33758])).
% 3.52/3.74 tff(33760,plain,
% 3.52/3.74 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[7087, 121, 33759, 28095, 33757])).
% 3.52/3.74 tff(33761,plain,
% 3.52/3.74 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[12887, 27998, 307, 2618])).
% 3.52/3.74 tff(33762,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[681, 33761, 17291, 676])).
% 3.52/3.74 tff(33763,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33764,plain,
% 3.52/3.74 (~(s(s(s(z))) = elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33763, 33760, 307, 33441, 19776])).
% 3.52/3.74 tff(33765,plain,
% 3.52/3.74 (b(s(s(s(z))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[255, 33764, 33755])).
% 3.52/3.74 tff(33766,plain,
% 3.52/3.74 (~b(s(s(s(elem!1))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[23787, 33765, 19776, 307])).
% 3.52/3.74 tff(33767,plain,
% 3.52/3.74 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3790, 33766, 33441])).
% 3.52/3.74 tff(33768,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[78, 33767])).
% 3.52/3.74 tff(33769,plain,
% 3.52/3.74 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[681, 33768, 33760])).
% 3.52/3.74 tff(33770,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2562, 33749, 33747])).
% 3.52/3.74 tff(33771,plain,
% 3.52/3.74 (~b(elem!1, s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[12887, 33769, 307, 33441])).
% 3.52/3.74 tff(33772,plain,
% 3.52/3.74 (~r(elem!1, s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[21266, 33771, 33750, 1, 33770, 33766, 33749, 33769])).
% 3.52/3.74 tff(33773,plain,
% 3.52/3.74 (b(elem!1, s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[599, 33772, 33767])).
% 3.52/3.74 tff(33774,plain,
% 3.52/3.74 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[84, 33768])).
% 3.52/3.74 tff(33775,plain,
% 3.52/3.74 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[13101, 33754, 33318, 28095])).
% 3.52/3.74 tff(33776,plain,
% 3.52/3.74 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2293, 21, 33775])).
% 3.52/3.74 tff(33777,plain,
% 3.52/3.74 (b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33776, 33774])).
% 3.52/3.74 tff(33778,plain,
% 3.52/3.74 (~b(s(s(elem!1)), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[18873, 33773, 307, 33777])).
% 3.52/3.74 tff(33779,plain,
% 3.52/3.74 (r(s(s(elem!1)), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[701, 33778, 3313])).
% 3.52/3.74 tff(33780,plain,
% 3.52/3.74 (~b(s(s(s(z))), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2081, 33752, 19776, 33749])).
% 3.52/3.74 tff(33781,plain,
% 3.52/3.74 (r(s(s(s(z))), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2325, 33780])).
% 3.52/3.74 tff(33782,plain,
% 3.52/3.74 (~r(elem!1, s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[11254, 33781, 33745, 33750])).
% 3.52/3.74 tff(33783,plain,
% 3.52/3.74 (~(elem!1 = s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1100, 33764])).
% 3.52/3.74 tff(33784,plain,
% 3.52/3.74 (b(elem!1, s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1192, 33783, 33782])).
% 3.52/3.74 tff(33785,plain,
% 3.52/3.74 (s(s(s(z))) = s(elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[13144, 33784, 307, 28095, 33441, 33765, 33743])).
% 3.52/3.74 tff(33786,plain,
% 3.52/3.74 (~b(s(z), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[9276, 33785, 71])).
% 3.52/3.74 tff(33787,plain,
% 3.52/3.74 (r(s(z), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[444, 33786, 348])).
% 3.52/3.74 tff(33788,plain,
% 3.52/3.74 (~r(s(s(elem!1)), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[14657, 33779, 28095, 33759])).
% 3.52/3.74 tff(33789,plain,
% 3.52/3.74 (b(s(s(elem!1)), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2430, 33788])).
% 3.52/3.74 tff(33790,plain,
% 3.52/3.74 (~b(s(z), s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[17014, 33789, 19197, 220])).
% 3.52/3.74 tff(33791,plain,
% 3.52/3.74 (r(s(z), s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2167, 33790])).
% 3.52/3.74 tff(33792,plain,
% 3.52/3.74 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3275, 33791, 33787, 33779])).
% 3.52/3.74 tff(33793,plain,
% 3.52/3.74 (b(s(elem!1), s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[526, 33792, 211])).
% 3.52/3.74 tff(33794,plain,
% 3.52/3.74 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[9687, 33793, 307, 33773])).
% 3.52/3.74 tff(33795,plain,
% 3.52/3.74 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[556, 33794, 1])).
% 3.52/3.74 tff(33796,plain,
% 3.52/3.74 (~(s(s(elem!1)) = elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[197, 33767])).
% 3.52/3.74 tff(33797,plain,
% 3.52/3.74 (~b(s(s(elem!1)), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[11355, 33789, 33743, 33784])).
% 3.52/3.74 tff(33798,plain,
% 3.52/3.74 (r(s(s(elem!1)), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[862, 33797, 33796])).
% 3.52/3.74 tff(33799,plain,
% 3.52/3.74 (~b(s(s(elem!1)), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[16949, 33789, 19197, 220])).
% 3.52/3.74 tff(33800,plain,
% 3.52/3.74 (r(s(s(elem!1)), s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2143, 33799])).
% 3.52/3.74 tff(33801,plain,
% 3.52/3.74 (~r(elem!1, z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[26043, 33800, 33745, 33798])).
% 3.52/3.74 tff(33802,plain,
% 3.52/3.74 (b(elem!1, z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[284, 33801, 9298])).
% 3.52/3.74 tff(33803,plain,
% 3.52/3.74 (~b(z, s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[20129, 33802, 33773, 33789])).
% 3.52/3.74 tff(33804,plain,
% 3.52/3.74 (r(z, s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2106, 33803])).
% 3.52/3.74 tff(33805,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3425, 33804, 33795, 33318, 33754])).
% 3.52/3.74 tff(33806,plain,(r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | b(s(z), s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33807,plain,
% 3.52/3.74 (r(elem!1, s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33806, 33317, 1, 11199, 348, 71, 108, 906])).
% 3.52/3.74 tff(33808,plain,
% 3.52/3.74 (~b(s(elem!1), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[27984, 33807, 11199, 348, 1, 906, 108, 71])).
% 3.52/3.74 tff(33809,plain,
% 3.52/3.74 (r(s(elem!1), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[409, 33808])).
% 3.52/3.74 tff(33810,plain,
% 3.52/3.74 (~r(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3683, 8563, 379, 412])).
% 3.52/3.74 tff(33811,plain,
% 3.52/3.74 (b(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[355, 33810, 331])).
% 3.52/3.74 tff(33812,plain,
% 3.52/3.74 (~b(elem!1, s(z))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[20398, 33811, 19197, 220])).
% 3.52/3.74 tff(33813,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[23545, 33812, 33811, 412, 422, 307, 147, 2073, 2467, 1])).
% 3.52/3.74 tff(33814,plain,(b(s(elem!1), elem!1) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(elem!1, s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (z = elem!1) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33815,plain,
% 3.52/3.74 (b(s(elem!1), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33814, 147, 422, 307, 412, 2073, 1, 220, 331, 379])).
% 3.52/3.74 tff(33816,plain,
% 3.52/3.74 (b(s(s(s(z))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[28109, 1326, 412, 1281, 220, 147, 108, 307, 2618, 2073, 907])).
% 3.52/3.74 tff(33817,plain,
% 3.52/3.74 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[26813, 33816, 307, 2073, 147])).
% 3.52/3.74 tff(33818,plain,
% 3.52/3.74 (~b(z, s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1978, 33816, 307, 1326])).
% 3.52/3.74 tff(33819,plain,
% 3.52/3.74 (r(z, s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1214, 33818])).
% 3.52/3.74 tff(33820,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[13140, 33819, 33817, 307, 412, 2618, 33816])).
% 3.52/3.74 tff(33821,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33822,plain,
% 3.52/3.74 (s(s(s(z))) = elem!1),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33821, 1326, 412, 2618, 2073, 147, 1281, 220, 108, 307])).
% 3.52/3.74 tff(33823,plain,
% 3.52/3.74 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3906, 33822])).
% 3.52/3.74 tff(33824,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[78, 33823])).
% 3.52/3.74 tff(33825,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2611, 33822])).
% 3.52/3.74 tff(33826,plain,
% 3.52/3.74 (b(s(s(s(elem!1))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[486, 33825, 147])).
% 3.52/3.74 tff(33827,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[23507, 33826, 33824, 307, 412, 1326])).
% 3.52/3.74 tff(33828,plain,((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33829,plain,
% 3.52/3.74 (~b(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33828, 147, 412, 307, 33815, 2073, 19197, 220, 108])).
% 3.52/3.74 tff(33830,plain,
% 3.52/3.74 (r(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[355, 33829, 331])).
% 3.52/3.74 tff(33831,plain,
% 3.52/3.74 (~r(z, s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[12090, 33830, 379, 412])).
% 3.52/3.74 tff(33832,plain,
% 3.52/3.74 (b(z, s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1439, 33831])).
% 3.52/3.74 tff(33833,plain,
% 3.52/3.74 (~r(elem!1, z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[24723, 33830, 379, 412])).
% 3.52/3.74 tff(33834,plain,
% 3.52/3.74 (b(elem!1, z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[284, 33833, 358])).
% 3.52/3.74 tff(33835,plain,
% 3.52/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))),
% 3.52/3.74 inference(rewrite,[status(thm)],[])).
% 3.52/3.74 tff(33836,plain,
% 3.52/3.74 (((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 3.52/3.74 inference(rewrite,[status(thm)],[])).
% 3.52/3.74 tff(33837,plain,
% 3.52/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1)))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33836])).
% 3.52/3.74 tff(33838,plain,
% 3.52/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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, z)) | (~b(z, s(elem!1))))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33837, 33835])).
% 3.52/3.74 tff(33839,plain,
% 3.52/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 3.52/3.74 inference(quant_inst,[status(thm)],[])).
% 3.52/3.74 tff(33840,plain,
% 3.52/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1)))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33839, 33838])).
% 3.52/3.74 tff(33841,plain,
% 3.52/3.74 ($false),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33840, 271, 307, 33815, 33834, 33832])).
% 3.52/3.74 tff(33842,plain,(r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (z = elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.74 tff(33843,plain,
% 3.52/3.74 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33842, 33317, 33807, 33809, 9297, 19776, 11199, 108, 2282, 1])).
% 3.52/3.74 tff(33844,plain,
% 3.52/3.74 (r(elem!1, s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33806, 307, 1, 220, 348, 71, 108, 906])).
% 3.52/3.74 tff(33845,plain,
% 3.52/3.74 (~b(s(elem!1), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[27984, 33844, 220, 348, 1, 906, 108, 71])).
% 3.52/3.74 tff(33846,plain,
% 3.52/3.74 (r(s(elem!1), z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[409, 33845])).
% 3.52/3.74 tff(33847,plain,
% 3.52/3.74 (~r(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[3683, 622, 33844, 33846])).
% 3.52/3.74 tff(33848,plain,
% 3.52/3.74 (b(z, elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[355, 33847, 9297])).
% 3.52/3.74 tff(33849,plain,
% 3.52/3.74 (~b(s(z), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[20382, 33848, 19197, 307])).
% 3.52/3.74 tff(33850,plain,
% 3.52/3.74 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33842, 307, 33844, 33846, 9297, 19776, 220, 108, 2282, 1])).
% 3.52/3.74 tff(33851,plain,
% 3.52/3.74 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[25513, 33850, 33844, 33846])).
% 3.52/3.74 tff(33852,plain,
% 3.52/3.74 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33321])).
% 3.52/3.74 tff(33853,plain,
% 3.52/3.74 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33852])).
% 3.52/3.74 tff(33854,plain,
% 3.52/3.74 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33324, 33853])).
% 3.52/3.74 tff(33855,plain,
% 3.52/3.74 (r(s(z), s(s(elem!1)))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33326, 33854])).
% 3.52/3.74 tff(33856,plain,
% 3.52/3.74 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33321])).
% 3.52/3.74 tff(33857,plain,
% 3.52/3.74 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33856])).
% 3.52/3.74 tff(33858,plain,
% 3.52/3.74 (r(s(z), s(elem!1))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[379, 33857])).
% 3.52/3.74 tff(33859,plain,
% 3.52/3.74 (elem!1 = s(z)),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[1221, 33321])).
% 3.52/3.74 tff(33860,plain,
% 3.52/3.74 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33321])).
% 3.52/3.74 tff(33861,plain,
% 3.52/3.74 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33860])).
% 3.52/3.74 tff(33862,plain,
% 3.52/3.74 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33322])).
% 3.52/3.74 tff(33863,plain,
% 3.52/3.74 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33862])).
% 3.52/3.74 tff(33864,plain,
% 3.52/3.74 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33863, 33861])).
% 3.52/3.74 tff(33865,plain,
% 3.52/3.74 (r(s(z), s(s(z)))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[379, 33864])).
% 3.52/3.74 tff(33866,plain,
% 3.52/3.74 (r(elem!1, s(s(z)))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[379, 33863])).
% 3.52/3.74 tff(33867,plain,
% 3.52/3.74 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33323])).
% 3.52/3.74 tff(33868,plain,
% 3.52/3.74 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33867])).
% 3.52/3.74 tff(33869,plain,
% 3.52/3.74 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33868, 200])).
% 3.52/3.74 tff(33870,plain,
% 3.52/3.74 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33869])).
% 3.52/3.74 tff(33871,plain,
% 3.52/3.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33460, 33870])).
% 3.52/3.74 tff(33872,plain,
% 3.52/3.74 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33867, 33321])).
% 3.52/3.74 tff(33873,plain,
% 3.52/3.74 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 3.52/3.74 inference(symmetry,[status(thm)],[33872])).
% 3.52/3.74 tff(33874,plain,
% 3.52/3.74 (r(s(s(s(s(z)))), s(z))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[139, 33873])).
% 3.52/3.74 tff(33875,plain,
% 3.52/3.74 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33322])).
% 3.52/3.74 tff(33876,plain,
% 3.52/3.74 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 3.52/3.74 inference(symmetry,[status(thm)],[33875])).
% 3.52/3.74 tff(33877,plain,
% 3.52/3.74 (r(s(s(z)), elem!1)),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[622, 33876])).
% 3.52/3.74 tff(33878,plain,
% 3.52/3.74 (~b(s(elem!1), s(s(s(z))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[22811, 33877, 2073, 33859, 33874, 33871, 33866, 33865])).
% 3.52/3.74 tff(33879,plain,
% 3.52/3.74 (~b(s(elem!1), s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2369, 33878, 33859])).
% 3.52/3.74 tff(33880,plain,
% 3.52/3.74 (r(s(elem!1), s(s(elem!1)))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[526, 33879, 216])).
% 3.52/3.74 tff(33881,plain,
% 3.52/3.74 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[681, 33871, 676])).
% 3.52/3.74 tff(33882,plain,
% 3.52/3.74 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33323])).
% 3.52/3.74 tff(33883,plain,
% 3.52/3.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[2073, 33882])).
% 3.52/3.74 tff(33884,plain,
% 3.52/3.74 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.74 inference(transitivity,[status(thm)],[33869, 2839])).
% 3.52/3.74 tff(33885,plain,
% 3.52/3.74 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 3.52/3.74 inference(monotonicity,[status(thm)],[33884])).
% 3.52/3.74 tff(33886,plain,
% 3.52/3.74 (~(s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.74 inference(modus_ponens,[status(thm)],[33460, 33885])).
% 3.52/3.74 tff(33887,plain,
% 3.52/3.74 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[9184, 622, 379, 139])).
% 3.52/3.74 tff(33888,plain,
% 3.52/3.74 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[2293, 21, 33887])).
% 3.52/3.74 tff(33889,plain,
% 3.52/3.74 (b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.74 inference(unit_resolution,[status(thm)],[33888, 33886])).
% 3.52/3.75 tff(33890,plain,
% 3.52/3.75 (~b(s(s(elem!1)), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[5254, 33889, 33883, 33881])).
% 3.52/3.75 tff(33891,plain,
% 3.52/3.75 (r(s(s(elem!1)), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[701, 33890, 8423])).
% 3.52/3.75 tff(33892,plain,
% 3.52/3.75 ($false),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[3275, 33891, 33880, 33858, 33855])).
% 3.52/3.75 tff(33893,plain,(r(s(z), elem!1) | (s(elem!1) = s(s(elem!1))) | r(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.75 tff(33894,plain,
% 3.52/3.75 (r(s(z), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33893, 622, 33851, 19776, 33850, 33844, 211, 108, 33849])).
% 3.52/3.75 tff(33895,plain,
% 3.52/3.75 (~(elem!1 = s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[25463, 33894])).
% 3.52/3.75 tff(33896,plain,
% 3.52/3.75 (~(s(z) = elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1221, 33895])).
% 3.52/3.75 tff(33897,plain,
% 3.52/3.75 (~b(elem!1, s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20398, 33848, 19197, 220])).
% 3.52/3.75 tff(33898,plain,
% 3.52/3.75 (~r(s(elem!1), s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[23287, 33896, 33844, 33897, 33849])).
% 3.52/3.75 tff(33899,plain,
% 3.52/3.75 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[32989, 33898, 33844, 108, 33846, 220, 1, 33896, 348, 19776, 33848, 71, 33849])).
% 3.52/3.75 tff(33900,plain,
% 3.52/3.75 (b(s(elem!1), s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[429, 33898, 2282])).
% 3.52/3.75 tff(33901,plain,
% 3.52/3.75 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[9637, 33894, 348, 33844, 33850, 622])).
% 3.52/3.75 tff(33902,plain,
% 3.52/3.75 (s(s(s(elem!1))) = s(elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[681, 33901, 33851])).
% 3.52/3.75 tff(33903,plain,
% 3.52/3.75 (elem!1 = s(s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[78, 33902])).
% 3.52/3.75 tff(33904,plain,
% 3.52/3.75 (~(s(s(s(z))) = elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[3906, 33903])).
% 3.52/3.75 tff(33905,plain,
% 3.52/3.75 ($false),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33092, 33904, 33900, 220, 33844, 33896, 33847, 1, 906, 33849, 33899, 71, 348, 108])).
% 3.52/3.75 tff(33906,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), s(s(s(z)))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.75 tff(33907,plain,
% 3.52/3.75 (~r(s(elem!1), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33906, 348, 1, 906, 71, 11199, 108, 33317])).
% 3.52/3.75 tff(33908,plain,
% 3.52/3.75 (b(s(elem!1), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[2243, 33907, 2207])).
% 3.52/3.75 tff(33909,plain,
% 3.52/3.75 (r(s(z), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33625, 33908, 71, 33317, 11199, 33843, 1, 33809, 348, 19776, 108])).
% 3.52/3.75 tff(33910,plain,
% 3.52/3.75 (~(elem!1 = s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[25463, 33909])).
% 3.52/3.75 tff(33911,plain,
% 3.52/3.75 (~(s(z) = elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1221, 33910])).
% 3.52/3.75 tff(33912,plain,
% 3.52/3.75 (~r(z, elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33741, 33908, 33317, 33843, 33809, 11199, 108, 348, 19776, 1, 71])).
% 3.52/3.75 tff(33913,plain,
% 3.52/3.75 (b(z, elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[355, 33912, 9297])).
% 3.52/3.75 tff(33914,plain,
% 3.52/3.75 (~b(s(z), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20382, 33913, 19197, 33317])).
% 3.52/3.75 tff(33915,plain,
% 3.52/3.75 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[25513, 33843, 33807, 33809])).
% 3.52/3.75 tff(33916,plain,
% 3.52/3.75 (~(s(s(s(z))) = elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33763, 33908, 33317, 33915, 19776])).
% 3.52/3.75 tff(33917,plain,
% 3.52/3.75 (~b(elem!1, s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20398, 33913, 19197, 11199])).
% 3.52/3.75 tff(33918,plain,
% 3.52/3.75 (~r(s(elem!1), s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[23287, 33911, 33807, 33917, 33914])).
% 3.52/3.75 tff(33919,plain,
% 3.52/3.75 (b(s(elem!1), s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[429, 33918, 2282])).
% 3.52/3.75 tff(33920,plain,
% 3.52/3.75 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[32989, 33918, 33807, 108, 33809, 11199, 1, 33911, 348, 19776, 33913, 71, 33914])).
% 3.52/3.75 tff(33921,plain,
% 3.52/3.75 ($false),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33092, 33920, 33919, 11199, 33807, 33916, 33912, 1, 906, 33914, 33911, 71, 348, 108])).
% 3.52/3.75 tff(33922,plain,((s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | b(s(z), s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.75 tff(33923,plain,
% 3.52/3.75 (s(z) = s(elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33922, 71, 906, 1, 108, 899])).
% 3.52/3.75 tff(33924,plain,
% 3.52/3.75 (z = elem!1),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[343, 33923])).
% 3.52/3.75 tff(33925,plain,
% 3.52/3.75 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[10142, 33924])).
% 3.52/3.75 tff(33926,plain,
% 3.52/3.75 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[33925, 19053])).
% 3.52/3.75 tff(33927,plain,
% 3.52/3.75 (b(elem!1, s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[327, 33924, 11199])).
% 3.52/3.75 tff(33928,plain,
% 3.52/3.75 (elem!1 = z),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[364, 33924])).
% 3.52/3.75 tff(33929,plain,
% 3.52/3.75 (b(s(elem!1), z)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20985, 33928, 19197])).
% 3.52/3.75 tff(33930,plain,
% 3.52/3.75 (b(s(elem!1), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[2488, 33929, 33924])).
% 3.52/3.75 tff(33931,plain,
% 3.52/3.75 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33923])).
% 3.52/3.75 tff(33932,plain,
% 3.52/3.75 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33931, 1927])).
% 3.52/3.75 tff(33933,plain,
% 3.52/3.75 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33932, 10146])).
% 3.52/3.75 tff(33934,plain,
% 3.52/3.75 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33933])).
% 3.52/3.75 tff(33935,plain,
% 3.52/3.75 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[927, 33934])).
% 3.52/3.75 tff(33936,plain,
% 3.52/3.75 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33924])).
% 3.52/3.75 tff(33937,plain,
% 3.52/3.75 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33936, 2211])).
% 3.52/3.75 tff(33938,plain,
% 3.52/3.75 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33937])).
% 3.52/3.75 tff(33939,plain,
% 3.52/3.75 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[59, 33938])).
% 3.52/3.75 tff(33940,plain,
% 3.52/3.75 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33923])).
% 3.52/3.75 tff(33941,plain,
% 3.52/3.75 (~b(s(z), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[12838, 33924, 71])).
% 3.52/3.75 tff(33942,plain,
% 3.52/3.75 (r(s(z), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[760, 33941])).
% 3.52/3.75 tff(33943,plain,
% 3.52/3.75 (r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[33942, 33940])).
% 3.52/3.75 tff(33944,plain,
% 3.52/3.75 (b(elem!1, s(z))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[324, 9878, 220])).
% 3.52/3.75 tff(33945,plain,
% 3.52/3.75 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = s(elem!1))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.75 tff(33946,plain,
% 3.52/3.75 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33945])).
% 3.52/3.75 tff(33947,plain,
% 3.52/3.75 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[97, 33946])).
% 3.52/3.75 tff(33948,plain,
% 3.52/3.75 (b(z, s(z)) <=> b(z, s(elem!1))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.75 tff(33949,plain,
% 3.52/3.75 (b(z, s(elem!1))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[220, 33948])).
% 3.52/3.75 tff(33950,plain,
% 3.52/3.75 (b(s(elem!1), z)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20985, 19216, 19197])).
% 3.52/3.75 tff(33951,plain,
% 3.52/3.75 (~r(s(s(s(z))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[149, 147, 9878])).
% 3.52/3.75 tff(33952,plain,
% 3.52/3.75 (~r(s(s(s(z))), z)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[475, 33951, 9878])).
% 3.52/3.75 tff(33953,plain,
% 3.52/3.75 (~b(s(s(s(z))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1427, 33952, 33950, 33949])).
% 3.52/3.75 tff(33954,plain,
% 3.52/3.75 (r(s(s(s(z))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1816, 33953, 33947])).
% 3.52/3.75 tff(33955,plain,
% 3.52/3.75 (b(elem!1, s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[327, 9878, 220])).
% 3.52/3.75 tff(33956,plain,
% 3.52/3.75 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 3.52/3.75 inference(symmetry,[status(thm)],[19400])).
% 3.52/3.75 tff(33957,plain,
% 3.52/3.75 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[9937])).
% 3.52/3.75 tff(33958,plain,
% 3.52/3.75 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 3.52/3.75 inference(symmetry,[status(thm)],[33957])).
% 3.52/3.75 tff(33959,plain,
% 3.52/3.75 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.75 tff(33960,plain,
% 3.52/3.75 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33959, 33958, 33956])).
% 3.52/3.75 tff(33961,plain,
% 3.52/3.75 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.75 tff(33962,plain,
% 3.52/3.75 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33961, 1927])).
% 3.52/3.75 tff(33963,plain,
% 3.52/3.75 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33962, 10146])).
% 3.52/3.75 tff(33964,plain,
% 3.52/3.75 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33963])).
% 3.52/3.75 tff(33965,plain,
% 3.52/3.75 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[927, 33964])).
% 3.52/3.75 tff(33966,plain,
% 3.52/3.75 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.52/3.75 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.75 tff(33967,plain,
% 3.52/3.75 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33966, 2211])).
% 3.52/3.75 tff(33968,plain,
% 3.52/3.75 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33967])).
% 3.52/3.75 tff(33969,plain,
% 3.52/3.75 (~(elem!1 = s(s(elem!1)))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[59, 33968])).
% 3.52/3.75 tff(33970,plain,
% 3.52/3.75 ((~r(z, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33959])).
% 3.52/3.75 tff(33971,plain,
% 3.52/3.75 (~r(elem!1, s(s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[19734, 33970])).
% 3.52/3.75 tff(33972,plain,
% 3.52/3.75 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.75 tff(33973,plain,
% 3.52/3.75 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33972, 200])).
% 3.52/3.75 tff(33974,plain,
% 3.52/3.75 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33973])).
% 3.52/3.75 tff(33975,plain,
% 3.52/3.75 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[61, 33974])).
% 3.52/3.75 tff(33976,plain,
% 3.52/3.75 (b(s(s(s(elem!1))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[486, 147, 19261])).
% 3.52/3.75 tff(33977,plain,
% 3.52/3.75 (b(s(elem!1), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[2488, 33950, 9878])).
% 3.52/3.75 tff(33978,plain,
% 3.52/3.75 (b(s(s(s(z))), z)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1155, 33952])).
% 3.52/3.75 tff(33979,plain,
% 3.52/3.75 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.52/3.75 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.75 tff(33980,plain,
% 3.52/3.75 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33979, 159])).
% 3.52/3.75 tff(33981,plain,
% 3.52/3.75 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33980])).
% 3.52/3.75 tff(33982,plain,
% 3.52/3.75 (~(elem!1 = s(s(s(z))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[166, 33981])).
% 3.52/3.75 tff(33983,plain,
% 3.52/3.75 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 3.52/3.75 inference(symmetry,[status(thm)],[33959])).
% 3.52/3.75 tff(33984,plain,
% 3.52/3.75 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[33957, 33983])).
% 3.52/3.75 tff(33985,plain,
% 3.52/3.75 (r(z, s(s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[1184, 33984])).
% 3.52/3.75 tff(33986,plain,
% 3.52/3.75 ($false),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[19734, 33985])).
% 3.52/3.75 tff(33987,plain,((~r(elem!1, s(s(s(z))))) | r(z, s(s(s(elem!1)))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.75 tff(33988,plain,
% 3.52/3.75 (~r(elem!1, s(s(s(z))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[33987, 19734, 338])).
% 3.52/3.75 tff(33989,plain,
% 3.52/3.75 (b(elem!1, s(s(s(z))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1192, 33988, 33982])).
% 3.52/3.75 tff(33990,plain,
% 3.52/3.75 (b(elem!1, s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1198, 33989, 9878])).
% 3.52/3.75 tff(33991,plain,
% 3.52/3.75 (b(z, s(s(s(z))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[6057, 33990, 9878])).
% 3.52/3.75 tff(33992,plain,
% 3.52/3.75 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.75 inference(symmetry,[status(thm)],[19547])).
% 3.52/3.75 tff(33993,plain,
% 3.52/3.75 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[19545, 33992])).
% 3.52/3.75 tff(33994,plain,
% 3.52/3.75 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[33993])).
% 3.52/3.75 tff(33995,plain,
% 3.52/3.75 (b(s(z), s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[521, 517, 338])).
% 3.52/3.75 tff(33996,plain,
% 3.52/3.75 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[19650, 504, 33977, 448])).
% 3.52/3.75 tff(33997,plain,
% 3.52/3.75 (r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[681, 33996, 33975])).
% 3.52/3.75 tff(33998,plain,
% 3.52/3.75 (b(s(s(s(elem!1))), z)),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[504, 19220])).
% 3.52/3.75 tff(33999,plain,
% 3.52/3.75 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[828, 517, 9878, 798, 307, 33997, 504])).
% 3.52/3.75 tff(34000,plain,
% 3.52/3.75 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[835, 33999, 9878])).
% 3.52/3.75 tff(34001,plain,
% 3.52/3.75 (r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[840, 34000, 9949])).
% 3.52/3.75 tff(34002,plain,
% 3.52/3.75 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[19592])).
% 3.52/3.75 tff(34003,plain,
% 3.52/3.75 (b(s(elem!1), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[2488, 394, 9878])).
% 3.52/3.75 tff(34004,plain,
% 3.52/3.75 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[5833, 33975])).
% 3.52/3.75 tff(34005,plain,
% 3.52/3.75 (~b(s(s(z)), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20726, 517, 9878, 34003, 307])).
% 3.52/3.75 tff(34006,plain,
% 3.52/3.75 (r(s(s(z)), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[3613, 34005, 19438])).
% 3.52/3.75 tff(34007,plain,
% 3.52/3.75 (r(s(s(elem!1)), elem!1)),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34006, 19440])).
% 3.52/3.75 tff(34008,plain,
% 3.52/3.75 (~b(elem!1, s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[3324, 2494, 307, 394])).
% 3.52/3.75 tff(34009,plain,
% 3.52/3.75 (r(elem!1, s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[599, 34008, 33969])).
% 3.52/3.75 tff(34010,plain,
% 3.52/3.75 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[10196, 20548, 10160])).
% 3.52/3.75 tff(34011,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.52/3.75 inference(rewrite,[status(thm)],[])).
% 3.52/3.75 tff(34012,plain,
% 3.52/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.52/3.75 inference(quant_inst,[status(thm)],[])).
% 3.52/3.75 tff(34013,plain,
% 3.52/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34012, 34011])).
% 3.52/3.75 tff(34014,plain,
% 3.52/3.75 ($false),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[34013, 121, 624, 1624, 34010, 19328])).
% 3.52/3.75 tff(34015,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.75 tff(34016,plain,
% 3.52/3.75 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[34015, 34009, 34007, 34004, 19305, 34003, 2494, 307])).
% 3.52/3.75 tff(34017,plain,
% 3.52/3.75 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1566, 34016, 9878])).
% 3.52/3.75 tff(34018,plain,
% 3.52/3.75 (r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1559, 34017, 33965])).
% 3.52/3.75 tff(34019,plain,
% 3.52/3.75 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[10182, 34018, 9878])).
% 3.52/3.75 tff(34020,plain,
% 3.52/3.75 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[7940, 121, 684, 798, 34019])).
% 3.52/3.75 tff(34021,plain,
% 3.52/3.75 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[8221, 34020, 1591])).
% 3.52/3.75 tff(34022,plain,
% 3.52/3.75 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34021, 34002])).
% 3.52/3.75 tff(34023,plain,
% 3.52/3.75 ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~b(s(z), s(s(s(s(s(z)))))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[32356])).
% 3.52/3.75 tff(34024,plain,
% 3.52/3.75 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[9962, 3061, 338])).
% 3.52/3.75 tff(34025,plain,
% 3.52/3.75 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[17096, 34009, 34024, 34007])).
% 3.52/3.75 tff(34026,plain,
% 3.52/3.75 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[18291, 34025, 32393])).
% 3.52/3.75 tff(34027,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.75 inference(rewrite,[status(thm)],[])).
% 3.52/3.75 tff(34028,plain,
% 3.52/3.75 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.75 inference(rewrite,[status(thm)],[])).
% 3.52/3.75 tff(34029,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[34028])).
% 3.52/3.75 tff(34030,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[34029, 34027])).
% 3.52/3.75 tff(34031,plain,
% 3.52/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.52/3.75 inference(quant_inst,[status(thm)],[])).
% 3.52/3.75 tff(34032,plain,
% 3.52/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34031, 34030])).
% 3.52/3.75 tff(34033,plain,
% 3.52/3.75 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[34032, 271, 517, 34026, 2494])).
% 3.52/3.75 tff(34034,plain,
% 3.52/3.75 (~b(s(z), s(s(s(s(s(z))))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34033, 34023])).
% 3.52/3.75 tff(34035,plain,
% 3.52/3.75 (r(s(z), s(s(s(s(s(z))))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1756, 34034])).
% 3.52/3.75 tff(34036,plain,
% 3.52/3.75 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[18909, 34035, 108, 3061])).
% 3.52/3.75 tff(34037,plain,
% 3.52/3.75 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1494, 34036])).
% 3.52/3.75 tff(34038,plain,
% 3.52/3.75 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[888, 271, 517, 34026, 2494])).
% 3.52/3.75 tff(34039,plain,
% 3.52/3.75 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[9896, 34038, 9878])).
% 3.52/3.75 tff(34040,plain,
% 3.52/3.75 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[4138, 34039, 31834])).
% 3.52/3.75 tff(34041,plain,
% 3.52/3.75 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[18190, 34040, 9878])).
% 3.52/3.75 tff(34042,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.75 inference(rewrite,[status(thm)],[])).
% 3.52/3.75 tff(34043,plain,
% 3.52/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.75 inference(quant_inst,[status(thm)],[])).
% 3.52/3.75 tff(34044,plain,
% 3.52/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34043, 34042])).
% 3.52/3.75 tff(34045,plain,
% 3.52/3.75 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[34044, 121, 684, 798, 34041])).
% 3.52/3.75 tff(34046,plain,
% 3.52/3.75 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[6039, 34045, 9878])).
% 3.52/3.75 tff(34047,plain,
% 3.52/3.75 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1733, 34046])).
% 3.52/3.75 tff(34048,plain,
% 3.52/3.75 (~b(z, s(s(s(s(s(z))))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[4072, 34047, 1935, 34037])).
% 3.52/3.75 tff(34049,plain,
% 3.52/3.75 (r(z, s(s(s(s(s(z))))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1658, 34048])).
% 3.52/3.75 tff(34050,plain,
% 3.52/3.75 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34047, 19547])).
% 3.52/3.75 tff(34051,plain,
% 3.52/3.75 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[9937])).
% 3.52/3.75 tff(34052,plain,
% 3.52/3.75 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.75 inference(symmetry,[status(thm)],[34051])).
% 3.52/3.75 tff(34053,plain,
% 3.52/3.75 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[19592])).
% 3.52/3.75 tff(34054,plain,
% 3.52/3.75 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.75 inference(transitivity,[status(thm)],[34053, 34052])).
% 3.52/3.75 tff(34055,plain,
% 3.52/3.75 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[34054])).
% 3.52/3.75 tff(34056,plain,
% 3.52/3.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34020, 34055])).
% 3.52/3.75 tff(34057,plain,
% 3.52/3.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[10426, 34056])).
% 3.52/3.75 tff(34058,plain,
% 3.52/3.75 (~b(s(s(s(s(z)))), z)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[13513, 34057, 1935, 1307])).
% 3.52/3.75 tff(34059,plain,
% 3.52/3.75 (r(s(s(s(s(z)))), z)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[1095, 34058])).
% 3.52/3.75 tff(34060,plain,
% 3.52/3.75 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[29482, 34059, 1638, 34050, 34049])).
% 3.52/3.75 tff(34061,plain,
% 3.52/3.75 ($false),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[34060, 34022])).
% 3.52/3.75 tff(34062,plain,((~b(s(s(elem!1)), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.75 tff(34063,plain,
% 3.52/3.75 (~b(s(s(elem!1)), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[34062, 34001, 33998, 1935, 1307, 1577, 33997, 798, 307, 108, 338, 517, 33950])).
% 3.52/3.75 tff(34064,plain,
% 3.52/3.75 (r(s(s(elem!1)), s(elem!1))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[701, 34063, 3313])).
% 3.52/3.75 tff(34065,plain,
% 3.52/3.75 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[3132, 34064, 798, 33997])).
% 3.52/3.75 tff(34066,plain,
% 3.52/3.75 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[556, 34065, 1])).
% 3.52/3.75 tff(34067,plain,
% 3.52/3.75 (~b(elem!1, s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[4433, 34066, 448, 33995])).
% 3.52/3.75 tff(34068,plain,
% 3.52/3.75 (r(elem!1, s(s(elem!1)))),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[599, 34067, 33969])).
% 3.52/3.75 tff(34069,plain,
% 3.52/3.75 (~b(s(s(z)), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[20726, 517, 9878, 33977, 307])).
% 3.52/3.75 tff(34070,plain,
% 3.52/3.75 (r(s(s(z)), elem!1)),
% 3.52/3.75 inference(unit_resolution,[status(thm)],[3613, 34069, 19438])).
% 3.52/3.75 tff(34071,plain,
% 3.52/3.75 (r(s(s(elem!1)), elem!1)),
% 3.52/3.75 inference(modus_ponens,[status(thm)],[34070, 19440])).
% 3.52/3.75 tff(34072,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.75 inference(rewrite,[status(thm)],[])).
% 3.52/3.75 tff(34073,plain,
% 3.52/3.75 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.75 inference(rewrite,[status(thm)],[])).
% 3.52/3.75 tff(34074,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 3.52/3.75 inference(monotonicity,[status(thm)],[34073])).
% 3.52/3.75 tff(34075,plain,
% 3.52/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.76 inference(transitivity,[status(thm)],[34074, 34072])).
% 3.52/3.76 tff(34076,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34077,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34076, 34075])).
% 3.52/3.76 tff(34078,plain,
% 3.52/3.76 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34077, 121, 33997, 798, 34064])).
% 3.52/3.76 tff(34079,plain,
% 3.52/3.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[586, 34078, 563])).
% 3.52/3.76 tff(34080,plain,
% 3.52/3.76 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.76 inference(symmetry,[status(thm)],[17064])).
% 3.52/3.76 tff(34081,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34082,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34083,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34082, 34081])).
% 3.52/3.76 tff(34084,plain,
% 3.52/3.76 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34083, 271, 543, 589])).
% 3.52/3.76 tff(34085,plain,
% 3.52/3.76 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34084, 18990])).
% 3.52/3.76 tff(34086,plain,
% 3.52/3.76 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[881, 21, 17091, 34085])).
% 3.52/3.76 tff(34087,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34088,plain,
% 3.52/3.76 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34089,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34088])).
% 3.52/3.76 tff(34090,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.76 inference(transitivity,[status(thm)],[34089, 34087])).
% 3.52/3.76 tff(34091,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34092,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34091, 34090])).
% 3.52/3.76 tff(34093,plain,
% 3.52/3.76 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34092, 121, 624, 1624, 34086])).
% 3.52/3.76 tff(34094,plain,
% 3.52/3.76 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34093, 20602])).
% 3.52/3.76 tff(34095,plain,
% 3.52/3.76 (b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[840, 34094, 712])).
% 3.52/3.76 tff(34096,plain,
% 3.52/3.76 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34095, 34080])).
% 3.52/3.76 tff(34097,plain,
% 3.52/3.76 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[788, 271, 307, 504, 18990])).
% 3.52/3.76 tff(34098,plain,
% 3.52/3.76 ($false),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34097, 34096])).
% 3.52/3.76 tff(34099,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.76 tff(34100,plain,
% 3.52/3.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34099, 34079, 9878, 307, 34071, 34066, 34068, 504])).
% 3.52/3.76 tff(34101,plain,
% 3.52/3.76 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34100, 33994])).
% 3.52/3.76 tff(34102,plain,
% 3.52/3.76 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[9962, 34001, 338])).
% 3.52/3.76 tff(34103,plain,
% 3.52/3.76 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[17096, 34068, 34102, 34071])).
% 3.52/3.76 tff(34104,plain,
% 3.52/3.76 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[18291, 34103, 32393])).
% 3.52/3.76 tff(34105,plain,
% 3.52/3.76 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[17089, 34104, 34066, 517])).
% 3.52/3.76 tff(34106,plain,
% 3.52/3.76 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[9896, 34105, 9878])).
% 3.52/3.76 tff(34107,plain,
% 3.52/3.76 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[4138, 34106, 31834])).
% 3.52/3.76 tff(34108,plain,
% 3.52/3.76 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[18190, 34107, 9878])).
% 3.52/3.76 tff(34109,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34110,plain,
% 3.52/3.76 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34111,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34110])).
% 3.52/3.76 tff(34112,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.76 inference(transitivity,[status(thm)],[34111, 34109])).
% 3.52/3.76 tff(34113,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34114,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34113, 34112])).
% 3.52/3.76 tff(34115,plain,
% 3.52/3.76 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34114, 271, 34066, 34079, 34104])).
% 3.52/3.76 tff(34116,plain,
% 3.52/3.76 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[18038, 34115, 9878])).
% 3.52/3.76 tff(34117,plain,
% 3.52/3.76 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1494, 34116])).
% 3.52/3.76 tff(34118,plain,
% 3.52/3.76 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[7296, 34117, 9878])).
% 3.52/3.76 tff(34119,plain,
% 3.52/3.76 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[7481, 34118, 798, 34108])).
% 3.52/3.76 tff(34120,plain,
% 3.52/3.76 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[6039, 34119, 9878])).
% 3.52/3.76 tff(34121,plain,
% 3.52/3.76 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1733, 34120])).
% 3.52/3.76 tff(34122,plain,
% 3.52/3.76 ($false),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34121, 34101])).
% 3.52/3.76 tff(34123,plain,((~b(s(elem!1), s(s(elem!1)))) | (~(s(z) = s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.76 tff(34124,plain,
% 3.52/3.76 (~b(s(elem!1), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34123, 33991, 798, 307, 33976, 448, 1, 33978, 338, 108])).
% 3.52/3.76 tff(34125,plain,
% 3.52/3.76 (r(s(elem!1), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[526, 34124, 211])).
% 3.52/3.76 tff(34126,plain,
% 3.52/3.76 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[3192, 34125, 307, 33977, 33976, 33975])).
% 3.52/3.76 tff(34127,plain,
% 3.52/3.76 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[556, 34126, 1])).
% 3.52/3.76 tff(34128,plain,
% 3.52/3.76 (~b(elem!1, s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[11908, 34127, 147, 19261, 33971])).
% 3.52/3.76 tff(34129,plain,
% 3.52/3.76 (r(elem!1, s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[599, 34128, 33969])).
% 3.52/3.76 tff(34130,plain,
% 3.52/3.76 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.52/3.76 inference(transitivity,[status(thm)],[33967, 2212])).
% 3.52/3.76 tff(34131,plain,
% 3.52/3.76 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34130])).
% 3.52/3.76 tff(34132,plain,
% 3.52/3.76 (~(s(s(elem!1)) = elem!1)),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[59, 34131])).
% 3.52/3.76 tff(34133,plain,
% 3.52/3.76 (~b(s(s(elem!1)), elem!1)),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[551, 34127, 307, 33976])).
% 3.52/3.76 tff(34134,plain,
% 3.52/3.76 (r(s(s(elem!1)), elem!1)),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[862, 34133, 34132])).
% 3.52/3.76 tff(34135,plain,
% 3.52/3.76 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[19650, 33976, 33977, 448])).
% 3.52/3.76 tff(34136,plain,
% 3.52/3.76 (r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[681, 34135, 33975])).
% 3.52/3.76 tff(34137,plain,
% 3.52/3.76 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.76 tff(34138,plain,
% 3.52/3.76 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 3.52/3.76 inference(symmetry,[status(thm)],[34137])).
% 3.52/3.76 tff(34139,plain,
% 3.52/3.76 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[9938])).
% 3.52/3.76 tff(34140,plain,
% 3.52/3.76 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.52/3.76 inference(symmetry,[status(thm)],[34139])).
% 3.52/3.76 tff(34141,plain,
% 3.52/3.76 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 3.52/3.76 inference(transitivity,[status(thm)],[34140, 34138])).
% 3.52/3.76 tff(34142,plain,
% 3.52/3.76 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(z, s(s(s(s(z))))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34141])).
% 3.52/3.76 tff(34143,plain,
% 3.52/3.76 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[14922, 121, 684, 627, 683])).
% 3.52/3.76 tff(34144,plain,
% 3.52/3.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[586, 34143, 6943])).
% 3.52/3.76 tff(34145,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34146,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34147,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34146, 34145])).
% 3.52/3.76 tff(34148,plain,
% 3.52/3.76 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34147, 121, 684, 627, 6898])).
% 3.52/3.76 tff(34149,plain,
% 3.52/3.76 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[8221, 34148, 1591])).
% 3.52/3.76 tff(34150,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34151,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34152,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34151, 34150])).
% 3.52/3.76 tff(34153,plain,
% 3.52/3.76 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34152, 121, 627, 683, 6898])).
% 3.52/3.76 tff(34154,plain,
% 3.52/3.76 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[5954, 21, 5951, 34153])).
% 3.52/3.76 tff(34155,plain,
% 3.52/3.76 ($false),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[7997, 271, 543, 589, 34154, 34149])).
% 3.52/3.76 tff(34156,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.76 tff(34157,plain,
% 3.52/3.76 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34156, 34144, 543, 34004, 1591, 627, 683, 684])).
% 3.52/3.76 tff(34158,plain,
% 3.52/3.76 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[10182, 34157, 9878])).
% 3.52/3.76 tff(34159,plain,
% 3.52/3.76 (b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1559, 34158, 33965])).
% 3.52/3.76 tff(34160,plain,
% 3.52/3.76 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1566, 34159, 9878])).
% 3.52/3.76 tff(34161,plain,
% 3.52/3.76 (~b(elem!1, s(s(s(s(elem!1)))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[23711, 34160, 2618, 307])).
% 3.52/3.76 tff(34162,plain,
% 3.52/3.76 (~b(z, s(s(s(s(z)))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34161, 34142])).
% 3.52/3.76 tff(34163,plain,
% 3.52/3.76 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[20617, 683, 307, 9878, 2618, 624, 627])).
% 3.52/3.76 tff(34164,plain,
% 3.52/3.76 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[18291, 34163, 32393])).
% 3.52/3.76 tff(34165,plain,
% 3.52/3.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[20650, 34164, 627, 543, 683, 33975])).
% 3.52/3.76 tff(34166,plain,
% 3.52/3.76 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[19552, 34165, 338])).
% 3.52/3.76 tff(34167,plain,
% 3.52/3.76 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1733, 34166])).
% 3.52/3.76 tff(34168,plain,
% 3.52/3.76 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[15217, 34167, 108, 1500, 448])).
% 3.52/3.76 tff(34169,plain,
% 3.52/3.76 (r(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1847, 34168, 9912])).
% 3.52/3.76 tff(34170,plain,
% 3.52/3.76 (r(z, s(s(s(s(s(z))))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34169, 9985])).
% 3.52/3.76 tff(34171,plain,
% 3.52/3.76 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.76 tff(34172,plain,
% 3.52/3.76 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(symmetry,[status(thm)],[34171])).
% 3.52/3.76 tff(34173,plain,
% 3.52/3.76 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[9940])).
% 3.52/3.76 tff(34174,plain,
% 3.52/3.76 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(transitivity,[status(thm)],[34173, 34172])).
% 3.52/3.76 tff(34175,plain,
% 3.52/3.76 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34174])).
% 3.52/3.76 tff(34176,plain,
% 3.52/3.76 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[6039, 34167, 9878])).
% 3.52/3.76 tff(34177,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34178,plain,
% 3.52/3.76 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.76 inference(rewrite,[status(thm)],[])).
% 3.52/3.76 tff(34179,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34178])).
% 3.52/3.76 tff(34180,plain,
% 3.52/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.76 inference(transitivity,[status(thm)],[34179, 34177])).
% 3.52/3.76 tff(34181,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.52/3.76 inference(quant_inst,[status(thm)],[])).
% 3.52/3.76 tff(34182,plain,
% 3.52/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34181, 34180])).
% 3.52/3.76 tff(34183,plain,
% 3.52/3.76 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34182, 121, 684, 798, 34176])).
% 3.52/3.76 tff(34184,plain,
% 3.52/3.76 (~r(s(z), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34183, 34175])).
% 3.52/3.76 tff(34185,plain,
% 3.52/3.76 (b(s(z), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1756, 34184])).
% 3.52/3.76 tff(34186,plain,
% 3.52/3.76 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.76 tff(34187,plain,
% 3.52/3.76 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 3.52/3.76 inference(symmetry,[status(thm)],[34186])).
% 3.52/3.76 tff(34188,plain,
% 3.52/3.76 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34187])).
% 3.52/3.76 tff(34189,plain,
% 3.52/3.76 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[801, 121, 684, 798, 34176])).
% 3.52/3.76 tff(34190,plain,
% 3.52/3.76 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[18190, 34189, 9878])).
% 3.52/3.76 tff(34191,plain,
% 3.52/3.76 (~r(s(s(s(s(s(z))))), s(z))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34190, 34188])).
% 3.52/3.76 tff(34192,plain,
% 3.52/3.76 (b(s(s(s(s(s(z))))), s(z))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1682, 34191])).
% 3.52/3.76 tff(34193,plain,
% 3.52/3.76 (~r(s(s(s(s(z)))), s(z))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[18101, 34158, 9878])).
% 3.52/3.76 tff(34194,plain,
% 3.52/3.76 (b(s(s(s(s(z)))), s(z))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[932, 34193])).
% 3.52/3.76 tff(34195,plain,
% 3.52/3.76 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1785, 34194, 34192, 34185])).
% 3.52/3.76 tff(34196,plain,
% 3.52/3.76 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1777, 34195])).
% 3.52/3.76 tff(34197,plain,
% 3.52/3.76 (~r(z, s(s(s(s(z)))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1766, 34196, 34167, 34170])).
% 3.52/3.76 tff(34198,plain,
% 3.52/3.76 (b(z, s(s(s(s(z)))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1121, 34197])).
% 3.52/3.76 tff(34199,plain,
% 3.52/3.76 ($false),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34198, 34162])).
% 3.52/3.76 tff(34200,plain,((~r(s(s(elem!1)), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.76 tff(34201,plain,
% 3.52/3.76 (~r(s(s(elem!1)), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34200, 34127, 33977, 307, 338, 1577, 34125, 34136, 563, 798, 108, 1500, 448, 34129])).
% 3.52/3.76 tff(34202,plain,
% 3.52/3.76 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[701, 34201, 3313])).
% 3.52/3.76 tff(34203,plain,
% 3.52/3.76 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34015, 34202, 34134, 34004, 19305, 33977, 34129, 307])).
% 3.52/3.76 tff(34204,plain,
% 3.52/3.76 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1566, 34203, 9878])).
% 3.52/3.76 tff(34205,plain,
% 3.52/3.76 (r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[1559, 34204, 33965])).
% 3.52/3.76 tff(34206,plain,
% 3.52/3.76 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[10182, 34205, 9878])).
% 3.52/3.76 tff(34207,plain,
% 3.52/3.76 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[34147, 121, 34136, 34125, 34206])).
% 3.52/3.76 tff(34208,plain,
% 3.52/3.76 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[8221, 34207, 1577])).
% 3.52/3.76 tff(34209,plain,
% 3.52/3.76 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[8017, 271, 34127, 33976, 34208])).
% 3.52/3.76 tff(34210,plain,
% 3.52/3.76 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[5954, 21, 34004, 34209])).
% 3.52/3.76 tff(34211,plain,
% 3.52/3.76 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.52/3.76 inference(monotonicity,[status(thm)],[19592])).
% 3.52/3.76 tff(34212,plain,
% 3.52/3.76 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.76 inference(symmetry,[status(thm)],[34211])).
% 3.52/3.76 tff(34213,plain,
% 3.52/3.76 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 3.52/3.76 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.76 tff(34214,plain,
% 3.52/3.76 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.76 inference(transitivity,[status(thm)],[34213, 34212])).
% 3.52/3.76 tff(34215,plain,
% 3.52/3.76 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 3.52/3.76 inference(monotonicity,[status(thm)],[34214])).
% 3.52/3.76 tff(34216,plain,
% 3.52/3.76 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.76 inference(modus_ponens,[status(thm)],[34207, 34055])).
% 3.52/3.76 tff(34217,plain,
% 3.52/3.76 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.52/3.76 inference(unit_resolution,[status(thm)],[10426, 34216])).
% 3.52/3.77 tff(34218,plain,
% 3.52/3.77 (~b(s(s(s(s(z)))), z)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[13513, 34217, 33978, 33991])).
% 3.52/3.77 tff(34219,plain,
% 3.52/3.77 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34218, 34215])).
% 3.52/3.77 tff(34220,plain,
% 3.52/3.77 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[5877, 21, 34219, 19305])).
% 3.52/3.77 tff(34221,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34013, 121, 34129, 34134, 34220, 34210])).
% 3.52/3.77 tff(34222,plain,(r(z, s(s(s(elem!1)))) | (~(s(z) = s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(z))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34223,plain,
% 3.52/3.77 (r(z, s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34222, 33954, 33955, 798, 108, 338, 33944, 147, 1])).
% 3.52/3.77 tff(34224,plain,
% 3.52/3.77 (r(z, s(s(s(z))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34223, 33960])).
% 3.52/3.77 tff(34225,plain,
% 3.52/3.77 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[15217, 1736, 108, 1500, 448])).
% 3.52/3.77 tff(34226,plain,
% 3.52/3.77 (r(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1847, 34225, 18042])).
% 3.52/3.77 tff(34227,plain,
% 3.52/3.77 (r(z, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34226, 19005])).
% 3.52/3.77 tff(34228,plain,
% 3.52/3.77 (~r(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[16283, 1736, 1661, 1140])).
% 3.52/3.77 tff(34229,plain,
% 3.52/3.77 (b(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[255, 34228, 907])).
% 3.52/3.77 tff(34230,plain,
% 3.52/3.77 (~b(s(s(s(z))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[3288, 34229, 394, 307])).
% 3.52/3.77 tff(34231,plain,
% 3.52/3.77 (r(s(s(s(z))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1816, 34230, 2033])).
% 3.52/3.77 tff(34232,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34233,plain,
% 3.52/3.77 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34234,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34233])).
% 3.52/3.77 tff(34235,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.52/3.77 inference(transitivity,[status(thm)],[34234, 34232])).
% 3.52/3.77 tff(34236,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.52/3.77 inference(quant_inst,[status(thm)],[])).
% 3.52/3.77 tff(34237,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34236, 34235])).
% 3.52/3.77 tff(34238,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34237, 121, 1661, 34231, 1736, 1140])).
% 3.52/3.77 tff(34239,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34240,plain,
% 3.52/3.77 (~r(z, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34239, 1736, 394, 307, 2033, 167, 1140])).
% 3.52/3.77 tff(34241,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34240, 34227])).
% 3.52/3.77 tff(34242,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(z = elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34243,plain,
% 3.52/3.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34242, 34224, 33950, 33955, 33947, 9878, 108, 33954, 33944])).
% 3.52/3.77 tff(34244,plain,
% 3.52/3.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1733, 34243])).
% 3.52/3.77 tff(34245,plain,
% 3.52/3.77 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.52/3.77 inference(transitivity,[status(thm)],[33980, 160])).
% 3.52/3.77 tff(34246,plain,
% 3.52/3.77 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34245])).
% 3.52/3.77 tff(34247,plain,
% 3.52/3.77 (~(s(s(s(z))) = elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[166, 34246])).
% 3.52/3.77 tff(34248,plain,
% 3.52/3.77 (b(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[255, 33951, 34247])).
% 3.52/3.77 tff(34249,plain,
% 3.52/3.77 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[5007, 34244, 34248, 33955])).
% 3.52/3.77 tff(34250,plain,
% 3.52/3.77 (r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[840, 34249, 9949])).
% 3.52/3.77 tff(34251,plain,
% 3.52/3.77 (~b(z, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[28932, 34250, 220, 33978, 108, 34244])).
% 3.52/3.77 tff(34252,plain,
% 3.52/3.77 (r(z, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1658, 34251])).
% 3.52/3.77 tff(34253,plain,
% 3.52/3.77 (r(elem!1, s(s(s(s(s(z))))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34252, 9984])).
% 3.52/3.77 tff(34254,plain,
% 3.52/3.77 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34253, 19015])).
% 3.52/3.77 tff(34255,plain,
% 3.52/3.77 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[9939])).
% 3.52/3.77 tff(34256,plain,
% 3.52/3.77 (b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.52/3.77 inference(symmetry,[status(thm)],[34255])).
% 3.52/3.77 tff(34257,plain,
% 3.52/3.77 ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34256])).
% 3.52/3.77 tff(34258,plain,
% 3.52/3.77 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[19552, 34244, 338])).
% 3.52/3.77 tff(34259,plain,
% 3.52/3.77 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[19650, 33976, 33977, 33944])).
% 3.52/3.77 tff(34260,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[681, 34259, 33975])).
% 3.52/3.77 tff(34261,plain,
% 3.52/3.77 (r(elem!1, s(s(s(elem!1))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34223, 33959])).
% 3.52/3.77 tff(34262,plain,
% 3.52/3.77 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[4719, 34261, 33955, 798, 34132, 34260, 3313, 33977])).
% 3.52/3.77 tff(34263,plain,
% 3.52/3.77 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[556, 34262, 1])).
% 3.52/3.77 tff(34264,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34265,plain,
% 3.52/3.77 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34266,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34265])).
% 3.52/3.77 tff(34267,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.77 inference(transitivity,[status(thm)],[34266, 34264])).
% 3.52/3.77 tff(34268,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 3.52/3.77 inference(quant_inst,[status(thm)],[])).
% 3.52/3.77 tff(34269,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34268, 34267])).
% 3.52/3.77 tff(34270,plain,
% 3.52/3.77 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34269, 271, 34263, 33976, 34258])).
% 3.52/3.77 tff(34271,plain,
% 3.52/3.77 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34270, 34257])).
% 3.52/3.77 tff(34272,plain,
% 3.52/3.77 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1719, 34271, 9878])).
% 3.52/3.77 tff(34273,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34274,plain,
% 3.52/3.77 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34275,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34274])).
% 3.52/3.77 tff(34276,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.77 inference(transitivity,[status(thm)],[34275, 34273])).
% 3.52/3.77 tff(34277,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.52/3.77 inference(quant_inst,[status(thm)],[])).
% 3.52/3.77 tff(34278,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34277, 34276])).
% 3.52/3.77 tff(34279,plain,
% 3.52/3.77 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34278, 271, 34263, 33976, 34258])).
% 3.52/3.77 tff(34280,plain,
% 3.52/3.77 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[18291, 34279, 32393])).
% 3.52/3.77 tff(34281,plain,
% 3.52/3.77 (~b(s(s(elem!1)), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[551, 34263, 33955, 33976])).
% 3.52/3.77 tff(34282,plain,
% 3.52/3.77 (r(s(s(elem!1)), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[862, 34281, 34132])).
% 3.52/3.77 tff(34283,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34284,plain,
% 3.52/3.77 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34285,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34284])).
% 3.52/3.77 tff(34286,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(transitivity,[status(thm)],[34285, 34283])).
% 3.52/3.77 tff(34287,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(quant_inst,[status(thm)],[])).
% 3.52/3.77 tff(34288,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34287, 34286])).
% 3.52/3.77 tff(34289,plain,
% 3.52/3.77 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34288, 121, 34282, 34280, 34272])).
% 3.52/3.77 tff(34290,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34289, 34254])).
% 3.52/3.77 tff(34291,plain,(r(s(s(s(elem!1))), elem!1) | (~(s(z) = s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34292,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34291, 33923, 11199, 108, 1, 33943])).
% 3.52/3.77 tff(34293,plain,
% 3.52/3.77 (~r(s(s(s(z))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[4527, 676, 9878])).
% 3.52/3.77 tff(34294,plain,
% 3.52/3.77 (b(s(s(s(z))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1816, 34293, 33947])).
% 3.52/3.77 tff(34295,plain,
% 3.52/3.77 (~b(elem!1, s(s(s(z))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1811, 34294, 307, 33950])).
% 3.52/3.77 tff(34296,plain,
% 3.52/3.77 (r(elem!1, s(s(s(z))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[1192, 34295, 33982])).
% 3.52/3.77 tff(34297,plain,
% 3.52/3.77 (r(elem!1, s(s(s(elem!1))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34296, 33957])).
% 3.52/3.77 tff(34298,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 3.52/3.77 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.77 tff(34299,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.52/3.77 inference(symmetry,[status(thm)],[34298])).
% 3.52/3.77 tff(34300,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), z)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[139, 34299])).
% 3.52/3.77 tff(34301,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34302,plain,
% 3.52/3.77 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34303,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34302])).
% 3.52/3.77 tff(34304,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 3.52/3.77 inference(transitivity,[status(thm)],[34303, 34301])).
% 3.52/3.77 tff(34305,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.52/3.77 inference(quant_inst,[status(thm)],[])).
% 3.52/3.77 tff(34306,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34305, 34304])).
% 3.52/3.77 tff(34307,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34306, 121, 623, 627, 798, 6842])).
% 3.52/3.77 tff(34308,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34309,plain,
% 3.52/3.77 (~r(s(elem!1), s(s(elem!1)))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34308, 623, 798, 34300])).
% 3.52/3.77 tff(34310,plain,
% 3.52/3.77 (b(s(elem!1), s(s(elem!1)))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[526, 34309, 216])).
% 3.52/3.77 tff(34311,plain,
% 3.52/3.77 (~b(s(s(z)), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[20726, 34310, 9878, 2618, 307])).
% 3.52/3.77 tff(34312,plain,
% 3.52/3.77 (r(s(s(z)), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[3613, 34311, 19438])).
% 3.52/3.77 tff(34313,plain,
% 3.52/3.77 (r(s(s(elem!1)), elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34312, 19440])).
% 3.52/3.77 tff(34314,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34315,plain,
% 3.52/3.77 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(rewrite,[status(thm)],[])).
% 3.52/3.77 tff(34316,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[34315])).
% 3.52/3.77 tff(34317,plain,
% 3.52/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(transitivity,[status(thm)],[34316, 34314])).
% 3.52/3.77 tff(34318,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.77 inference(quant_inst,[status(thm)],[])).
% 3.52/3.77 tff(34319,plain,
% 3.52/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34318, 34317])).
% 3.52/3.77 tff(34320,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34319, 121, 623, 139, 727, 34313])).
% 3.52/3.77 tff(34321,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34322,plain,
% 3.52/3.77 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34321, 34297, 139, 338, 33977, 307, 211, 798])).
% 3.52/3.77 tff(34323,plain,
% 3.52/3.77 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[556, 34322, 1])).
% 3.52/3.77 tff(34324,plain,
% 3.52/3.77 (b(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[681, 676, 33975])).
% 3.52/3.77 tff(34325,plain,
% 3.52/3.77 (~b(elem!1, s(s(elem!1)))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[9687, 517, 307, 543])).
% 3.52/3.77 tff(34326,plain,
% 3.52/3.77 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[10055])).
% 3.52/3.77 tff(34327,plain,
% 3.52/3.77 (~b(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[645, 17058])).
% 3.52/3.77 tff(34328,plain,
% 3.52/3.77 (r(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[255, 34327, 167])).
% 3.52/3.77 tff(34329,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34328, 136])).
% 3.52/3.77 tff(34330,plain,
% 3.52/3.77 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[134])).
% 3.52/3.77 tff(34331,plain,
% 3.52/3.77 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 3.52/3.77 inference(symmetry,[status(thm)],[34330])).
% 3.52/3.77 tff(34332,plain,
% 3.52/3.77 (r(elem!1, s(s(z)))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[624, 34331])).
% 3.52/3.77 tff(34333,plain,
% 3.52/3.77 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 3.52/3.77 inference(monotonicity,[status(thm)],[17067])).
% 3.52/3.77 tff(34334,plain,
% 3.52/3.77 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[644, 271, 307, 517])).
% 3.52/3.77 tff(34335,plain,
% 3.52/3.77 (~b(s(s(s(elem!1))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34334, 638])).
% 3.52/3.77 tff(34336,plain,
% 3.52/3.77 (~b(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34335, 17058])).
% 3.52/3.77 tff(34337,plain,
% 3.52/3.77 (r(s(s(s(z))), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[255, 34336, 167])).
% 3.52/3.77 tff(34338,plain,
% 3.52/3.77 (r(s(s(s(elem!1))), elem!1)),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34337, 136])).
% 3.52/3.77 tff(34339,plain,
% 3.52/3.77 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[13873, 121, 622, 624, 34338])).
% 3.52/3.77 tff(34340,plain,
% 3.52/3.77 (~r(s(z), s(s(s(elem!1))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34339, 34333])).
% 3.52/3.77 tff(34341,plain,
% 3.52/3.77 (b(s(z), s(s(s(elem!1))))),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[759, 34340, 11298])).
% 3.52/3.77 tff(34342,plain,
% 3.52/3.77 (b(s(elem!1), s(s(s(elem!1))))),
% 3.52/3.77 inference(modus_ponens,[status(thm)],[34341, 749])).
% 3.52/3.77 tff(34343,plain,
% 3.52/3.77 ($false),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[13882, 271, 543, 517, 34342, 638])).
% 3.52/3.77 tff(34344,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (s(z) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.77 tff(34345,plain,
% 3.52/3.77 (~r(s(elem!1), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[34344, 638, 517, 107, 11298, 543, 624, 307])).
% 3.52/3.77 tff(34346,plain,
% 3.52/3.77 (b(s(elem!1), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[2243, 34345, 2564])).
% 3.52/3.77 tff(34347,plain,
% 3.52/3.77 (~b(s(s(z)), elem!1)),
% 3.52/3.77 inference(unit_resolution,[status(thm)],[20726, 34346, 307, 107, 517])).
% 3.52/3.78 tff(34348,plain,
% 3.52/3.78 (r(s(s(z)), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[3613, 34347, 10121])).
% 3.52/3.78 tff(34349,plain,
% 3.52/3.78 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[14387, 34348, 34332, 34329])).
% 3.52/3.78 tff(34350,plain,
% 3.52/3.78 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34349, 34326])).
% 3.52/3.78 tff(34351,plain,
% 3.52/3.78 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[586, 34350, 6943])).
% 3.52/3.78 tff(34352,plain,
% 3.52/3.78 ($false),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1457, 271, 543, 517, 34351, 638])).
% 3.52/3.78 tff(34353,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (s(z) = s(s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.78 tff(34354,plain,
% 3.52/3.78 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~r(elem!1, s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34353, 61])).
% 3.52/3.78 tff(34355,plain,
% 3.52/3.78 (~r(elem!1, s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34354, 517, 107, 307, 6943, 638, 2564, 543])).
% 3.52/3.78 tff(34356,plain,
% 3.52/3.78 ($false),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[599, 34355, 34325, 18438])).
% 3.52/3.78 tff(34357,plain,((~b(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.78 tff(34358,plain,
% 3.52/3.78 (~b(s(elem!1), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34357, 34324, 307, 563, 9878, 2207, 34323])).
% 3.52/3.78 tff(34359,plain,
% 3.52/3.78 (r(s(elem!1), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[526, 34358, 211])).
% 3.52/3.78 tff(34360,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34361,plain,
% 3.52/3.78 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34362,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[34361])).
% 3.52/3.78 tff(34363,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(transitivity,[status(thm)],[34362, 34360])).
% 3.52/3.78 tff(34364,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 3.52/3.78 inference(quant_inst,[status(thm)],[])).
% 3.52/3.78 tff(34365,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34364, 34363])).
% 3.52/3.78 tff(34366,plain,
% 3.52/3.78 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34365, 271, 543, 638, 18990])).
% 3.52/3.78 tff(34367,plain,
% 3.52/3.78 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34366, 34257])).
% 3.52/3.78 tff(34368,plain,
% 3.52/3.78 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1719, 34367, 9878])).
% 3.52/3.78 tff(34369,plain,
% 3.52/3.78 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20641, 18990, 638, 543])).
% 3.52/3.78 tff(34370,plain,
% 3.52/3.78 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[18291, 34369, 32393])).
% 3.52/3.78 tff(34371,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34372,plain,
% 3.52/3.78 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34373,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[34372])).
% 3.52/3.78 tff(34374,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.78 inference(transitivity,[status(thm)],[34373, 34371])).
% 3.52/3.78 tff(34375,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.78 inference(quant_inst,[status(thm)],[])).
% 3.52/3.78 tff(34376,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34375, 34374])).
% 3.52/3.78 tff(34377,plain,
% 3.52/3.78 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34376, 121, 627, 34370, 34368])).
% 3.52/3.78 tff(34378,plain,
% 3.52/3.78 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[18190, 34377, 9878])).
% 3.52/3.78 tff(34379,plain,
% 3.52/3.78 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[4138, 34378, 31834])).
% 3.52/3.78 tff(34380,plain,
% 3.52/3.78 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[9896, 34379, 9878])).
% 3.52/3.78 tff(34381,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34382,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(quant_inst,[status(thm)],[])).
% 3.52/3.78 tff(34383,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34382, 34381])).
% 3.52/3.78 tff(34384,plain,
% 3.52/3.78 ($false),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34383, 271, 2618, 638, 18990, 34380])).
% 3.52/3.78 tff(34385,plain,((~b(s(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))) | (~r(s(elem!1), s(s(elem!1)))) | (~(s(z) = s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.78 tff(34386,plain,
% 3.52/3.78 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34385, 34324, 33977, 34359, 338, 34323])).
% 3.52/3.78 tff(34387,plain,
% 3.52/3.78 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[19552, 34386, 338])).
% 3.52/3.78 tff(34388,plain,
% 3.52/3.78 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1733, 34387])).
% 3.52/3.78 tff(34389,plain,
% 3.52/3.78 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[6039, 34388, 9878])).
% 3.52/3.78 tff(34390,plain,
% 3.52/3.78 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 3.52/3.78 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.78 tff(34391,plain,
% 3.52/3.78 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 3.52/3.78 inference(symmetry,[status(thm)],[34390])).
% 3.52/3.78 tff(34392,plain,
% 3.52/3.78 (b(s(z), elem!1)),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[33977, 34391])).
% 3.52/3.78 tff(34393,plain,
% 3.52/3.78 (r(s(s(s(z))), z)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[143, 139, 9878])).
% 3.52/3.78 tff(34394,plain,
% 3.52/3.78 (r(s(s(s(z))), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[475, 34393, 9878])).
% 3.52/3.78 tff(34395,plain,
% 3.52/3.78 (~r(s(s(s(s(s(z))))), s(z))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[23750, 34388, 108, 34394])).
% 3.52/3.78 tff(34396,plain,
% 3.52/3.78 (b(s(s(s(s(s(z))))), s(z))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1682, 34395])).
% 3.52/3.78 tff(34397,plain,
% 3.52/3.78 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[5398, 34396, 307, 34392])).
% 3.52/3.78 tff(34398,plain,
% 3.52/3.78 (r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[840, 34397, 9949])).
% 3.52/3.78 tff(34399,plain,
% 3.52/3.78 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[9962, 34398, 338])).
% 3.52/3.78 tff(34400,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34401,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.52/3.78 inference(quant_inst,[status(thm)],[])).
% 3.52/3.78 tff(34402,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34401, 34400])).
% 3.52/3.78 tff(34403,plain,
% 3.52/3.78 ($false),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34402, 121, 139, 34297, 34399, 34389])).
% 3.52/3.78 tff(34404,plain,(r(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.78 tff(34405,plain,
% 3.52/3.78 (r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34404, 34292, 33923, 33927, 108, 1, 33943])).
% 3.52/3.78 tff(34406,plain,
% 3.52/3.78 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.52/3.78 inference(transitivity,[status(thm)],[33937, 2212])).
% 3.52/3.78 tff(34407,plain,
% 3.52/3.78 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[34406])).
% 3.52/3.78 tff(34408,plain,
% 3.52/3.78 (~(s(s(elem!1)) = elem!1)),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[59, 34407])).
% 3.52/3.78 tff(34409,plain,
% 3.52/3.78 (~r(s(s(elem!1)), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[3132, 623, 798, 684])).
% 3.52/3.78 tff(34410,plain,
% 3.52/3.78 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[701, 34409, 694])).
% 3.52/3.78 tff(34411,plain,
% 3.52/3.78 (~b(s(s(elem!1)), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[6807, 34410, 307, 2618])).
% 3.52/3.78 tff(34412,plain,
% 3.52/3.78 (r(s(s(elem!1)), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[862, 34411, 851])).
% 3.52/3.78 tff(34413,plain,
% 3.52/3.78 (~b(elem!1, s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[3324, 34410, 307, 394])).
% 3.52/3.78 tff(34414,plain,
% 3.52/3.78 (r(elem!1, s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[599, 34413, 68])).
% 3.52/3.78 tff(34415,plain,
% 3.52/3.78 ($false),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[2670, 34414, 34412, 139, 623])).
% 3.52/3.78 tff(34416,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.78 tff(34417,plain,
% 3.52/3.78 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34416, 34292, 33939, 34408, 33927, 33929, 33930, 3313, 33943, 34405])).
% 3.52/3.78 tff(34418,plain,
% 3.52/3.78 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[556, 34417, 1])).
% 3.52/3.78 tff(34419,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.52/3.78 tff(34420,plain,
% 3.52/3.78 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 3.52/3.78 inference(transitivity,[status(thm)],[9938, 34419, 9940])).
% 3.52/3.78 tff(34421,plain,
% 3.52/3.78 ($false),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1772, 34420])).
% 3.52/3.78 tff(34422,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.78 tff(34423,plain,
% 3.52/3.78 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34422, 338])).
% 3.52/3.78 tff(34424,plain,
% 3.52/3.78 (b(s(elem!1), z)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20985, 19216, 1281])).
% 3.52/3.78 tff(34425,plain,
% 3.52/3.78 (b(s(elem!1), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[2488, 34424, 9878])).
% 3.52/3.78 tff(34426,plain,
% 3.52/3.78 (b(s(s(elem!1)), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[862, 860, 34132])).
% 3.52/3.78 tff(34427,plain,
% 3.52/3.78 (~b(s(s(elem!1)), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[6807, 34426, 33955, 34425])).
% 3.52/3.78 tff(34428,plain,
% 3.52/3.78 (r(s(s(elem!1)), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[701, 34427, 8423])).
% 3.52/3.78 tff(34429,plain,
% 3.52/3.78 (~r(s(s(z)), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[19443, 860, 338])).
% 3.52/3.78 tff(34430,plain,
% 3.52/3.78 (b(s(s(z)), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[3613, 34429, 19438])).
% 3.52/3.78 tff(34431,plain,
% 3.52/3.78 (~b(s(elem!1), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20726, 34430, 9878, 34425, 33955])).
% 3.52/3.78 tff(34432,plain,
% 3.52/3.78 (r(s(elem!1), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[526, 34431, 216])).
% 3.52/3.78 tff(34433,plain,
% 3.52/3.78 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 3.52/3.78 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.78 tff(34434,plain,
% 3.52/3.78 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.52/3.78 inference(symmetry,[status(thm)],[34433])).
% 3.52/3.78 tff(34435,plain,
% 3.52/3.78 (b(s(s(elem!1)), z)),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34426, 34434])).
% 3.52/3.78 tff(34436,plain,
% 3.52/3.78 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.78 tff(34437,plain,
% 3.52/3.78 (~b(z, elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20398, 33944, 1281, 220])).
% 3.52/3.78 tff(34438,plain,
% 3.52/3.78 (~(s(z) = elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[229, 34437, 220])).
% 3.52/3.78 tff(34439,plain,
% 3.52/3.78 (~(elem!1 = s(z))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[242, 34438])).
% 3.52/3.78 tff(34440,plain,
% 3.52/3.78 (~r(z, s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20669, 34435, 34439, 33969, 220, 543])).
% 3.52/3.78 tff(34441,plain,
% 3.52/3.78 (b(z, s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[2106, 34440])).
% 3.52/3.78 tff(34442,plain,
% 3.52/3.78 (b(elem!1, s(s(elem!1)))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34441, 34436])).
% 3.52/3.78 tff(34443,plain,
% 3.52/3.78 (~b(elem!1, s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20573, 34442, 9878, 34425, 139, 33949, 1591, 684, 543, 216, 33955])).
% 3.52/3.78 tff(34444,plain,
% 3.52/3.78 (~b(elem!1, s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1198, 34443, 9878])).
% 3.52/3.78 tff(34445,plain,
% 3.52/3.78 (r(elem!1, s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1192, 34444, 33982])).
% 3.52/3.78 tff(34446,plain,
% 3.52/3.78 (r(z, s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[33987, 34445, 338])).
% 3.52/3.78 tff(34447,plain,
% 3.52/3.78 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[10857, 34446, 572, 34435])).
% 3.52/3.78 tff(34448,plain,
% 3.52/3.78 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[586, 34447, 6943])).
% 3.52/3.78 tff(34449,plain,
% 3.52/3.78 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34156, 34448, 684, 34004, 1591, 543, 34432, 34428])).
% 3.52/3.78 tff(34450,plain,
% 3.52/3.78 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[10182, 34449, 9878])).
% 3.52/3.78 tff(34451,plain,
% 3.52/3.78 (~r(s(s(s(s(z)))), s(z))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[18101, 34450, 9878])).
% 3.52/3.78 tff(34452,plain,
% 3.52/3.78 (b(s(s(s(s(z)))), s(z))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[932, 34451])).
% 3.52/3.78 tff(34453,plain,
% 3.52/3.78 (~b(s(s(s(s(z)))), z)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[22548, 34452, 1281, 220])).
% 3.52/3.78 tff(34454,plain,
% 3.52/3.78 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34453, 34215])).
% 3.52/3.78 tff(34455,plain,
% 3.52/3.78 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[5877, 21, 34454, 19305])).
% 3.52/3.78 tff(34456,plain,
% 3.52/3.78 (r(elem!1, s(s(s(elem!1))))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34445, 33957])).
% 3.52/3.78 tff(34457,plain,
% 3.52/3.78 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[10171, 121, 139, 34456, 34455])).
% 3.52/3.78 tff(34458,plain,
% 3.52/3.78 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[8221, 34457, 1591])).
% 3.52/3.78 tff(34459,plain,
% 3.52/3.78 (r(z, s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1187, 34445, 9878])).
% 3.52/3.78 tff(34460,plain,
% 3.52/3.78 (~(s(s(z)) = s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[960, 34438])).
% 3.52/3.78 tff(34461,plain,
% 3.52/3.78 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[953, 34460])).
% 3.52/3.78 tff(34462,plain,
% 3.52/3.78 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[946, 34461])).
% 3.52/3.78 tff(34463,plain,
% 3.52/3.78 (b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1559, 34450, 33965])).
% 3.52/3.78 tff(34464,plain,
% 3.52/3.78 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1566, 34463, 9878])).
% 3.52/3.78 tff(34465,plain,
% 3.52/3.78 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[20558, 34464, 34425, 9878, 33955, 139])).
% 3.52/3.78 tff(34466,plain,
% 3.52/3.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[18820, 34465, 9878])).
% 3.52/3.78 tff(34467,plain,
% 3.52/3.78 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[18811, 34466, 9878])).
% 3.52/3.78 tff(34468,plain,
% 3.52/3.78 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1014, 34467, 34462])).
% 3.52/3.78 tff(34469,plain,
% 3.52/3.78 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.78 tff(34470,plain,
% 3.52/3.78 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 3.52/3.78 inference(symmetry,[status(thm)],[34469])).
% 3.52/3.78 tff(34471,plain,
% 3.52/3.78 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[19592])).
% 3.52/3.78 tff(34472,plain,
% 3.52/3.78 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(z)))))),
% 3.52/3.78 inference(transitivity,[status(thm)],[34471, 34470])).
% 3.52/3.78 tff(34473,plain,
% 3.52/3.78 ((~r(s(elem!1), s(s(s(s(elem!1)))))) <=> (~r(s(z), s(s(s(s(z))))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[34472])).
% 3.52/3.78 tff(34474,plain,
% 3.52/3.78 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[7997, 271, 543, 34448, 34458])).
% 3.52/3.78 tff(34475,plain,
% 3.52/3.78 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[5954, 21, 34004, 34474])).
% 3.52/3.78 tff(34476,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34477,plain,
% 3.52/3.78 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34478,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[34477])).
% 3.52/3.78 tff(34479,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.52/3.78 inference(transitivity,[status(thm)],[34478, 34476])).
% 3.52/3.78 tff(34480,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.52/3.78 inference(quant_inst,[status(thm)],[])).
% 3.52/3.78 tff(34481,plain,
% 3.52/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34480, 34479])).
% 3.52/3.78 tff(34482,plain,
% 3.52/3.78 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34481, 121, 34432, 34428, 34475])).
% 3.52/3.78 tff(34483,plain,
% 3.52/3.78 (~r(s(z), s(s(s(s(z)))))),
% 3.52/3.78 inference(modus_ponens,[status(thm)],[34482, 34473])).
% 3.52/3.78 tff(34484,plain,
% 3.52/3.78 (b(s(z), s(s(s(s(z)))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[16482, 34483])).
% 3.52/3.78 tff(34485,plain,
% 3.52/3.78 (~b(s(s(s(elem!1))), s(z))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1075, 34484, 34452, 34468])).
% 3.52/3.78 tff(34486,plain,
% 3.52/3.78 (~b(s(s(s(z))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[19370, 34485, 338])).
% 3.52/3.78 tff(34487,plain,
% 3.52/3.78 (r(s(s(s(z))), s(elem!1))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1816, 34486, 33947])).
% 3.52/3.78 tff(34488,plain,
% 3.52/3.78 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[34242, 34487, 34424, 33955, 33947, 9878, 108, 34459, 33944])).
% 3.52/3.78 tff(34489,plain,
% 3.52/3.78 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[1733, 34488])).
% 3.52/3.78 tff(34490,plain,
% 3.52/3.78 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.78 inference(unit_resolution,[status(thm)],[19552, 34489, 338])).
% 3.52/3.78 tff(34491,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34492,plain,
% 3.52/3.78 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(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(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.78 inference(rewrite,[status(thm)],[])).
% 3.52/3.78 tff(34493,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 3.52/3.78 inference(monotonicity,[status(thm)],[34492])).
% 3.52/3.78 tff(34494,plain,
% 3.52/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34493, 34491])).
% 3.52/3.79 tff(34495,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34496,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34495, 34494])).
% 3.52/3.79 tff(34497,plain,
% 3.52/3.79 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34496, 271, 34448, 34490, 34458])).
% 3.52/3.79 tff(34498,plain,
% 3.52/3.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34499,plain,
% 3.52/3.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34500,plain,
% 3.52/3.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34499, 34498])).
% 3.52/3.79 tff(34501,plain,
% 3.52/3.79 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34500, 21, 34497, 34423])).
% 3.52/3.79 tff(34502,plain,
% 3.52/3.79 (b(s(z), elem!1)),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34425, 34391])).
% 3.52/3.79 tff(34503,plain,
% 3.52/3.79 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[338, 9936])).
% 3.52/3.79 tff(34504,plain,
% 3.52/3.79 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 3.52/3.79 inference(symmetry,[status(thm)],[34503])).
% 3.52/3.79 tff(34505,plain,
% 3.52/3.79 (r(s(z), s(s(z)))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34432, 34504])).
% 3.52/3.79 tff(34506,plain,
% 3.52/3.79 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[9936, 338])).
% 3.52/3.79 tff(34507,plain,
% 3.52/3.79 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 3.52/3.79 inference(symmetry,[status(thm)],[34506])).
% 3.52/3.79 tff(34508,plain,
% 3.52/3.79 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(z)), s(z)))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34507])).
% 3.52/3.79 tff(34509,plain,
% 3.52/3.79 (~b(s(s(z)), s(z))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34427, 34508])).
% 3.52/3.79 tff(34510,plain,
% 3.52/3.79 (r(s(s(z)), s(z))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[4670, 34509])).
% 3.52/3.79 tff(34511,plain,
% 3.52/3.79 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[338])).
% 3.52/3.79 tff(34512,plain,
% 3.52/3.79 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 3.52/3.79 inference(symmetry,[status(thm)],[34511])).
% 3.52/3.79 tff(34513,plain,
% 3.52/3.79 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[9937])).
% 3.52/3.79 tff(34514,plain,
% 3.52/3.79 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.52/3.79 inference(symmetry,[status(thm)],[34513])).
% 3.52/3.79 tff(34515,plain,
% 3.52/3.79 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34514, 34512])).
% 3.52/3.79 tff(34516,plain,
% 3.52/3.79 (r(s(s(s(z))), s(z))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[684, 34515])).
% 3.52/3.79 tff(34517,plain,
% 3.52/3.79 (~r(s(s(s(s(s(z))))), s(z))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[27722, 34516, 34510, 34505])).
% 3.52/3.79 tff(34518,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), s(z))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1682, 34517])).
% 3.52/3.79 tff(34519,plain,
% 3.52/3.79 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[5398, 34518, 33955, 34502])).
% 3.52/3.79 tff(34520,plain,
% 3.52/3.79 (r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[840, 34519, 9949])).
% 3.52/3.79 tff(34521,plain,
% 3.52/3.79 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[9962, 34520, 338])).
% 3.52/3.79 tff(34522,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34523,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34524,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34523, 34522])).
% 3.52/3.79 tff(34525,plain,
% 3.52/3.79 ($false),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34524, 121, 34456, 34521, 34455, 34501])).
% 3.52/3.79 tff(34526,plain,(r(s(s(elem!1)), elem!1) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.79 tff(34527,plain,
% 3.52/3.79 (r(s(s(elem!1)), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34526, 33923, 34405, 108, 34418, 1577, 34292, 19197, 11199, 563, 33942, 211])).
% 3.52/3.79 tff(34528,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[20662, 19550, 139, 107, 624])).
% 3.52/3.79 tff(34529,plain,
% 3.52/3.79 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34528, 830])).
% 3.52/3.79 tff(34530,plain,
% 3.52/3.79 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[20819, 271, 307, 2618, 34529])).
% 3.52/3.79 tff(34531,plain,
% 3.52/3.79 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[818, 21, 815, 34530])).
% 3.52/3.79 tff(34532,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34533,plain,
% 3.52/3.79 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34534,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34533])).
% 3.52/3.79 tff(34535,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34534, 34532])).
% 3.52/3.79 tff(34536,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34537,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34536, 34535])).
% 3.52/3.79 tff(34538,plain,
% 3.52/3.79 ($false),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34537, 121, 139, 798, 20654, 34531])).
% 3.52/3.79 tff(34539,plain,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.79 tff(34540,plain,
% 3.52/3.79 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34539, 624, 9878, 798, 33955, 34003, 139])).
% 3.52/3.79 tff(34541,plain,
% 3.52/3.79 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 3.52/3.79 inference(monotonicity,[status(thm)],[9878])).
% 3.52/3.79 tff(34542,plain,
% 3.52/3.79 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 3.52/3.79 inference(symmetry,[status(thm)],[34541])).
% 3.52/3.79 tff(34543,plain,
% 3.52/3.79 (r(s(s(elem!1)), z)),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[1624, 34542])).
% 3.52/3.79 tff(34544,plain,
% 3.52/3.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[14145, 624, 139, 34543])).
% 3.52/3.79 tff(34545,plain,
% 3.52/3.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[586, 34544, 6943])).
% 3.52/3.79 tff(34546,plain,
% 3.52/3.79 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34083, 271, 543, 34545, 34540])).
% 3.52/3.79 tff(34547,plain,
% 3.52/3.79 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[18291, 34546, 32393])).
% 3.52/3.79 tff(34548,plain,
% 3.52/3.79 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[17096, 34547, 624, 1624])).
% 3.52/3.79 tff(34549,plain,
% 3.52/3.79 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[9962, 34548, 338])).
% 3.52/3.79 tff(34550,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[840, 34549, 9949])).
% 3.52/3.79 tff(34551,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), z)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[32429, 34550, 9878])).
% 3.52/3.79 tff(34552,plain,
% 3.52/3.79 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[24620, 34551, 220, 394])).
% 3.52/3.79 tff(34553,plain,
% 3.52/3.79 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[4138, 34552, 31834])).
% 3.52/3.79 tff(34554,plain,
% 3.52/3.79 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[18190, 34553, 9878])).
% 3.52/3.79 tff(34555,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[18990, 33993])).
% 3.52/3.79 tff(34556,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 3.52/3.79 tff(34557,plain,
% 3.52/3.79 ($false),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34556, 34555])).
% 3.52/3.79 tff(34558,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.79 tff(34559,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34558, 34540, 338])).
% 3.52/3.79 tff(34560,plain,
% 3.52/3.79 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[32357])).
% 3.52/3.79 tff(34561,plain,
% 3.52/3.79 (b(s(z), elem!1)),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34003, 34391])).
% 3.52/3.79 tff(34562,plain,
% 3.52/3.79 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34083, 271, 543, 589, 18990])).
% 3.52/3.79 tff(34563,plain,
% 3.52/3.79 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[18291, 34562, 32393])).
% 3.52/3.79 tff(34564,plain,
% 3.52/3.79 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[17096, 34563, 624, 1624])).
% 3.52/3.79 tff(34565,plain,
% 3.52/3.79 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[9962, 34564, 338])).
% 3.52/3.79 tff(34566,plain,
% 3.52/3.79 (b(s(s(s(s(s(z))))), elem!1)),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[840, 34565, 9949])).
% 3.52/3.79 tff(34567,plain,
% 3.52/3.79 (~b(s(z), s(s(s(s(s(z))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[5389, 34566, 33955, 34561])).
% 3.52/3.79 tff(34568,plain,
% 3.52/3.79 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34567, 34560])).
% 3.52/3.79 tff(34569,plain,
% 3.52/3.79 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[814, 9878])).
% 3.52/3.79 tff(34570,plain,
% 3.52/3.79 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34569, 7608])).
% 3.52/3.79 tff(34571,plain,
% 3.52/3.79 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[18925, 34570, 34568])).
% 3.52/3.79 tff(34572,plain,
% 3.52/3.79 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[9937])).
% 3.52/3.79 tff(34573,plain,
% 3.52/3.79 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 3.52/3.79 inference(symmetry,[status(thm)],[34572])).
% 3.52/3.79 tff(34574,plain,
% 3.52/3.79 (b(s(s(elem!1)), s(s(s(z))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[543, 34573])).
% 3.52/3.79 tff(34575,plain,
% 3.52/3.79 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[31858, 34566, 9878, 684, 31834, 220, 394])).
% 3.52/3.79 tff(34576,plain,
% 3.52/3.79 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[7296, 34575, 9878])).
% 3.52/3.79 tff(34577,plain,
% 3.52/3.79 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1494, 34576])).
% 3.52/3.79 tff(34578,plain,
% 3.52/3.79 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1731, 34577, 34574, 1723])).
% 3.52/3.79 tff(34579,plain,
% 3.52/3.79 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1719, 34578, 9878])).
% 3.52/3.79 tff(34580,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34581,plain,
% 3.52/3.79 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34582,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34581])).
% 3.52/3.79 tff(34583,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34582, 34580])).
% 3.52/3.79 tff(34584,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34585,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34584, 34583])).
% 3.52/3.79 tff(34586,plain,
% 3.52/3.79 ($false),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34585, 121, 34563, 683, 34579, 34571])).
% 3.52/3.79 tff(34587,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.79 tff(34588,plain,
% 3.52/3.79 (~r(s(s(elem!1)), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34587, 34559, 338, 684, 220, 394, 624, 1624, 543, 34545, 34540])).
% 3.52/3.79 tff(34589,plain,
% 3.52/3.79 (b(s(s(elem!1)), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[701, 34588, 694])).
% 3.52/3.79 tff(34590,plain,
% 3.52/3.79 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34015, 34589, 1624, 34004, 19305, 34003, 624, 33955])).
% 3.52/3.79 tff(34591,plain,
% 3.52/3.79 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1566, 34590, 9878])).
% 3.52/3.79 tff(34592,plain,
% 3.52/3.79 (r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1559, 34591, 33965])).
% 3.52/3.79 tff(34593,plain,
% 3.52/3.79 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[10182, 34592, 9878])).
% 3.52/3.79 tff(34594,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(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(s(s(elem!1))))))))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34595,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1))))))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34596,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34595, 34594])).
% 3.52/3.79 tff(34597,plain,
% 3.52/3.79 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34596, 121, 798, 34593, 34554])).
% 3.52/3.79 tff(34598,plain,
% 3.52/3.79 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[7940, 121, 684, 798, 34593])).
% 3.52/3.79 tff(34599,plain,
% 3.52/3.79 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[8221, 34598, 1591])).
% 3.52/3.79 tff(34600,plain,
% 3.52/3.79 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34496, 271, 34545, 34540, 34599])).
% 3.52/3.79 tff(34601,plain,
% 3.52/3.79 ($false),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34500, 21, 34600, 34423, 34597])).
% 3.52/3.79 tff(34602,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~(s(z) = s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.52/3.79 tff(34603,plain,
% 3.52/3.79 (~r(elem!1, s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34602, 33943, 11199, 33929, 33923, 34527, 1577, 34405, 34418, 3313, 563, 34292])).
% 3.52/3.79 tff(34604,plain,
% 3.52/3.79 (b(elem!1, s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[599, 34603, 33939])).
% 3.52/3.79 tff(34605,plain,
% 3.52/3.79 (~b(s(s(elem!1)), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[3324, 34604, 33927, 33929])).
% 3.52/3.79 tff(34606,plain,
% 3.52/3.79 (r(s(s(elem!1)), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[701, 34605, 3313])).
% 3.52/3.79 tff(34607,plain,
% 3.52/3.79 (~b(s(elem!1), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[9687, 34604, 33927, 34418])).
% 3.52/3.79 tff(34608,plain,
% 3.52/3.79 (r(s(elem!1), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[526, 34607, 211])).
% 3.52/3.79 tff(34609,plain,
% 3.52/3.79 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[33923])).
% 3.52/3.79 tff(34610,plain,
% 3.52/3.79 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34609, 200])).
% 3.52/3.79 tff(34611,plain,
% 3.52/3.79 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34610])).
% 3.52/3.79 tff(34612,plain,
% 3.52/3.79 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[61, 34611])).
% 3.52/3.79 tff(34613,plain,
% 3.52/3.79 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[5833, 34612])).
% 3.52/3.79 tff(34614,plain,
% 3.52/3.79 (s(s(z)) = s(s(elem!1))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[33923])).
% 3.52/3.79 tff(34615,plain,
% 3.52/3.79 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34614])).
% 3.52/3.79 tff(34616,plain,
% 3.52/3.79 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34615])).
% 3.52/3.79 tff(34617,plain,
% 3.52/3.79 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.52/3.79 inference(monotonicity,[status(thm)],[33924])).
% 3.52/3.79 tff(34618,plain,
% 3.52/3.79 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34617, 159])).
% 3.52/3.79 tff(34619,plain,
% 3.52/3.79 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34618])).
% 3.52/3.79 tff(34620,plain,
% 3.52/3.79 (~(elem!1 = s(s(s(z))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[166, 34619])).
% 3.52/3.79 tff(34621,plain,
% 3.52/3.79 (b(z, s(z)) <=> b(z, s(elem!1))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[33923])).
% 3.52/3.79 tff(34622,plain,
% 3.52/3.79 (b(z, s(elem!1))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[11199, 34621])).
% 3.52/3.79 tff(34623,plain,
% 3.52/3.79 (~b(elem!1, s(s(s(elem!1))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[20573, 34604, 33924, 33930, 34292, 34622, 1577, 34405, 34418, 211, 33927])).
% 3.52/3.79 tff(34624,plain,
% 3.52/3.79 (~b(elem!1, s(s(s(z))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1198, 34623, 33924])).
% 3.52/3.79 tff(34625,plain,
% 3.52/3.79 (r(elem!1, s(s(s(z))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1192, 34624, 34620])).
% 3.52/3.79 tff(34626,plain,
% 3.52/3.79 (r(elem!1, s(s(s(elem!1))))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34625, 34616])).
% 3.52/3.79 tff(34627,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34628,plain,
% 3.52/3.79 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.79 inference(rewrite,[status(thm)],[])).
% 3.52/3.79 tff(34629,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))))),
% 3.52/3.79 inference(monotonicity,[status(thm)],[34628])).
% 3.52/3.79 tff(34630,plain,
% 3.52/3.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.79 inference(transitivity,[status(thm)],[34629, 34627])).
% 3.52/3.79 tff(34631,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.52/3.79 inference(quant_inst,[status(thm)],[])).
% 3.52/3.79 tff(34632,plain,
% 3.52/3.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 3.52/3.79 inference(modus_ponens,[status(thm)],[34631, 34630])).
% 3.52/3.79 tff(34633,plain,
% 3.52/3.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34632, 121, 34292, 34626, 34527])).
% 3.52/3.79 tff(34634,plain,
% 3.52/3.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[586, 34633, 563])).
% 3.52/3.79 tff(34635,plain,
% 3.52/3.79 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34156, 34634, 34405, 34613, 1577, 34418, 34608, 34606])).
% 3.52/3.79 tff(34636,plain,
% 3.52/3.79 (~r(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[10182, 34635, 33924])).
% 3.52/3.79 tff(34637,plain,
% 3.52/3.79 (b(s(s(s(s(z)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1559, 34636, 33935])).
% 3.52/3.79 tff(34638,plain,
% 3.52/3.79 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[1566, 34637, 33924])).
% 3.52/3.79 tff(34639,plain,
% 3.52/3.79 (~b(elem!1, s(s(s(s(elem!1)))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[23711, 34638, 33930, 33927])).
% 3.52/3.79 tff(34640,plain,
% 3.52/3.79 ((elem!1 = s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[19067, 21, 34639])).
% 3.52/3.79 tff(34641,plain,
% 3.52/3.79 (r(elem!1, s(s(s(s(elem!1)))))),
% 3.52/3.79 inference(unit_resolution,[status(thm)],[34640, 33926])).
% 3.52/3.79 tff(34642,plain,
% 3.52/3.79 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34615])).
% 3.52/3.80 tff(34643,plain,
% 3.52/3.80 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34642])).
% 3.52/3.80 tff(34644,plain,
% 3.52/3.80 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34643, 34614])).
% 3.52/3.80 tff(34645,plain,
% 3.52/3.80 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34644])).
% 3.52/3.80 tff(34646,plain,
% 3.52/3.80 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 3.52/3.80 inference(modus_ponens,[status(thm)],[877, 34645])).
% 3.52/3.80 tff(34647,plain,
% 3.52/3.80 (b(elem!1, s(z))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[324, 33924, 11199])).
% 3.52/3.80 tff(34648,plain,
% 3.52/3.80 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34615])).
% 3.52/3.80 tff(34649,plain,
% 3.52/3.80 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 3.52/3.80 inference(symmetry,[status(thm)],[34648])).
% 3.52/3.80 tff(34650,plain,
% 3.52/3.80 (r(s(s(s(z))), s(elem!1))),
% 3.52/3.80 inference(modus_ponens,[status(thm)],[34405, 34649])).
% 3.52/3.80 tff(34651,plain,
% 3.52/3.80 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = s(elem!1))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[33923])).
% 3.52/3.80 tff(34652,plain,
% 3.52/3.80 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34651])).
% 3.52/3.80 tff(34653,plain,
% 3.52/3.80 (~(s(s(s(z))) = s(elem!1))),
% 3.52/3.80 inference(modus_ponens,[status(thm)],[97, 34652])).
% 3.52/3.80 tff(34654,plain,
% 3.52/3.80 (r(z, s(s(s(z))))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[1187, 34625, 33924])).
% 3.52/3.80 tff(34655,plain,
% 3.52/3.80 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[34242, 34654, 33929, 33927, 34653, 33924, 108, 34650, 34647])).
% 3.52/3.80 tff(34656,plain,
% 3.52/3.80 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[1733, 34655])).
% 3.52/3.80 tff(34657,plain,
% 3.52/3.80 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[19552, 34656, 33923])).
% 3.52/3.80 tff(34658,plain,
% 3.52/3.80 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[20650, 34657, 34608, 34418, 34606, 34612])).
% 3.52/3.80 tff(34659,plain,
% 3.52/3.80 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.52/3.80 inference(unit_resolution,[status(thm)],[18291, 34658, 34646])).
% 3.52/3.80 tff(34660,plain,
% 3.52/3.80 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.52/3.80 inference(monotonicity,[status(thm)],[33924])).
% 3.52/3.80 tff(34661,plain,
% 3.52/3.80 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34660])).
% 3.52/3.80 tff(34662,plain,
% 3.52/3.80 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.52/3.80 inference(modus_ponens,[status(thm)],[711, 34661])).
% 3.52/3.80 tff(34663,plain,
% 3.52/3.80 (s(elem!1) = s(z)),
% 3.52/3.80 inference(symmetry,[status(thm)],[33923])).
% 3.52/3.80 tff(34664,plain,
% 3.52/3.80 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34663])).
% 3.52/3.80 tff(34665,plain,
% 3.52/3.80 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 3.52/3.80 inference(symmetry,[status(thm)],[34664])).
% 3.52/3.80 tff(34666,plain,
% 3.52/3.80 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 3.52/3.80 inference(monotonicity,[status(thm)],[34665])).
% 3.52/3.80 tff(34667,plain,
% 3.52/3.80 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.52/3.80 inference(modus_ponens,[status(thm)],[1677, 34666])).
% 3.52/3.80 tff(34668,plain,
% 3.52/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.52/3.80 inference(rewrite,[status(thm)],[])).
% 3.52/3.80 tff(34669,plain,
% 3.52/3.80 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.62/3.80 inference(rewrite,[status(thm)],[])).
% 3.62/3.80 tff(34670,plain,
% 3.62/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 3.62/3.80 inference(monotonicity,[status(thm)],[34669])).
% 3.62/3.80 tff(34671,plain,
% 3.62/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.62/3.80 inference(transitivity,[status(thm)],[34670, 34668])).
% 3.62/3.80 tff(34672,plain,
% 3.62/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.62/3.80 inference(quant_inst,[status(thm)],[])).
% 3.62/3.80 tff(34673,plain,
% 3.62/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[34672, 34671])).
% 3.62/3.80 tff(34674,plain,
% 3.62/3.80 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34673, 121, 34608, 34527, 34659])).
% 3.62/3.80 tff(34675,plain,
% 3.62/3.80 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[18190, 34674, 33924])).
% 3.62/3.80 tff(34676,plain,
% 3.62/3.80 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[4138, 34675, 34667])).
% 3.62/3.80 tff(34677,plain,
% 3.62/3.80 (~b(s(s(s(s(s(z))))), z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24620, 34676, 11199, 33929])).
% 3.62/3.80 tff(34678,plain,
% 3.62/3.80 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32429, 34677, 33924])).
% 3.62/3.80 tff(34679,plain,
% 3.62/3.80 (r(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[840, 34678, 34662])).
% 3.62/3.80 tff(34680,plain,
% 3.62/3.80 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[9962, 34679, 33923])).
% 3.62/3.80 tff(34681,plain,
% 3.62/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 3.62/3.80 inference(rewrite,[status(thm)],[])).
% 3.62/3.80 tff(34682,plain,
% 3.62/3.80 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 3.62/3.80 inference(rewrite,[status(thm)],[])).
% 3.62/3.80 tff(34683,plain,
% 3.62/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 3.62/3.80 inference(monotonicity,[status(thm)],[34682])).
% 3.62/3.80 tff(34684,plain,
% 3.62/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 3.62/3.80 inference(transitivity,[status(thm)],[34683, 34681])).
% 3.62/3.80 tff(34685,plain,
% 3.62/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.62/3.80 inference(quant_inst,[status(thm)],[])).
% 3.62/3.80 tff(34686,plain,
% 3.62/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[34685, 34684])).
% 3.62/3.80 tff(34687,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34686, 121, 34527, 34680, 34659, 34641])).
% 3.62/3.80 tff(34688,plain,(b(s(z), s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34689,plain,
% 3.62/3.80 (b(s(z), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34688, 32850, 1, 906, 899])).
% 3.62/3.80 tff(34690,plain,
% 3.62/3.80 (~b(z, s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[19817, 19776, 19197, 3871])).
% 3.62/3.80 tff(34691,plain,
% 3.62/3.80 (r(z, s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1214, 34690])).
% 3.62/3.80 tff(34692,plain,
% 3.62/3.80 (~b(s(s(s(elem!1))), z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32797, 111, 211, 3871, 220, 2073, 317, 19197])).
% 3.62/3.80 tff(34693,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32693, 34692, 111, 220, 3871, 906, 1, 31518])).
% 3.62/3.80 tff(34694,plain,((~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), z) | (~b(s(s(s(z))), s(s(s(elem!1))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34695,plain,
% 3.62/3.80 (~r(z, s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34694, 317, 3871, 906, 1, 31518, 19776, 220])).
% 3.62/3.80 tff(34696,plain,
% 3.62/3.80 (b(z, s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[19736, 34695])).
% 3.62/3.80 tff(34697,plain,
% 3.62/3.80 (r(s(elem!1), z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24348, 34696, 3871, 1])).
% 3.62/3.80 tff(34698,plain,
% 3.62/3.80 (~r(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24748, 34697, 34691, 9983])).
% 3.62/3.80 tff(34699,plain,
% 3.62/3.80 (b(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[284, 34698, 9298])).
% 3.62/3.80 tff(34700,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[22265, 337, 10219, 109, 1209, 317, 412, 3871, 348, 377])).
% 3.62/3.80 tff(34701,plain,(b(z, elem!1) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34702,plain,
% 3.62/3.80 (b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34701, 317, 34690, 24432, 34697, 3871, 348, 219, 220])).
% 3.62/3.80 tff(34703,plain,
% 3.62/3.80 (r(s(z), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32849, 906, 1, 220, 31518])).
% 3.62/3.80 tff(34704,plain,
% 3.62/3.80 (~r(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3683, 622, 19000, 412])).
% 3.62/3.80 tff(34705,plain,
% 3.62/3.80 (b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[355, 34704, 9297])).
% 3.62/3.80 tff(34706,plain,
% 3.62/3.80 (~b(elem!1, s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[20398, 34705, 1281, 220])).
% 3.62/3.80 tff(34707,plain,
% 3.62/3.80 (~r(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24748, 412, 1140, 379])).
% 3.62/3.80 tff(34708,plain,
% 3.62/3.80 (b(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[284, 34707, 358])).
% 3.62/3.80 tff(34709,plain,
% 3.62/3.80 (~r(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3683, 412, 379, 622])).
% 3.62/3.80 tff(34710,plain,
% 3.62/3.80 (b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[355, 34709, 331])).
% 3.62/3.80 tff(34711,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[7173, 34710, 34708, 3407, 504])).
% 3.62/3.80 tff(34712,plain,((~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34713,plain,
% 3.62/3.80 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34712, 622, 3407, 9297, 19000, 412, 32731])).
% 3.62/3.80 tff(34714,plain,
% 3.62/3.80 (~r(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24748, 412, 32731, 19000])).
% 3.62/3.80 tff(34715,plain,
% 3.62/3.80 (b(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[284, 34714, 9298])).
% 3.62/3.80 tff(34716,plain,
% 3.62/3.80 (~b(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[21030, 34715, 1281, 3407])).
% 3.62/3.80 tff(34717,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[15486, 121, 412, 24356, 32731])).
% 3.62/3.80 tff(34718,plain,
% 3.62/3.80 (r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[7179, 2505, 379])).
% 3.62/3.80 tff(34719,plain,
% 3.62/3.80 (~b(s(z), s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2562, 2505, 1242])).
% 3.62/3.80 tff(34720,plain,
% 3.62/3.80 (r(s(z), s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[760, 34719])).
% 3.62/3.80 tff(34721,plain,
% 3.62/3.80 (~r(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[9617, 34720, 622, 34718])).
% 3.62/3.80 tff(34722,plain,
% 3.62/3.80 (elem!1 = s(s(s(elem!1)))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[13222, 2505])).
% 3.62/3.80 tff(34723,plain,
% 3.62/3.80 (b(s(s(s(z))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[19808, 34722, 2073])).
% 3.62/3.80 tff(34724,plain,
% 3.62/3.80 (b(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2044, 3841, 2038])).
% 3.62/3.80 tff(34725,plain,
% 3.62/3.80 (~b(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3879, 34724, 3871, 34723])).
% 3.62/3.80 tff(34726,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[444, 34725, 34721, 348])).
% 3.62/3.80 tff(34727,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | r(s(elem!1), s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34728,plain,
% 3.62/3.80 (~(s(s(s(elem!1))) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34727, 622, 3871, 348, 34717, 2073, 19000, 34716])).
% 3.62/3.80 tff(34729,plain,
% 3.62/3.80 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[486, 34728, 34713])).
% 3.62/3.80 tff(34730,plain,
% 3.62/3.80 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[25513, 34729, 19000, 412])).
% 3.62/3.80 tff(34731,plain,
% 3.62/3.80 (r(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[33893, 34729, 622, 2073, 34730, 19000, 216, 108, 34716])).
% 3.62/3.80 tff(34732,plain,
% 3.62/3.80 (~(elem!1 = s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[25463, 34731])).
% 3.62/3.80 tff(34733,plain,
% 3.62/3.80 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[18965, 34732, 34716, 34729, 34706])).
% 3.62/3.80 tff(34734,plain,
% 3.62/3.80 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[760, 34733])).
% 3.62/3.80 tff(34735,plain,
% 3.62/3.80 (~b(s(s(s(elem!1))), s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[12484, 34734, 3871, 2073])).
% 3.62/3.80 tff(34736,plain,
% 3.62/3.80 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[9637, 34731, 348, 19000, 622, 34729])).
% 3.62/3.80 tff(34737,plain,
% 3.62/3.80 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[681, 34736, 34730])).
% 3.62/3.80 tff(34738,plain,
% 3.62/3.80 (elem!1 = s(s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[78, 34737])).
% 3.62/3.80 tff(34739,plain,
% 3.62/3.80 (~r(s(s(s(elem!1))), s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32597, 34738, 3871, 1281, 220, 317, 9298, 412, 32730, 8336])).
% 3.62/3.80 tff(34740,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[16580, 34739, 34735])).
% 3.62/3.80 tff(34741,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | b(elem!1, s(elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34742,plain,
% 3.62/3.80 (~r(s(elem!1), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34741, 317, 19197, 220, 3871, 34697, 19776, 348, 211, 34703, 34696])).
% 3.62/3.80 tff(34743,plain,
% 3.62/3.80 (b(s(elem!1), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2243, 34742, 2207])).
% 3.62/3.80 tff(34744,plain,
% 3.62/3.80 (~b(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[21030, 34699, 19197, 34696])).
% 3.62/3.80 tff(34745,plain,
% 3.62/3.80 (~(s(s(s(z))) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[10599, 34744, 3871])).
% 3.62/3.80 tff(34746,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[15486, 121, 34697, 24432, 34691])).
% 3.62/3.80 tff(34747,plain,
% 3.62/3.80 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 3.62/3.80 inference(symmetry,[status(thm)],[14244])).
% 3.62/3.80 tff(34748,plain,
% 3.62/3.80 ((~b(s(elem!1), s(z))) <=> (~b(s(elem!1), elem!1))),
% 3.62/3.80 inference(monotonicity,[status(thm)],[34747])).
% 3.62/3.80 tff(34749,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24187, 2359, 2038])).
% 3.62/3.80 tff(34750,plain,
% 3.62/3.80 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[526, 34749, 216])).
% 3.62/3.80 tff(34751,plain,
% 3.62/3.80 (b(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2369, 34750, 239])).
% 3.62/3.80 tff(34752,plain,
% 3.62/3.80 (~b(s(elem!1), s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[7781, 34751, 3871, 2073])).
% 3.62/3.80 tff(34753,plain,
% 3.62/3.80 (~b(s(elem!1), elem!1)),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[34752, 34748])).
% 3.62/3.80 tff(34754,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2618, 34753])).
% 3.62/3.80 tff(34755,plain,((~(elem!1 = s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34756,plain,
% 3.62/3.80 (~(elem!1 = s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34755, 34743, 3871, 19776, 211, 34746])).
% 3.62/3.80 tff(34757,plain,
% 3.62/3.80 (~(s(z) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1221, 34756])).
% 3.62/3.80 tff(34758,plain,
% 3.62/3.80 (r(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[236, 34757, 34744])).
% 3.62/3.80 tff(34759,plain,
% 3.62/3.80 (~b(elem!1, s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[20398, 34702, 19197, 220])).
% 3.62/3.80 tff(34760,plain,
% 3.62/3.80 (r(elem!1, s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[299, 34756, 34759])).
% 3.62/3.80 tff(34761,plain,
% 3.62/3.80 (~r(s(s(s(z))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[4112, 34760, 34703, 34758])).
% 3.62/3.80 tff(34762,plain,
% 3.62/3.80 (b(s(s(s(z))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[255, 34761, 34745])).
% 3.62/3.80 tff(34763,plain,
% 3.62/3.80 (s(s(s(z))) = s(elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[23566, 34762, 34743, 34702, 34699])).
% 3.62/3.80 tff(34764,plain,
% 3.62/3.80 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[7173, 34702, 34696, 34699])).
% 3.62/3.80 tff(34765,plain,
% 3.62/3.80 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3790, 34764, 34743])).
% 3.62/3.80 tff(34766,plain,
% 3.62/3.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[78, 34765])).
% 3.62/3.80 tff(34767,plain,
% 3.62/3.80 (~r(s(elem!1), s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[23287, 34757, 9983, 34759, 34744])).
% 3.62/3.80 tff(34768,plain,
% 3.62/3.80 (b(s(elem!1), s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[429, 34767, 2282])).
% 3.62/3.80 tff(34769,plain,
% 3.62/3.80 (~r(s(s(s(elem!1))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3823, 34768, 9983, 34766, 34697, 34758])).
% 3.62/3.80 tff(34770,plain,
% 3.62/3.80 (s(s(s(elem!1))) = elem!1),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[486, 34769, 34764])).
% 3.62/3.80 tff(34771,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2596, 34770, 34763])).
% 3.62/3.80 tff(34772,plain,(b(elem!1, s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34773,plain,
% 3.62/3.80 (b(elem!1, s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34772, 348, 220, 3871, 1, 906, 31518])).
% 3.62/3.80 tff(34774,plain,
% 3.62/3.80 (~b(z, s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24348, 10994, 3871, 1])).
% 3.62/3.80 tff(34775,plain,
% 3.62/3.80 (~b(s(s(s(elem!1))), z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32824, 10994, 1, 220, 3871, 906, 307])).
% 3.62/3.80 tff(34776,plain,
% 3.62/3.80 (~r(z, s(s(s(elem!1))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[32693, 34775, 220, 3871, 906, 1, 31518])).
% 3.62/3.80 tff(34777,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[19736, 34776, 34774])).
% 3.62/3.80 tff(34778,plain,(r(s(elem!1), z) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), z) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34779,plain,
% 3.62/3.80 (r(s(elem!1), z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34778, 34773, 3871, 906, 1, 31518, 220])).
% 3.62/3.80 tff(34780,plain,
% 3.62/3.80 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[26349, 34691, 220, 24432, 34703, 19197])).
% 3.62/3.80 tff(34781,plain,
% 3.62/3.80 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1733, 34780])).
% 3.62/3.80 tff(34782,plain,
% 3.62/3.80 (~r(elem!1, s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[33842, 147, 307, 412, 331, 2073, 220, 108, 422, 1])).
% 3.62/3.80 tff(34783,plain,
% 3.62/3.80 (~b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[20398, 448, 19197, 220])).
% 3.62/3.80 tff(34784,plain,
% 3.62/3.80 (r(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[355, 34783, 331])).
% 3.62/3.80 tff(34785,plain,
% 3.62/3.80 (~r(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[5358, 34784, 412, 8563])).
% 3.62/3.80 tff(34786,plain,
% 3.62/3.80 (b(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[284, 34785, 358])).
% 3.62/3.80 tff(34787,plain,
% 3.62/3.80 (~b(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[8962, 34786, 220, 448])).
% 3.62/3.80 tff(34788,plain,
% 3.62/3.80 (~(s(s(s(z))) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[10599, 34787, 3871])).
% 3.62/3.80 tff(34789,plain,
% 3.62/3.80 (~(elem!1 = s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1100, 34788])).
% 3.62/3.80 tff(34790,plain,
% 3.62/3.80 (s(elem!1) = s(s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[26949, 34787, 412, 147, 220, 2467, 2344, 2073, 307, 34783, 34784, 358, 422, 1])).
% 3.62/3.80 tff(34791,plain,
% 3.62/3.80 (s(s(s(s(z)))) = s(elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[17419, 34790])).
% 3.62/3.80 tff(34792,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1516, 34791, 34789])).
% 3.62/3.80 tff(34793,plain,((~b(elem!1, s(z))) | (~r(s(elem!1), z)) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | b(s(elem!1), elem!1) | r(elem!1, s(elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34794,plain,
% 3.62/3.80 (~b(elem!1, s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34793, 147, 412, 220, 2467, 34782, 2073, 307, 422, 1, 3871, 331])).
% 3.62/3.80 tff(34795,plain,
% 3.62/3.80 (elem!1 = s(z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[23549, 34794, 331, 412, 307, 422, 2467, 2073, 147, 1])).
% 3.62/3.80 tff(34796,plain,
% 3.62/3.80 (~b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[23545, 34794, 307, 422, 412, 2467, 2073, 147, 1])).
% 3.62/3.80 tff(34797,plain,
% 3.62/3.80 (~(s(z) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[229, 34796, 220])).
% 3.62/3.80 tff(34798,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[242, 34797, 34795])).
% 3.62/3.80 tff(34799,plain,(r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (z = elem!1) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34800,plain,
% 3.62/3.80 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34799, 2467, 9297, 412, 307, 2282, 220, 19776, 1, 3871, 108])).
% 3.62/3.80 tff(34801,plain,
% 3.62/3.80 (b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[26201, 294, 412, 8448, 9297, 220])).
% 3.62/3.80 tff(34802,plain,
% 3.62/3.80 (~b(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[20382, 34801, 1281, 307])).
% 3.62/3.80 tff(34803,plain,
% 3.62/3.80 (~b(z, s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[19817, 19776, 1281, 3871])).
% 3.62/3.80 tff(34804,plain,
% 3.62/3.80 (r(z, s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1214, 34803])).
% 3.62/3.80 tff(34805,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[15486, 121, 412, 24356, 34804])).
% 3.62/3.80 tff(34806,plain,
% 3.62/3.80 (~(s(s(s(z))) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[6548, 34801, 34803])).
% 3.62/3.80 tff(34807,plain,
% 3.62/3.80 (~r(s(s(s(z))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[4112, 1256, 108, 1258])).
% 3.62/3.80 tff(34808,plain,
% 3.62/3.80 (b(s(s(s(z))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[255, 34807, 907])).
% 3.62/3.80 tff(34809,plain,
% 3.62/3.80 (~(s(elem!1) = s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[8462, 34808, 2467])).
% 3.62/3.80 tff(34810,plain,
% 3.62/3.80 (~r(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[6525, 1258, 622, 1256])).
% 3.62/3.80 tff(34811,plain,
% 3.62/3.80 (b(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[444, 34810, 348])).
% 3.62/3.80 tff(34812,plain,
% 3.62/3.80 (~b(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3879, 34811, 3871, 34808])).
% 3.62/3.80 tff(34813,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2044, 34812, 34809, 2038])).
% 3.62/3.80 tff(34814,plain,((elem!1 = s(z)) | r(s(elem!1), s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | b(s(elem!1), elem!1) | (s(z) = s(elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34815,plain,
% 3.62/3.80 (elem!1 = s(z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34814, 34806, 3871, 2467, 348, 34805, 8448, 108, 34802, 294])).
% 3.62/3.80 tff(34816,plain,
% 3.62/3.80 (~r(s(z), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[25463, 34815])).
% 3.62/3.80 tff(34817,plain,
% 3.62/3.80 (s(z) = elem!1),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[242, 34815])).
% 3.62/3.80 tff(34818,plain,
% 3.62/3.80 (b(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1276, 34817, 307])).
% 3.62/3.80 tff(34819,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[24187, 34817, 34805])).
% 3.62/3.80 tff(34820,plain,
% 3.62/3.80 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[526, 34819, 216])).
% 3.62/3.80 tff(34821,plain,
% 3.62/3.80 (b(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[2369, 34820, 34815])).
% 3.62/3.80 tff(34822,plain,
% 3.62/3.80 (~b(s(s(s(z))), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3879, 34821, 3871, 34818])).
% 3.62/3.80 tff(34823,plain,
% 3.62/3.80 (r(elem!1, s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[33376, 34822, 348, 139, 108, 8448, 2467, 294, 906, 34802])).
% 3.62/3.80 tff(34824,plain,
% 3.62/3.80 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[25513, 34823, 139, 412])).
% 3.62/3.80 tff(34825,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[33893, 34824, 34823, 8448, 19776, 139, 34816, 216, 108, 34802])).
% 3.62/3.80 tff(34826,plain,(b(elem!1, s(z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | b(s(elem!1), elem!1) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34827,plain,
% 3.62/3.80 (b(elem!1, s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34826, 34800, 211, 108, 412, 348, 2467, 906, 3871, 307, 19197, 220])).
% 3.62/3.80 tff(34828,plain,
% 3.62/3.80 (~b(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[20398, 34827, 19197, 220])).
% 3.62/3.80 tff(34829,plain,
% 3.62/3.80 (r(z, elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[355, 34828, 9297])).
% 3.62/3.80 tff(34830,plain,
% 3.62/3.80 (~r(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[5358, 34829, 412, 8563])).
% 3.62/3.80 tff(34831,plain,
% 3.62/3.80 (b(elem!1, z)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[284, 34830, 9298])).
% 3.62/3.80 tff(34832,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[22281, 271, 19197, 34831, 34827, 220])).
% 3.62/3.80 tff(34833,plain,(b(s(elem!1), elem!1) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (s(z) = s(elem!1)) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34834,plain,
% 3.62/3.80 (b(s(elem!1), elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34833, 34779, 220, 34703, 348, 906, 3871, 34773, 1])).
% 3.62/3.80 tff(34835,plain,
% 3.62/3.80 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.62/3.80 inference(monotonicity,[status(thm)],[2606])).
% 3.62/3.80 tff(34836,plain,
% 3.62/3.80 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.62/3.80 inference(monotonicity,[status(thm)],[34835])).
% 3.62/3.80 tff(34837,plain,
% 3.62/3.80 (~b(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[3435, 31605, 307, 2618])).
% 3.62/3.80 tff(34838,plain,
% 3.62/3.80 (r(s(z), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[444, 34837, 348])).
% 3.62/3.80 tff(34839,plain,
% 3.62/3.80 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[17876, 34838, 412, 220])).
% 3.62/3.80 tff(34840,plain,
% 3.62/3.80 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[34839, 34836])).
% 3.62/3.80 tff(34841,plain,
% 3.62/3.80 (b(s(s(s(s(z)))), elem!1)),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[2618, 9466])).
% 3.62/3.80 tff(34842,plain,
% 3.62/3.80 (b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[1723, 27367])).
% 3.62/3.80 tff(34843,plain,
% 3.62/3.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.62/3.80 inference(rewrite,[status(thm)],[])).
% 3.62/3.80 tff(34844,plain,
% 3.62/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.62/3.80 inference(quant_inst,[status(thm)],[])).
% 3.62/3.80 tff(34845,plain,
% 3.62/3.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.62/3.80 inference(modus_ponens,[status(thm)],[34844, 34843])).
% 3.62/3.80 tff(34846,plain,
% 3.62/3.80 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34845, 271, 34842, 27998, 34841])).
% 3.62/3.80 tff(34847,plain,
% 3.62/3.80 ($false),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[9512, 34846, 34840])).
% 3.62/3.80 tff(34848,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.80 tff(34849,plain,
% 3.62/3.80 (~(s(s(s(z))) = elem!1)),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34848, 34834, 34781, 34779, 220, 348, 34773, 19776, 3871])).
% 3.62/3.80 tff(34850,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[15486, 121, 34779, 24432, 34691])).
% 3.62/3.80 tff(34851,plain,
% 3.62/3.80 (~(elem!1 = s(z))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[34755, 34834, 3871, 19776, 211, 34850])).
% 3.62/3.80 tff(34852,plain,
% 3.62/3.80 (~b(z, s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[19817, 2073, 19197, 3871])).
% 3.62/3.80 tff(34853,plain,
% 3.62/3.80 (r(z, s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[1214, 34852])).
% 3.62/3.80 tff(34854,plain,
% 3.62/3.80 (~r(s(elem!1), s(s(s(z))))),
% 3.62/3.80 inference(unit_resolution,[status(thm)],[15486, 121, 412, 24432, 34853])).
% 3.62/3.81 tff(34855,plain,
% 3.62/3.81 (~(elem!1 = s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34755, 2618, 3871, 2073, 211, 34854])).
% 3.62/3.81 tff(34856,plain,
% 3.62/3.81 (~(s(z) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1221, 34855])).
% 3.62/3.81 tff(34857,plain,
% 3.62/3.81 (b(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[236, 232, 34856])).
% 3.62/3.81 tff(34858,plain,
% 3.62/3.81 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26349, 34853, 220, 24432, 108, 19197])).
% 3.62/3.81 tff(34859,plain,
% 3.62/3.81 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1733, 34858])).
% 3.62/3.81 tff(34860,plain,
% 3.62/3.81 (~(s(s(s(z))) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34848, 2618, 34859, 412, 220, 348, 307, 2073, 3871])).
% 3.62/3.81 tff(34861,plain,
% 3.62/3.81 (~b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33821, 251, 412, 2618, 2073, 147, 1281, 220, 108, 307])).
% 3.62/3.81 tff(34862,plain,
% 3.62/3.81 (~(s(z) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[229, 34861, 220])).
% 3.62/3.81 tff(34863,plain,
% 3.62/3.81 (~(elem!1 = s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[242, 34862])).
% 3.62/3.81 tff(34864,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[355, 34861, 9297])).
% 3.62/3.81 tff(34865,plain,
% 3.62/3.81 (b(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[236, 34862, 232])).
% 3.62/3.81 tff(34866,plain,
% 3.62/3.81 (~b(s(z), s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3435, 34865, 307, 2618])).
% 3.62/3.81 tff(34867,plain,
% 3.62/3.81 (r(s(z), s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[444, 34866, 348])).
% 3.62/3.81 tff(34868,plain,
% 3.62/3.81 (~(s(s(z)) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[960, 34862])).
% 3.62/3.81 tff(34869,plain,
% 3.62/3.81 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[953, 34868])).
% 3.62/3.81 tff(34870,plain,
% 3.62/3.81 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[946, 34869])).
% 3.62/3.81 tff(34871,plain,
% 3.62/3.81 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[25008, 34870])).
% 3.62/3.81 tff(34872,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26892, 34871, 34867, 2073, 147, 220, 307, 412, 1281, 348, 34865, 34864, 108, 251, 2564, 34863])).
% 3.62/3.81 tff(34873,plain,(r(s(z), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34874,plain,
% 3.62/3.81 (r(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34873, 147, 2073, 220, 307, 412, 1281, 348, 108, 2564, 2618])).
% 3.62/3.81 tff(34875,plain,
% 3.62/3.81 (~b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33828, 147, 307, 412, 2618, 2073, 1281, 220, 108])).
% 3.62/3.81 tff(34876,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[355, 34875, 9297])).
% 3.62/3.81 tff(34877,plain,
% 3.62/3.81 (s(s(s(z))) = s(elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[13140, 257, 1140, 307, 412, 2618])).
% 3.62/3.81 tff(34878,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26813, 34877, 257, 307, 2073, 147])).
% 3.62/3.81 tff(34879,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34880,plain,
% 3.62/3.81 (~b(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34879, 147, 2073, 307, 1140, 412, 2618])).
% 3.62/3.81 tff(34881,plain,
% 3.62/3.81 (r(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[255, 34880, 907])).
% 3.62/3.81 tff(34882,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26024, 34881, 34876, 34874, 220, 9298, 1281, 258, 108])).
% 3.62/3.81 tff(34883,plain,(r(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34884,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34883, 34855, 19197, 220, 108, 34860, 2073, 307, 34853, 412, 2618, 348, 2207])).
% 3.62/3.81 tff(34885,plain,
% 3.62/3.81 (b(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33615, 232, 307, 220, 108, 412, 2618, 2073, 1, 348, 34884])).
% 3.62/3.81 tff(34886,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24003, 34885, 34857, 3871, 307])).
% 3.62/3.81 tff(34887,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34888,plain,
% 3.62/3.81 (r(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34887, 34773, 3871, 220, 34703, 34779, 34834, 19776, 1, 348])).
% 3.62/3.81 tff(34889,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34883, 34851, 19197, 220, 34703, 34849, 19776, 34773, 34691, 34779, 34834, 348, 2207])).
% 3.62/3.81 tff(34890,plain,
% 3.62/3.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.62/3.81 inference(rewrite,[status(thm)],[])).
% 3.62/3.81 tff(34891,plain,
% 3.62/3.81 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.62/3.81 inference(rewrite,[status(thm)],[])).
% 3.62/3.81 tff(34892,plain,
% 3.62/3.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34891])).
% 3.62/3.81 tff(34893,plain,
% 3.62/3.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.62/3.81 inference(transitivity,[status(thm)],[34892, 34890])).
% 3.62/3.81 tff(34894,plain,
% 3.62/3.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.62/3.81 inference(quant_inst,[status(thm)],[])).
% 3.62/3.81 tff(34895,plain,
% 3.62/3.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[34894, 34893])).
% 3.62/3.81 tff(34896,plain,
% 3.62/3.81 (~b(s(z), s(s(s(s(s(z))))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34895, 271, 19776, 3871, 34781])).
% 3.62/3.81 tff(34897,plain,
% 3.62/3.81 (~r(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[4112, 23518, 108, 357])).
% 3.62/3.81 tff(34898,plain,
% 3.62/3.81 (b(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[255, 34897, 907])).
% 3.62/3.81 tff(34899,plain,
% 3.62/3.81 (s(s(s(z))) = s(elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[13140, 34898, 1140, 307, 412, 2618])).
% 3.62/3.81 tff(34900,plain,
% 3.62/3.81 (s(s(s(s(z)))) = s(s(elem!1))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34899])).
% 3.62/3.81 tff(34901,plain,
% 3.62/3.81 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34900])).
% 3.62/3.81 tff(34902,plain,
% 3.62/3.81 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34901])).
% 3.62/3.81 tff(34903,plain,
% 3.62/3.81 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(z))))))),
% 3.62/3.81 inference(symmetry,[status(thm)],[34902])).
% 3.62/3.81 tff(34904,plain,
% 3.62/3.81 (~b(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24003, 34898, 3871, 307])).
% 3.62/3.81 tff(34905,plain,
% 3.62/3.81 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[18965, 34904, 139, 258, 294])).
% 3.62/3.81 tff(34906,plain,
% 3.62/3.81 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[760, 34905])).
% 3.62/3.81 tff(34907,plain,
% 3.62/3.81 (b(s(z), s(s(s(s(s(z))))))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[34906, 34903])).
% 3.62/3.81 tff(34908,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1751, 34907])).
% 3.62/3.81 tff(34909,plain,(b(elem!1, s(z)) | b(s(z), s(s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34910,plain,
% 3.62/3.81 (b(elem!1, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34909, 34896, 34889, 34851, 34691, 34773, 34779, 34834, 3871, 34849, 34703, 34888])).
% 3.62/3.81 tff(34911,plain,
% 3.62/3.81 (~b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[20398, 34910, 19197, 220])).
% 3.62/3.81 tff(34912,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[355, 34911, 9297])).
% 3.62/3.81 tff(34913,plain,
% 3.62/3.81 (~r(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26024, 34912, 34888, 220, 9298, 19197, 34851, 34703])).
% 3.62/3.81 tff(34914,plain,
% 3.62/3.81 (~b(s(z), s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3019, 34910, 34773, 34834])).
% 3.62/3.81 tff(34915,plain,
% 3.62/3.81 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[4929, 34914, 3871])).
% 3.62/3.81 tff(34916,plain,
% 3.62/3.81 (~b(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[13140, 34915, 34691, 34773, 34779, 34834])).
% 3.62/3.81 tff(34917,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[255, 34916, 34913, 34849])).
% 3.62/3.81 tff(34918,plain,((s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34919,plain,
% 3.62/3.81 (s(z) = s(elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34918, 34689, 11199, 1, 906, 31518])).
% 3.62/3.81 tff(34920,plain,
% 3.62/3.81 (r(s(z), z) <=> r(s(elem!1), z)),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34919])).
% 3.62/3.81 tff(34921,plain,
% 3.62/3.81 (r(s(elem!1), z) <=> r(s(z), z)),
% 3.62/3.81 inference(symmetry,[status(thm)],[34920])).
% 3.62/3.81 tff(34922,plain,
% 3.62/3.81 (z = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[343, 34919])).
% 3.62/3.81 tff(34923,plain,
% 3.62/3.81 (b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[327, 34922, 11199])).
% 3.62/3.81 tff(34924,plain,
% 3.62/3.81 (r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34778, 34923, 34689, 906, 1, 31518, 11199])).
% 3.62/3.81 tff(34925,plain,
% 3.62/3.81 (r(s(z), z)),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[34924, 34921])).
% 3.62/3.81 tff(34926,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[31518, 34925])).
% 3.62/3.81 tff(34927,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | r(s(z), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34928,plain,
% 3.62/3.81 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34927, 899, 1, 31518])).
% 3.62/3.81 tff(34929,plain,
% 3.62/3.81 (~(s(z) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24229, 34928])).
% 3.62/3.81 tff(34930,plain,
% 3.62/3.81 (~(z = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[500, 34929])).
% 3.62/3.81 tff(34931,plain,
% 3.62/3.81 (r(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27575, 11199, 1, 34928])).
% 3.62/3.81 tff(34932,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27657, 220, 1, 5499])).
% 3.62/3.81 tff(34933,plain,
% 3.62/3.81 (~r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24738, 199, 2564, 379, 220, 1281, 331])).
% 3.62/3.81 tff(34934,plain,
% 3.62/3.81 (~b(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[13607, 1243, 220, 379, 139, 82])).
% 3.62/3.81 tff(34935,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[409, 34934, 34933])).
% 3.62/3.81 tff(34936,plain,(b(z, elem!1) | (~b(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = elem!1) | (~b(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34937,plain,
% 3.62/3.81 (b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34936, 82, 27576, 34932, 220, 2207, 19197, 25633])).
% 3.62/3.81 tff(34938,plain,
% 3.62/3.81 (~b(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[20382, 34937, 19197, 25632])).
% 3.62/3.81 tff(34939,plain,
% 3.62/3.81 (~b(elem!1, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[20398, 34937, 19197, 220])).
% 3.62/3.81 tff(34940,plain,
% 3.62/3.81 (elem!1 = s(z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27280, 907, 19197, 220, 25632, 34932, 34937, 5499])).
% 3.62/3.81 tff(34941,plain,
% 3.62/3.81 (s(elem!1) = s(s(z))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34940])).
% 3.62/3.81 tff(34942,plain,
% 3.62/3.81 (s(s(elem!1)) = s(s(s(z)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34941])).
% 3.62/3.81 tff(34943,plain,
% 3.62/3.81 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34942])).
% 3.62/3.81 tff(34944,plain,
% 3.62/3.81 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.81 inference(symmetry,[status(thm)],[34943])).
% 3.62/3.81 tff(34945,plain,
% 3.62/3.81 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[5499, 34944])).
% 3.62/3.81 tff(34946,plain,
% 3.62/3.81 (s(z) = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[242, 34940])).
% 3.62/3.81 tff(34947,plain,
% 3.62/3.81 (~b(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26193, 34937, 19197, 25632, 24230, 219, 220])).
% 3.62/3.81 tff(34948,plain,
% 3.62/3.81 (r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[409, 34947])).
% 3.62/3.81 tff(34949,plain,
% 3.62/3.81 (~b(s(elem!1), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27315, 907, 220, 82, 5499, 34932, 34948, 1])).
% 3.62/3.81 tff(34950,plain,
% 3.62/3.81 (r(s(elem!1), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2243, 34949, 2207])).
% 3.62/3.81 tff(34951,plain,
% 3.62/3.81 (b(elem!1, z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[20120, 34946, 19197])).
% 3.62/3.81 tff(34952,plain,
% 3.62/3.81 (~r(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[25562, 34951, 27576, 34932, 34937, 19197, 5499, 907, 34948, 25634, 24230, 34950, 34939])).
% 3.62/3.81 tff(34953,plain,
% 3.62/3.81 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[26325, 34952, 34932, 220, 34946, 1])).
% 3.62/3.81 tff(34954,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34953, 34945])).
% 3.62/3.81 tff(34955,plain,((s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34956,plain,
% 3.62/3.81 (s(s(s(z))) = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34955, 82, 220, 1, 5499])).
% 3.62/3.81 tff(34957,plain,
% 3.62/3.81 (~b(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[10599, 34956, 34938])).
% 3.62/3.81 tff(34958,plain,
% 3.62/3.81 (r(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[105, 34957])).
% 3.62/3.81 tff(34959,plain,
% 3.62/3.81 (r(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[250, 34958, 34956])).
% 3.62/3.81 tff(34960,plain,
% 3.62/3.81 (~(elem!1 = s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[25463, 34959])).
% 3.62/3.81 tff(34961,plain,
% 3.62/3.81 (~(s(z) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1221, 34960])).
% 3.62/3.81 tff(34962,plain,
% 3.62/3.81 (~b(s(elem!1), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3823, 34959, 27576, 34932, 34948, 82])).
% 3.62/3.81 tff(34963,plain,
% 3.62/3.81 (r(s(elem!1), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[429, 34962, 26198])).
% 3.62/3.81 tff(34964,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[23287, 34963, 34961, 27576, 34939, 34938])).
% 3.62/3.81 tff(34965,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34966,plain,
% 3.62/3.81 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34965, 11199, 1, 34928])).
% 3.62/3.81 tff(34967,plain,
% 3.62/3.81 (elem!1 = s(s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[78, 34966])).
% 3.62/3.81 tff(34968,plain,
% 3.62/3.81 (~(s(s(s(z))) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3906, 34967])).
% 3.62/3.81 tff(34969,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27657, 11199, 1, 34928])).
% 3.62/3.81 tff(34970,plain,
% 3.62/3.81 (b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[25631, 34928, 11199, 1])).
% 3.62/3.81 tff(34971,plain,
% 3.62/3.81 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34967])).
% 3.62/3.81 tff(34972,plain,
% 3.62/3.81 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 3.62/3.81 inference(symmetry,[status(thm)],[34971])).
% 3.62/3.81 tff(34973,plain,
% 3.62/3.81 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 3.62/3.81 inference(transitivity,[status(thm)],[34972, 1218])).
% 3.62/3.81 tff(34974,plain,
% 3.62/3.81 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34973])).
% 3.62/3.81 tff(34975,plain,
% 3.62/3.81 (~(elem!1 = s(z))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[2137, 34974])).
% 3.62/3.81 tff(34976,plain,
% 3.62/3.81 (~b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27280, 34975, 19197, 11199, 34970, 34969, 34968, 34928])).
% 3.62/3.81 tff(34977,plain,
% 3.62/3.81 (~r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24738, 34976, 2207, 34931, 11199, 19197, 34930])).
% 3.62/3.81 tff(34978,plain,
% 3.62/3.81 (b(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[409, 34977])).
% 3.62/3.81 tff(34979,plain,
% 3.62/3.81 (~b(s(z), s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[9241, 34978, 19197, 11199])).
% 3.62/3.81 tff(34980,plain,
% 3.62/3.81 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3917, 34967, 34929])).
% 3.62/3.81 tff(34981,plain,
% 3.62/3.81 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = elem!1))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34972])).
% 3.62/3.81 tff(34982,plain,
% 3.62/3.81 (~(s(z) = elem!1)),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[2137, 34981])).
% 3.62/3.81 tff(34983,plain,
% 3.62/3.81 (~(elem!1 = z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[333, 34930])).
% 3.62/3.81 tff(34984,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[355, 34976, 34930])).
% 3.62/3.81 tff(34985,plain,
% 3.62/3.81 (~r(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27152, 34984, 34969, 11199, 34983, 19197, 34975])).
% 3.62/3.81 tff(34986,plain,
% 3.62/3.81 (b(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[236, 34985, 34982])).
% 3.62/3.81 tff(34987,plain,
% 3.62/3.81 (r(s(s(s(z))), s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[23458, 34966, 34928])).
% 3.62/3.81 tff(34988,plain,
% 3.62/3.81 (s(elem!1) = s(s(s(elem!1)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34967])).
% 3.62/3.81 tff(34989,plain,
% 3.62/3.81 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34988])).
% 3.62/3.81 tff(34990,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.62/3.81 inference(symmetry,[status(thm)],[34989])).
% 3.62/3.81 tff(34991,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[34967])).
% 3.62/3.81 tff(34992,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[34969, 34991])).
% 3.62/3.81 tff(34993,plain,
% 3.62/3.81 (r(s(elem!1), s(s(elem!1)))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[34992, 34990])).
% 3.62/3.81 tff(34994,plain,
% 3.62/3.81 (~r(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24763, 34993, 34931, 34987])).
% 3.62/3.81 tff(34995,plain,
% 3.62/3.81 (b(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[255, 34994, 34968])).
% 3.62/3.81 tff(34996,plain,
% 3.62/3.81 (~r(s(z), s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3299, 34978, 34970, 34993, 34995, 34986, 34980])).
% 3.62/3.81 tff(34997,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[444, 34996, 34979, 34929])).
% 3.62/3.81 tff(34998,plain,(r(z, s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(34999,plain,
% 3.62/3.81 (r(z, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34998, 1, 31518])).
% 3.62/3.81 tff(35000,plain,
% 3.62/3.81 (b(z, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24220, 34999, 147, 1])).
% 3.62/3.81 tff(35001,plain,
% 3.62/3.81 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27657, 35000, 147, 1])).
% 3.62/3.81 tff(35002,plain,
% 3.62/3.81 (~b(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34918, 35001, 1, 35000, 348, 31518])).
% 3.62/3.81 tff(35003,plain,
% 3.62/3.81 (r(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[32849, 35000, 1, 35001, 31518])).
% 3.62/3.81 tff(35004,plain,
% 3.62/3.81 (~b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33906, 35002, 1, 35001, 348, 35000, 35003, 2468])).
% 3.62/3.81 tff(35005,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33301, 35004, 1, 35000, 35001, 348, 35003, 35002])).
% 3.62/3.81 tff(35006,plain,
% 3.62/3.81 (r(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[392, 35004, 219])).
% 3.62/3.81 tff(35007,plain,
% 3.62/3.81 (~r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3683, 35006, 35005, 2468])).
% 3.62/3.81 tff(35008,plain,
% 3.62/3.81 (~b(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27984, 35006, 1, 348, 35000, 35001, 35003, 35002])).
% 3.62/3.81 tff(35009,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[409, 35008, 35007])).
% 3.62/3.81 tff(35010,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | r(s(z), z) | b(s(elem!1), elem!1) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35011,plain,
% 3.62/3.81 (r(s(z), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35010, 31517, 348, 2467, 147])).
% 3.62/3.81 tff(35012,plain,
% 3.62/3.81 (~b(z, s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[17920, 35011, 31517, 9297])).
% 3.62/3.81 tff(35013,plain,
% 3.62/3.81 (r(z, s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19736, 35012])).
% 3.62/3.81 tff(35014,plain,
% 3.62/3.81 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12364, 31517, 147, 2467])).
% 3.62/3.81 tff(35015,plain,
% 3.62/3.81 (~(s(elem!1) = s(s(elem!1)))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[210, 31517])).
% 3.62/3.81 tff(35016,plain,
% 3.62/3.81 (~(elem!1 = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[218, 35015])).
% 3.62/3.81 tff(35017,plain,
% 3.62/3.81 (~(s(elem!1) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2206, 35016])).
% 3.62/3.81 tff(35018,plain,
% 3.62/3.81 (r(s(elem!1), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2243, 35017, 2467])).
% 3.62/3.81 tff(35019,plain,
% 3.62/3.81 (b(z, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24222, 31517, 147])).
% 3.62/3.81 tff(35020,plain,
% 3.62/3.81 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27657, 35019, 147, 31517])).
% 3.62/3.81 tff(35021,plain,
% 3.62/3.81 (~b(z, s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[17920, 110, 1, 9297])).
% 3.62/3.81 tff(35022,plain,
% 3.62/3.81 (r(z, s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19736, 35021])).
% 3.62/3.81 tff(35023,plain,
% 3.62/3.81 (b(s(s(s(elem!1))), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[16580, 38])).
% 3.62/3.81 tff(35024,plain,
% 3.62/3.81 (~r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2312, 35023, 79, 110, 35022, 348])).
% 3.62/3.81 tff(35025,plain,
% 3.62/3.81 (b(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[409, 35024])).
% 3.62/3.81 tff(35026,plain,
% 3.62/3.81 (r(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[11196, 3871, 68, 110, 35022, 1, 38, 348, 35025])).
% 3.62/3.81 tff(35027,plain,
% 3.62/3.81 (b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[11998, 3871, 68, 110, 35022, 38, 35025, 348, 1])).
% 3.62/3.81 tff(35028,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12011, 35027, 3871, 110, 85, 35022, 220, 35025, 35023, 35026, 219, 348])).
% 3.62/3.81 tff(35029,plain,((~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (elem!1 = s(s(elem!1))) | r(s(s(s(elem!1))), s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35030,plain,
% 3.62/3.81 (~b(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35029, 38, 220, 348, 68, 110, 1])).
% 3.62/3.81 tff(35031,plain,
% 3.62/3.81 (r(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[105, 35030])).
% 3.62/3.81 tff(35032,plain,
% 3.62/3.81 (~b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33906, 35030, 1, 906, 348, 220, 35031, 622])).
% 3.62/3.81 tff(35033,plain,
% 3.62/3.81 (~r(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[27984, 35031, 1, 348, 220, 906, 35025, 35030])).
% 3.62/3.81 tff(35034,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[392, 35033, 35032, 219])).
% 3.62/3.81 tff(35035,plain,(r(s(s(s(elem!1))), s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(z, s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35036,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35035, 31517, 348, 35019, 35020, 35018, 35014, 35011])).
% 3.62/3.81 tff(35037,plain,
% 3.62/3.81 (~r(z, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12779, 35036, 35011, 35013])).
% 3.62/3.81 tff(35038,plain,
% 3.62/3.81 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12769, 35036, 35011, 35013])).
% 3.62/3.81 tff(35039,plain,
% 3.62/3.81 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[760, 35038])).
% 3.62/3.81 tff(35040,plain,
% 3.62/3.81 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2071, 35020, 9149])).
% 3.62/3.81 tff(35041,plain,
% 3.62/3.81 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19800, 3871, 2073, 750])).
% 3.62/3.81 tff(35042,plain,
% 3.62/3.81 (s(s(s(elem!1))) = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[486, 35041, 147])).
% 3.62/3.81 tff(35043,plain,
% 3.62/3.81 (r(elem!1, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12809, 35042, 12761])).
% 3.62/3.81 tff(35044,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[11073, 35042, 111])).
% 3.62/3.81 tff(35045,plain,
% 3.62/3.81 (~r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[5343, 35044, 622, 35043])).
% 3.62/3.81 tff(35046,plain,
% 3.62/3.81 (b(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2562, 35042, 750])).
% 3.62/3.81 tff(35047,plain,
% 3.62/3.81 (elem!1 = s(s(s(elem!1)))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[13222, 35042])).
% 3.62/3.81 tff(35048,plain,
% 3.62/3.81 (b(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19808, 35047, 2073])).
% 3.62/3.81 tff(35049,plain,
% 3.62/3.81 (~b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24003, 35048, 35046, 3871])).
% 3.62/3.81 tff(35050,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24634, 35049, 35045, 1, 24223, 3871, 622, 147])).
% 3.62/3.81 tff(35051,plain,((~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35052,plain,
% 3.62/3.81 (~b(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35051, 31517, 35018, 147, 35040, 35039, 35036, 35013])).
% 3.62/3.81 tff(35053,plain,
% 3.62/3.81 (r(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[105, 35052])).
% 3.62/3.81 tff(35054,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33922, 35053, 35052, 31517, 35020, 348, 35037])).
% 3.62/3.81 tff(35055,plain,((s(z) = s(elem!1)) | r(s(s(s(elem!1))), elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35056,plain,
% 3.62/3.81 (s(z) = s(elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35055, 2467, 147])).
% 3.62/3.81 tff(35057,plain,
% 3.62/3.81 (z = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[343, 35056])).
% 3.62/3.81 tff(35058,plain,
% 3.62/3.81 (elem!1 = z),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[364, 35057])).
% 3.62/3.81 tff(35059,plain,
% 3.62/3.81 (~b(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2488, 35057, 2467])).
% 3.62/3.81 tff(35060,plain,
% 3.62/3.81 (~b(s(z), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[20985, 35059, 35058])).
% 3.62/3.81 tff(35061,plain,
% 3.62/3.81 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19196, 35060])).
% 3.62/3.81 tff(35062,plain,
% 3.62/3.81 (~r(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[149, 35057, 147])).
% 3.62/3.81 tff(35063,plain,
% 3.62/3.81 (~r(s(s(s(z))), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[475, 35057, 35062])).
% 3.62/3.81 tff(35064,plain,
% 3.62/3.81 (b(s(s(s(elem!1))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[490, 35063, 35057])).
% 3.62/3.81 tff(35065,plain,
% 3.62/3.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[7281, 35064, 2467])).
% 3.62/3.81 tff(35066,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[614, 35065, 35061])).
% 3.62/3.81 tff(35067,plain,(b(s(elem!1), elem!1) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35068,plain,
% 3.62/3.81 (b(s(elem!1), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35067, 147])).
% 3.62/3.81 tff(35069,plain,
% 3.62/3.81 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2071, 9149, 27658])).
% 3.62/3.81 tff(35070,plain,
% 3.62/3.81 (r(z, s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34688, 106, 1, 27658, 71])).
% 3.62/3.81 tff(35071,plain,
% 3.62/3.81 (~r(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24738, 199, 220, 3500, 412, 1281, 9297])).
% 3.62/3.81 tff(35072,plain,
% 3.62/3.81 (~b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3490, 10219, 909, 108, 412, 337, 2282, 348])).
% 3.62/3.81 tff(35073,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[392, 35072, 35071, 377])).
% 3.62/3.81 tff(35074,plain,(b(z, elem!1) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35075,plain,
% 3.62/3.81 (b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35074, 28189, 35070, 106, 219, 348, 24223, 19197])).
% 3.62/3.81 tff(35076,plain,
% 3.62/3.81 (~b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33828, 35075, 147, 24223, 35069, 35068, 19197, 106, 28189])).
% 3.62/3.81 tff(35077,plain,
% 3.62/3.81 (b(elem!1, z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[21021, 28189, 219, 19197, 35070, 9298])).
% 3.62/3.81 tff(35078,plain,
% 3.62/3.81 (r(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[392, 35076, 219])).
% 3.62/3.81 tff(35079,plain,
% 3.62/3.81 (s(s(s(z))) = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[25418, 35078, 35077, 35076, 147, 24223, 19197, 35068, 28189])).
% 3.62/3.81 tff(35080,plain,
% 3.62/3.81 (r(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[33301, 35076, 1, 24223, 27658, 348, 106, 71])).
% 3.62/3.81 tff(35081,plain,
% 3.62/3.81 (~r(s(z), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[3673, 35080, 35070, 35078])).
% 3.62/3.81 tff(35082,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[250, 35081, 35079, 106])).
% 3.62/3.81 tff(35083,plain,((s(z) = s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35084,plain,
% 3.62/3.81 (s(z) = s(elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35083, 71, 1, 147])).
% 3.62/3.81 tff(35085,plain,
% 3.62/3.81 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[338])).
% 3.62/3.81 tff(35086,plain,
% 3.62/3.81 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(symmetry,[status(thm)],[35085])).
% 3.62/3.81 tff(35087,plain,
% 3.62/3.81 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 3.62/3.81 inference(monotonicity,[status(thm)],[35086])).
% 3.62/3.81 tff(35088,plain,
% 3.62/3.81 (~r(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34291, 338, 24223, 108, 1, 147])).
% 3.62/3.81 tff(35089,plain,
% 3.62/3.81 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(modus_ponens,[status(thm)],[35088, 35087])).
% 3.62/3.81 tff(35090,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[572, 35089])).
% 3.62/3.81 tff(35091,plain,((~(s(z) = s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35092,plain,
% 3.62/3.81 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35091, 35084, 106, 1, 147])).
% 3.62/3.81 tff(35093,plain,
% 3.62/3.81 (z = elem!1),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[343, 35084])).
% 3.62/3.81 tff(35094,plain,
% 3.62/3.81 (~b(s(z), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12838, 35093, 71])).
% 3.62/3.81 tff(35095,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[760, 35094, 35092])).
% 3.62/3.81 tff(35096,plain,(b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35097,plain,
% 3.62/3.81 (b(s(z), s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35096, 1, 147])).
% 3.62/3.81 tff(35098,plain,
% 3.62/3.81 (~b(s(s(s(z))), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[21058, 35097, 19197, 24223])).
% 3.62/3.81 tff(35099,plain,
% 3.62/3.81 (r(s(s(s(z))), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1155, 35098])).
% 3.62/3.81 tff(35100,plain,
% 3.62/3.81 (~r(s(s(s(z))), elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[149, 107, 147])).
% 3.62/3.81 tff(35101,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[475, 35100, 107, 109])).
% 3.62/3.81 tff(35102,plain,((~(z = elem!1)) | (~r(s(s(s(z))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35103,plain,
% 3.62/3.81 (~(z = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35102, 35099, 147])).
% 3.62/3.81 tff(35104,plain,
% 3.62/3.81 (~(s(z) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[343, 35103])).
% 3.62/3.81 tff(35105,plain,
% 3.62/3.81 (~(s(elem!1) = s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[350, 35104])).
% 3.62/3.81 tff(35106,plain,
% 3.62/3.81 (r(s(z), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[34918, 35104, 1, 24223, 35097, 27658])).
% 3.62/3.81 tff(35107,plain,
% 3.62/3.81 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2063, 35104])).
% 3.62/3.81 tff(35108,plain,
% 3.62/3.81 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[2071, 35107, 27658])).
% 3.62/3.81 tff(35109,plain,
% 3.62/3.81 (~b(z, s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19817, 35108, 19197, 35097])).
% 3.62/3.81 tff(35110,plain,
% 3.62/3.81 (r(z, s(s(s(z))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1214, 35109])).
% 3.62/3.81 tff(35111,plain,
% 3.62/3.81 (~b(z, s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[17920, 35106, 1, 35103])).
% 3.62/3.81 tff(35112,plain,
% 3.62/3.81 (r(z, s(s(s(elem!1))))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[19736, 35111])).
% 3.62/3.81 tff(35113,plain,
% 3.62/3.81 (~b(s(s(s(s(z)))), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[24371, 35112, 19197, 24223, 35097])).
% 3.62/3.81 tff(35114,plain,
% 3.62/3.81 (r(s(s(s(s(z)))), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[932, 35113])).
% 3.62/3.81 tff(35115,plain,
% 3.62/3.81 (~(elem!1 = s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1234, 35114, 147])).
% 3.62/3.81 tff(35116,plain,
% 3.62/3.81 (~(s(z) = elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[1221, 35115])).
% 3.62/3.81 tff(35117,plain,
% 3.62/3.81 (b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[32797, 1638, 211, 220, 3871, 2073, 111, 19197])).
% 3.62/3.81 tff(35118,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[32824, 35117, 1638, 1, 906, 220, 3871, 10994])).
% 3.62/3.81 tff(35119,plain,((~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | r(s(elem!1), z) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35120,plain,
% 3.62/3.81 (~b(s(s(s(elem!1))), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35119, 19776, 906, 220, 3871, 10994, 1, 111])).
% 3.62/3.81 tff(35121,plain,
% 3.62/3.81 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12308, 35120, 11211])).
% 3.62/3.81 tff(35122,plain,
% 3.62/3.81 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35029, 35121, 220, 3871, 348, 110, 1])).
% 3.62/3.81 tff(35123,plain,
% 3.62/3.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[78, 35121])).
% 3.62/3.81 tff(35124,plain,
% 3.62/3.81 (~b(z, elem!1)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[13049, 35122, 219, 110, 111, 231])).
% 3.62/3.81 tff(35125,plain,
% 3.62/3.81 (b(elem!1, s(elem!1))),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12823, 35124, 219, 110, 111, 35122])).
% 3.62/3.81 tff(35126,plain,
% 3.62/3.81 ($false),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[12891, 35125, 35124, 110, 35123, 111, 9297, 220, 35122, 219, 231, 11211])).
% 3.62/3.81 tff(35127,plain,((s(z) = s(elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(z) = elem!1) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.81 tff(35128,plain,
% 3.62/3.81 (r(s(elem!1), z)),
% 3.62/3.81 inference(unit_resolution,[status(thm)],[35127, 35116, 35104, 24223, 35112, 35097, 1, 27658, 35106])).
% 3.62/3.81 tff(35129,plain,
% 3.62/3.81 (~r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[15256, 35128, 35110, 35106])).
% 3.62/3.82 tff(35130,plain,
% 3.62/3.82 (b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35129, 35105])).
% 3.62/3.82 tff(35131,plain,
% 3.62/3.82 (~b(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[24719, 35130, 19197, 24223])).
% 3.62/3.82 tff(35132,plain,
% 3.62/3.82 (b(z, elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[12800, 35128, 219, 35106, 35103, 24223])).
% 3.62/3.82 tff(35133,plain,
% 3.62/3.82 (~r(s(s(s(elem!1))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[13049, 35132, 219, 35106, 35112, 35116])).
% 3.62/3.82 tff(35134,plain,
% 3.62/3.82 (b(s(s(s(elem!1))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[16580, 35133])).
% 3.62/3.82 tff(35135,plain,
% 3.62/3.82 (elem!1 = s(s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35029, 35133, 24223, 35097, 35104, 35106, 1])).
% 3.62/3.82 tff(35136,plain,
% 3.62/3.82 (~r(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[12628, 35135, 219, 35106, 35128, 35112, 35097, 35132, 35134])).
% 3.62/3.82 tff(35137,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1439, 35136, 35131])).
% 3.62/3.82 tff(35138,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35139,plain,
% 3.62/3.82 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35138, 147])).
% 3.62/3.82 tff(35140,plain,
% 3.62/3.82 (s(elem!1) = s(s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[608, 35139])).
% 3.62/3.82 tff(35141,plain,
% 3.62/3.82 (s(elem!1) = s(s(s(elem!1)))),
% 3.62/3.82 inference(transitivity,[status(thm)],[35140, 35139])).
% 3.62/3.82 tff(35142,plain,
% 3.62/3.82 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35141])).
% 3.62/3.82 tff(35143,plain,
% 3.62/3.82 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.82 inference(symmetry,[status(thm)],[35142])).
% 3.62/3.82 tff(35144,plain,
% 3.62/3.82 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35143])).
% 3.62/3.82 tff(35145,plain,
% 3.62/3.82 (~b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[12265, 35144])).
% 3.62/3.82 tff(35146,plain,
% 3.62/3.82 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35139])).
% 3.62/3.82 tff(35147,plain,
% 3.62/3.82 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[614, 35139])).
% 3.62/3.82 tff(35148,plain,
% 3.62/3.82 (elem!1 = s(s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[78, 35147])).
% 3.62/3.82 tff(35149,plain,
% 3.62/3.82 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3787, 35148, 35068])).
% 3.62/3.82 tff(35150,plain,
% 3.62/3.82 (b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35149, 35146])).
% 3.62/3.82 tff(35151,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35150, 35145])).
% 3.62/3.82 tff(35152,plain,(r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35153,plain,
% 3.62/3.82 (~b(s(z), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[12838, 71, 107])).
% 3.62/3.82 tff(35154,plain,
% 3.62/3.82 (r(s(z), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[760, 35153])).
% 3.62/3.82 tff(35155,plain,
% 3.62/3.82 (r(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35154, 723])).
% 3.62/3.82 tff(35156,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.62/3.82 inference(symmetry,[status(thm)],[20462])).
% 3.62/3.82 tff(35157,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), z)),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[139, 35156])).
% 3.62/3.82 tff(35158,plain,
% 3.62/3.82 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[10022])).
% 3.62/3.82 tff(35159,plain,
% 3.62/3.82 (r(z, s(z)) <=> r(elem!1, s(z))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[107])).
% 3.62/3.82 tff(35160,plain,
% 3.62/3.82 (r(elem!1, s(z))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[909, 35159])).
% 3.62/3.82 tff(35161,plain,
% 3.62/3.82 (~r(s(s(s(elem!1))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[22268, 35154, 139, 35160])).
% 3.62/3.82 tff(35162,plain,
% 3.62/3.82 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35161, 35158])).
% 3.62/3.82 tff(35163,plain,
% 3.62/3.82 (b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[679, 21, 35162, 3512])).
% 3.62/3.82 tff(35164,plain,
% 3.62/3.82 (~r(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1148, 106, 909, 5903])).
% 3.62/3.82 tff(35165,plain,
% 3.62/3.82 (~r(elem!1, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1187, 35164, 107])).
% 3.62/3.82 tff(35166,plain,
% 3.62/3.82 (b(elem!1, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1192, 35165, 10087])).
% 3.62/3.82 tff(35167,plain,
% 3.62/3.82 (b(elem!1, s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1198, 35166, 107])).
% 3.62/3.82 tff(35168,plain,
% 3.62/3.82 (b(s(elem!1), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20985, 18839, 19197])).
% 3.62/3.82 tff(35169,plain,
% 3.62/3.82 (b(s(elem!1), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2488, 35168, 107])).
% 3.62/3.82 tff(35170,plain,
% 3.62/3.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[6906, 588, 738, 638])).
% 3.62/3.82 tff(35171,plain,
% 3.62/3.82 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[556, 35170, 1])).
% 3.62/3.82 tff(35172,plain,
% 3.62/3.82 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[34308, 35171, 6842, 798])).
% 3.62/3.82 tff(35173,plain,
% 3.62/3.82 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[526, 35172, 211])).
% 3.62/3.82 tff(35174,plain,
% 3.62/3.82 (~b(s(s(elem!1)), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19336, 35173, 2618, 588])).
% 3.62/3.82 tff(35175,plain,
% 3.62/3.82 (r(s(s(elem!1)), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[701, 35174, 3313])).
% 3.62/3.82 tff(35176,plain,
% 3.62/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.62/3.82 inference(rewrite,[status(thm)],[])).
% 3.62/3.82 tff(35177,plain,
% 3.62/3.82 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.62/3.82 inference(rewrite,[status(thm)],[])).
% 3.62/3.82 tff(35178,plain,
% 3.62/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35177])).
% 3.62/3.82 tff(35179,plain,
% 3.62/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.62/3.82 inference(transitivity,[status(thm)],[35178, 35176])).
% 3.62/3.82 tff(35180,plain,
% 3.62/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.62/3.82 inference(quant_inst,[status(thm)],[])).
% 3.62/3.82 tff(35181,plain,
% 3.62/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35180, 35179])).
% 3.62/3.82 tff(35182,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35181, 121, 35171, 139, 798, 35175])).
% 3.62/3.82 tff(35183,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(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)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35184,plain,
% 3.62/3.82 (~b(elem!1, s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35183, 35155, 139, 35169, 35157, 1, 35167, 35163])).
% 3.62/3.82 tff(35185,plain,
% 3.62/3.82 (r(elem!1, s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[599, 35184, 18438])).
% 3.62/3.82 tff(35186,plain,
% 3.62/3.82 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[135])).
% 3.62/3.82 tff(35187,plain,
% 3.62/3.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19552, 19550, 1536])).
% 3.62/3.82 tff(35188,plain,
% 3.62/3.82 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1733, 35187])).
% 3.62/3.82 tff(35189,plain,
% 3.62/3.82 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35188, 35186])).
% 3.62/3.82 tff(35190,plain,
% 3.62/3.82 (~r(s(z), s(s(s(s(s(z))))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[17287, 35189, 139, 572])).
% 3.62/3.82 tff(35191,plain,
% 3.62/3.82 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[835, 34528, 107])).
% 3.62/3.82 tff(35192,plain,
% 3.62/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.62/3.82 inference(rewrite,[status(thm)],[])).
% 3.62/3.82 tff(35193,plain,
% 3.62/3.82 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.62/3.82 inference(rewrite,[status(thm)],[])).
% 3.62/3.82 tff(35194,plain,
% 3.62/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35193])).
% 3.62/3.82 tff(35195,plain,
% 3.62/3.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.62/3.82 inference(transitivity,[status(thm)],[35194, 35192])).
% 3.62/3.82 tff(35196,plain,
% 3.62/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.62/3.82 inference(quant_inst,[status(thm)],[])).
% 3.62/3.82 tff(35197,plain,
% 3.62/3.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35196, 35195])).
% 3.62/3.82 tff(35198,plain,
% 3.62/3.82 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35197, 271, 2618, 35191, 738])).
% 3.62/3.82 tff(35199,plain,
% 3.62/3.82 (~b(s(z), s(s(s(s(s(z))))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19528, 35198, 107])).
% 3.62/3.82 tff(35200,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1756, 35199, 35190])).
% 3.62/3.82 tff(35201,plain,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35202,plain,
% 3.62/3.82 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35201, 35154, 139, 107, 35169, 35167, 35185])).
% 3.62/3.82 tff(35203,plain,
% 3.62/3.82 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[34308, 627, 6842, 798])).
% 3.62/3.82 tff(35204,plain,
% 3.62/3.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[34385, 627, 338, 2618, 638, 18990])).
% 3.62/3.82 tff(35205,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[556, 35204, 35203, 1])).
% 3.62/3.82 tff(35206,plain,((~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35207,plain,
% 3.62/3.82 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35206, 35163, 1536, 35169, 1, 35202, 35157, 35155])).
% 3.62/3.82 tff(35208,plain,
% 3.62/3.82 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[526, 35207, 211])).
% 3.62/3.82 tff(35209,plain,
% 3.62/3.82 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1459, 543, 638, 517])).
% 3.62/3.82 tff(35210,plain,
% 3.62/3.82 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20495, 543, 139, 1536, 10121, 738, 517, 18438, 2618])).
% 3.62/3.82 tff(35211,plain,
% 3.62/3.82 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[18861, 35210, 107])).
% 3.62/3.82 tff(35212,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[586, 35211, 35209, 6943])).
% 3.62/3.82 tff(35213,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35214,plain,
% 3.62/3.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35213, 35163, 107, 563, 35208, 139, 35167, 35169])).
% 3.62/3.82 tff(35215,plain,
% 3.62/3.82 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[556, 35214, 1])).
% 3.62/3.82 tff(35216,plain,
% 3.62/3.82 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2670, 35215, 139, 35185])).
% 3.62/3.82 tff(35217,plain,
% 3.62/3.82 (b(s(s(elem!1)), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[862, 35216, 18443])).
% 3.62/3.82 tff(35218,plain,
% 3.62/3.82 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[17916, 35215, 139, 35185])).
% 3.62/3.82 tff(35219,plain,
% 3.62/3.82 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[586, 35218, 563])).
% 3.62/3.82 tff(35220,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19511, 35219, 35217, 35163, 35208])).
% 3.62/3.82 tff(35221,plain,(b(s(z), s(s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(z = elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35222,plain,
% 3.62/3.82 (~(z = elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35221, 71, 35152, 1, 905])).
% 3.62/3.82 tff(35223,plain,
% 3.62/3.82 (~(elem!1 = z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[333, 35222])).
% 3.62/3.82 tff(35224,plain,
% 3.62/3.82 (~b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20261, 271, 394, 19197, 3407])).
% 3.62/3.82 tff(35225,plain,
% 3.62/3.82 (r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35224, 351])).
% 3.62/3.82 tff(35226,plain,
% 3.62/3.82 (~r(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2186, 35225, 905, 108])).
% 3.62/3.82 tff(35227,plain,
% 3.62/3.82 (b(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1439, 35226])).
% 3.62/3.82 tff(35228,plain,
% 3.62/3.82 (~b(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20253, 271, 394, 19197, 3407])).
% 3.62/3.82 tff(35229,plain,
% 3.62/3.82 (r(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[444, 35228, 344])).
% 3.62/3.82 tff(35230,plain,
% 3.62/3.82 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23235, 35229, 108, 35225])).
% 3.62/3.82 tff(35231,plain,
% 3.62/3.82 (~b(s(s(s(elem!1))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[22147, 85, 351, 19197, 3407, 394])).
% 3.62/3.82 tff(35232,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[8229, 35231])).
% 3.62/3.82 tff(35233,plain,
% 3.62/3.82 (~r(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[8972, 1243, 35152, 6842])).
% 3.62/3.82 tff(35234,plain,
% 3.62/3.82 (b(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[392, 35233, 377])).
% 3.62/3.82 tff(35235,plain,
% 3.62/3.82 (r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 20262, 351])).
% 3.62/3.82 tff(35236,plain,
% 3.62/3.82 (r(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[444, 20254, 344])).
% 3.62/3.82 tff(35237,plain,
% 3.62/3.82 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23235, 35236, 108, 35235])).
% 3.62/3.82 tff(35238,plain,
% 3.62/3.82 (~b(elem!1, z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3415, 35234, 394, 3407])).
% 3.62/3.82 tff(35239,plain,
% 3.62/3.82 (r(elem!1, z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[284, 35238, 358])).
% 3.62/3.82 tff(35240,plain,
% 3.62/3.82 (s(s(s(z))) = elem!1),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[25677, 35239, 35152, 394, 35237, 344, 1281, 1243, 35234])).
% 3.62/3.82 tff(35241,plain,
% 3.62/3.82 (~b(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[4210, 35240, 199])).
% 3.62/3.82 tff(35242,plain,
% 3.62/3.82 (r(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1214, 35241])).
% 3.62/3.82 tff(35243,plain,
% 3.62/3.82 (~r(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2186, 35235, 909, 108])).
% 3.62/3.82 tff(35244,plain,
% 3.62/3.82 (b(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1439, 35243])).
% 3.62/3.82 tff(35245,plain,
% 3.62/3.82 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[4909, 35240, 35234])).
% 3.62/3.82 tff(35246,plain,
% 3.62/3.82 (r(s(s(s(z))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1427, 35245, 394, 35244])).
% 3.62/3.82 tff(35247,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1148, 35246, 35242, 108, 909])).
% 3.62/3.82 tff(35248,plain,(b(z, elem!1) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35249,plain,
% 3.62/3.82 (b(z, elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35248, 35232, 905, 394, 19197, 3407, 219, 108, 331])).
% 3.62/3.82 tff(35250,plain,
% 3.62/3.82 (~(elem!1 = s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1397, 35249, 894])).
% 3.62/3.82 tff(35251,plain,
% 3.62/3.82 (r(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20888, 35249, 35152, 1, 394, 3407, 358, 35225, 35229, 68, 19197])).
% 3.62/3.82 tff(35252,plain,
% 3.62/3.82 (~r(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23250, 35251, 35228, 344, 19197, 35249])).
% 3.62/3.82 tff(35253,plain,
% 3.62/3.82 (~b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[9252, 271, 1326, 394, 1281])).
% 3.62/3.82 tff(35254,plain,
% 3.62/3.82 (r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35253, 2282])).
% 3.62/3.82 tff(35255,plain,
% 3.62/3.82 (~b(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23220, 394, 1281, 1326])).
% 3.62/3.82 tff(35256,plain,
% 3.62/3.82 (r(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[444, 35255, 348])).
% 3.62/3.82 tff(35257,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20297, 121, 379, 357, 35256, 35254])).
% 3.62/3.82 tff(35258,plain,((~b(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35259,plain,
% 3.62/3.82 (~r(s(z), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35258, 35251, 394, 35249, 19197, 344])).
% 3.62/3.82 tff(35260,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20894, 35259, 35252, 19197, 35249, 35250])).
% 3.62/3.82 tff(35261,plain,((elem!1 = s(s(elem!1))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | b(z, s(z)) | (~r(s(z), s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35262,plain,
% 3.62/3.82 (elem!1 = s(s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35261, 3407, 1, 394, 894, 108, 331])).
% 3.62/3.82 tff(35263,plain,
% 3.62/3.82 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3917, 35262, 344])).
% 3.62/3.82 tff(35264,plain,
% 3.62/3.82 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1816, 35263, 35230])).
% 3.62/3.82 tff(35265,plain,
% 3.62/3.82 (r(s(s(s(z))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1427, 35264, 394, 35227])).
% 3.62/3.82 tff(35266,plain,
% 3.62/3.82 (~b(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19710, 35264, 394, 35227])).
% 3.62/3.82 tff(35267,plain,
% 3.62/3.82 (r(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1214, 35266])).
% 3.62/3.82 tff(35268,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1148, 35267, 35265, 108, 905])).
% 3.62/3.82 tff(35269,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35270,plain,
% 3.62/3.82 (~b(z, s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35269, 394, 106, 1, 894, 35222])).
% 3.62/3.82 tff(35271,plain,
% 3.62/3.82 (r(z, s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19736, 35270])).
% 3.62/3.82 tff(35272,plain,
% 3.62/3.82 (~r(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3464, 1243, 909, 106])).
% 3.62/3.82 tff(35273,plain,
% 3.62/3.82 (~r(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[10227, 1243, 35152, 111])).
% 3.62/3.82 tff(35274,plain,
% 3.62/3.82 (b(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[392, 35273, 377])).
% 3.62/3.82 tff(35275,plain,
% 3.62/3.82 (~b(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19761, 1307, 1281, 394])).
% 3.62/3.82 tff(35276,plain,
% 3.62/3.82 (r(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[444, 35275, 348])).
% 3.62/3.82 tff(35277,plain,
% 3.62/3.82 (~b(elem!1, z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1315, 1307, 394, 307])).
% 3.62/3.82 tff(35278,plain,
% 3.62/3.82 (r(elem!1, z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[284, 35277, 259])).
% 3.62/3.82 tff(35279,plain,
% 3.62/3.82 (r(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[25677, 35278, 35152, 394, 378, 348, 1281, 4211, 307])).
% 3.62/3.82 tff(35280,plain,
% 3.62/3.82 (~r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23235, 35279, 108, 35276])).
% 3.62/3.82 tff(35281,plain,
% 3.62/3.82 (~(s(z) = elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20120, 35277, 1281])).
% 3.62/3.82 tff(35282,plain,
% 3.62/3.82 (~(elem!1 = s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[242, 35281])).
% 3.62/3.82 tff(35283,plain,
% 3.62/3.82 (b(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[299, 35282, 293])).
% 3.62/3.82 tff(35284,plain,
% 3.62/3.82 (~b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1290, 35283, 1281, 307])).
% 3.62/3.82 tff(35285,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35284, 35280, 2282])).
% 3.62/3.82 tff(35286,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(z)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (elem!1 = z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35287,plain,
% 3.62/3.82 (~b(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35286, 35274, 1281, 106, 35272, 394, 1243, 344, 358, 199])).
% 3.62/3.82 tff(35288,plain,
% 3.62/3.82 (r(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1214, 35287])).
% 3.62/3.82 tff(35289,plain,
% 3.62/3.82 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1508, 6533, 106, 909])).
% 3.62/3.82 tff(35290,plain,
% 3.62/3.82 (~b(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1427, 1421, 394, 141])).
% 3.62/3.82 tff(35291,plain,
% 3.62/3.82 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[16218, 1421, 1209])).
% 3.62/3.82 tff(35292,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1816, 35291, 35290, 1510])).
% 3.62/3.82 tff(35293,plain,((~b(z, s(elem!1))) | r(s(s(s(z))), s(elem!1)) | b(z, s(s(s(z)))) | (~b(s(elem!1), z)) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35294,plain,
% 3.62/3.82 (~b(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35293, 35289, 1209, 394, 141])).
% 3.62/3.82 tff(35295,plain,
% 3.62/3.82 (r(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1439, 35294])).
% 3.62/3.82 tff(35296,plain,
% 3.62/3.82 (~r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2186, 35295, 909, 106])).
% 3.62/3.82 tff(35297,plain,
% 3.62/3.82 (b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35296, 422])).
% 3.62/3.82 tff(35298,plain,
% 3.62/3.82 (~b(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1290, 35297, 1281, 307])).
% 3.62/3.82 tff(35299,plain,
% 3.62/3.82 (elem!1 = s(z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[299, 35298, 293])).
% 3.62/3.82 tff(35300,plain,
% 3.62/3.82 (s(z) = elem!1),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[242, 35299])).
% 3.62/3.82 tff(35301,plain,
% 3.62/3.82 (b(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1276, 35300, 307])).
% 3.62/3.82 tff(35302,plain,
% 3.62/3.82 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[9276, 35301, 71])).
% 3.62/3.82 tff(35303,plain,
% 3.62/3.82 (~r(s(s(s(z))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2335, 6533, 106, 909])).
% 3.62/3.82 tff(35304,plain,
% 3.62/3.82 (b(s(s(s(z))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2325, 35303])).
% 3.62/3.82 tff(35305,plain,
% 3.62/3.82 (~b(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[24796, 35301, 35304, 35297])).
% 3.62/3.82 tff(35306,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1816, 35305, 35302, 35289])).
% 3.62/3.82 tff(35307,plain,(b(z, s(s(s(z)))) | b(s(z), s(s(s(z)))) | (~b(elem!1, s(elem!1))) | r(elem!1, s(z)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~b(s(elem!1), z)) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35308,plain,
% 3.62/3.82 (r(s(s(s(z))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35307, 35287, 35274, 35272, 1281, 351, 909, 394, 71])).
% 3.62/3.82 tff(35309,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1148, 35308, 35288, 106, 909])).
% 3.62/3.82 tff(35310,plain,(b(z, elem!1) | (~r(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | b(s(z), s(s(s(z)))) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35311,plain,
% 3.62/3.82 (b(z, elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35310, 394, 19197, 905, 71, 219, 35271, 35222])).
% 3.62/3.82 tff(35312,plain,
% 3.62/3.82 (~(elem!1 = s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1397, 35311, 894])).
% 3.62/3.82 tff(35313,plain,
% 3.62/3.82 (~(s(z) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[343, 35222])).
% 3.62/3.82 tff(35314,plain,
% 3.62/3.82 (~b(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23220, 35311, 19197, 394])).
% 3.62/3.82 tff(35315,plain,
% 3.62/3.82 (~(s(elem!1) = s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[350, 35313])).
% 3.62/3.82 tff(35316,plain,
% 3.62/3.82 (~b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[9252, 271, 35311, 394, 19197])).
% 3.62/3.82 tff(35317,plain,
% 3.62/3.82 (r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35316, 35315])).
% 3.62/3.82 tff(35318,plain,
% 3.62/3.82 (~r(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2186, 35317, 905, 106])).
% 3.62/3.82 tff(35319,plain,
% 3.62/3.82 (b(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1439, 35318])).
% 3.62/3.82 tff(35320,plain,
% 3.62/3.82 (~b(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[9091, 35319, 394, 35311])).
% 3.62/3.82 tff(35321,plain,
% 3.62/3.82 (r(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[392, 35320, 219])).
% 3.62/3.82 tff(35322,plain,
% 3.62/3.82 (~r(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23250, 35321, 35314, 35313, 19197, 35311])).
% 3.62/3.82 tff(35323,plain,
% 3.62/3.82 (~r(s(z), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35258, 35321, 394, 35311, 19197, 35313])).
% 3.62/3.82 tff(35324,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[20894, 35323, 35322, 19197, 35311, 35312])).
% 3.62/3.82 tff(35325,plain,((~b(s(elem!1), z)) | b(z, s(z)) | b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35326,plain,
% 3.62/3.82 (~b(s(elem!1), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35325, 71, 894, 1])).
% 3.62/3.82 tff(35327,plain,
% 3.62/3.82 (r(s(elem!1), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[409, 35326])).
% 3.62/3.82 tff(35328,plain,
% 3.62/3.82 (b(elem!1, z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[21021, 35327, 219, 19197, 905, 35223])).
% 3.62/3.82 tff(35329,plain,
% 3.62/3.82 (~r(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[12090, 3502, 412, 1243])).
% 3.62/3.82 tff(35330,plain,
% 3.62/3.82 (b(z, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1439, 35329])).
% 3.62/3.82 tff(35331,plain,
% 3.62/3.82 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3724, 317, 909, 3500, 331, 199, 3502, 412])).
% 3.62/3.82 tff(35332,plain,
% 3.62/3.82 (~r(s(elem!1), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3683, 3502, 412, 1243])).
% 3.62/3.82 tff(35333,plain,
% 3.62/3.82 (b(s(elem!1), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2243, 35332, 3500])).
% 3.62/3.82 tff(35334,plain,
% 3.62/3.82 (~b(s(s(s(z))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23209, 35333, 35331, 35330])).
% 3.62/3.82 tff(35335,plain,
% 3.62/3.82 (r(s(s(s(z))), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1155, 35334])).
% 3.62/3.82 tff(35336,plain,
% 3.62/3.82 (~(s(s(s(z))) = elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[6165, 35331, 317])).
% 3.62/3.82 tff(35337,plain,
% 3.62/3.82 (~b(s(s(s(z))), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23200, 35333, 35331, 261])).
% 3.62/3.82 tff(35338,plain,
% 3.62/3.82 (r(s(s(s(z))), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[255, 35337, 35336])).
% 3.62/3.82 tff(35339,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[19765, 35338, 35335, 3502, 1243])).
% 3.62/3.82 tff(35340,plain,(b(elem!1, s(elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (z = elem!1) | b(z, elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35341,plain,
% 3.62/3.82 (b(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35340, 199, 412, 909, 331, 261, 377])).
% 3.62/3.82 tff(35342,plain,
% 3.62/3.82 (elem!1 = s(z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3490, 35341, 909, 106, 412, 1243, 351, 344])).
% 3.62/3.82 tff(35343,plain,
% 3.62/3.82 (s(elem!1) = s(s(z))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35342])).
% 3.62/3.82 tff(35344,plain,
% 3.62/3.82 (s(s(z)) = s(elem!1)),
% 3.62/3.82 inference(symmetry,[status(thm)],[35343])).
% 3.62/3.82 tff(35345,plain,
% 3.62/3.82 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35344])).
% 3.62/3.82 tff(35346,plain,
% 3.62/3.82 (s(s(elem!1)) = s(s(s(z)))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35343])).
% 3.62/3.82 tff(35347,plain,
% 3.62/3.82 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35346])).
% 3.62/3.82 tff(35348,plain,
% 3.62/3.82 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.62/3.82 inference(symmetry,[status(thm)],[35347])).
% 3.62/3.82 tff(35349,plain,
% 3.62/3.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35343, 35348])).
% 3.62/3.82 tff(35350,plain,
% 3.62/3.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.62/3.82 inference(transitivity,[status(thm)],[35349, 10493])).
% 3.62/3.82 tff(35351,plain,
% 3.62/3.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.82 inference(transitivity,[status(thm)],[35350, 35345])).
% 3.62/3.82 tff(35352,plain,
% 3.62/3.82 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35351])).
% 3.62/3.82 tff(35353,plain,
% 3.62/3.82 (~r(s(z), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[25463, 35342])).
% 3.62/3.82 tff(35354,plain,
% 3.62/3.82 (~(s(s(s(z))) = elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[250, 35353, 106])).
% 3.62/3.82 tff(35355,plain,
% 3.62/3.82 (~(elem!1 = s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1100, 35354])).
% 3.62/3.82 tff(35356,plain,
% 3.62/3.82 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1516, 35355])).
% 3.62/3.82 tff(35357,plain,
% 3.62/3.82 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[17419, 35356])).
% 3.62/3.82 tff(35358,plain,
% 3.62/3.82 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35357, 35352])).
% 3.62/3.82 tff(35359,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35347])).
% 3.62/3.82 tff(35360,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35342])).
% 3.62/3.82 tff(35361,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35152, 35360])).
% 3.62/3.82 tff(35362,plain,
% 3.62/3.82 (r(s(s(s(s(z)))), s(z))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[35361, 35359])).
% 3.62/3.82 tff(35363,plain,
% 3.62/3.82 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35342])).
% 3.62/3.82 tff(35364,plain,
% 3.62/3.82 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.62/3.82 inference(symmetry,[status(thm)],[35363])).
% 3.62/3.82 tff(35365,plain,
% 3.62/3.82 (r(elem!1, s(s(s(z))))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[106, 35364])).
% 3.62/3.82 tff(35366,plain,
% 3.62/3.82 (s(z) = elem!1),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[242, 35342])).
% 3.62/3.82 tff(35367,plain,
% 3.62/3.82 (b(s(z), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1276, 35366, 35341])).
% 3.62/3.82 tff(35368,plain,
% 3.62/3.82 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[9276, 35367, 71])).
% 3.62/3.82 tff(35369,plain,
% 3.62/3.82 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 3.62/3.82 inference(monotonicity,[status(thm)],[35346])).
% 3.62/3.82 tff(35370,plain,
% 3.62/3.82 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 3.62/3.82 inference(symmetry,[status(thm)],[35369])).
% 3.62/3.82 tff(35371,plain,
% 3.62/3.82 (r(s(z), s(s(elem!1)))),
% 3.62/3.82 inference(modus_ponens,[status(thm)],[106, 35370])).
% 3.62/3.82 tff(35372,plain,
% 3.62/3.82 (~r(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[4423, 35371, 909, 412])).
% 3.62/3.82 tff(35373,plain,
% 3.62/3.82 (b(s(elem!1), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[429, 35372, 351])).
% 3.62/3.82 tff(35374,plain,
% 3.62/3.82 (~r(s(s(s(z))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[30241, 35362, 106, 909])).
% 3.62/3.82 tff(35375,plain,
% 3.62/3.82 (b(s(s(s(z))), s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[2325, 35374])).
% 3.62/3.82 tff(35376,plain,
% 3.62/3.82 (~b(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[24796, 35375, 35367, 35373])).
% 3.62/3.82 tff(35377,plain,
% 3.62/3.82 (r(s(s(s(z))), s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1816, 35376, 35368])).
% 3.62/3.82 tff(35378,plain,
% 3.62/3.82 (~r(elem!1, s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[17626, 35377, 412, 35365])).
% 3.62/3.82 tff(35379,plain,
% 3.62/3.82 (~r(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1508, 35377, 106, 909])).
% 3.62/3.82 tff(35380,plain,
% 3.62/3.82 (b(z, s(s(s(z))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1214, 35379])).
% 3.62/3.82 tff(35381,plain,
% 3.62/3.82 ($false),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[6708, 35380, 35378, 909, 35342, 71, 35362, 199, 331, 35358])).
% 3.62/3.82 tff(35382,plain,(b(z, elem!1) | (~r(z, s(z))) | b(s(z), s(s(s(z)))) | (z = elem!1) | (~r(s(elem!1), z)) | (~b(elem!1, z)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.82 tff(35383,plain,
% 3.62/3.82 (b(z, elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[35382, 71, 905, 35222, 35327, 35328, 219])).
% 3.62/3.82 tff(35384,plain,
% 3.62/3.82 (~b(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[21813, 35383, 219, 19197, 35327, 35223])).
% 3.62/3.82 tff(35385,plain,
% 3.62/3.82 (~(elem!1 = s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[1397, 35383, 894])).
% 3.62/3.82 tff(35386,plain,
% 3.62/3.82 (~b(s(z), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[3964, 35383, 19197, 35328])).
% 3.62/3.82 tff(35387,plain,
% 3.62/3.82 (r(s(s(s(elem!1))), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[24220, 894, 1, 909])).
% 3.62/3.82 tff(35388,plain,
% 3.62/3.82 (r(s(z), elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[236, 1242, 5772])).
% 3.62/3.82 tff(35389,plain,
% 3.62/3.82 (~(s(s(z)) = s(elem!1))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[960, 5772])).
% 3.62/3.82 tff(35390,plain,
% 3.62/3.82 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[953, 35389])).
% 3.62/3.82 tff(35391,plain,
% 3.62/3.82 (b(z, elem!1)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[355, 6509, 1391])).
% 3.62/3.82 tff(35392,plain,
% 3.62/3.82 (~b(s(elem!1), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[23827, 307, 2207, 19197, 1391, 1242, 894])).
% 3.62/3.82 tff(35393,plain,
% 3.62/3.82 (r(s(elem!1), z)),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[409, 35392])).
% 3.62/3.82 tff(35394,plain,
% 3.62/3.82 (~b(elem!1, s(z))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[21813, 35393, 219, 19197, 35391, 23812])).
% 3.62/3.82 tff(35395,plain,
% 3.62/3.82 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.82 inference(unit_resolution,[status(thm)],[18965, 35394, 35387, 5773, 1242])).
% 3.62/3.83 tff(35396,plain,
% 3.62/3.83 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[760, 35395])).
% 3.62/3.83 tff(35397,plain,
% 3.62/3.83 (r(elem!1, s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[299, 35394, 5773])).
% 3.62/3.83 tff(35398,plain,
% 3.62/3.83 (b(elem!1, z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21021, 412, 377, 1281, 909, 23812])).
% 3.62/3.83 tff(35399,plain,
% 3.62/3.83 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3888, 622, 139, 3456])).
% 3.62/3.83 tff(35400,plain,
% 3.62/3.83 (b(s(elem!1), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[429, 23395, 6511])).
% 3.62/3.83 tff(35401,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3813, 271, 750, 35400, 26172])).
% 3.62/3.83 tff(35402,plain,
% 3.62/3.83 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[681, 35401, 35399])).
% 3.62/3.83 tff(35403,plain,
% 3.62/3.83 (elem!1 = s(s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[78, 35402])).
% 3.62/3.83 tff(35404,plain,
% 3.62/3.83 (~(s(s(s(z))) = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3906, 35403])).
% 3.62/3.83 tff(35405,plain,
% 3.62/3.83 (~r(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23313, 35404, 909, 357, 1326, 3456, 35398])).
% 3.62/3.83 tff(35406,plain,
% 3.62/3.83 (b(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[105, 35405])).
% 3.62/3.83 tff(35407,plain,
% 3.62/3.83 (~r(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6525, 622, 357, 3456])).
% 3.62/3.83 tff(35408,plain,
% 3.62/3.83 (b(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[444, 35407, 6510])).
% 3.62/3.83 tff(35409,plain,
% 3.62/3.83 (~b(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[12508, 35406, 307, 412, 26172, 35403, 1326, 35408])).
% 3.62/3.83 tff(35410,plain,
% 3.62/3.83 (r(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[255, 35409, 35404])).
% 3.62/3.83 tff(35411,plain,
% 3.62/3.83 (~b(z, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[4122, 35400, 307, 1326])).
% 3.62/3.83 tff(35412,plain,
% 3.62/3.83 (r(z, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1439, 35411])).
% 3.62/3.83 tff(35413,plain,
% 3.62/3.83 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3917, 35403, 6510])).
% 3.62/3.83 tff(35414,plain,
% 3.62/3.83 (~(s(elem!1) = s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2035, 35413])).
% 3.62/3.83 tff(35415,plain,
% 3.62/3.83 (b(z, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6558, 35409, 909, 1326, 357, 35406, 35414, 35400, 35412])).
% 3.62/3.83 tff(35416,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21465, 35415, 35410, 377, 1281, 894, 1326, 412, 35406, 23812])).
% 3.62/3.83 tff(35417,plain,((~r(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | b(z, s(z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35418,plain,
% 3.62/3.83 (~r(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35417, 35391, 19197, 894, 219, 35393, 909, 35388, 307, 35397, 35396, 35387])).
% 3.62/3.83 tff(35419,plain,
% 3.62/3.83 (b(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2243, 35418, 2207])).
% 3.62/3.83 tff(35420,plain,
% 3.62/3.83 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[8078, 35392, 219, 894])).
% 3.62/3.83 tff(35421,plain,
% 3.62/3.83 (~r(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35417, 1326, 19197, 894, 219, 412, 909, 357, 307, 3456, 750, 35387])).
% 3.62/3.83 tff(35422,plain,
% 3.62/3.83 (b(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2243, 35421, 2207])).
% 3.62/3.83 tff(35423,plain,
% 3.62/3.83 (b(elem!1, z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21021, 412, 219, 19197, 909, 23812])).
% 3.62/3.83 tff(35424,plain,
% 3.62/3.83 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[33648, 2606, 9894])).
% 3.62/3.83 tff(35425,plain,
% 3.62/3.83 (b(s(s(elem!1)), s(elem!1))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35424, 9441])).
% 3.62/3.83 tff(35426,plain,
% 3.62/3.83 (~b(s(s(elem!1)), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6807, 35425, 307, 2618])).
% 3.62/3.83 tff(35427,plain,
% 3.62/3.83 (r(s(s(elem!1)), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[862, 35426, 10064])).
% 3.62/3.83 tff(35428,plain,
% 3.62/3.83 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 3.62/3.83 inference(symmetry,[status(thm)],[15691])).
% 3.62/3.83 tff(35429,plain,
% 3.62/3.83 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[33663, 271, 35424, 34841, 27343])).
% 3.62/3.83 tff(35430,plain,
% 3.62/3.83 (r(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1847, 35429, 33634])).
% 3.62/3.83 tff(35431,plain,
% 3.62/3.83 (r(elem!1, s(s(elem!1)))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35430, 35428])).
% 3.62/3.83 tff(35432,plain,
% 3.62/3.83 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2670, 35431, 139, 35427])).
% 3.62/3.83 tff(35433,plain,
% 3.62/3.83 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[556, 35432, 1])).
% 3.62/3.83 tff(35434,plain,
% 3.62/3.83 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[33655, 271, 35424, 34841, 27343])).
% 3.62/3.83 tff(35435,plain,
% 3.62/3.83 (r(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[840, 35434, 28006])).
% 3.62/3.83 tff(35436,plain,
% 3.62/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.62/3.83 inference(rewrite,[status(thm)],[])).
% 3.62/3.83 tff(35437,plain,
% 3.62/3.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.62/3.83 inference(quant_inst,[status(thm)],[])).
% 3.62/3.83 tff(35438,plain,
% 3.62/3.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35437, 35436])).
% 3.62/3.83 tff(35439,plain,
% 3.62/3.83 (~r(s(z), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35438, 121, 357, 3456, 35435])).
% 3.62/3.83 tff(35440,plain,
% 3.62/3.83 (~r(s(z), s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[9700, 35439, 2606])).
% 3.62/3.83 tff(35441,plain,
% 3.62/3.83 (b(s(z), s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2167, 35440])).
% 3.62/3.83 tff(35442,plain,
% 3.62/3.83 (~b(z, s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[19354, 35441, 19197, 35433])).
% 3.62/3.83 tff(35443,plain,
% 3.62/3.83 (r(z, s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2106, 35442])).
% 3.62/3.83 tff(35444,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5852, 35433, 750, 35431, 3456])).
% 3.62/3.83 tff(35445,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[681, 35444, 82])).
% 3.62/3.83 tff(35446,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[13843, 35441, 750, 35433])).
% 3.62/3.83 tff(35447,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[8229, 35446])).
% 3.62/3.83 tff(35448,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6850, 35447, 35445, 412, 35443])).
% 3.62/3.83 tff(35449,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35450,plain,
% 3.62/3.83 (~(s(s(s(z))) = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35449, 82, 412, 750, 3456, 1, 35387, 357, 307, 35422, 9894])).
% 3.62/3.83 tff(35451,plain,
% 3.62/3.83 (~r(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23313, 35450, 909, 357, 1326, 3456, 35423])).
% 3.62/3.83 tff(35452,plain,
% 3.62/3.83 (b(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[105, 35451])).
% 3.62/3.83 tff(35453,plain,
% 3.62/3.83 (b(z, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6558, 2346, 909, 1326, 357, 3871, 8606, 447, 1441])).
% 3.62/3.83 tff(35454,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21465, 35453, 17770, 377, 1281, 894, 1326, 412, 3871, 259])).
% 3.62/3.83 tff(35455,plain,(b(s(s(s(z))), elem!1) | (elem!1 = s(elem!1)) | (~b(s(z), z)) | b(z, s(z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (elem!1 = z) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35456,plain,
% 3.62/3.83 (b(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35455, 35452, 19197, 894, 1326, 412, 219, 23812, 909, 357, 35400, 35412, 35450, 35422])).
% 3.62/3.83 tff(35457,plain,
% 3.62/3.83 (s(s(s(z))) = s(elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23566, 35456, 1326, 35423, 35422])).
% 3.62/3.83 tff(35458,plain,
% 3.62/3.83 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35457])).
% 3.62/3.83 tff(35459,plain,
% 3.62/3.83 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35458])).
% 3.62/3.83 tff(35460,plain,
% 3.62/3.83 (~r(s(s(s(elem!1))), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[4618, 121, 357, 35387, 3456])).
% 3.62/3.83 tff(35461,plain,
% 3.62/3.83 (b(s(s(s(elem!1))), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[16580, 35460])).
% 3.62/3.83 tff(35462,plain,
% 3.62/3.83 (r(z, s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23127, 35451, 1, 19197])).
% 3.62/3.83 tff(35463,plain,
% 3.62/3.83 (r(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2310, 35462, 6510, 35461, 82, 412, 23395])).
% 3.62/3.83 tff(35464,plain,
% 3.62/3.83 (r(s(z), s(s(s(z))))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35463, 35459])).
% 3.62/3.83 tff(35465,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35451, 35464])).
% 3.62/3.83 tff(35466,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | b(z, s(z)) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35467,plain,
% 3.62/3.83 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35466, 35391, 894, 35393, 909, 35388, 1, 35397, 35396, 307, 35420])).
% 3.62/3.83 tff(35468,plain,
% 3.62/3.83 (elem!1 = s(s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[78, 35467])).
% 3.62/3.83 tff(35469,plain,
% 3.62/3.83 (~(s(s(s(z))) = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3906, 35468])).
% 3.62/3.83 tff(35470,plain,
% 3.62/3.83 (~r(s(elem!1), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1254, 35393, 909, 35388])).
% 3.62/3.83 tff(35471,plain,
% 3.62/3.83 (b(s(elem!1), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[429, 35470, 6511])).
% 3.62/3.83 tff(35472,plain,
% 3.62/3.83 (~b(z, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[4122, 35471, 307, 35391])).
% 3.62/3.83 tff(35473,plain,
% 3.62/3.83 (r(z, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1439, 35472])).
% 3.62/3.83 tff(35474,plain,
% 3.62/3.83 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[11663, 6983])).
% 3.62/3.83 tff(35475,plain,
% 3.62/3.83 (b(elem!1, z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21021, 35393, 219, 19197, 909, 23812])).
% 3.62/3.83 tff(35476,plain,
% 3.62/3.83 (b(s(s(s(elem!1))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3790, 35468, 35419])).
% 3.62/3.83 tff(35477,plain,
% 3.62/3.83 (~b(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[11686, 35476, 35391, 35475, 35474])).
% 3.62/3.83 tff(35478,plain,
% 3.62/3.83 (~r(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23313, 35469, 909, 35388, 35391, 35397, 35475])).
% 3.62/3.83 tff(35479,plain,
% 3.62/3.83 (b(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[105, 35478])).
% 3.62/3.83 tff(35480,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35455, 35479, 35477, 19197, 894, 35391, 35393, 219, 23812, 909, 35388, 35471, 35473, 35469, 35419])).
% 3.62/3.83 tff(35481,plain,((~b(elem!1, s(elem!1))) | b(z, s(z)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35482,plain,
% 3.62/3.83 (~b(elem!1, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35481, 1242, 909, 1, 894, 1391])).
% 3.62/3.83 tff(35483,plain,
% 3.62/3.83 (r(elem!1, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[392, 35482, 219])).
% 3.62/3.83 tff(35484,plain,
% 3.62/3.83 (~r(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[17391, 8448, 357, 379])).
% 3.62/3.83 tff(35485,plain,
% 3.62/3.83 (b(z, elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[355, 16802, 1391])).
% 3.62/3.83 tff(35486,plain,
% 3.62/3.83 (b(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[444, 16929, 438])).
% 3.62/3.83 tff(35487,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23220, 35486, 35485, 1281, 394])).
% 3.62/3.83 tff(35488,plain,((~b(s(elem!1), z)) | (~b(s(z), z)) | r(s(z), s(elem!1)) | r(z, elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35489,plain,
% 3.62/3.83 (~b(s(elem!1), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35488, 35484, 1281, 1391, 2467])).
% 3.62/3.83 tff(35490,plain,
% 3.62/3.83 (~(elem!1 = z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[20985, 35489, 1281])).
% 3.62/3.83 tff(35491,plain,
% 3.62/3.83 (~(z = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[364, 35490])).
% 3.62/3.83 tff(35492,plain,
% 3.62/3.83 (r(s(elem!1), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[409, 35489])).
% 3.62/3.83 tff(35493,plain,
% 3.62/3.83 (~(s(z) = s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[343, 35491])).
% 3.62/3.83 tff(35494,plain,
% 3.62/3.83 (~(s(elem!1) = s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[350, 35493])).
% 3.62/3.83 tff(35495,plain,
% 3.62/3.83 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3826, 35494, 909, 139, 379, 35492, 357])).
% 3.62/3.83 tff(35496,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[7281, 35495, 2467])).
% 3.62/3.83 tff(35497,plain,
% 3.62/3.83 (b(z, elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[355, 35491, 1391])).
% 3.62/3.83 tff(35498,plain,
% 3.62/3.83 (b(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5661, 35491, 909, 379, 35492, 1391, 258])).
% 3.62/3.83 tff(35499,plain,
% 3.62/3.83 (elem!1 = s(s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[78, 35495])).
% 3.62/3.83 tff(35500,plain,
% 3.62/3.83 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3952, 35499, 909, 379, 2467, 944, 35492, 35491, 35498, 35497, 216])).
% 3.62/3.83 tff(35501,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5759, 35500, 35496, 909, 379, 35492, 35491, 944, 357, 1391, 258])).
% 3.62/3.83 tff(35502,plain,(b(s(elem!1), elem!1) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), elem!1)) | r(z, elem!1) | (elem!1 = s(z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35503,plain,
% 3.62/3.83 (b(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35502, 35483, 909, 35390, 35388, 1391, 5773, 211, 35387, 19197])).
% 3.62/3.83 tff(35504,plain,
% 3.62/3.83 (b(s(z), elem!1) <=> b(s(z), z)),
% 3.62/3.83 inference(symmetry,[status(thm)],[20677])).
% 3.62/3.83 tff(35505,plain,
% 3.62/3.83 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35504])).
% 3.62/3.83 tff(35506,plain,
% 3.62/3.83 (~b(s(z), z)),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[1242, 35505])).
% 3.62/3.83 tff(35507,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1281, 35506])).
% 3.62/3.83 tff(35508,plain,((~(z = elem!1)) | (~b(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35509,plain,
% 3.62/3.83 (~(z = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35508, 1242, 19197])).
% 3.62/3.83 tff(35510,plain,
% 3.62/3.83 (~(s(z) = s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[343, 35509])).
% 3.62/3.83 tff(35511,plain,
% 3.62/3.83 (~(s(elem!1) = s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[350, 35510])).
% 3.62/3.83 tff(35512,plain,
% 3.62/3.83 (b(z, elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[355, 35509, 1391])).
% 3.62/3.83 tff(35513,plain,
% 3.62/3.83 (~b(s(elem!1), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35258, 35483, 35388, 35512, 19197, 35510])).
% 3.62/3.83 tff(35514,plain,
% 3.62/3.83 (r(s(elem!1), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[409, 35513])).
% 3.62/3.83 tff(35515,plain,
% 3.62/3.83 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3826, 35514, 909, 35387, 35483, 35511, 35388])).
% 3.62/3.83 tff(35516,plain,
% 3.62/3.83 (elem!1 = s(s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[78, 35515])).
% 3.62/3.83 tff(35517,plain,
% 3.62/3.83 (~(elem!1 = z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[333, 35509])).
% 3.62/3.83 tff(35518,plain,
% 3.62/3.83 (b(elem!1, z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21021, 35514, 219, 19197, 909, 35517])).
% 3.62/3.83 tff(35519,plain,
% 3.62/3.83 (b(s(s(s(elem!1))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[17387, 35518, 909, 35387, 35483, 35388, 35503, 35512, 35511])).
% 3.62/3.83 tff(35520,plain,
% 3.62/3.83 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23410, 35516, 19197, 909, 35483, 35510, 35511, 894, 219, 35388, 35519])).
% 3.62/3.83 tff(35521,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3787, 35520, 35516, 35503])).
% 3.62/3.83 tff(35522,plain,(b(s(z), elem!1) | (~r(z, s(z))) | b(z, s(z)) | r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35523,plain,
% 3.62/3.83 (r(z, elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35522, 35386, 1, 894, 905])).
% 3.62/3.83 tff(35524,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1266, 35523, 35386, 905, 35385, 35384])).
% 3.62/3.83 tff(35525,plain,(b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35526,plain,
% 3.62/3.83 (b(s(z), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35525, 894, 1])).
% 3.62/3.83 tff(35527,plain,
% 3.62/3.83 (b(elem!1, z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21021, 412, 219, 19197, 905, 358])).
% 3.62/3.83 tff(35528,plain,
% 3.62/3.83 (b(elem!1, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35340, 199, 412, 909, 331, 23687, 219])).
% 3.62/3.83 tff(35529,plain,
% 3.62/3.83 (b(s(z), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1293, 258, 1281, 909, 412, 2282, 378, 307])).
% 3.62/3.83 tff(35530,plain,
% 3.62/3.83 (~b(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23931, 35529, 412, 909, 307, 378, 8337, 348])).
% 3.62/3.83 tff(35531,plain,
% 3.62/3.83 (r(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2243, 35530, 8337])).
% 3.62/3.83 tff(35532,plain,
% 3.62/3.83 (~r(elem!1, s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5343, 35531, 412, 378])).
% 3.62/3.83 tff(35533,plain,
% 3.62/3.83 (b(elem!1, s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[299, 35532, 258])).
% 3.62/3.83 tff(35534,plain,
% 3.62/3.83 (~b(z, s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5420, 35533, 1281, 261])).
% 3.62/3.83 tff(35535,plain,
% 3.62/3.83 (r(z, s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2106, 35534])).
% 3.62/3.83 tff(35536,plain,
% 3.62/3.83 (elem!1 = s(s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23946, 35535, 1281, 8336, 909, 412, 199, 258, 378, 348, 35532])).
% 3.62/3.83 tff(35537,plain,
% 3.62/3.83 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[7490, 35536])).
% 3.62/3.83 tff(35538,plain,
% 3.62/3.83 (b(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5347, 35529, 909, 412, 307, 8337, 378, 348])).
% 3.62/3.83 tff(35539,plain,
% 3.62/3.83 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[4497, 35529, 35538, 307])).
% 3.62/3.83 tff(35540,plain,
% 3.62/3.83 (r(s(elem!1), s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[526, 35539, 216])).
% 3.62/3.83 tff(35541,plain,
% 3.62/3.83 (~r(s(s(elem!1)), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5431, 35535, 35540, 412])).
% 3.62/3.83 tff(35542,plain,
% 3.62/3.83 (b(s(s(elem!1)), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2143, 35541])).
% 3.62/3.83 tff(35543,plain,
% 3.62/3.83 (~b(s(s(s(z))), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[22517, 35542, 1281, 35536, 378, 3871])).
% 3.62/3.83 tff(35544,plain,
% 3.62/3.83 (r(s(s(s(z))), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2325, 35543])).
% 3.62/3.83 tff(35545,plain,
% 3.62/3.83 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35536])).
% 3.62/3.83 tff(35546,plain,
% 3.62/3.83 (b(s(s(elem!1)), z)),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[261, 35545])).
% 3.62/3.83 tff(35547,plain,
% 3.62/3.83 (~b(z, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6481, 35546, 1281, 35542])).
% 3.62/3.83 tff(35548,plain,
% 3.62/3.83 (r(z, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1658, 35547])).
% 3.62/3.83 tff(35549,plain,
% 3.62/3.83 (~b(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[24003, 35529, 3871, 307])).
% 3.62/3.83 tff(35550,plain,
% 3.62/3.83 (~(s(s(s(z))) = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3906, 35536])).
% 3.62/3.83 tff(35551,plain,
% 3.62/3.83 (r(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[255, 35550, 35549])).
% 3.62/3.83 tff(35552,plain,
% 3.62/3.83 (~b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5408, 1661, 909, 307, 260])).
% 3.62/3.83 tff(35553,plain,
% 3.62/3.83 (r(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[840, 35552, 4997])).
% 3.62/3.83 tff(35554,plain,
% 3.62/3.83 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5017, 35553, 378, 1661])).
% 3.62/3.83 tff(35555,plain,
% 3.62/3.83 (b(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1847, 35554, 5002])).
% 3.62/3.83 tff(35556,plain,
% 3.62/3.83 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35555, 16272])).
% 3.62/3.83 tff(35557,plain,
% 3.62/3.83 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5462, 35553, 2470])).
% 3.62/3.83 tff(35558,plain,
% 3.62/3.83 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5531, 35557, 1140, 1661])).
% 3.62/3.83 tff(35559,plain,
% 3.62/3.83 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1494, 35558])).
% 3.62/3.83 tff(35560,plain,
% 3.62/3.83 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1731, 35559, 1721, 17468])).
% 3.62/3.83 tff(35561,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35560, 35556])).
% 3.62/3.83 tff(35562,plain,((~r(z, s(s(s(s(s(z))))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35563,plain,
% 3.62/3.83 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35562, 1140, 260, 307, 378, 145, 17421, 1661, 909, 2470])).
% 3.62/3.83 tff(35564,plain,
% 3.62/3.83 (~r(elem!1, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[19831, 1140, 378, 2327])).
% 3.62/3.83 tff(35565,plain,
% 3.62/3.83 (b(elem!1, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1192, 35564, 12183])).
% 3.62/3.83 tff(35566,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5482, 35565, 35563, 2470])).
% 3.62/3.83 tff(35567,plain,((~r(z, s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35568,plain,
% 3.62/3.83 (~r(z, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35567, 35536, 35529, 307, 378, 35551, 35548, 909, 35544])).
% 3.62/3.83 tff(35569,plain,
% 3.62/3.83 (b(z, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1214, 35568])).
% 3.62/3.83 tff(35570,plain,
% 3.62/3.83 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[19817, 35569, 1281, 3871])).
% 3.62/3.83 tff(35571,plain,
% 3.62/3.83 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2071, 35570, 9149])).
% 3.62/3.83 tff(35572,plain,
% 3.62/3.83 (r(s(s(s(z))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23458, 35571, 35537])).
% 3.62/3.83 tff(35573,plain,
% 3.62/3.83 (~r(s(s(s(z))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3650, 35572, 378, 412])).
% 3.62/3.83 tff(35574,plain,
% 3.62/3.83 (b(s(s(s(z))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1155, 35573])).
% 3.62/3.83 tff(35575,plain,
% 3.62/3.83 (~(elem!1 = s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1100, 35550])).
% 3.62/3.83 tff(35576,plain,
% 3.62/3.83 (~r(elem!1, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5181, 35572, 35531, 35551])).
% 3.62/3.83 tff(35577,plain,
% 3.62/3.83 (b(elem!1, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1192, 35576, 35575])).
% 3.62/3.83 tff(35578,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[11038, 35577, 35574, 3871, 35533])).
% 3.62/3.83 tff(35579,plain,((elem!1 = s(z)) | (~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(z))) | (~b(elem!1, z)) | b(z, elem!1) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35580,plain,
% 3.62/3.83 (elem!1 = s(z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35579, 1243, 3871, 412, 19197, 35528, 909, 23687, 199, 344, 211])).
% 3.62/3.83 tff(35581,plain,
% 3.62/3.83 (s(z) = elem!1),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[242, 35580])).
% 3.62/3.83 tff(35582,plain,
% 3.62/3.83 (~b(z, s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21421, 35581, 909, 3871, 23687, 412])).
% 3.62/3.83 tff(35583,plain,
% 3.62/3.83 (~b(z, s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23691, 35582, 35581])).
% 3.62/3.83 tff(35584,plain,
% 3.62/3.83 (r(z, s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2106, 35583])).
% 3.62/3.83 tff(35585,plain,
% 3.62/3.83 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3425, 35584, 35152, 111])).
% 3.62/3.83 tff(35586,plain,
% 3.62/3.83 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[556, 35585, 1])).
% 3.62/3.83 tff(35587,plain,
% 3.62/3.83 (~r(elem!1, s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[10623, 1243, 35152, 111])).
% 3.62/3.83 tff(35588,plain,
% 3.62/3.83 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1045, 35581, 35587])).
% 3.62/3.83 tff(35589,plain,
% 3.62/3.83 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[760, 35588])).
% 3.62/3.83 tff(35590,plain,
% 3.62/3.83 (s(elem!1) = s(s(z))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35580])).
% 3.62/3.83 tff(35591,plain,
% 3.62/3.83 (s(s(elem!1)) = s(s(s(z)))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35590])).
% 3.62/3.83 tff(35592,plain,
% 3.62/3.83 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35591])).
% 3.62/3.83 tff(35593,plain,
% 3.62/3.83 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35592])).
% 3.62/3.83 tff(35594,plain,
% 3.62/3.83 (b(s(z), s(s(elem!1)))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[3871, 35593])).
% 3.62/3.83 tff(35595,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[13843, 35594, 35589, 35586])).
% 3.62/3.83 tff(35596,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[8229, 35595])).
% 3.62/3.83 tff(35597,plain,
% 3.62/3.83 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35580])).
% 3.62/3.83 tff(35598,plain,
% 3.62/3.83 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35597])).
% 3.62/3.83 tff(35599,plain,
% 3.62/3.83 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35598])).
% 3.62/3.83 tff(35600,plain,
% 3.62/3.83 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[2137, 35599])).
% 3.62/3.83 tff(35601,plain,
% 3.62/3.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[78, 35600])).
% 3.62/3.83 tff(35602,plain,
% 3.62/3.83 (b(elem!1, s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[8233, 35589, 35581])).
% 3.62/3.83 tff(35603,plain,
% 3.62/3.83 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35580])).
% 3.62/3.83 tff(35604,plain,
% 3.62/3.83 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35603])).
% 3.62/3.83 tff(35605,plain,
% 3.62/3.83 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 3.62/3.83 inference(transitivity,[status(thm)],[35593, 35604])).
% 3.62/3.83 tff(35606,plain,
% 3.62/3.83 (b(elem!1, s(s(elem!1)))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[3871, 35605])).
% 3.62/3.83 tff(35607,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6906, 35606, 35586, 35602])).
% 3.62/3.83 tff(35608,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[681, 35607, 35601])).
% 3.62/3.83 tff(35609,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6850, 35608, 35596, 412, 35584])).
% 3.62/3.83 tff(35610,plain,(b(z, elem!1) | (~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35611,plain,
% 3.62/3.83 (b(z, elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35610, 412, 35526, 1, 111, 905, 331])).
% 3.62/3.83 tff(35612,plain,
% 3.62/3.83 (~b(s(z), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3964, 35611, 19197, 35527])).
% 3.62/3.83 tff(35613,plain,
% 3.62/3.83 (~(elem!1 = s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1397, 35611, 894])).
% 3.62/3.83 tff(35614,plain,
% 3.62/3.83 (~b(elem!1, s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[21813, 35611, 219, 19197, 412, 358])).
% 3.62/3.83 tff(35615,plain,
% 3.62/3.83 (~r(z, elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1266, 35614, 905, 35613, 35612])).
% 3.62/3.83 tff(35616,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35522, 35615, 35612, 1, 894, 905])).
% 3.62/3.83 tff(35617,plain,((~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z)) | (~r(z, s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35618,plain,
% 3.62/3.83 (~r(s(elem!1), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35617, 331, 894, 111, 1])).
% 3.62/3.83 tff(35619,plain,
% 3.62/3.83 (b(elem!1, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[392, 35273, 219])).
% 3.62/3.83 tff(35620,plain,
% 3.62/3.83 ($false),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[26178, 121, 378, 111, 35152, 3456])).
% 3.62/3.83 tff(35621,plain,((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.83 tff(35622,plain,
% 3.62/3.83 (~r(elem!1, s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[35621, 378, 111])).
% 3.62/3.83 tff(35623,plain,
% 3.62/3.83 (b(elem!1, s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[299, 258, 35622])).
% 3.62/3.83 tff(35624,plain,
% 3.62/3.83 (~r(elem!1, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[10227, 378, 35152, 111])).
% 3.62/3.83 tff(35625,plain,
% 3.62/3.83 (b(elem!1, s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[392, 35624, 219])).
% 3.62/3.83 tff(35626,plain,
% 3.62/3.83 (b(s(z), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23843, 258, 909, 259, 11211, 378, 2282, 19197, 35625])).
% 3.62/3.83 tff(35627,plain,
% 3.62/3.83 (~b(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[24003, 260, 3871, 35625])).
% 3.62/3.83 tff(35628,plain,
% 3.62/3.83 (~r(elem!1, s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[10623, 378, 35152, 111])).
% 3.62/3.83 tff(35629,plain,
% 3.62/3.83 (~r(s(s(s(z))), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[19871, 1409, 1140, 378])).
% 3.62/3.83 tff(35630,plain,
% 3.62/3.83 (s(s(s(z))) = elem!1),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[255, 35629, 2346])).
% 3.62/3.83 tff(35631,plain,
% 3.62/3.83 (s(elem!1) = s(s(s(s(z))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2605, 35630])).
% 3.62/3.83 tff(35632,plain,
% 3.62/3.83 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35631])).
% 3.62/3.83 tff(35633,plain,
% 3.62/3.83 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[3906, 35630])).
% 3.62/3.83 tff(35634,plain,
% 3.62/3.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[78, 35633])).
% 3.62/3.83 tff(35635,plain,
% 3.62/3.83 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[4909, 35630, 307])).
% 3.62/3.83 tff(35636,plain,
% 3.62/3.83 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35630])).
% 3.62/3.83 tff(35637,plain,
% 3.62/3.83 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35636])).
% 3.62/3.83 tff(35638,plain,
% 3.62/3.83 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35637])).
% 3.62/3.83 tff(35639,plain,
% 3.62/3.83 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[1043, 35638])).
% 3.62/3.83 tff(35640,plain,
% 3.62/3.83 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2071, 35639, 9149])).
% 3.62/3.83 tff(35641,plain,
% 3.62/3.83 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2114, 35640, 35635, 394])).
% 3.62/3.83 tff(35642,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[681, 35641, 35634])).
% 3.62/3.83 tff(35643,plain,
% 3.62/3.83 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35631])).
% 3.62/3.83 tff(35644,plain,
% 3.62/3.83 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35643])).
% 3.62/3.83 tff(35645,plain,
% 3.62/3.83 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[6958, 1409, 35152, 1, 563, 378])).
% 3.62/3.83 tff(35646,plain,
% 3.62/3.83 (~(s(s(elem!1)) = elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[197, 35633])).
% 3.62/3.83 tff(35647,plain,
% 3.62/3.83 (b(s(s(elem!1)), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[862, 35646, 35645])).
% 3.62/3.83 tff(35648,plain,
% 3.62/3.83 (b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35647, 35644])).
% 3.62/3.83 tff(35649,plain,
% 3.62/3.83 (~r(z, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[5408, 35648, 909, 260, 307])).
% 3.62/3.83 tff(35650,plain,
% 3.62/3.83 (b(z, s(s(s(s(s(z))))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[1658, 35649])).
% 3.62/3.83 tff(35651,plain,
% 3.62/3.83 (~b(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[23890, 35650, 19197, 394])).
% 3.62/3.83 tff(35652,plain,
% 3.62/3.83 (r(s(z), s(elem!1))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[444, 35651, 348])).
% 3.62/3.83 tff(35653,plain,
% 3.62/3.83 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35630])).
% 3.62/3.83 tff(35654,plain,
% 3.62/3.83 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.62/3.83 inference(symmetry,[status(thm)],[35653])).
% 3.62/3.83 tff(35655,plain,
% 3.62/3.83 (r(s(s(s(z))), z)),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[1409, 35654])).
% 3.62/3.83 tff(35656,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35630])).
% 3.62/3.83 tff(35657,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35656])).
% 3.62/3.83 tff(35658,plain,
% 3.62/3.83 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35152, 35657])).
% 3.62/3.83 tff(35659,plain,
% 3.62/3.83 (~r(s(s(s(elem!1))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[11676, 35658, 35655, 1140])).
% 3.62/3.83 tff(35660,plain,
% 3.62/3.83 (b(s(s(s(elem!1))), z)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[8229, 35659])).
% 3.62/3.83 tff(35661,plain,
% 3.62/3.83 (~r(s(s(s(z))), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[10317, 35652, 909, 35655])).
% 3.62/3.83 tff(35662,plain,
% 3.62/3.83 (b(s(s(s(z))), s(z))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2325, 35661])).
% 3.62/3.83 tff(35663,plain,
% 3.62/3.83 (~b(s(z), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[14970, 35662, 35660, 35640])).
% 3.62/3.83 tff(35664,plain,
% 3.62/3.83 (r(s(z), s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[760, 35663])).
% 3.62/3.83 tff(35665,plain,
% 3.62/3.83 (~r(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[9617, 35664, 35652, 35642])).
% 3.62/3.83 tff(35666,plain,
% 3.62/3.83 (b(s(elem!1), elem!1)),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[2243, 35665, 2207])).
% 3.62/3.83 tff(35667,plain,
% 3.62/3.83 (b(s(s(s(s(z)))), elem!1)),
% 3.62/3.83 inference(modus_ponens,[status(thm)],[35666, 35632])).
% 3.62/3.83 tff(35668,plain,
% 3.62/3.83 (b(elem!1, s(s(s(elem!1))))),
% 3.62/3.83 inference(unit_resolution,[status(thm)],[9580, 35640, 35630])).
% 3.62/3.83 tff(35669,plain,
% 3.62/3.83 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35643])).
% 3.62/3.83 tff(35670,plain,
% 3.62/3.83 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35669])).
% 3.62/3.83 tff(35671,plain,
% 3.62/3.83 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(symmetry,[status(thm)],[35670])).
% 3.62/3.83 tff(35672,plain,
% 3.62/3.83 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 3.62/3.83 inference(monotonicity,[status(thm)],[35631])).
% 3.62/3.83 tff(35673,plain,
% 3.62/3.83 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.62/3.83 inference(transitivity,[status(thm)],[35672, 35671])).
% 3.62/3.83 tff(35674,plain,
% 3.62/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.83 inference(rewrite,[status(thm)],[])).
% 3.62/3.83 tff(35675,plain,
% 3.62/3.83 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.83 inference(rewrite,[status(thm)],[])).
% 3.62/3.83 tff(35676,plain,
% 3.62/3.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35675])).
% 3.62/3.84 tff(35677,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.84 inference(transitivity,[status(thm)],[35676, 35674])).
% 3.62/3.84 tff(35678,plain,
% 3.62/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.62/3.84 inference(quant_inst,[status(thm)],[])).
% 3.62/3.84 tff(35679,plain,
% 3.62/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35678, 35677])).
% 3.62/3.84 tff(35680,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35679, 271, 2618, 542, 2494, 738])).
% 3.62/3.84 tff(35681,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35682,plain,
% 3.62/3.84 (~b(s(s(elem!1)), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35681, 35666, 35647, 35668])).
% 3.62/3.84 tff(35683,plain,
% 3.62/3.84 (r(s(s(elem!1)), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[701, 35682, 3313])).
% 3.62/3.84 tff(35684,plain,
% 3.62/3.84 (b(elem!1, s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23140, 35662, 35630])).
% 3.62/3.84 tff(35685,plain,
% 3.62/3.84 (~b(s(s(elem!1)), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[5441, 35684, 260, 35647])).
% 3.62/3.84 tff(35686,plain,
% 3.62/3.84 (r(s(s(elem!1)), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2143, 35685])).
% 3.62/3.84 tff(35687,plain,
% 3.62/3.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2125, 35664, 35642, 35686])).
% 3.62/3.84 tff(35688,plain,
% 3.62/3.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[556, 35687, 1])).
% 3.62/3.84 tff(35689,plain,
% 3.62/3.84 (~r(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[8581, 35686, 909, 35664])).
% 3.62/3.84 tff(35690,plain,
% 3.62/3.84 (b(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2106, 35689])).
% 3.62/3.84 tff(35691,plain,
% 3.62/3.84 (~b(s(z), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[19354, 35690, 19197, 35688])).
% 3.62/3.84 tff(35692,plain,
% 3.62/3.84 (r(s(z), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2167, 35691])).
% 3.62/3.84 tff(35693,plain,
% 3.62/3.84 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3275, 35692, 35652, 35683])).
% 3.62/3.84 tff(35694,plain,
% 3.62/3.84 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[526, 35693, 211])).
% 3.62/3.84 tff(35695,plain,
% 3.62/3.84 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35694, 35673])).
% 3.62/3.84 tff(35696,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.62/3.84 inference(rewrite,[status(thm)],[])).
% 3.62/3.84 tff(35697,plain,
% 3.62/3.84 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.62/3.84 inference(rewrite,[status(thm)],[])).
% 3.62/3.84 tff(35698,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35697])).
% 3.62/3.84 tff(35699,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 3.62/3.84 inference(transitivity,[status(thm)],[35698, 35696])).
% 3.62/3.84 tff(35700,plain,
% 3.62/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.62/3.84 inference(quant_inst,[status(thm)],[])).
% 3.62/3.84 tff(35701,plain,
% 3.62/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35700, 35699])).
% 3.62/3.84 tff(35702,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35701, 271, 35695, 35648, 35668, 35667])).
% 3.62/3.84 tff(35703,plain,((~r(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(z))))) | r(elem!1, s(s(s(elem!1)))) | b(s(s(s(z))), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35704,plain,
% 3.62/3.84 (~r(elem!1, z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35703, 1140, 909, 260, 348, 11211, 35625, 1, 35628, 35627, 378])).
% 3.62/3.84 tff(35705,plain,
% 3.62/3.84 (b(elem!1, z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[284, 35704, 259])).
% 3.62/3.84 tff(35706,plain,
% 3.62/3.84 (~b(z, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10660, 35705, 11211, 35625])).
% 3.62/3.84 tff(35707,plain,
% 3.62/3.84 (r(z, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1439, 35706])).
% 3.62/3.84 tff(35708,plain,
% 3.62/3.84 (~b(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3404, 35705, 11211, 35625])).
% 3.62/3.84 tff(35709,plain,
% 3.62/3.84 (r(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2106, 35708])).
% 3.62/3.84 tff(35710,plain,
% 3.62/3.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3425, 35709, 35152, 111])).
% 3.62/3.84 tff(35711,plain,
% 3.62/3.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[556, 35710, 1])).
% 3.62/3.84 tff(35712,plain,
% 3.62/3.84 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23132, 448, 909, 111, 260])).
% 3.62/3.84 tff(35713,plain,
% 3.62/3.84 (b(elem!1, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[392, 35624, 8336])).
% 3.62/3.84 tff(35714,plain,
% 3.62/3.84 (~b(s(s(s(z))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[24003, 260, 3871, 35713])).
% 3.62/3.84 tff(35715,plain,
% 3.62/3.84 (~b(s(elem!1), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1290, 448, 1281, 35713])).
% 3.62/3.84 tff(35716,plain,
% 3.62/3.84 (r(s(elem!1), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[429, 35715, 2282])).
% 3.62/3.84 tff(35717,plain,
% 3.62/3.84 (b(elem!1, s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[12884, 9552, 111, 378, 479])).
% 3.62/3.84 tff(35718,plain,
% 3.62/3.84 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35717, 9576])).
% 3.62/3.84 tff(35719,plain,
% 3.62/3.84 (~b(s(s(s(elem!1))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[30266, 35718, 3871, 222])).
% 3.62/3.84 tff(35720,plain,
% 3.62/3.84 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[16580, 35719])).
% 3.62/3.84 tff(35721,plain,
% 3.62/3.84 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[2606])).
% 3.62/3.84 tff(35722,plain,
% 3.62/3.84 (r(z, s(s(s(s(z)))))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[1441, 35721])).
% 3.62/3.84 tff(35723,plain,
% 3.62/3.84 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[2606])).
% 3.62/3.84 tff(35724,plain,
% 3.62/3.84 (r(s(s(s(s(z)))), s(z))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[411, 35723])).
% 3.62/3.84 tff(35725,plain,
% 3.62/3.84 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9490, 35724, 909, 35722])).
% 3.62/3.84 tff(35726,plain,
% 3.62/3.84 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[760, 35725])).
% 3.62/3.84 tff(35727,plain,
% 3.62/3.84 (~b(s(s(s(elem!1))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[14970, 35726, 222, 35718])).
% 3.62/3.84 tff(35728,plain,
% 3.62/3.84 (r(s(s(s(elem!1))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[8229, 35727])).
% 3.62/3.84 tff(35729,plain,
% 3.62/3.84 (~r(s(z), s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[19684, 35728, 909, 35720])).
% 3.62/3.84 tff(35730,plain,
% 3.62/3.84 (~r(s(z), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9700, 35729, 2606])).
% 3.62/3.84 tff(35731,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2678, 121, 378, 624, 139, 6842])).
% 3.62/3.84 tff(35732,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35733,plain,
% 3.62/3.84 (~r(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35732, 35728, 35152, 378])).
% 3.62/3.84 tff(35734,plain,
% 3.62/3.84 (b(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[599, 35733, 68])).
% 3.62/3.84 tff(35735,plain,
% 3.62/3.84 (~b(s(z), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4433, 35734, 448, 543])).
% 3.62/3.84 tff(35736,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2167, 35735, 35730])).
% 3.62/3.84 tff(35737,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35738,plain,
% 3.62/3.84 (~b(s(s(s(z))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35737, 244, 543, 68, 909, 378, 448, 3871, 411, 1441, 111, 479])).
% 3.62/3.84 tff(35739,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35738, 10641])).
% 3.62/3.84 tff(35740,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35741,plain,
% 3.62/3.84 (~(s(s(s(z))) = elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35740, 68, 543, 448, 909, 378, 3871, 35716, 1441, 111, 35712])).
% 3.62/3.84 tff(35742,plain,
% 3.62/3.84 (r(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1192, 1101, 11112])).
% 3.62/3.84 tff(35743,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[6723, 35742, 23300, 1140, 378])).
% 3.62/3.84 tff(35744,plain,((s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35745,plain,
% 3.62/3.84 (b(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35744, 35741, 378, 1140, 35714])).
% 3.62/3.84 tff(35746,plain,
% 3.62/3.84 (~b(s(s(s(z))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[11038, 35745, 3871, 448])).
% 3.62/3.84 tff(35747,plain,
% 3.62/3.84 (r(s(s(s(z))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1155, 35746])).
% 3.62/3.84 tff(35748,plain,
% 3.62/3.84 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[11011, 35747, 10994])).
% 3.62/3.84 tff(35749,plain,
% 3.62/3.84 (~(s(elem!1) = s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2035, 35748])).
% 3.62/3.84 tff(35750,plain,
% 3.62/3.84 (~b(s(s(s(z))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1811, 35745, 11211, 35713])).
% 3.62/3.84 tff(35751,plain,
% 3.62/3.84 (r(s(s(s(z))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1816, 35748, 35750])).
% 3.62/3.84 tff(35752,plain,
% 3.62/3.84 (~r(s(elem!1), s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10701, 35751, 1140, 1441])).
% 3.62/3.84 tff(35753,plain,
% 3.62/3.84 (b(s(elem!1), s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2044, 35752, 35749])).
% 3.62/3.84 tff(35754,plain,
% 3.62/3.84 (~b(s(s(s(z))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10690, 35753, 35713, 35745])).
% 3.62/3.84 tff(35755,plain,
% 3.62/3.84 (r(s(s(s(z))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2325, 35754])).
% 3.62/3.84 tff(35756,plain,
% 3.62/3.84 (~r(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10317, 35755, 909, 35747])).
% 3.62/3.84 tff(35757,plain,
% 3.62/3.84 (b(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[444, 35756, 348])).
% 3.62/3.84 tff(35758,plain,
% 3.62/3.84 (~b(s(elem!1), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3435, 35757, 35713, 260])).
% 3.62/3.84 tff(35759,plain,
% 3.62/3.84 (r(s(elem!1), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2243, 35758, 8337])).
% 3.62/3.84 tff(35760,plain,
% 3.62/3.84 (~r(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2697, 35759, 35152, 378, 79])).
% 3.62/3.84 tff(35761,plain,
% 3.62/3.84 (b(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[599, 35760, 68])).
% 3.62/3.84 tff(35762,plain,
% 3.62/3.84 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[7694, 35759, 1441, 111])).
% 3.62/3.84 tff(35763,plain,
% 3.62/3.84 (b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[681, 35762, 79])).
% 3.62/3.84 tff(35764,plain,
% 3.62/3.84 (~b(elem!1, s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[6906, 35763, 543, 35761])).
% 3.62/3.84 tff(35765,plain,
% 3.62/3.84 (~b(z, s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23890, 35757, 1281, 11211])).
% 3.62/3.84 tff(35766,plain,
% 3.62/3.84 (r(z, s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1658, 35765])).
% 3.62/3.84 tff(35767,plain,
% 3.62/3.84 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[11865, 35766, 11211, 35757, 909])).
% 3.62/3.84 tff(35768,plain,
% 3.62/3.84 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4497, 35757, 260, 35713])).
% 3.62/3.84 tff(35769,plain,
% 3.62/3.84 (r(s(elem!1), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[526, 35768, 216])).
% 3.62/3.84 tff(35770,plain,
% 3.62/3.84 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[6368, 35769, 35766, 1441])).
% 3.62/3.84 tff(35771,plain,
% 3.62/3.84 (s(s(s(s(s(z))))) = s(elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4138, 35770, 35767])).
% 3.62/3.84 tff(35772,plain,
% 3.62/3.84 (~(s(s(s(elem!1))) = elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[6264, 35771, 944])).
% 3.62/3.84 tff(35773,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[12884, 35772, 35764, 111, 378, 35712])).
% 3.62/3.84 tff(35774,plain,((elem!1 = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (~r(z, s(s(s(z))))) | r(s(elem!1), z) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35775,plain,
% 3.62/3.84 (elem!1 = s(s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35774, 35711, 378, 944, 111, 35707, 909, 211, 260, 19197, 348, 1140, 10994, 3871, 448])).
% 3.62/3.84 tff(35776,plain,
% 3.62/3.84 (~(s(s(s(z))) = elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3906, 35775])).
% 3.62/3.84 tff(35777,plain,
% 3.62/3.84 (b(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35744, 35776, 378, 1140, 35627])).
% 3.62/3.84 tff(35778,plain,
% 3.62/3.84 (~b(s(s(s(z))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[11038, 35777, 3871, 448])).
% 3.62/3.84 tff(35779,plain,
% 3.62/3.84 (r(s(s(s(z))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1155, 35778])).
% 3.62/3.84 tff(35780,plain,
% 3.62/3.84 (~r(s(s(elem!1)), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[12129, 35775, 35622])).
% 3.62/3.84 tff(35781,plain,
% 3.62/3.84 (b(s(s(elem!1)), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2143, 35780])).
% 3.62/3.84 tff(35782,plain,
% 3.62/3.84 (~b(s(s(s(z))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[22517, 35781, 19197, 35775, 378, 3871])).
% 3.62/3.84 tff(35783,plain,
% 3.62/3.84 (r(s(s(s(z))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2325, 35782])).
% 3.62/3.84 tff(35784,plain,
% 3.62/3.84 (~r(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10317, 35783, 909, 35779])).
% 3.62/3.84 tff(35785,plain,
% 3.62/3.84 (b(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[444, 35784, 348])).
% 3.62/3.84 tff(35786,plain,
% 3.62/3.84 (r(s(s(s(z))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[255, 35776, 35627])).
% 3.62/3.84 tff(35787,plain,
% 3.62/3.84 (~r(z, s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35567, 35783, 260, 35625, 378, 1140, 35775, 909, 35786])).
% 3.62/3.84 tff(35788,plain,
% 3.62/3.84 (b(z, s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1658, 35787])).
% 3.62/3.84 tff(35789,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23890, 35788, 35785, 19197, 11211])).
% 3.62/3.84 tff(35790,plain,((~r(z, s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35791,plain,
% 3.62/3.84 (~r(z, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35790, 35626, 348, 378, 909, 3871, 35623, 19199, 111, 10994, 1, 259])).
% 3.62/3.84 tff(35792,plain,
% 3.62/3.84 (b(z, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1214, 35791])).
% 3.62/3.84 tff(35793,plain,
% 3.62/3.84 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[19817, 35792, 19197, 3871])).
% 3.62/3.84 tff(35794,plain,
% 3.62/3.84 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2071, 35793, 9149])).
% 3.62/3.84 tff(35795,plain,
% 3.62/3.84 (r(s(s(s(z))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4220, 35792, 19197, 3871, 199])).
% 3.62/3.84 tff(35796,plain,
% 3.62/3.84 (~(s(s(s(z))) = elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4210, 35792, 199])).
% 3.62/3.84 tff(35797,plain,
% 3.62/3.84 (~(elem!1 = s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1100, 35796])).
% 3.62/3.84 tff(35798,plain,
% 3.62/3.84 (~b(elem!1, z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1315, 35792, 11211, 35625])).
% 3.62/3.84 tff(35799,plain,
% 3.62/3.84 (r(elem!1, z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[284, 35798, 259])).
% 3.62/3.84 tff(35800,plain,
% 3.62/3.84 (~r(s(s(s(z))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[15900, 35799, 909, 35795])).
% 3.62/3.84 tff(35801,plain,
% 3.62/3.84 (b(s(s(s(z))), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1155, 35800])).
% 3.62/3.84 tff(35802,plain,
% 3.62/3.84 (~b(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[11038, 35801, 3871, 35623])).
% 3.62/3.84 tff(35803,plain,
% 3.62/3.84 (r(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1192, 35802, 35797])).
% 3.62/3.84 tff(35804,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[5301, 121, 35803, 35152, 35795, 35794])).
% 3.62/3.84 tff(35805,plain,((elem!1 = s(z)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (elem!1 = z) | b(z, elem!1) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | r(s(elem!1), z) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35806,plain,
% 3.62/3.84 (elem!1 = s(z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35805, 199, 909, 358, 3871, 344, 1243, 111, 10994, 1])).
% 3.62/3.84 tff(35807,plain,
% 3.62/3.84 (s(z) = elem!1),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[242, 35806])).
% 3.62/3.84 tff(35808,plain,
% 3.62/3.84 (b(elem!1, z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[20120, 35807, 19197])).
% 3.62/3.84 tff(35809,plain,
% 3.62/3.84 (~b(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3404, 35808, 11211, 35619])).
% 3.62/3.84 tff(35810,plain,
% 3.62/3.84 (r(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2106, 35809])).
% 3.62/3.84 tff(35811,plain,
% 3.62/3.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3425, 35810, 35152, 111])).
% 3.62/3.84 tff(35812,plain,
% 3.62/3.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[556, 35811, 1])).
% 3.62/3.84 tff(35813,plain,
% 3.62/3.84 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35806])).
% 3.62/3.84 tff(35814,plain,
% 3.62/3.84 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(symmetry,[status(thm)],[35813])).
% 3.62/3.84 tff(35815,plain,
% 3.62/3.84 (s(elem!1) = s(s(z))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35806])).
% 3.62/3.84 tff(35816,plain,
% 3.62/3.84 (s(s(elem!1)) = s(s(s(z)))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35815])).
% 3.62/3.84 tff(35817,plain,
% 3.62/3.84 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35816])).
% 3.62/3.84 tff(35818,plain,
% 3.62/3.84 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 3.62/3.84 inference(symmetry,[status(thm)],[35817])).
% 3.62/3.84 tff(35819,plain,
% 3.62/3.84 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(transitivity,[status(thm)],[35818, 35814])).
% 3.62/3.84 tff(35820,plain,
% 3.62/3.84 (b(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[3871, 35819])).
% 3.62/3.84 tff(35821,plain,
% 3.62/3.84 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9687, 35820, 35812, 35619])).
% 3.62/3.84 tff(35822,plain,
% 3.62/3.84 (~b(z, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10660, 35808, 11211, 35619])).
% 3.62/3.84 tff(35823,plain,
% 3.62/3.84 (r(z, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1439, 35822])).
% 3.62/3.84 tff(35824,plain,
% 3.62/3.84 (b(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1276, 35807, 35619])).
% 3.62/3.84 tff(35825,plain,
% 3.62/3.84 (~b(z, s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23890, 35824, 19197, 11211])).
% 3.62/3.84 tff(35826,plain,
% 3.62/3.84 (r(z, s(s(s(s(s(z))))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1658, 35825])).
% 3.62/3.84 tff(35827,plain,
% 3.62/3.84 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[11865, 35826, 11211, 35824, 909])).
% 3.62/3.84 tff(35828,plain,
% 3.62/3.84 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35815])).
% 3.62/3.84 tff(35829,plain,
% 3.62/3.84 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 3.62/3.84 inference(symmetry,[status(thm)],[35828])).
% 3.62/3.84 tff(35830,plain,
% 3.62/3.84 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35829])).
% 3.62/3.84 tff(35831,plain,
% 3.62/3.84 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[877, 35830])).
% 3.62/3.84 tff(35832,plain,
% 3.62/3.84 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4138, 35831, 35827])).
% 3.62/3.84 tff(35833,plain,
% 3.62/3.84 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[6368, 35832, 35826, 35823])).
% 3.62/3.84 tff(35834,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[526, 35833, 35821, 211])).
% 3.62/3.84 tff(35835,plain,(b(z, elem!1) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | r(s(elem!1), z) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35836,plain,
% 3.62/3.84 (b(z, elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35835, 35618, 1, 905, 111, 35526, 331])).
% 3.62/3.84 tff(35837,plain,
% 3.62/3.84 (~(elem!1 = s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1397, 35836, 894])).
% 3.62/3.84 tff(35838,plain,
% 3.62/3.84 (b(s(elem!1), z)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[409, 35618])).
% 3.62/3.84 tff(35839,plain,
% 3.62/3.84 (~b(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23220, 35836, 19197, 35838])).
% 3.62/3.84 tff(35840,plain,
% 3.62/3.84 (~b(s(elem!1), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9252, 271, 35836, 35838, 19197])).
% 3.62/3.84 tff(35841,plain,
% 3.62/3.84 (r(s(elem!1), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[429, 35840, 351])).
% 3.62/3.84 tff(35842,plain,
% 3.62/3.84 (r(s(z), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[444, 35839, 344])).
% 3.62/3.84 tff(35843,plain,
% 3.62/3.84 (~r(z, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[10292, 121, 905, 35842, 35841])).
% 3.62/3.84 tff(35844,plain,
% 3.62/3.84 (b(z, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1439, 35843])).
% 3.62/3.84 tff(35845,plain,
% 3.62/3.84 (~b(elem!1, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9091, 35844, 35838, 35836])).
% 3.62/3.84 tff(35846,plain,
% 3.62/3.84 (r(elem!1, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[392, 35845, 219])).
% 3.62/3.84 tff(35847,plain,
% 3.62/3.84 (~r(elem!1, s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[23250, 35846, 35839, 344, 19197, 35836])).
% 3.62/3.84 tff(35848,plain,
% 3.62/3.84 (~r(s(z), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35258, 35846, 35838, 35836, 19197, 344])).
% 3.62/3.84 tff(35849,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[20894, 35848, 35847, 19197, 35836, 35837])).
% 3.62/3.84 tff(35850,plain,((z = elem!1) | b(z, s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.84 tff(35851,plain,
% 3.62/3.84 (z = elem!1),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35850, 111, 1, 894])).
% 3.62/3.84 tff(35852,plain,
% 3.62/3.84 (s(z) = s(elem!1)),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.84 tff(35853,plain,
% 3.62/3.84 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35852])).
% 3.62/3.84 tff(35854,plain,
% 3.62/3.84 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 3.62/3.84 inference(symmetry,[status(thm)],[35853])).
% 3.62/3.84 tff(35855,plain,
% 3.62/3.84 (s(s(z)) = s(s(elem!1))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35852])).
% 3.62/3.84 tff(35856,plain,
% 3.62/3.84 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35855])).
% 3.62/3.84 tff(35857,plain,
% 3.62/3.84 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35856])).
% 3.62/3.84 tff(35858,plain,
% 3.62/3.84 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 3.62/3.84 inference(symmetry,[status(thm)],[35857])).
% 3.62/3.84 tff(35859,plain,
% 3.62/3.84 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 3.62/3.84 inference(transitivity,[status(thm)],[35858, 35854])).
% 3.62/3.84 tff(35860,plain,
% 3.62/3.84 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35859])).
% 3.62/3.84 tff(35861,plain,
% 3.62/3.84 (elem!1 = z),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[364, 35851])).
% 3.62/3.84 tff(35862,plain,
% 3.62/3.84 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9876, 35861, 35526])).
% 3.62/3.84 tff(35863,plain,
% 3.62/3.84 (b(s(z), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35508, 35851, 19197])).
% 3.62/3.84 tff(35864,plain,
% 3.62/3.84 (~b(elem!1, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1543, 35851, 894])).
% 3.62/3.84 tff(35865,plain,
% 3.62/3.84 (r(elem!1, s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[392, 35864, 219])).
% 3.62/3.84 tff(35866,plain,
% 3.62/3.84 (r(z, s(z)) <=> r(elem!1, s(z))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.84 tff(35867,plain,
% 3.62/3.84 (r(elem!1, s(z))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[905, 35866])).
% 3.62/3.84 tff(35868,plain,
% 3.62/3.84 (~r(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[3425, 623, 139, 111])).
% 3.62/3.84 tff(35869,plain,
% 3.62/3.84 (b(z, s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[2106, 35868])).
% 3.62/3.84 tff(35870,plain,
% 3.62/3.84 (b(elem!1, s(s(elem!1)))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35869, 7508])).
% 3.62/3.84 tff(35871,plain,
% 3.62/3.84 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[20691, 35870, 139, 379, 1536, 260, 10121, 216, 623])).
% 3.62/3.84 tff(35872,plain,
% 3.62/3.84 (b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[681, 35871, 3512])).
% 3.62/3.84 tff(35873,plain,
% 3.62/3.84 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9876, 3871, 18839])).
% 3.62/3.84 tff(35874,plain,
% 3.62/3.84 (b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[754, 35873, 107])).
% 3.62/3.84 tff(35875,plain,
% 3.62/3.84 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[4527, 35871, 107])).
% 3.62/3.84 tff(35876,plain,
% 3.62/3.84 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1816, 35875, 18832])).
% 3.62/3.84 tff(35877,plain,
% 3.62/3.84 (b(s(s(s(elem!1))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[19370, 35876, 1536])).
% 3.62/3.84 tff(35878,plain,
% 3.62/3.84 (b(s(s(s(z))), s(z))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[19469, 35877, 1536])).
% 3.62/3.84 tff(35879,plain,
% 3.62/3.84 (~b(z, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[21149, 35878, 1281, 3871])).
% 3.62/3.84 tff(35880,plain,
% 3.62/3.84 (~b(elem!1, s(s(s(elem!1))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[6057, 35879, 107])).
% 3.62/3.84 tff(35881,plain,
% 3.62/3.84 (~b(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1198, 35880, 107])).
% 3.62/3.84 tff(35882,plain,
% 3.62/3.84 (r(elem!1, s(s(s(z))))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[1192, 35881, 10087])).
% 3.62/3.84 tff(35883,plain,
% 3.62/3.84 (r(elem!1, s(s(s(elem!1))))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35882, 10085])).
% 3.62/3.84 tff(35884,plain,
% 3.62/3.84 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[34319, 121, 623, 139, 727])).
% 3.62/3.84 tff(35885,plain,
% 3.62/3.84 (b(s(s(elem!1)), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[862, 35884, 18443])).
% 3.62/3.84 tff(35886,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.62/3.84 inference(rewrite,[status(thm)],[])).
% 3.62/3.84 tff(35887,plain,
% 3.62/3.84 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.62/3.84 inference(rewrite,[status(thm)],[])).
% 3.62/3.84 tff(35888,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 3.62/3.84 inference(monotonicity,[status(thm)],[35887])).
% 3.62/3.84 tff(35889,plain,
% 3.62/3.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 3.62/3.84 inference(transitivity,[status(thm)],[35888, 35886])).
% 3.62/3.84 tff(35890,plain,
% 3.62/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.62/3.84 inference(quant_inst,[status(thm)],[])).
% 3.62/3.84 tff(35891,plain,
% 3.62/3.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 3.62/3.84 inference(modus_ponens,[status(thm)],[35890, 35889])).
% 3.62/3.84 tff(35892,plain,
% 3.62/3.84 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[35891, 121, 623, 139, 6026])).
% 3.62/3.84 tff(35893,plain,
% 3.62/3.84 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[18291, 35892, 878])).
% 3.62/3.84 tff(35894,plain,
% 3.62/3.84 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[34402, 121, 139, 727, 6026])).
% 3.62/3.84 tff(35895,plain,
% 3.62/3.84 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[9962, 35894, 1536])).
% 3.62/3.84 tff(35896,plain,
% 3.62/3.84 (b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[840, 35895, 712])).
% 3.62/3.84 tff(35897,plain,
% 3.62/3.84 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[835, 35896, 107])).
% 3.62/3.84 tff(35898,plain,
% 3.62/3.84 ($false),
% 3.62/3.84 inference(unit_resolution,[status(thm)],[5958, 271, 588, 35897, 35893, 35885])).
% 3.62/3.85 tff(35899,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.85 tff(35900,plain,
% 3.62/3.85 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35899, 35870, 107, 139, 35883, 623])).
% 3.62/3.85 tff(35901,plain,
% 3.62/3.85 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[6039, 35900, 107])).
% 3.62/3.85 tff(35902,plain,
% 3.62/3.85 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[1733, 35901])).
% 3.62/3.85 tff(35903,plain,
% 3.62/3.85 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[19552, 35902, 1536])).
% 3.62/3.85 tff(35904,plain,
% 3.62/3.85 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[18992, 35903, 35874, 35872])).
% 3.62/3.85 tff(35905,plain,
% 3.62/3.85 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[9896, 35904, 107])).
% 3.62/3.85 tff(35906,plain,
% 3.62/3.85 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[4138, 35905, 18174])).
% 3.62/3.85 tff(35907,plain,
% 3.62/3.85 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[18190, 35906, 107])).
% 3.62/3.85 tff(35908,plain,
% 3.62/3.85 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[34319, 121, 623, 139, 35883])).
% 3.62/3.85 tff(35909,plain,
% 3.62/3.85 (b(s(s(elem!1)), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[862, 35908, 18443])).
% 3.62/3.85 tff(35910,plain,
% 3.62/3.85 (b(s(elem!1), z)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[20985, 18839, 1281])).
% 3.62/3.85 tff(35911,plain,
% 3.62/3.85 (b(s(elem!1), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[2488, 35910, 107])).
% 3.62/3.85 tff(35912,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35913,plain,
% 3.62/3.85 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35914,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35913])).
% 3.62/3.85 tff(35915,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(transitivity,[status(thm)],[35914, 35912])).
% 3.62/3.85 tff(35916,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 3.62/3.85 inference(quant_inst,[status(thm)],[])).
% 3.62/3.85 tff(35917,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35916, 35915])).
% 3.62/3.85 tff(35918,plain,
% 3.62/3.85 (~b(s(s(elem!1)), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35917, 271, 35911, 35870, 35909])).
% 3.62/3.85 tff(35919,plain,
% 3.62/3.85 (r(s(s(elem!1)), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[701, 35918, 8423])).
% 3.62/3.85 tff(35920,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35921,plain,
% 3.62/3.85 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35922,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35921])).
% 3.62/3.85 tff(35923,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(transitivity,[status(thm)],[35922, 35920])).
% 3.62/3.85 tff(35924,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 3.62/3.85 inference(quant_inst,[status(thm)],[])).
% 3.62/3.85 tff(35925,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35924, 35923])).
% 3.62/3.85 tff(35926,plain,
% 3.62/3.85 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35925, 271, 35911, 35870, 35909])).
% 3.62/3.85 tff(35927,plain,
% 3.62/3.85 (r(s(elem!1), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[526, 35926, 216])).
% 3.62/3.85 tff(35928,plain,
% 3.62/3.85 (r(s(z), s(s(elem!1)))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35927, 1547])).
% 3.62/3.85 tff(35929,plain,
% 3.62/3.85 (~b(s(s(s(s(s(z))))), s(z))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[28576, 35902, 3871, 35878])).
% 3.62/3.85 tff(35930,plain,
% 3.62/3.85 (r(s(s(s(s(s(z))))), s(z))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[1682, 35929])).
% 3.62/3.85 tff(35931,plain,
% 3.62/3.85 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[25896, 35930, 3456, 35928])).
% 3.62/3.85 tff(35932,plain,
% 3.62/3.85 (b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[840, 35931, 712])).
% 3.62/3.85 tff(35933,plain,
% 3.62/3.85 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[835, 35932, 107])).
% 3.62/3.85 tff(35934,plain,
% 3.62/3.85 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[5958, 271, 35870, 35933, 35909])).
% 3.62/3.85 tff(35935,plain,
% 3.62/3.85 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[18291, 35934, 878])).
% 3.62/3.85 tff(35936,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35937,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 3.62/3.85 inference(quant_inst,[status(thm)],[])).
% 3.62/3.85 tff(35938,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35937, 35936])).
% 3.62/3.85 tff(35939,plain,
% 3.62/3.85 ($false),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35938, 121, 35927, 35935, 35919, 35907])).
% 3.62/3.85 tff(35940,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), z)) | (~r(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.85 tff(35941,plain,
% 3.62/3.85 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35940, 35867, 35851, 35526, 35152, 211, 19197, 35865, 35863, 111])).
% 3.62/3.85 tff(35942,plain,
% 3.62/3.85 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[556, 35941, 1])).
% 3.62/3.85 tff(35943,plain,
% 3.62/3.85 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.85 tff(35944,plain,
% 3.62/3.85 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 3.62/3.85 inference(transitivity,[status(thm)],[35943, 2211])).
% 3.62/3.85 tff(35945,plain,
% 3.62/3.85 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35944])).
% 3.62/3.85 tff(35946,plain,
% 3.62/3.85 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[59, 35945])).
% 3.62/3.85 tff(35947,plain,
% 3.62/3.85 (b(s(elem!1), z)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[20985, 35861, 19197])).
% 3.62/3.85 tff(35948,plain,
% 3.62/3.85 (b(s(elem!1), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[2488, 35947, 35851])).
% 3.62/3.85 tff(35949,plain,
% 3.62/3.85 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.85 tff(35950,plain,
% 3.62/3.85 (r(elem!1, s(s(s(elem!1))))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[111, 35949])).
% 3.62/3.85 tff(35951,plain,
% 3.62/3.85 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[11463, 627, 139, 379])).
% 3.62/3.85 tff(35952,plain,
% 3.62/3.85 (b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[681, 35951, 3512])).
% 3.62/3.85 tff(35953,plain,
% 3.62/3.85 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[34385, 35952, 1536, 2618, 543, 627])).
% 3.62/3.85 tff(35954,plain,
% 3.62/3.85 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[19552, 35953, 1536])).
% 3.62/3.85 tff(35955,plain,
% 3.62/3.85 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[1733, 35954])).
% 3.62/3.85 tff(35956,plain,
% 3.62/3.85 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[6039, 35955, 107])).
% 3.62/3.85 tff(35957,plain,
% 3.62/3.85 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[34402, 121, 139, 727, 35956])).
% 3.62/3.85 tff(35958,plain,
% 3.62/3.85 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[9962, 35957, 1536])).
% 3.62/3.85 tff(35959,plain,
% 3.62/3.85 (b(s(s(s(s(s(z))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[840, 35958, 712])).
% 3.62/3.85 tff(35960,plain,
% 3.62/3.85 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[835, 35959, 107])).
% 3.62/3.85 tff(35961,plain,
% 3.62/3.85 (~r(elem!1, s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[5852, 35952, 750, 543, 3456])).
% 3.62/3.85 tff(35962,plain,
% 3.62/3.85 (b(elem!1, s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[599, 35961, 18438])).
% 3.62/3.85 tff(35963,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35964,plain,
% 3.62/3.85 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35965,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35964])).
% 3.62/3.85 tff(35966,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 3.62/3.85 inference(transitivity,[status(thm)],[35965, 35963])).
% 3.62/3.85 tff(35967,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 3.62/3.85 inference(quant_inst,[status(thm)],[])).
% 3.62/3.85 tff(35968,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35967, 35966])).
% 3.62/3.85 tff(35969,plain,
% 3.62/3.85 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35968, 271, 2618, 35962, 35960])).
% 3.62/3.85 tff(35970,plain,
% 3.62/3.85 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[9896, 35969, 107])).
% 3.62/3.85 tff(35971,plain,
% 3.62/3.85 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[4138, 35970, 18174])).
% 3.62/3.85 tff(35972,plain,
% 3.62/3.85 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[18190, 35971, 107])).
% 3.62/3.85 tff(35973,plain,
% 3.62/3.85 (b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[754, 750, 107])).
% 3.62/3.85 tff(35974,plain,
% 3.62/3.85 (~b(s(s(elem!1)), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[5254, 35952, 35973, 543])).
% 3.62/3.85 tff(35975,plain,
% 3.62/3.85 (r(s(s(elem!1)), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[701, 35974, 694])).
% 3.62/3.85 tff(35976,plain,
% 3.62/3.85 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35938, 121, 627, 35975, 35972])).
% 3.62/3.85 tff(35977,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35978,plain,
% 3.62/3.85 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(35979,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35978])).
% 3.62/3.85 tff(35980,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(transitivity,[status(thm)],[35979, 35977])).
% 3.62/3.85 tff(35981,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 3.62/3.85 inference(quant_inst,[status(thm)],[])).
% 3.62/3.85 tff(35982,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35981, 35980])).
% 3.62/3.85 tff(35983,plain,
% 3.62/3.85 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35982, 121, 379, 627, 35975])).
% 3.62/3.85 tff(35984,plain,
% 3.62/3.85 (b(s(s(elem!1)), elem!1)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[862, 35983, 18443])).
% 3.62/3.85 tff(35985,plain,
% 3.62/3.85 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[5958, 271, 35962, 35960, 35984])).
% 3.62/3.85 tff(35986,plain,
% 3.62/3.85 ($false),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[18291, 35985, 35976, 878])).
% 3.62/3.85 tff(35987,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.85 tff(35988,plain,
% 3.62/3.85 (~r(s(elem!1), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[35987, 35942, 35851, 35948, 35152, 35865, 3313, 35862, 35950, 35867])).
% 3.62/3.85 tff(35989,plain,
% 3.62/3.85 (b(s(elem!1), s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[526, 35988, 211])).
% 3.62/3.85 tff(35990,plain,
% 3.62/3.85 (~b(elem!1, s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[14419, 35989, 35942, 35948])).
% 3.62/3.85 tff(35991,plain,
% 3.62/3.85 (r(elem!1, s(s(elem!1)))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[599, 35990, 35946])).
% 3.62/3.85 tff(35992,plain,
% 3.62/3.85 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[5852, 35991, 35867, 35942, 35862])).
% 3.62/3.85 tff(35993,plain,
% 3.62/3.85 (~b(s(s(s(z))), s(z))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35992, 35860])).
% 3.62/3.85 tff(35994,plain,
% 3.62/3.85 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.85 tff(35995,plain,
% 3.62/3.85 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 3.62/3.85 inference(symmetry,[status(thm)],[35994])).
% 3.62/3.85 tff(35996,plain,
% 3.62/3.85 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35856])).
% 3.62/3.85 tff(35997,plain,
% 3.62/3.85 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 3.62/3.85 inference(symmetry,[status(thm)],[35996])).
% 3.62/3.85 tff(35998,plain,
% 3.62/3.85 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 3.62/3.85 inference(transitivity,[status(thm)],[35997, 35995])).
% 3.62/3.85 tff(35999,plain,
% 3.62/3.85 (r(z, s(s(s(z))))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[35950, 35998])).
% 3.62/3.85 tff(36000,plain,
% 3.62/3.85 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35856])).
% 3.62/3.85 tff(36001,plain,
% 3.62/3.85 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[36000])).
% 3.62/3.85 tff(36002,plain,
% 3.62/3.85 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[36001, 36000])).
% 3.62/3.85 tff(36003,plain,
% 3.62/3.85 (r(s(s(s(z))), z)),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[143, 35851, 35152])).
% 3.62/3.85 tff(36004,plain,
% 3.62/3.85 (b(s(elem!1), s(s(s(elem!1))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[754, 35862, 35851])).
% 3.62/3.85 tff(36005,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(36006,plain,
% 3.62/3.85 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.62/3.85 inference(rewrite,[status(thm)],[])).
% 3.62/3.85 tff(36007,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[36006])).
% 3.62/3.85 tff(36008,plain,
% 3.62/3.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 3.62/3.85 inference(transitivity,[status(thm)],[36007, 36005])).
% 3.62/3.85 tff(36009,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 3.62/3.85 inference(quant_inst,[status(thm)],[])).
% 3.62/3.85 tff(36010,plain,
% 3.62/3.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 3.62/3.85 inference(modus_ponens,[status(thm)],[36009, 36008])).
% 3.62/3.85 tff(36011,plain,
% 3.62/3.85 ($false),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[36010, 271, 543, 517, 739, 18043])).
% 3.62/3.85 tff(36012,plain,((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.85 tff(36013,plain,
% 3.62/3.85 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[36012, 35989, 36004, 35942])).
% 3.62/3.85 tff(36014,plain,
% 3.62/3.85 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[18038, 36013, 35851])).
% 3.62/3.85 tff(36015,plain,
% 3.62/3.85 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.62/3.85 inference(unit_resolution,[status(thm)],[1494, 36014])).
% 3.62/3.85 tff(36016,plain,
% 3.62/3.85 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.85 tff(36017,plain,
% 3.62/3.85 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 3.62/3.85 inference(symmetry,[status(thm)],[36016])).
% 3.62/3.85 tff(36018,plain,
% 3.62/3.85 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 3.62/3.85 inference(monotonicity,[status(thm)],[35851])).
% 3.62/3.85 tff(36019,plain,
% 3.62/3.85 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 3.62/3.85 inference(transitivity,[status(thm)],[36018, 1837])).
% 3.62/3.85 tff(36020,plain,
% 3.62/3.85 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36019])).
% 3.62/3.86 tff(36021,plain,
% 3.62/3.86 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[711, 36020])).
% 3.62/3.86 tff(36022,plain,
% 3.62/3.86 (s(z) = s(elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[500, 35851])).
% 3.62/3.86 tff(36023,plain,
% 3.62/3.86 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.62/3.86 inference(transitivity,[status(thm)],[35944, 2212])).
% 3.62/3.86 tff(36024,plain,
% 3.62/3.86 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36023])).
% 3.62/3.86 tff(36025,plain,
% 3.62/3.86 (~(s(s(elem!1)) = elem!1)),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[59, 36024])).
% 3.62/3.86 tff(36026,plain,
% 3.62/3.86 (b(s(z), s(s(elem!1)))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[521, 35989, 36022])).
% 3.62/3.86 tff(36027,plain,
% 3.62/3.86 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[15399, 36026, 35942, 35526])).
% 3.62/3.86 tff(36028,plain,
% 3.62/3.86 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[20478, 36027, 36022])).
% 3.62/3.86 tff(36029,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[586, 36028, 563])).
% 3.62/3.86 tff(36030,plain,
% 3.62/3.86 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[17619, 36029, 35950, 35991])).
% 3.62/3.86 tff(36031,plain,
% 3.62/3.86 (b(s(s(elem!1)), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[862, 36030, 36025])).
% 3.62/3.86 tff(36032,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36033,plain,
% 3.62/3.86 (((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36034,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36033])).
% 3.62/3.86 tff(36035,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 3.62/3.86 inference(transitivity,[status(thm)],[36034, 36032])).
% 3.62/3.86 tff(36036,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 3.62/3.86 inference(quant_inst,[status(thm)],[])).
% 3.62/3.86 tff(36037,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36036, 36035])).
% 3.62/3.86 tff(36038,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36037, 271, 2618, 517, 542, 6004])).
% 3.62/3.86 tff(36039,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36040,plain,
% 3.62/3.86 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36039, 36031, 35989, 35948])).
% 3.62/3.86 tff(36041,plain,
% 3.62/3.86 (~b(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[9946, 36040, 36022])).
% 3.62/3.86 tff(36042,plain,
% 3.62/3.86 (r(elem!1, s(s(s(s(s(z))))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1847, 36041, 36021])).
% 3.62/3.86 tff(36043,plain,
% 3.62/3.86 (r(z, s(s(s(s(s(z))))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36042, 36017])).
% 3.62/3.86 tff(36044,plain,
% 3.62/3.86 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19088, 36043, 36015, 36003])).
% 3.62/3.86 tff(36045,plain,
% 3.62/3.86 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[9512, 36044])).
% 3.62/3.86 tff(36046,plain,
% 3.62/3.86 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36045, 36002])).
% 3.62/3.86 tff(36047,plain,
% 3.62/3.86 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[35852])).
% 3.62/3.86 tff(36048,plain,
% 3.62/3.86 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 3.62/3.86 inference(transitivity,[status(thm)],[36047, 1927])).
% 3.62/3.86 tff(36049,plain,
% 3.62/3.86 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36048])).
% 3.62/3.86 tff(36050,plain,
% 3.62/3.86 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[927, 36049])).
% 3.62/3.86 tff(36051,plain,
% 3.62/3.86 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[35852])).
% 3.62/3.86 tff(36052,plain,
% 3.62/3.86 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.86 inference(transitivity,[status(thm)],[36051, 200])).
% 3.62/3.86 tff(36053,plain,
% 3.62/3.86 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36052])).
% 3.62/3.86 tff(36054,plain,
% 3.62/3.86 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[61, 36053])).
% 3.62/3.86 tff(36055,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[681, 35992, 36054])).
% 3.62/3.86 tff(36056,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36057,plain,
% 3.62/3.86 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36058,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36057])).
% 3.62/3.86 tff(36059,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(transitivity,[status(thm)],[36058, 36056])).
% 3.62/3.86 tff(36060,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.62/3.86 inference(quant_inst,[status(thm)],[])).
% 3.62/3.86 tff(36061,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36060, 36059])).
% 3.62/3.86 tff(36062,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36061, 121, 379, 684, 139, 31928])).
% 3.62/3.86 tff(36063,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36064,plain,
% 3.62/3.86 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36063, 36055, 35152, 35865])).
% 3.62/3.86 tff(36065,assumption,(~r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.62/3.86 tff(36066,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36065, 18940])).
% 3.62/3.86 tff(36067,plain,((~r(s(elem!1), s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36068,plain,
% 3.62/3.86 (~r(s(elem!1), s(s(s(s(z)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36067, 36064, 35851])).
% 3.62/3.86 tff(36069,plain,
% 3.62/3.86 (b(s(elem!1), s(s(s(s(z)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1995, 36068, 36050])).
% 3.62/3.86 tff(36070,plain,
% 3.62/3.86 (b(s(z), s(s(s(s(z)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19605, 36069, 35851])).
% 3.62/3.86 tff(36071,plain,
% 3.62/3.86 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19599, 36070, 36022])).
% 3.62/3.86 tff(36072,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.62/3.86 tff(36073,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), z)),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[35152, 35156])).
% 3.62/3.86 tff(36074,plain,
% 3.62/3.86 (~b(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19469, 2319, 1536])).
% 3.62/3.86 tff(36075,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[16580, 36074])).
% 3.62/3.86 tff(36076,plain,
% 3.62/3.86 (~r(s(z), s(s(s(s(s(z))))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19684, 36075, 909, 36073])).
% 3.62/3.86 tff(36077,plain,
% 3.62/3.86 (b(s(z), s(s(s(s(s(z))))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1756, 36076])).
% 3.62/3.86 tff(36078,plain,
% 3.62/3.86 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19528, 36077, 107])).
% 3.62/3.86 tff(36079,plain,
% 3.62/3.86 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.62/3.86 inference(symmetry,[status(thm)],[19292])).
% 3.62/3.86 tff(36080,plain,
% 3.62/3.86 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.62/3.86 inference(transitivity,[status(thm)],[19290, 36079])).
% 3.62/3.86 tff(36081,plain,
% 3.62/3.86 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36080])).
% 3.62/3.86 tff(36082,plain,
% 3.62/3.86 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 3.62/3.86 inference(transitivity,[status(thm)],[18573, 10146])).
% 3.62/3.86 tff(36083,plain,
% 3.62/3.86 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36082])).
% 3.62/3.86 tff(36084,plain,
% 3.62/3.86 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[927, 36083])).
% 3.62/3.86 tff(36085,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36086,plain,
% 3.62/3.86 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36087,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36086])).
% 3.62/3.86 tff(36088,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(transitivity,[status(thm)],[36087, 36085])).
% 3.62/3.86 tff(36089,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.62/3.86 inference(quant_inst,[status(thm)],[])).
% 3.62/3.86 tff(36090,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36089, 36088])).
% 3.62/3.86 tff(36091,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36090, 271, 1586, 31874, 19535, 36072])).
% 3.62/3.86 tff(36092,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36093,plain,
% 3.62/3.86 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36092, 36078, 36072, 31874])).
% 3.62/3.86 tff(36094,plain,
% 3.62/3.86 (~b(s(s(s(s(z)))), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1566, 36093, 107])).
% 3.62/3.86 tff(36095,plain,
% 3.62/3.86 (r(s(s(s(s(z)))), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1559, 36094, 36084])).
% 3.62/3.86 tff(36096,plain,
% 3.62/3.86 (r(s(s(s(s(z)))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1554, 36095, 1536])).
% 3.62/3.86 tff(36097,plain,
% 3.62/3.86 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[24945, 36096, 1281, 2326, 1140])).
% 3.62/3.86 tff(36098,plain,
% 3.62/3.86 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36097, 36081])).
% 3.62/3.86 tff(36099,plain,
% 3.62/3.86 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1594, 21, 1591, 36098])).
% 3.62/3.86 tff(36100,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36101,plain,
% 3.62/3.86 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(rewrite,[status(thm)],[])).
% 3.62/3.86 tff(36102,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 3.62/3.86 inference(monotonicity,[status(thm)],[36101])).
% 3.62/3.86 tff(36103,plain,
% 3.62/3.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 3.62/3.86 inference(transitivity,[status(thm)],[36102, 36100])).
% 3.62/3.86 tff(36104,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 3.62/3.86 inference(quant_inst,[status(thm)],[])).
% 3.62/3.86 tff(36105,plain,
% 3.62/3.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 3.62/3.86 inference(modus_ponens,[status(thm)],[36104, 36103])).
% 3.62/3.86 tff(36106,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36105, 271, 36099, 31874, 36078, 36072])).
% 3.62/3.86 tff(36107,plain,(b(s(s(s(z))), s(z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36108,plain,
% 3.62/3.86 (b(s(s(s(z))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36107, 36071, 36046, 1577, 35851, 19197, 35999, 905])).
% 3.62/3.86 tff(36109,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36108, 35993])).
% 3.62/3.86 tff(36110,plain,((~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36111,plain,
% 3.62/3.86 (~r(z, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36110, 894, 1])).
% 3.62/3.86 tff(36112,plain,
% 3.62/3.86 (b(z, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19736, 36111])).
% 3.62/3.86 tff(36113,plain,
% 3.62/3.86 (r(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[24348, 36112, 1, 35526])).
% 3.62/3.86 tff(36114,plain,
% 3.62/3.86 (b(elem!1, z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[21021, 9298, 219, 19197, 905, 36113])).
% 3.62/3.86 tff(36115,plain,
% 3.62/3.86 (~b(s(z), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[21030, 36114, 19197, 36112])).
% 3.62/3.86 tff(36116,plain,
% 3.62/3.86 (r(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[35522, 36115, 1, 894, 905])).
% 3.62/3.86 tff(36117,plain,
% 3.62/3.86 (~b(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[23060, 36116, 219, 19197, 894, 36113, 36112, 9298])).
% 3.62/3.86 tff(36118,plain,
% 3.62/3.86 (~r(s(s(s(elem!1))), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[21798, 36117, 19197, 35526, 36112, 36113, 35152, 1])).
% 3.62/3.86 tff(36119,plain,
% 3.62/3.86 (b(s(s(s(elem!1))), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[8229, 36118])).
% 3.62/3.86 tff(36120,plain,
% 3.62/3.86 (r(s(z), s(s(s(z))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[23127, 36111, 1, 19197])).
% 3.62/3.86 tff(36121,plain,
% 3.62/3.86 (~r(elem!1, s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[3464, 36116, 905, 36120])).
% 3.62/3.86 tff(36122,plain,
% 3.62/3.86 (~b(z, s(s(s(z))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[21426, 36117, 35526, 36113, 36112, 36121, 19197, 36114])).
% 3.62/3.86 tff(36123,plain,
% 3.62/3.86 (r(z, s(s(s(z))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1214, 36122])).
% 3.62/3.86 tff(36124,plain,
% 3.62/3.86 (~r(s(s(s(z))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2335, 36123, 36120, 905])).
% 3.62/3.86 tff(36125,plain,
% 3.62/3.86 (b(s(s(s(z))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2325, 36124])).
% 3.62/3.86 tff(36126,plain,
% 3.62/3.86 (b(elem!1, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[35340, 36117, 36113, 905, 9297, 36114, 219])).
% 3.62/3.86 tff(36127,plain,
% 3.62/3.86 (b(s(z), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1303, 36117, 905, 36113, 36115, 9297, 36126])).
% 3.62/3.86 tff(36128,plain,
% 3.62/3.86 (~r(s(s(s(z))), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1148, 36123, 36120, 905])).
% 3.62/3.86 tff(36129,plain,
% 3.62/3.86 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[4006, 36128, 36113])).
% 3.62/3.86 tff(36130,plain,
% 3.62/3.86 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1508, 36123, 36120, 905])).
% 3.62/3.86 tff(36131,plain,
% 3.62/3.86 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1816, 36130, 36129])).
% 3.62/3.86 tff(36132,plain,
% 3.62/3.86 (~b(s(elem!1), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[24796, 36131, 36127, 36125])).
% 3.62/3.86 tff(36133,plain,
% 3.62/3.86 (r(s(elem!1), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[429, 36132, 2282])).
% 3.62/3.86 tff(36134,plain,
% 3.62/3.86 (~r(z, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2186, 36133, 905, 36120])).
% 3.62/3.86 tff(36135,plain,
% 3.62/3.86 (b(z, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1439, 36134])).
% 3.62/3.86 tff(36136,plain,
% 3.62/3.86 (s(z) = elem!1),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[21036, 36117, 19197, 219, 905, 36112, 36113, 9298])).
% 3.62/3.86 tff(36137,plain,
% 3.62/3.86 (elem!1 = s(z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1221, 36136])).
% 3.62/3.86 tff(36138,plain,
% 3.62/3.86 (b(elem!1, s(s(s(z))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[11114, 36137, 35526])).
% 3.62/3.86 tff(36139,plain,
% 3.62/3.86 (~b(s(elem!1), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[26482, 36131, 36126, 36138])).
% 3.62/3.86 tff(36140,plain,
% 3.62/3.86 (r(s(elem!1), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2243, 36139, 2207])).
% 3.62/3.86 tff(36141,plain,
% 3.62/3.86 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[8568, 36140, 905, 36113, 36120, 36126, 348, 36116])).
% 3.62/3.86 tff(36142,plain,
% 3.62/3.86 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[760, 36141])).
% 3.62/3.86 tff(36143,plain,
% 3.62/3.86 (b(elem!1, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[8233, 36142, 36136])).
% 3.62/3.86 tff(36144,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[6839, 36143, 36135, 36114, 36119])).
% 3.62/3.86 tff(36145,plain,((s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36146,plain,
% 3.62/3.86 (s(z) = s(elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36145, 894, 1])).
% 3.62/3.86 tff(36147,plain,
% 3.62/3.86 (z = elem!1),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[343, 36146])).
% 3.62/3.86 tff(36148,plain,
% 3.62/3.86 (elem!1 = z),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[364, 36147])).
% 3.62/3.86 tff(36149,plain,
% 3.62/3.86 (b(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[20985, 36148, 19197])).
% 3.62/3.86 tff(36150,plain,
% 3.62/3.86 (~b(s(s(s(elem!1))), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[22605, 36149, 1, 19197, 35526, 36112])).
% 3.62/3.86 tff(36151,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[8229, 36150])).
% 3.62/3.86 tff(36152,plain,
% 3.62/3.86 (b(s(z), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[35508, 36147, 19197])).
% 3.62/3.86 tff(36153,plain,
% 3.62/3.86 (~b(elem!1, z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[21030, 36152, 19197, 36112])).
% 3.62/3.86 tff(36154,plain,
% 3.62/3.86 (~(s(z) = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[20120, 36153, 19197])).
% 3.62/3.86 tff(36155,plain,
% 3.62/3.86 (~(elem!1 = s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[242, 36154])).
% 3.62/3.86 tff(36156,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[20833, 36155, 36151, 1, 19197, 35526, 36112, 36147, 36149])).
% 3.62/3.86 tff(36157,plain,(b(z, s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36158,plain,
% 3.62/3.86 (b(z, s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36157, 1])).
% 3.62/3.86 tff(36159,plain,
% 3.62/3.86 (r(s(z), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[34998, 899, 1])).
% 3.62/3.86 tff(36160,plain,
% 3.62/3.86 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[34688, 106, 1, 899, 71])).
% 3.62/3.86 tff(36161,plain,
% 3.62/3.86 (b(elem!1, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[25631, 36160, 1, 36158])).
% 3.62/3.86 tff(36162,plain,
% 3.62/3.86 (~(s(z) = s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[24229, 36160])).
% 3.62/3.86 tff(36163,plain,
% 3.62/3.86 (~(z = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[500, 36162])).
% 3.62/3.86 tff(36164,plain,
% 3.62/3.86 (~b(z, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[17920, 36163, 1, 36159])).
% 3.62/3.86 tff(36165,plain,
% 3.62/3.86 (r(z, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19736, 36164])).
% 3.62/3.86 tff(36166,plain,
% 3.62/3.86 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[34965, 36160, 1, 36158])).
% 3.62/3.86 tff(36167,plain,
% 3.62/3.86 (elem!1 = s(s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[78, 36166])).
% 3.62/3.86 tff(36168,plain,
% 3.62/3.86 (r(elem!1, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[27575, 36160, 1, 36158])).
% 3.62/3.86 tff(36169,plain,
% 3.62/3.86 (~r(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[10227, 36165, 35152, 36168])).
% 3.62/3.86 tff(36170,plain,
% 3.62/3.86 (b(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[355, 36169, 36163])).
% 3.62/3.86 tff(36171,plain,
% 3.62/3.86 (~b(s(z), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12178, 36170, 36159, 106, 36158, 36167, 36165])).
% 3.62/3.86 tff(36172,plain,
% 3.62/3.86 (~(s(z) = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1276, 36171, 36161])).
% 3.62/3.86 tff(36173,plain,
% 3.62/3.86 (~b(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[26193, 36170, 19197, 36158, 36161, 219, 36162])).
% 3.62/3.86 tff(36174,plain,
% 3.62/3.86 (~b(z, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[6491, 36164, 36167])).
% 3.62/3.86 tff(36175,plain,
% 3.62/3.86 (r(z, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1439, 36174])).
% 3.62/3.86 tff(36176,plain,
% 3.62/3.86 (~b(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12449, 36175, 1, 36159, 106, 36167, 36165])).
% 3.62/3.86 tff(36177,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[16580, 36176])).
% 3.62/3.86 tff(36178,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12985, 36177, 36173, 36159, 36165, 36170, 219, 36172])).
% 3.62/3.86 tff(36179,plain,(b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36180,plain,
% 3.62/3.86 (b(s(z), s(s(s(z))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36179, 899, 1])).
% 3.62/3.86 tff(36181,plain,
% 3.62/3.86 (~b(z, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[17920, 9297, 1, 110])).
% 3.62/3.86 tff(36182,plain,
% 3.62/3.86 (r(z, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[19736, 36181])).
% 3.62/3.86 tff(36183,plain,
% 3.62/3.86 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[10632, 36182, 35152, 110])).
% 3.62/3.86 tff(36184,plain,
% 3.62/3.86 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[760, 36183])).
% 3.62/3.86 tff(36185,plain,
% 3.62/3.86 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[10632, 111, 35152, 110])).
% 3.62/3.86 tff(36186,plain,
% 3.62/3.86 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[760, 36185])).
% 3.62/3.86 tff(36187,plain,
% 3.62/3.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[25631, 317, 1, 36158])).
% 3.62/3.86 tff(36188,plain,
% 3.62/3.86 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2071, 36187, 2065])).
% 3.62/3.86 tff(36189,plain,
% 3.62/3.86 (~b(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12484, 36188, 3871, 36186])).
% 3.62/3.86 tff(36190,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[16580, 36189])).
% 3.62/3.86 tff(36191,plain,
% 3.62/3.86 (s(z) = elem!1),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13049, 36190, 219, 110, 111, 1326])).
% 3.62/3.86 tff(36192,plain,
% 3.62/3.86 (b(elem!1, s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[8233, 36191, 36186])).
% 3.62/3.86 tff(36193,plain,
% 3.62/3.86 (~r(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13149, 36191, 110, 36186, 111, 35152, 563, 1326, 219, 422])).
% 3.62/3.86 tff(36194,plain,
% 3.62/3.86 (~r(s(elem!1), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13186, 36193, 35152, 1, 36158, 110, 9983, 111, 1391, 1326, 36192, 36191])).
% 3.62/3.86 tff(36195,plain,
% 3.62/3.86 (b(elem!1, z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[20120, 36191, 19197])).
% 3.62/3.86 tff(36196,plain,
% 3.62/3.86 (b(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[409, 36193])).
% 3.62/3.86 tff(36197,plain,
% 3.62/3.86 (~b(s(elem!1), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[11634, 36196, 1326, 36195])).
% 3.62/3.86 tff(36198,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2243, 36197, 36194, 2207])).
% 3.62/3.86 tff(36199,plain,(b(elem!1, s(elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | r(z, elem!1) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36200,plain,
% 3.62/3.86 (b(elem!1, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36199, 32853, 1, 110, 36182, 1391, 2282, 3871, 9149])).
% 3.62/3.86 tff(36201,plain,
% 3.62/3.86 (~b(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[26193, 36200, 19197, 36158, 32853, 219, 348])).
% 3.62/3.86 tff(36202,plain,
% 3.62/3.86 (r(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[409, 36201])).
% 3.62/3.86 tff(36203,plain,
% 3.62/3.86 (~(s(z) = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13149, 36202, 110, 36184, 36182, 35152, 563, 32853, 219, 2282])).
% 3.62/3.86 tff(36204,plain,
% 3.62/3.86 (~r(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13049, 36203, 219, 110, 36182, 32853])).
% 3.62/3.86 tff(36205,plain,
% 3.62/3.86 (b(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[16580, 36204])).
% 3.62/3.86 tff(36206,plain,
% 3.62/3.86 (~b(s(z), elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[20382, 36200, 19197, 32853])).
% 3.62/3.86 tff(36207,plain,
% 3.62/3.86 (~(s(s(s(z))) = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[10599, 36206, 3871])).
% 3.62/3.86 tff(36208,plain,
% 3.62/3.86 (~(elem!1 = s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[242, 36203])).
% 3.62/3.86 tff(36209,plain,
% 3.62/3.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[27280, 36208, 35152, 19197, 36158, 32853, 36200, 36207])).
% 3.62/3.86 tff(36210,plain,
% 3.62/3.86 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2071, 36209, 9149])).
% 3.62/3.86 tff(36211,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12484, 36210, 36205, 3871, 36184])).
% 3.62/3.86 tff(36212,plain,(r(z, elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36213,plain,
% 3.62/3.86 (r(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36212, 348, 110, 3871, 1])).
% 3.62/3.86 tff(36214,plain,
% 3.62/3.86 (~r(elem!1, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[10227, 36213, 35152, 36182])).
% 3.62/3.86 tff(36215,plain,
% 3.62/3.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[27575, 36214, 1, 36158])).
% 3.62/3.86 tff(36216,plain,
% 3.62/3.86 (b(elem!1, s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[392, 36214, 219])).
% 3.62/3.86 tff(36217,plain,
% 3.62/3.86 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[2071, 36215, 9149])).
% 3.62/3.86 tff(36218,plain,
% 3.62/3.86 (~b(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12484, 36217, 3871, 36184])).
% 3.62/3.86 tff(36219,plain,
% 3.62/3.86 (r(s(s(s(elem!1))), s(z))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[16580, 36218])).
% 3.62/3.86 tff(36220,plain,
% 3.62/3.86 (b(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[12848, 3498, 110, 111, 12761, 377])).
% 3.62/3.86 tff(36221,plain,
% 3.62/3.86 (~(s(z) = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13149, 3501, 110, 36186, 111, 35152, 6943, 36220, 377, 422])).
% 3.62/3.86 tff(36222,plain,
% 3.62/3.86 ($false),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[13049, 36221, 36220, 377, 110, 111, 12761])).
% 3.62/3.86 tff(36223,plain,(b(s(elem!1), z) | (elem!1 = s(elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.86 tff(36224,plain,
% 3.62/3.86 (b(s(elem!1), z)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[36223, 36182, 110, 219, 36219, 563, 2282])).
% 3.62/3.86 tff(36225,plain,
% 3.62/3.86 (~b(s(z), s(elem!1))),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[9241, 36224, 19197, 36158])).
% 3.62/3.86 tff(36226,plain,
% 3.62/3.86 (~(s(z) = elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[1276, 36225, 36216])).
% 3.62/3.86 tff(36227,plain,
% 3.62/3.86 (~b(z, elem!1)),
% 3.62/3.86 inference(unit_resolution,[status(thm)],[26193, 36224, 19197, 36158, 36216, 219, 348])).
% 3.62/3.86 tff(36228,plain,
% 3.62/3.87 (~r(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[12828, 36227, 36158, 110, 36216, 9297, 219, 36226])).
% 3.62/3.87 tff(36229,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35127, 36228, 36226, 36158, 348, 36182, 3871, 1, 36215, 110])).
% 3.62/3.87 tff(36230,plain,((s(z) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36231,plain,
% 3.62/3.87 (s(z) = s(elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36230, 36180, 1, 36159])).
% 3.62/3.87 tff(36232,plain,
% 3.62/3.87 (z = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[343, 36231])).
% 3.62/3.87 tff(36233,plain,
% 3.62/3.87 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[10142, 36232])).
% 3.62/3.87 tff(36234,plain,
% 3.62/3.87 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36235,plain,
% 3.62/3.87 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.62/3.87 inference(symmetry,[status(thm)],[36234])).
% 3.62/3.87 tff(36236,plain,
% 3.62/3.87 (r(s(s(s(elem!1))), z)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[35152, 36235])).
% 3.62/3.87 tff(36237,plain,
% 3.62/3.87 (elem!1 = z),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[364, 36232])).
% 3.62/3.87 tff(36238,plain,
% 3.62/3.87 (b(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20985, 36237, 19197])).
% 3.62/3.87 tff(36239,plain,
% 3.62/3.87 (b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[327, 36232, 36158])).
% 3.62/3.87 tff(36240,plain,
% 3.62/3.87 (b(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35508, 36232, 19197])).
% 3.62/3.87 tff(36241,plain,
% 3.62/3.87 (~b(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20382, 36240, 19197, 36239])).
% 3.62/3.87 tff(36242,plain,
% 3.62/3.87 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36243,plain,
% 3.62/3.87 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 3.62/3.87 inference(symmetry,[status(thm)],[36242])).
% 3.62/3.87 tff(36244,plain,
% 3.62/3.87 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36243])).
% 3.62/3.87 tff(36245,plain,
% 3.62/3.87 (~r(z, elem!1)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[9971, 36244])).
% 3.62/3.87 tff(36246,plain,
% 3.62/3.87 (~b(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20858, 36245, 19197, 36180, 36241, 36238, 36236, 1])).
% 3.62/3.87 tff(36247,plain,
% 3.62/3.87 (r(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19736, 36246])).
% 3.62/3.87 tff(36248,plain,
% 3.62/3.87 (~b(s(s(s(s(z)))), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[24371, 36247, 19197, 36158, 36180])).
% 3.62/3.87 tff(36249,plain,
% 3.62/3.87 (r(s(s(s(s(z)))), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[932, 36248])).
% 3.62/3.87 tff(36250,plain,
% 3.62/3.87 (r(s(s(s(s(z)))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[18101, 36249, 36232])).
% 3.62/3.87 tff(36251,plain,
% 3.62/3.87 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[10182, 36250, 36232])).
% 3.62/3.87 tff(36252,plain,
% 3.62/3.87 (s(z) = s(elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36253,plain,
% 3.62/3.87 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36252])).
% 3.62/3.87 tff(36254,plain,
% 3.62/3.87 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36255,plain,
% 3.62/3.87 (r(s(z), elem!1)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36159, 36254])).
% 3.62/3.87 tff(36256,plain,
% 3.62/3.87 (r(s(elem!1), elem!1)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36255, 36253])).
% 3.62/3.87 tff(36257,plain,
% 3.62/3.87 (s(s(z)) = s(s(elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36252])).
% 3.62/3.87 tff(36258,plain,
% 3.62/3.87 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36257])).
% 3.62/3.87 tff(36259,plain,
% 3.62/3.87 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36258])).
% 3.62/3.87 tff(36260,plain,
% 3.62/3.87 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36261,plain,
% 3.62/3.87 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.62/3.87 inference(transitivity,[status(thm)],[36260, 159])).
% 3.62/3.87 tff(36262,plain,
% 3.62/3.87 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36261])).
% 3.62/3.87 tff(36263,plain,
% 3.62/3.87 (~(elem!1 = s(s(s(z))))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[166, 36262])).
% 3.62/3.87 tff(36264,plain,
% 3.62/3.87 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[24229, 36231])).
% 3.62/3.87 tff(36265,plain,
% 3.62/3.87 (~b(z, s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[31543, 36236, 1, 36158, 36264, 36180])).
% 3.62/3.87 tff(36266,plain,
% 3.62/3.87 (~b(elem!1, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[6057, 36265, 36232])).
% 3.62/3.87 tff(36267,plain,
% 3.62/3.87 (~b(elem!1, s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1198, 36266, 36232])).
% 3.62/3.87 tff(36268,plain,
% 3.62/3.87 (r(elem!1, s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1192, 36267, 36263])).
% 3.62/3.87 tff(36269,plain,
% 3.62/3.87 (r(elem!1, s(s(s(elem!1))))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36268, 36259])).
% 3.62/3.87 tff(36270,plain,
% 3.62/3.87 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[10192, 36269, 36256, 36251])).
% 3.62/3.87 tff(36271,plain,
% 3.62/3.87 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[9876, 36237, 36180])).
% 3.62/3.87 tff(36272,plain,
% 3.62/3.87 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[13752, 36240, 36239, 36271])).
% 3.62/3.87 tff(36273,plain,
% 3.62/3.87 (b(s(elem!1), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2488, 36238, 36232])).
% 3.62/3.87 tff(36274,plain,
% 3.62/3.87 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[3790, 36273, 36272])).
% 3.62/3.87 tff(36275,plain,
% 3.62/3.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[78, 36274])).
% 3.62/3.87 tff(36276,plain,
% 3.62/3.87 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[5833, 36275])).
% 3.62/3.87 tff(36277,plain,
% 3.62/3.87 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[18062, 36276])).
% 3.62/3.87 tff(36278,plain,
% 3.62/3.87 (~(s(s(elem!1)) = elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[197, 36274])).
% 3.62/3.87 tff(36279,plain,
% 3.62/3.87 (~b(s(s(s(z))), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[21058, 36180, 19197, 36158])).
% 3.62/3.87 tff(36280,plain,
% 3.62/3.87 (r(s(s(s(z))), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1155, 36279])).
% 3.62/3.87 tff(36281,plain,
% 3.62/3.87 (r(s(s(s(z))), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[475, 36232, 36280])).
% 3.62/3.87 tff(36282,plain,
% 3.62/3.87 (~(s(z) = elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[229, 36241, 36158])).
% 3.62/3.87 tff(36283,plain,
% 3.62/3.87 (~(s(s(z)) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[960, 36282])).
% 3.62/3.87 tff(36284,plain,
% 3.62/3.87 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[953, 36283])).
% 3.62/3.87 tff(36285,plain,
% 3.62/3.87 (~b(s(z), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[9241, 36238, 19197, 36158])).
% 3.62/3.87 tff(36286,plain,
% 3.62/3.87 (~(s(s(s(z))) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[4929, 36285, 36180])).
% 3.62/3.87 tff(36287,plain,
% 3.62/3.87 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[5181, 36268, 36256, 36281])).
% 3.62/3.87 tff(36288,plain,
% 3.62/3.87 (b(s(s(s(z))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1816, 36287, 36286])).
% 3.62/3.87 tff(36289,plain,
% 3.62/3.87 (b(s(s(s(elem!1))), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19370, 36288, 36231])).
% 3.62/3.87 tff(36290,plain,
% 3.62/3.87 (b(s(s(s(z))), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19469, 36289, 36231])).
% 3.62/3.87 tff(36291,plain,
% 3.62/3.87 (~r(s(s(elem!1)), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[5239, 36290, 36255, 36268, 36284, 36281])).
% 3.62/3.87 tff(36292,plain,
% 3.62/3.87 (b(s(s(elem!1)), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[862, 36291, 36278])).
% 3.62/3.87 tff(36293,plain,
% 3.62/3.87 (~b(s(s(elem!1)), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[6807, 36292, 36239, 36273])).
% 3.62/3.87 tff(36294,plain,
% 3.62/3.87 (r(s(s(elem!1)), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[701, 36293, 3313])).
% 3.62/3.87 tff(36295,plain,
% 3.62/3.87 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[18095, 36294, 36256, 36251])).
% 3.62/3.87 tff(36296,plain,
% 3.62/3.87 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[18082, 36295, 36277])).
% 3.62/3.87 tff(36297,plain,
% 3.62/3.87 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36298,plain,
% 3.62/3.87 (b(elem!1, s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[324, 36232, 36158])).
% 3.62/3.87 tff(36299,plain,
% 3.62/3.87 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36300,plain,
% 3.62/3.87 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 3.62/3.87 inference(symmetry,[status(thm)],[36299])).
% 3.62/3.87 tff(36301,plain,
% 3.62/3.87 (r(s(z), elem!1) <=> r(s(elem!1), z)),
% 3.62/3.87 inference(transitivity,[status(thm)],[36253, 36300])).
% 3.62/3.87 tff(36302,plain,
% 3.62/3.87 (r(s(elem!1), z)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36255, 36301])).
% 3.62/3.87 tff(36303,plain,
% 3.62/3.87 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36232])).
% 3.62/3.87 tff(36304,plain,
% 3.62/3.87 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36303])).
% 3.62/3.87 tff(36305,plain,
% 3.62/3.87 (~(s(s(z)) = elem!1)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[95, 36304])).
% 3.62/3.87 tff(36306,plain,
% 3.62/3.87 (~r(s(s(z)), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19443, 36291, 36231])).
% 3.62/3.87 tff(36307,plain,
% 3.62/3.87 (b(s(s(z)), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[3613, 36306, 36305])).
% 3.62/3.87 tff(36308,plain,
% 3.62/3.87 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20726, 36307, 36239, 36232, 36273])).
% 3.62/3.87 tff(36309,plain,
% 3.62/3.87 (~r(z, s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[5454, 36308, 36302, 36240, 36274, 36298])).
% 3.62/3.87 tff(36310,plain,
% 3.62/3.87 (b(z, s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2106, 36309])).
% 3.62/3.87 tff(36311,plain,
% 3.62/3.87 (b(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36310, 36297])).
% 3.62/3.87 tff(36312,plain,
% 3.62/3.87 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[11438, 36311, 36292, 36296])).
% 3.62/3.87 tff(36313,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[10196, 36312, 36270, 36233])).
% 3.62/3.87 tff(36314,plain,(r(z, s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36315,plain,
% 3.62/3.87 (r(z, s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36314, 1])).
% 3.62/3.87 tff(36316,plain,
% 3.62/3.87 (~(z = elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35221, 71, 35152, 1, 36315])).
% 3.62/3.87 tff(36317,plain,
% 3.62/3.87 (~(s(z) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[343, 36316])).
% 3.62/3.87 tff(36318,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[27984, 36187, 9983, 1, 36158, 106, 394, 36317, 71])).
% 3.62/3.87 tff(36319,plain,(b(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), z)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36320,plain,
% 3.62/3.87 (b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36319, 394, 1, 71])).
% 3.62/3.87 tff(36321,plain,
% 3.62/3.87 (~b(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[26193, 36320, 19197, 36158, 394, 219, 36317])).
% 3.62/3.87 tff(36322,plain,
% 3.62/3.87 (r(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[355, 36321, 36316])).
% 3.62/3.87 tff(36323,plain,
% 3.62/3.87 (~(elem!1 = z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[333, 36316])).
% 3.62/3.87 tff(36324,plain,
% 3.62/3.87 (~b(s(z), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[9241, 394, 19197, 36158])).
% 3.62/3.87 tff(36325,plain,
% 3.62/3.87 (~(s(z) = elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1276, 36320, 36324])).
% 3.62/3.87 tff(36326,plain,
% 3.62/3.87 (~(elem!1 = s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[242, 36325])).
% 3.62/3.87 tff(36327,plain,
% 3.62/3.87 (~r(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[27152, 36326, 35152, 36158, 36323, 19197, 36322])).
% 3.62/3.87 tff(36328,plain,
% 3.62/3.87 (r(s(z), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[444, 36324, 36317])).
% 3.62/3.87 tff(36329,plain,
% 3.62/3.87 (~(s(elem!1) = s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[350, 36317])).
% 3.62/3.87 tff(36330,plain,
% 3.62/3.87 (~b(s(elem!1), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[16834, 271, 394, 19197, 36158])).
% 3.62/3.87 tff(36331,plain,
% 3.62/3.87 (r(s(elem!1), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[429, 36330, 36329])).
% 3.62/3.87 tff(36332,plain,
% 3.62/3.87 (~r(s(s(s(z))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[23235, 36331, 106, 36328])).
% 3.62/3.87 tff(36333,plain,
% 3.62/3.87 (~b(elem!1, z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[402, 36320, 36158, 394])).
% 3.62/3.87 tff(36334,plain,
% 3.62/3.87 (r(elem!1, z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[284, 36333, 36323])).
% 3.62/3.87 tff(36335,plain,
% 3.62/3.87 (s(s(s(z))) = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[25677, 36334, 35152, 36332, 394, 36317, 19197, 36322, 36320])).
% 3.62/3.87 tff(36336,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[250, 36335, 36327, 106])).
% 3.62/3.87 tff(36337,plain,((~b(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36338,plain,
% 3.62/3.87 (~b(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36337, 71, 1])).
% 3.62/3.87 tff(36339,plain,
% 3.62/3.87 (r(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[409, 36338])).
% 3.62/3.87 tff(36340,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[21036, 230, 199, 1281, 377, 909, 412, 3407, 259])).
% 3.62/3.87 tff(36341,plain,(b(z, elem!1) | (~b(s(z), z)) | (elem!1 = s(elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36342,plain,
% 3.62/3.87 (b(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36341, 412, 219, 36158, 36315, 19197, 36323, 3407])).
% 3.62/3.87 tff(36343,plain,
% 3.62/3.87 (~b(elem!1, s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20398, 36342, 19197, 36158])).
% 3.62/3.87 tff(36344,plain,
% 3.62/3.87 (b(elem!1, z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[21021, 412, 219, 19197, 36315, 36323])).
% 3.62/3.87 tff(36345,plain,
% 3.62/3.87 (~b(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[12145, 36344, 36158, 36342])).
% 3.62/3.87 tff(36346,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[33228, 36187, 317, 1, 106, 36158, 1242, 1391, 71, 36317])).
% 3.62/3.87 tff(36347,plain,(b(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), elem!1) | r(z, elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36348,plain,
% 3.62/3.87 (b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36347, 1391, 36345, 1, 71])).
% 3.62/3.87 tff(36349,plain,
% 3.62/3.87 (s(s(s(z))) = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[23313, 9232, 909, 108, 261, 1244, 1326])).
% 3.62/3.87 tff(36350,plain,
% 3.62/3.87 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[3906, 36349])).
% 3.62/3.87 tff(36351,plain,
% 3.62/3.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[78, 36350])).
% 3.62/3.87 tff(36352,plain,
% 3.62/3.87 (~r(s(z), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[18965, 243, 35152, 1242, 294])).
% 3.62/3.87 tff(36353,plain,
% 3.62/3.87 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[760, 36352])).
% 3.62/3.87 tff(36354,plain,
% 3.62/3.87 (~b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[21846, 36353, 1281, 3407])).
% 3.62/3.87 tff(36355,plain,
% 3.62/3.87 (b(s(elem!1), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[429, 1255, 2282])).
% 3.62/3.87 tff(36356,plain,
% 3.62/3.87 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[4636, 36355, 1281, 3407, 1326, 307, 2564, 243, 348, 35152])).
% 3.62/3.87 tff(36357,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[681, 36356, 36354, 36351])).
% 3.62/3.87 tff(36358,plain,((s(z) = elem!1) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36359,plain,
% 3.62/3.87 (s(z) = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36358, 36348, 3407, 36342, 19197, 2207, 36317, 36315, 106, 36344, 412, 36345, 36343])).
% 3.62/3.87 tff(36360,plain,
% 3.62/3.87 (r(z, s(z)) <=> r(z, elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36359])).
% 3.62/3.87 tff(36361,plain,
% 3.62/3.87 (r(z, elem!1) <=> r(z, s(z))),
% 3.62/3.87 inference(symmetry,[status(thm)],[36360])).
% 3.62/3.87 tff(36362,plain,
% 3.62/3.87 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36361])).
% 3.62/3.87 tff(36363,plain,
% 3.62/3.87 (~r(z, s(z))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[1391, 36362])).
% 3.62/3.87 tff(36364,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36315, 36363])).
% 3.62/3.87 tff(36365,plain,(r(z, elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36366,plain,
% 3.62/3.87 (r(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36365, 412, 3407, 1, 71])).
% 3.62/3.87 tff(36367,plain,
% 3.62/3.87 (elem!1 = s(z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1266, 36366, 36315, 36343, 36345])).
% 3.62/3.87 tff(36368,plain,
% 3.62/3.87 (s(elem!1) = s(s(z))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36367])).
% 3.62/3.87 tff(36369,plain,
% 3.62/3.87 (s(s(elem!1)) = s(s(s(z)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36368])).
% 3.62/3.87 tff(36370,plain,
% 3.62/3.87 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36369])).
% 3.62/3.87 tff(36371,plain,
% 3.62/3.87 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 3.62/3.87 inference(symmetry,[status(thm)],[36370])).
% 3.62/3.87 tff(36372,plain,
% 3.62/3.87 (r(s(z), s(s(elem!1)))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[106, 36371])).
% 3.62/3.87 tff(36373,plain,
% 3.62/3.87 (~r(s(elem!1), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[4423, 36372, 36315, 412])).
% 3.62/3.87 tff(36374,plain,
% 3.62/3.87 (b(s(elem!1), s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[429, 36373, 36329])).
% 3.62/3.87 tff(36375,plain,
% 3.62/3.87 (~b(z, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[24719, 36374, 19197, 36158])).
% 3.62/3.87 tff(36376,plain,
% 3.62/3.87 (r(z, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1439, 36375])).
% 3.62/3.87 tff(36377,plain,
% 3.62/3.87 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2063, 36317])).
% 3.62/3.87 tff(36378,plain,
% 3.62/3.87 (s(s(z)) = s(elem!1)),
% 3.62/3.87 inference(symmetry,[status(thm)],[36368])).
% 3.62/3.87 tff(36379,plain,
% 3.62/3.87 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36378])).
% 3.62/3.87 tff(36380,plain,
% 3.62/3.87 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36369])).
% 3.62/3.87 tff(36381,plain,
% 3.62/3.87 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.62/3.87 inference(symmetry,[status(thm)],[36380])).
% 3.62/3.87 tff(36382,plain,
% 3.62/3.87 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36368, 36381])).
% 3.62/3.87 tff(36383,plain,
% 3.62/3.87 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.62/3.87 inference(transitivity,[status(thm)],[36382, 10493])).
% 3.62/3.87 tff(36384,plain,
% 3.62/3.87 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.87 inference(transitivity,[status(thm)],[36383, 36379])).
% 3.62/3.87 tff(36385,plain,
% 3.62/3.87 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36384])).
% 3.62/3.87 tff(36386,plain,
% 3.62/3.87 (~r(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[25463, 36367])).
% 3.62/3.87 tff(36387,plain,
% 3.62/3.87 (~(s(s(s(z))) = elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[250, 36386, 106])).
% 3.62/3.87 tff(36388,plain,
% 3.62/3.87 (~(elem!1 = s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1100, 36387])).
% 3.62/3.87 tff(36389,plain,
% 3.62/3.87 (~(s(s(s(s(z)))) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1516, 36388])).
% 3.62/3.87 tff(36390,plain,
% 3.62/3.87 (~(s(elem!1) = s(s(s(s(z)))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[17419, 36389])).
% 3.62/3.87 tff(36391,plain,
% 3.62/3.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36390, 36385])).
% 3.62/3.87 tff(36392,plain,
% 3.62/3.87 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[34965, 36391, 1, 36158])).
% 3.62/3.87 tff(36393,plain,
% 3.62/3.87 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2071, 36392, 36377])).
% 3.62/3.87 tff(36394,plain,
% 3.62/3.87 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36367])).
% 3.62/3.87 tff(36395,plain,
% 3.62/3.87 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(symmetry,[status(thm)],[36394])).
% 3.62/3.87 tff(36396,plain,
% 3.62/3.87 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(transitivity,[status(thm)],[36371, 36395])).
% 3.62/3.87 tff(36397,plain,
% 3.62/3.87 (r(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[106, 36396])).
% 3.62/3.87 tff(36398,plain,
% 3.62/3.87 (~r(s(elem!1), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2697, 36391, 35152, 36366, 36397])).
% 3.62/3.87 tff(36399,plain,
% 3.62/3.87 (b(s(elem!1), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2243, 36398, 2207])).
% 3.62/3.87 tff(36400,plain,
% 3.62/3.87 (~b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[33741, 36399, 35152, 36158, 71, 36366, 36393, 36317, 412, 1, 106])).
% 3.62/3.87 tff(36401,plain,
% 3.62/3.87 (r(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[392, 36400, 219])).
% 3.62/3.87 tff(36402,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[12090, 36401, 36376, 36366, 412])).
% 3.62/3.87 tff(36403,plain,((~r(s(elem!1), z)) | b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36404,plain,
% 3.62/3.87 (~b(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36403, 36339, 1, 71])).
% 3.62/3.87 tff(36405,plain,
% 3.62/3.87 (r(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19736, 36404])).
% 3.62/3.87 tff(36406,plain,
% 3.62/3.87 (r(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[33301, 317, 1, 36158, 106, 36317, 36187, 71])).
% 3.62/3.87 tff(36407,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[10227, 36406, 9983, 35152, 36405])).
% 3.62/3.87 tff(36408,plain,(b(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36409,plain,
% 3.62/3.87 (b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36408, 71, 1])).
% 3.62/3.87 tff(36410,plain,
% 3.62/3.87 (b(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35074, 36339, 36158, 36315, 219, 106, 36317, 19197])).
% 3.62/3.87 tff(36411,plain,
% 3.62/3.87 (b(elem!1, z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[21021, 36339, 219, 19197, 36315, 36323])).
% 3.62/3.87 tff(36412,plain,
% 3.62/3.87 (~b(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[12145, 36411, 36158, 36410])).
% 3.62/3.87 tff(36413,plain,
% 3.62/3.87 (r(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[236, 231, 36412])).
% 3.62/3.87 tff(36414,plain,
% 3.62/3.87 (~b(elem!1, s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20398, 36410, 19197, 36158])).
% 3.62/3.87 tff(36415,plain,
% 3.62/3.87 (r(elem!1, s(z))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[299, 243, 36414])).
% 3.62/3.87 tff(36416,plain,
% 3.62/3.87 (s(s(s(z))) = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[23313, 36415, 36315, 106, 36411, 36413, 36410])).
% 3.62/3.87 tff(36417,plain,
% 3.62/3.87 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[3906, 36416])).
% 3.62/3.87 tff(36418,plain,
% 3.62/3.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[78, 36417])).
% 3.62/3.87 tff(36419,plain,
% 3.62/3.87 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[34965, 36418, 1, 36158])).
% 3.62/3.87 tff(36420,plain,
% 3.62/3.87 (~r(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[3826, 36418, 35152, 36315, 36339, 36329, 36413])).
% 3.62/3.87 tff(36421,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[33806, 36420, 36419, 1, 36158, 106, 36317, 36409, 71])).
% 3.62/3.87 tff(36422,plain,((s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36423,plain,
% 3.62/3.87 (s(z) = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36422, 71, 1])).
% 3.62/3.87 tff(36424,plain,
% 3.62/3.87 (s(s(z)) = s(elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36423])).
% 3.62/3.87 tff(36425,plain,
% 3.62/3.87 (s(s(s(z))) = s(s(elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36424])).
% 3.62/3.87 tff(36426,plain,
% 3.62/3.87 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36425])).
% 3.62/3.87 tff(36427,plain,
% 3.62/3.87 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36423])).
% 3.62/3.87 tff(36428,plain,
% 3.62/3.87 (r(elem!1, s(s(s(z))))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[106, 36427])).
% 3.62/3.87 tff(36429,plain,
% 3.62/3.87 (r(elem!1, s(s(elem!1)))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36428, 36426])).
% 3.62/3.87 tff(36430,plain,
% 3.62/3.87 (r(z, s(z)) <=> r(z, elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36423])).
% 3.62/3.87 tff(36431,plain,
% 3.62/3.87 (r(z, elem!1)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36315, 36430])).
% 3.62/3.87 tff(36432,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[3145, 121, 36431, 36405, 36429, 35152])).
% 3.62/3.87 tff(36433,plain,(b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36434,plain,
% 3.62/3.87 (b(s(z), s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36433, 1])).
% 3.62/3.87 tff(36435,plain,
% 3.62/3.87 (~b(s(s(s(z))), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[21058, 36434, 19197, 36158])).
% 3.62/3.87 tff(36436,plain,
% 3.62/3.87 (r(s(s(s(z))), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1155, 36435])).
% 3.62/3.87 tff(36437,plain,
% 3.62/3.87 (~r(s(z), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36230, 348, 1, 36434])).
% 3.62/3.87 tff(36438,plain,
% 3.62/3.87 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[34918, 36437, 1, 36158, 36434, 348])).
% 3.62/3.87 tff(36439,plain,
% 3.62/3.87 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[34965, 36438, 1, 36158])).
% 3.62/3.87 tff(36440,plain,
% 3.62/3.87 (r(s(s(s(z))), s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[23458, 36439, 36438])).
% 3.62/3.87 tff(36441,plain,
% 3.62/3.87 (~r(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[5155, 36440, 36315, 36436])).
% 3.62/3.87 tff(36442,plain,
% 3.62/3.87 (b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[25631, 36438, 1, 36158])).
% 3.62/3.87 tff(36443,plain,
% 3.62/3.87 (b(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[409, 36441])).
% 3.62/3.87 tff(36444,plain,
% 3.62/3.87 (~b(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[26193, 36443, 19197, 36158, 36442, 219, 348])).
% 3.62/3.87 tff(36445,plain,
% 3.62/3.87 (~b(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[24348, 36441, 1, 36434])).
% 3.62/3.87 tff(36446,plain,
% 3.62/3.87 (r(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19736, 36445])).
% 3.62/3.87 tff(36447,plain,
% 3.62/3.87 ($false),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35835, 36446, 36444, 1, 36315, 9297, 36434, 36441])).
% 3.62/3.87 tff(36448,plain,((s(z) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.87 tff(36449,plain,
% 3.62/3.87 (s(z) = s(elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[36448, 1])).
% 3.62/3.87 tff(36450,plain,
% 3.62/3.87 (z = elem!1),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[343, 36449])).
% 3.62/3.87 tff(36451,plain,
% 3.62/3.87 (s(z) = s(elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36450])).
% 3.62/3.87 tff(36452,plain,
% 3.62/3.87 (s(s(z)) = s(s(elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36451])).
% 3.62/3.87 tff(36453,plain,
% 3.62/3.87 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36452])).
% 3.62/3.87 tff(36454,plain,
% 3.62/3.87 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36453])).
% 3.62/3.87 tff(36455,plain,
% 3.62/3.87 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36450])).
% 3.62/3.87 tff(36456,plain,
% 3.62/3.87 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 3.62/3.87 inference(transitivity,[status(thm)],[36455, 159])).
% 3.62/3.87 tff(36457,plain,
% 3.62/3.87 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36456])).
% 3.62/3.87 tff(36458,plain,
% 3.62/3.87 (~(elem!1 = s(s(s(z))))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[166, 36457])).
% 3.62/3.87 tff(36459,plain,
% 3.62/3.87 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[24229, 36449])).
% 3.62/3.87 tff(36460,plain,
% 3.62/3.87 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36450])).
% 3.62/3.87 tff(36461,plain,
% 3.62/3.87 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.62/3.87 inference(symmetry,[status(thm)],[36460])).
% 3.62/3.87 tff(36462,plain,
% 3.62/3.87 (r(s(s(s(elem!1))), z)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[35152, 36461])).
% 3.62/3.87 tff(36463,plain,
% 3.62/3.87 (~b(z, s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[31543, 36462, 1, 36158, 36434, 36459])).
% 3.62/3.87 tff(36464,plain,
% 3.62/3.87 (~b(elem!1, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[6057, 36463, 36450])).
% 3.62/3.87 tff(36465,plain,
% 3.62/3.87 (~b(elem!1, s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1198, 36464, 36450])).
% 3.62/3.87 tff(36466,plain,
% 3.62/3.87 (r(elem!1, s(s(s(z))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[1192, 36465, 36458])).
% 3.62/3.87 tff(36467,plain,
% 3.62/3.87 (r(elem!1, s(s(s(elem!1))))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36466, 36454])).
% 3.62/3.87 tff(36468,plain,
% 3.62/3.87 (r(z, s(z)) <=> r(elem!1, s(z))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36450])).
% 3.62/3.87 tff(36469,plain,
% 3.62/3.87 (r(elem!1, s(z))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36315, 36468])).
% 3.62/3.87 tff(36470,plain,
% 3.62/3.87 (b(s(z), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35508, 36450, 19197])).
% 3.62/3.87 tff(36471,plain,
% 3.62/3.87 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36451])).
% 3.62/3.87 tff(36472,plain,
% 3.62/3.87 (r(elem!1, s(elem!1))),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[36469, 36471])).
% 3.62/3.87 tff(36473,plain,
% 3.62/3.87 (elem!1 = z),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[364, 36450])).
% 3.62/3.87 tff(36474,plain,
% 3.62/3.87 (b(s(elem!1), z)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20985, 36473, 19197])).
% 3.62/3.87 tff(36475,plain,
% 3.62/3.87 (b(elem!1, s(elem!1))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[327, 36450, 36158])).
% 3.62/3.87 tff(36476,plain,
% 3.62/3.87 (~b(z, elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20382, 36470, 19197, 36475])).
% 3.62/3.87 tff(36477,plain,
% 3.62/3.87 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36450])).
% 3.62/3.87 tff(36478,plain,
% 3.62/3.87 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 3.62/3.87 inference(symmetry,[status(thm)],[36477])).
% 3.62/3.87 tff(36479,plain,
% 3.62/3.87 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 3.62/3.87 inference(monotonicity,[status(thm)],[36478])).
% 3.62/3.87 tff(36480,plain,
% 3.62/3.87 (~r(z, elem!1)),
% 3.62/3.87 inference(modus_ponens,[status(thm)],[9971, 36479])).
% 3.62/3.87 tff(36481,plain,
% 3.62/3.87 (~b(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[20858, 36480, 19197, 36434, 36476, 36474, 36462, 1])).
% 3.62/3.87 tff(36482,plain,
% 3.62/3.87 (r(z, s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[19736, 36481])).
% 3.62/3.87 tff(36483,plain,
% 3.62/3.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[35940, 36482, 36450, 36434, 35152, 211, 19197, 36472, 36470, 36469])).
% 3.62/3.87 tff(36484,plain,
% 3.62/3.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[556, 36483, 1])).
% 3.62/3.87 tff(36485,plain,
% 3.62/3.87 (b(s(z), s(s(s(elem!1))))),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[9876, 36473, 36434])).
% 3.62/3.87 tff(36486,plain,
% 3.62/3.87 (b(s(elem!1), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[2488, 36474, 36450])).
% 3.62/3.87 tff(36487,plain,
% 3.62/3.87 (~b(s(s(s(elem!1))), elem!1)),
% 3.62/3.87 inference(unit_resolution,[status(thm)],[13752, 36470, 36475, 36485])).
% 3.62/3.89 tff(36488,plain,
% 3.62/3.89 (~(elem!1 = s(s(elem!1)))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[3790, 36486, 36487])).
% 3.62/3.89 tff(36489,plain,
% 3.62/3.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[78, 36488])).
% 3.62/3.89 tff(36490,plain,
% 3.62/3.89 (r(z, s(s(s(z))))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[1202, 36481, 36450, 36458])).
% 3.62/3.89 tff(36491,plain,
% 3.62/3.89 (r(s(z), z)),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[32539, 36482, 36158, 36434, 1, 36488, 36459, 36462, 36463])).
% 3.62/3.89 tff(36492,plain,
% 3.62/3.89 (~r(s(s(s(z))), s(z))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[11100, 36491, 36315, 36490])).
% 3.62/3.89 tff(36493,plain,
% 3.62/3.89 (b(s(s(s(z))), s(z))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[2325, 36492])).
% 3.62/3.89 tff(36494,plain,
% 3.62/3.89 (r(s(elem!1), z)),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[32440, 36493, 1, 36158, 36459, 36488, 36434, 36482, 36462, 36490])).
% 3.62/3.89 tff(36495,plain,
% 3.62/3.89 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[25513, 36494, 35152, 36472])).
% 3.62/3.89 tff(36496,plain,
% 3.62/3.89 (b(s(s(s(elem!1))), s(elem!1))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[681, 36495, 36489])).
% 3.62/3.89 tff(36497,plain,
% 3.62/3.89 (~b(s(elem!1), s(s(elem!1)))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[34357, 36496, 36475, 563, 36450, 2207, 36484])).
% 3.62/3.89 tff(36498,plain,
% 3.62/3.89 (r(s(elem!1), s(s(elem!1)))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[526, 36497, 211])).
% 3.62/3.89 tff(36499,plain,
% 3.62/3.89 (~r(elem!1, s(s(s(elem!1))))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[35987, 36498, 36450, 36486, 35152, 36472, 3313, 36485, 36484, 36469])).
% 3.62/3.89 tff(36500,plain,
% 3.62/3.89 ($false),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[36499, 36467])).
% 3.62/3.89 tff(36501,plain,(s(s(elem!1)) = s(s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.62/3.89 tff(36502,plain,
% 3.62/3.89 (s(s(s(elem!1))) = s(elem!1)),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[614, 36501])).
% 3.62/3.89 tff(36503,plain,
% 3.62/3.89 (elem!1 = s(s(elem!1))),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[78, 36502])).
% 3.62/3.89 tff(36504,plain,
% 3.62/3.89 (elem!1 = s(s(s(elem!1)))),
% 3.62/3.89 inference(transitivity,[status(thm)],[36503, 36501])).
% 3.62/3.89 tff(36505,plain,
% 3.62/3.89 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 3.62/3.89 inference(monotonicity,[status(thm)],[36504])).
% 3.62/3.89 tff(36506,plain,
% 3.62/3.89 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), elem!1)),
% 3.62/3.89 inference(symmetry,[status(thm)],[36505])).
% 3.62/3.89 tff(36507,plain,
% 3.62/3.89 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 3.62/3.89 inference(monotonicity,[status(thm)],[36506])).
% 3.62/3.89 tff(36508,plain,
% 3.62/3.89 (~r(s(s(s(elem!1))), elem!1)),
% 3.62/3.89 inference(modus_ponens,[status(thm)],[179, 36507])).
% 3.62/3.89 tff(36509,plain,
% 3.62/3.89 ($false),
% 3.62/3.89 inference(unit_resolution,[status(thm)],[35152, 36508])).
% 3.62/3.89 % SZS output end Proof
% 3.62/3.89 % E exiting
%------------------------------------------------------------------------------